This study aimed to describe the process of thinking by prospective teachers of mathematics in making arguments. It was a qualitative research involving the mathematics students of STKIP PGRI Jombang as the subject of the study. Test and task-based semi structural interview were conducted for data collection. The result showed that 163 of 260 mathematics students argued using inductive and deductive warrants. The process of thinking by the prospective teachers of mathematics in making arguments had begun since they constructed their very first idea by figuring out some objects to make a conclusion. However, they also found a rebuttal from that conclusion, though they did not further describe what such rebuttal was. Therefore, they decided to construct the second ideas in order to verify the first ones through some pieces of definition.
Bloom's Taxonomy is a classification of learning objectives within education which divides educational goals into three "domains": Cognitive, Affective, and Psychomotor. The Cognitive domain involves knowledge and intellectual skills and is further divided into six levels - from basic recall or recognition of facts to the more complex levels of analysis, synthesis, and evaluation. The taxonomy provides a useful framework for teachers to structure learning objectives, develop assessments, and ensure all levels of learning are addressed. Bloom's Taxonomy was later revised to update the language and relevance for 21st century education.
This document describes best practices in technical education used at Mount Zion College of Engineering & Technology. It discusses how the college uses Bloom's revised taxonomy as a framework to develop specific, measurable learning objectives aligned with cognitive levels and knowledge dimensions. Teachers create lesson plans and learning activities mapped to the taxonomy to systematically facilitate student learning. Assessment is also designed based on the taxonomy to evaluate if students achieved the objectives. The methods section provides an example mapping of an objective, activities, and assessment to the taxonomy table to illustrate how it ensures proper alignment of the educational components.
It discuss about Blooms Taxonomy in details. It explains on Benjamin SAMUEL Bloom's contribution, introduction about bloom, what is bloom's taxonomy, definition, purpose, classification - cognitive domain, affective domain, psychomotor domain's components with examples. Then Bloom’s Revised Taxonomy (2001) , educational implications, benefits and conclusion.
The document discusses a Table of Specifications (TOS), which is a tabular format used to map instructional goals and learning outcomes to assessments and activities. A TOS correlates each course unit to specific Bloom's taxonomy levels and learning outcomes. It is developed by identifying key topics, extracting concepts and terms, listing suggested readings, and noting formative assessments. The TOS provides transparency by communicating the expected intellectual rigor and content to students. It ensures assessments are aligned with course goals and outcomes.
This document outlines the adoption of new K-12 mathematics standards for the state of Washington. It discusses the process by which the standards were developed, including input from national experts, state educators, and thousands of stakeholders. The state superintendent officially adopts the revised standards, noting they set more rigorous expectations and provide clarity to support student understanding and problem solving abilities across grades and subjects. The standards are considered the first step in improving mathematics learning statewide.
This document discusses performance assessment tasks (PATs) in secondary mathematics classrooms. PATs require students to perform tasks rather than take formal exams. The document outlines reasons why PATs are beneficial, including that they actively demonstrate student knowledge and provide improvement in instruction. Research shows PATs improve problem solving skills compared to non-PAT driven instruction. However, PATs also have drawbacks like being time-consuming and difficult to score consistently. The document provides examples of PAT types like portfolios and discusses how to construct effective PATs aligned with learning goals.
Authentic assessment for improving cognitive skill,critical creative thinking...Alexander Decker
This document discusses authentic assessment and its benefits. It defines authentic assessment as assessment used to holistically and continuously record students' achievement, including both product and learning process. Authentic assessment improves students' cognitive skills, critical-creative thinking, and meta-cognitive awareness. It involves meaningful, real-world tasks like portfolios, performances, and projects. Authentic assessment is continuous and provides feedback to improve learning, unlike traditional tests. It also develops higher-order thinking skills like analysis and problem-solving.
Levels of Learning (Revised Bloom's of Taxonomy)lerise
The document discusses Bloom's Taxonomy, which classifies different levels of thinking. It provides an overview of the original 1956 taxonomy and the revised 2001 version. The revised taxonomy makes changes to terminology, structure, and emphasis. It uses verbs to describe cognitive processes and organizes thinking into a two-dimensional table with knowledge dimensions and cognitive process dimensions. This provides a more comprehensive framework for curriculum planning, instruction, and assessment. Sample questions are provided for each cognitive process to illustrate how they can be applied in teaching.
Bloom's Taxonomy is a classification of learning objectives within education which divides educational goals into three "domains": Cognitive, Affective, and Psychomotor. The Cognitive domain involves knowledge and intellectual skills and is further divided into six levels - from basic recall or recognition of facts to the more complex levels of analysis, synthesis, and evaluation. The taxonomy provides a useful framework for teachers to structure learning objectives, develop assessments, and ensure all levels of learning are addressed. Bloom's Taxonomy was later revised to update the language and relevance for 21st century education.
This document describes best practices in technical education used at Mount Zion College of Engineering & Technology. It discusses how the college uses Bloom's revised taxonomy as a framework to develop specific, measurable learning objectives aligned with cognitive levels and knowledge dimensions. Teachers create lesson plans and learning activities mapped to the taxonomy to systematically facilitate student learning. Assessment is also designed based on the taxonomy to evaluate if students achieved the objectives. The methods section provides an example mapping of an objective, activities, and assessment to the taxonomy table to illustrate how it ensures proper alignment of the educational components.
It discuss about Blooms Taxonomy in details. It explains on Benjamin SAMUEL Bloom's contribution, introduction about bloom, what is bloom's taxonomy, definition, purpose, classification - cognitive domain, affective domain, psychomotor domain's components with examples. Then Bloom’s Revised Taxonomy (2001) , educational implications, benefits and conclusion.
The document discusses a Table of Specifications (TOS), which is a tabular format used to map instructional goals and learning outcomes to assessments and activities. A TOS correlates each course unit to specific Bloom's taxonomy levels and learning outcomes. It is developed by identifying key topics, extracting concepts and terms, listing suggested readings, and noting formative assessments. The TOS provides transparency by communicating the expected intellectual rigor and content to students. It ensures assessments are aligned with course goals and outcomes.
This document outlines the adoption of new K-12 mathematics standards for the state of Washington. It discusses the process by which the standards were developed, including input from national experts, state educators, and thousands of stakeholders. The state superintendent officially adopts the revised standards, noting they set more rigorous expectations and provide clarity to support student understanding and problem solving abilities across grades and subjects. The standards are considered the first step in improving mathematics learning statewide.
This document discusses performance assessment tasks (PATs) in secondary mathematics classrooms. PATs require students to perform tasks rather than take formal exams. The document outlines reasons why PATs are beneficial, including that they actively demonstrate student knowledge and provide improvement in instruction. Research shows PATs improve problem solving skills compared to non-PAT driven instruction. However, PATs also have drawbacks like being time-consuming and difficult to score consistently. The document provides examples of PAT types like portfolios and discusses how to construct effective PATs aligned with learning goals.
Authentic assessment for improving cognitive skill,critical creative thinking...Alexander Decker
This document discusses authentic assessment and its benefits. It defines authentic assessment as assessment used to holistically and continuously record students' achievement, including both product and learning process. Authentic assessment improves students' cognitive skills, critical-creative thinking, and meta-cognitive awareness. It involves meaningful, real-world tasks like portfolios, performances, and projects. Authentic assessment is continuous and provides feedback to improve learning, unlike traditional tests. It also develops higher-order thinking skills like analysis and problem-solving.
Levels of Learning (Revised Bloom's of Taxonomy)lerise
The document discusses Bloom's Taxonomy, which classifies different levels of thinking. It provides an overview of the original 1956 taxonomy and the revised 2001 version. The revised taxonomy makes changes to terminology, structure, and emphasis. It uses verbs to describe cognitive processes and organizes thinking into a two-dimensional table with knowledge dimensions and cognitive process dimensions. This provides a more comprehensive framework for curriculum planning, instruction, and assessment. Sample questions are provided for each cognitive process to illustrate how they can be applied in teaching.
Applying Learning Principles based on Cognitive Science to Improve Training ...Dr.Kumuda Gururao
The document discusses applying cognitive science principles to improve training performance. It defines learning science and its relationship to cognitive science. Six cognitive strategies are described to enhance training: spaced practice, interleaving, retrieval practice, elaboration, dual coding, and concrete examples. The document recommends incorporating these strategies into learning design through effective organization, coherence, stories, and multiple examples. It also suggests offering learning environments that promote cognitive disequilibrium and flexibility to enhance performance.
The document provides an overview of the K to 12 Mathematics curriculum guide for the Philippines. It outlines the conceptual framework, which identifies critical thinking and problem solving as the twin goals of mathematics education. It also describes the five content areas - numbers and number sense, measurement, geometry, patterns and algebra, and probability and statistics. Additionally, it provides learning standards and competencies for each grade level from grade 1 to grade 10.
This was a field research (literature review and exploration) with descriptive quantitative approach. This study aims: (1) to develop a model (scheme) to assess mathematical power, (2) to test the validity of instruments of mathematical power assessment, and (3) to developa valid and reliable test and non-test instrument prototypes as a mathematical power measurement. The research instruments consist of 4 items of essay test, 20 sheets of observation on investigative activities, and 20 items of questionnaires. Validity test was conducted through constructions built up from 3 aspects of mathematical power ability. Result of instrument analysis showed that: (1) the r of instrument test = 0.947, meaning that the instrument is reliable, (2) the r of activity observation sheets = 0.912, meaning that the instrument is reliable, and (3) the r of questionnaires = 0.770, meaning that the questionnaire is reliable on 0.05 significance level. This study concludes: (a) the steps in the model (scheme) of mathematical power assessment may be used as a reference for assessing mathematical power, (b) test and non-test instruments are valid and reliable, and (c) prototypes of test and non-test instruments may be used as a measurement in mathematical power assessment.
Lorin Anderson revised Benjamin Bloom's taxonomy of educational objectives in the 1990s. The two main changes were changing the categories from nouns to verbs and rearranging the order. The categories are now Remembering, Understanding, Applying, Analyzing, Evaluating, and Creating. This revision provides examples and key verbs for each category to better illustrate how to assess learning in a domain from lower order to higher order thinking skills.
INTERPRETING PHYSICS TEACHERS’ FEEDBACK COMMENTS ON STUDENTS’ SOLUTIOijejournal
This paper investigates teachers’ intentions, when providing their feedback comments to hypothetical
students’ written solutions to linear motion tasks. To obtain an in-depth understanding of the teachers’
thinking when responding to student written solutions, a qualitative case study approach was employed
using two different data sources: a Problem Centred Questionnaire (PCQ) and a Problem Centred
Interview (PCI). Data processing was conducted in two main phases: Initial and Comparative. In both
phases we explored patterns about teachers’ foci across student strategies and motion tasks. A main finding
of this research is to categorising teachers’ interpretations and feedback on student solutions, based on the
extent of teachers’ attentions to Student Thinking and Disciplinary Thinking. This analysis approach
refines the previously held view that a high level of teacher content knowledge, and a concurrent focus to
both ‘student thinking’ and ‘disciplinary thinking’ are required to provide meaningful feedback on student
solutions. The findings indicated that their level of teachers’ propositional
The document provides an introduction to the Common Core Georgia Performance Standards for Mathematics. It discusses the focus of the Georgia mathematics curriculum on developing conceptual understanding through problem solving, representation, reasoning and communication. It emphasizes applying math concepts in authentic contexts. The standards are designed to increase coherence and focus from grade to grade to improve math achievement. They define what students should understand and be able to do at each grade level.
This research was conducted due to the importance value of mathematics for early childhood and the fact some researches showed the early childhood education (ECE) teachers' low level of basic mathematical knowledge, especially the one related to childhood developmental stages. The participants of this research were 35 ECE teachers from one of the cities in West Java province with teaching experience approximately ten years. In this research, 30 minutes was given to the participants to solve 20 questions, which tested teachers' knowledge related to verbal counting sequence, counting, the ordinal number of words, addition/subtraction, divisions of sets, written number symbols, and words. Besides, the interview was conducted to get more indepth information from the participants. The quantitative descriptive analysis was used to identify the frequency, percentage, mean value, and standard deviation. The result of the research showed that ECE teachers had limited knowledge of children's mathematical development. It was revealed by the result of the mean value of the teachers’ responses, which were only 33% correct answers and 16% no idea answers. This result can become input for the stakeholders to hold a professional development program which aims to increase the quality of ECE teachers related to mathematical development activity.
This document discusses best practices for designing assessments and tests. It outlines different types of assessments, including formative and summative assessments. It also describes various types of questions that can be used, such as true/false, multiple choice, matching, fill-in-the-blank, and essay questions. For each question type, it provides guidance on when to use each type and how to design the questions effectively. Throughout, it emphasizes the importance of clear learning targets and designing assessments that accurately measure what students need to learn.
This document discusses effective questioning techniques for instructors. It presents a taxonomy that categorizes questions as either high or low order and convergent or divergent. High order questions require deeper thinking while divergent questions have open-ended answers. Research shows that most teacher questions are low-level convergent, focusing on recall. The document outlines techniques for crafting higher-order, divergent questions like wait time and probing responses. When these techniques are used, students provide more thoughtful answers and teachers ask a greater variety of questions.
This document discusses effective questioning techniques for instructors. It presents a taxonomy that categorizes questions as either high or low order and convergent or divergent. High order questions require deeper thinking while divergent questions have open-ended answers. Research shows that most teacher questions are low-level convergent, focusing on recall. The document outlines techniques for crafting higher-order, divergent questions like wait time and probing responses. When these techniques are used, students provide more thoughtful answers and teachers ask a greater variety of questions.
The document describes the development of a construct map for teacher attentiveness based on responses to open-ended assessment items. It involved the following steps:
1. The researchers reviewed literature to identify potential levels of attentiveness and coded responses from teachers and teacher candidates to assessment items.
2. The coded responses were organized into qualitative categories that were hierarchically ordered to show increasing levels of attentiveness.
3. The ordered categories were organized into a construct map diagram to operationalize the attentiveness construct and show how it is measured by the assessment. The goal was to provide an example of developing a construct map for a complex teaching skill based on open-ended response data.
This document provides a guide for writing educational cases. It outlines a 6-step case writing process: 1) identifying needs, 2) establishing needs, 3) initial contact, 4) data collection, 5) writing process, and 6) release. The writing process involves planning, organizing, drafting, and revising. Planning involves identifying the purpose and intended learners. Organizing arranges ideas in a narrative structure. Drafting develops the ideas and materials. Revising improves the case through evaluation. The goal is to present a problem-based learning experience that engages students and leads to intended outcomes.
This research is aimed to know students‟ concept understanding profile on heat and temperature. This research is descriptive research using a qualitative approach. Subjects of this research are 10th-grade students in Surakarta in the academic year of 2016/ 2017. They represent high, medium, and low categorized school. Subject selection is based on the average score of physics at the latest four years. This research uses the question of extended response test through essay question. Before having given to the subjects, essay questions are validated by the experts. Based on the research result and the data analysis, students‟ concept understanding on heat and temperature as follows: (1) The average percentage of students‟ concept understanding at high categorized school is 60,66%, at medium categorized school is 51,47%, and at low categorized school is 48,83%, (2) Most students have misconception on basic concept of heat and temperature such as heat capacity, thermal conductivity, and expansion concept.
The document discusses revisions that were made to Bloom's Taxonomy of Learning. The original taxonomy classified learning objectives into six levels from simple to complex. It was revised in 1999 to address criticisms and broaden its applicability. The revised version distinguishes between factual, procedural, conceptual, and metacognitive knowledge. It also changes the names of the categories from nouns to verbs to better reflect thinking as an active process. The revision emphasizes higher-order thinking and has been widely adopted to improve curriculum, instruction, and assessment.
The purpose of this study is to determine the mathematics teacher performance category in building high order thinking skills (HOTS) of students. The study was conducted on 560 students taken randomly from ten junior high schools and eight high schools from eight districts in North Sumatra Province. Data collection techniques and instruments are carried out by giving questionnaires to students which contain a number of questions about students' assessment of the mathematics teacher's performance in constructing the HOTS indicator. Based on descriptive analysis, it was found that the performance of mathematics teachers built HOTS indicators, namely (1) understanding of concepts, (2) mathematical communication, (3) creativity, (4) problem solving, and (5) reasoning is enough category. The results of analysis of variance show that teacher performance builds (1) understanding of concepts, (2) mathematical communication, (3) creativity, (4) problem solving, and (5) reasoning significantly influences students' abilities.
OCAS Assessments adopted Bloom's Taxonomy to help students develop higher-order cognitive abilities and improve their thinking skills. Bloom's Taxonomy is a framework for categorizing levels of thinking skills, from basic recall to more complex skills, like evaluation and synthesis. It was developed by Benjamin Bloom in 1956 to classify intellectual behaviors important for learning. The taxonomy includes six cognitive levels - knowledge, comprehension, application, analysis, synthesis, and evaluation - which represent increasing sophistication in students' skills, advancing from memory to creative abilities.
This study aims to develop the teacher's perceptions of critical thinking in science learning in elementary schools. The samples in this study were 50 elementary school teachers in Central Java. Selection of samples employed convenience sampling. The instruments in this study used a modified Likert Scale. The validity tests used in this research were content validity and construct validity. Content validity was measured using CVR (Content Validity Ratio) and construct validity was measured using EFA (Exploratory Factor Analysis). By using SPSS, reliability estimation was obtained with the Cronbach Alpha formula 0.83 and it can be stated that the instruments for evaluating teacher perceptions of critical thinking in science learning are reliable.
Despite its central place in the mathematics curriculum the notion of mathematical proof has failed to permeate the curriculum at all scholastic levels. While the concept of mathematical proof can serve as a vehicle for inculcating mathematical thinking, studies have revealed that students experience serious difficulties with proving that include (a) not knowing how to begin the proving process, (b) the proclivity to use empirical verifications for tasks that call for axiomatic methods of proving, and (c) resorting to rote memorization of uncoordinated fragments of proof facts. While several studies have been conducted with the aim of addressing students’ fragile grasp of mathematical proof the majority of such studies have been based on activities that involve students reflecting and expressing their level of convincement in arguments supplied by the researchers, thereby compromising the voice of the informants. Further, research focus has been on the front instead of the back of mathematics. Hence, there is a dearth in research studies into students’ thinking processes around mathematical proof that are grounded in students’ own proof attempts. Therefore current investigations should aim at identifying critical elements of students’ knowledge of the notion of proof that are informed by students’ actual individual proof construction attempts.
One of the most fundamental subjects of primary school mathematics, the
concept of fraction plays a key role in students' educational background.
Students experience difficulties and misconceptions regarding this concept.
Therefore, it is of great importance to understand this subject well and to use
different teaching methods and techniques. Various methods can be used in
learning mathematics, such as invention method, computer-assisted
teaching, problem solving, creative drama and discussion. Argumentation
method is a scientific discussion of a claim on a subject by providing data,
warrant and backing, and by revealing the rebuttal and the invalidity of the
claim. Students gain more skills by interacting with teachers or collaborating
with their peers, and that they possess skills that have not been obtained
before or that are too difficult to achieve on their own. Therefore, the
argumentation method was chosen for its effect on the development of
primary school students’ fraction calculation strategies. Having a case study
design, this study was conducted with 28 primary school fourth-grade
students and 10 open-ended questions prepared by the researchers were used
during interviews. The results suggested that primary school students were
able to develop fraction calculation strategies through the argumentation
method. In general, inventing strategies, using representations, number
sense, addition and subtraction, using unit fractions and proportional
reasoning were used as fraction calculation strategies. It recommended to
use the argumentation method in other critical subjects of mathematics as
well.
The purpose of this study is to find out the critical thinking skills indicators and aspects of prospective elementary school teachers in mathematics-science integration lectures on electrical circuits and mathematical logic lesson. This research uses random sampling technique in which 30 first semester students were chosen randomly from one of university in Padang region West Sumatera Indonesia. This research uses Research and Development (R & D). The critical thinking skills are seen from processes, observations, and tests. The process of critical thinking skills of prospective elementary school teachers on the average of critical thinking skills indicator is 84% in strategies and tactics, 80% in advanced clarification and 83% in elementary clarification, basic support, and inference. The result of observing the critical thinking skills of prospective elementary school teachers on the average of each lectures is significantly increased to be 81.9%. The results of pre-test and post-test were increased significantly. It is shown from N-gain of 0.7 to be medium category.
Proving a proposition is emphasized in undergraduate mathematics learning. There are three strategies in proving or proof-production, i.e.: proceduralproof, syntactic-proof, and semantic-proof production. Students‟ difficulties in proving can occur in constructing a proof. In this article, we focused on students‟ thinking when proving using semantic-proof production. This research is qualitative research that conducted on students majored in mathematics education in public university in Banten province, Indonesia. Data was obtained through asking students to solve proving-task using thinkaloud and then following by interview based task. Results show that characterization of students‟ thinking using semantic-proof production can be classified into three categories, i.e.: (1) false-semantic, (2) proof-semantic for clarification of proposition, (3) proof-semantic for remembering concept. Both category (1) and (2) occurred before students proven formally in Representation System Proof (RSP). Nevertheless, category (3) occurred when students have proven the task in RSP then step out from RSP while proving. Based on the results, some suitable learning activities should be designed to support the construction of these mental categories.
Applying Learning Principles based on Cognitive Science to Improve Training ...Dr.Kumuda Gururao
The document discusses applying cognitive science principles to improve training performance. It defines learning science and its relationship to cognitive science. Six cognitive strategies are described to enhance training: spaced practice, interleaving, retrieval practice, elaboration, dual coding, and concrete examples. The document recommends incorporating these strategies into learning design through effective organization, coherence, stories, and multiple examples. It also suggests offering learning environments that promote cognitive disequilibrium and flexibility to enhance performance.
The document provides an overview of the K to 12 Mathematics curriculum guide for the Philippines. It outlines the conceptual framework, which identifies critical thinking and problem solving as the twin goals of mathematics education. It also describes the five content areas - numbers and number sense, measurement, geometry, patterns and algebra, and probability and statistics. Additionally, it provides learning standards and competencies for each grade level from grade 1 to grade 10.
This was a field research (literature review and exploration) with descriptive quantitative approach. This study aims: (1) to develop a model (scheme) to assess mathematical power, (2) to test the validity of instruments of mathematical power assessment, and (3) to developa valid and reliable test and non-test instrument prototypes as a mathematical power measurement. The research instruments consist of 4 items of essay test, 20 sheets of observation on investigative activities, and 20 items of questionnaires. Validity test was conducted through constructions built up from 3 aspects of mathematical power ability. Result of instrument analysis showed that: (1) the r of instrument test = 0.947, meaning that the instrument is reliable, (2) the r of activity observation sheets = 0.912, meaning that the instrument is reliable, and (3) the r of questionnaires = 0.770, meaning that the questionnaire is reliable on 0.05 significance level. This study concludes: (a) the steps in the model (scheme) of mathematical power assessment may be used as a reference for assessing mathematical power, (b) test and non-test instruments are valid and reliable, and (c) prototypes of test and non-test instruments may be used as a measurement in mathematical power assessment.
Lorin Anderson revised Benjamin Bloom's taxonomy of educational objectives in the 1990s. The two main changes were changing the categories from nouns to verbs and rearranging the order. The categories are now Remembering, Understanding, Applying, Analyzing, Evaluating, and Creating. This revision provides examples and key verbs for each category to better illustrate how to assess learning in a domain from lower order to higher order thinking skills.
INTERPRETING PHYSICS TEACHERS’ FEEDBACK COMMENTS ON STUDENTS’ SOLUTIOijejournal
This paper investigates teachers’ intentions, when providing their feedback comments to hypothetical
students’ written solutions to linear motion tasks. To obtain an in-depth understanding of the teachers’
thinking when responding to student written solutions, a qualitative case study approach was employed
using two different data sources: a Problem Centred Questionnaire (PCQ) and a Problem Centred
Interview (PCI). Data processing was conducted in two main phases: Initial and Comparative. In both
phases we explored patterns about teachers’ foci across student strategies and motion tasks. A main finding
of this research is to categorising teachers’ interpretations and feedback on student solutions, based on the
extent of teachers’ attentions to Student Thinking and Disciplinary Thinking. This analysis approach
refines the previously held view that a high level of teacher content knowledge, and a concurrent focus to
both ‘student thinking’ and ‘disciplinary thinking’ are required to provide meaningful feedback on student
solutions. The findings indicated that their level of teachers’ propositional
The document provides an introduction to the Common Core Georgia Performance Standards for Mathematics. It discusses the focus of the Georgia mathematics curriculum on developing conceptual understanding through problem solving, representation, reasoning and communication. It emphasizes applying math concepts in authentic contexts. The standards are designed to increase coherence and focus from grade to grade to improve math achievement. They define what students should understand and be able to do at each grade level.
This research was conducted due to the importance value of mathematics for early childhood and the fact some researches showed the early childhood education (ECE) teachers' low level of basic mathematical knowledge, especially the one related to childhood developmental stages. The participants of this research were 35 ECE teachers from one of the cities in West Java province with teaching experience approximately ten years. In this research, 30 minutes was given to the participants to solve 20 questions, which tested teachers' knowledge related to verbal counting sequence, counting, the ordinal number of words, addition/subtraction, divisions of sets, written number symbols, and words. Besides, the interview was conducted to get more indepth information from the participants. The quantitative descriptive analysis was used to identify the frequency, percentage, mean value, and standard deviation. The result of the research showed that ECE teachers had limited knowledge of children's mathematical development. It was revealed by the result of the mean value of the teachers’ responses, which were only 33% correct answers and 16% no idea answers. This result can become input for the stakeholders to hold a professional development program which aims to increase the quality of ECE teachers related to mathematical development activity.
This document discusses best practices for designing assessments and tests. It outlines different types of assessments, including formative and summative assessments. It also describes various types of questions that can be used, such as true/false, multiple choice, matching, fill-in-the-blank, and essay questions. For each question type, it provides guidance on when to use each type and how to design the questions effectively. Throughout, it emphasizes the importance of clear learning targets and designing assessments that accurately measure what students need to learn.
This document discusses effective questioning techniques for instructors. It presents a taxonomy that categorizes questions as either high or low order and convergent or divergent. High order questions require deeper thinking while divergent questions have open-ended answers. Research shows that most teacher questions are low-level convergent, focusing on recall. The document outlines techniques for crafting higher-order, divergent questions like wait time and probing responses. When these techniques are used, students provide more thoughtful answers and teachers ask a greater variety of questions.
This document discusses effective questioning techniques for instructors. It presents a taxonomy that categorizes questions as either high or low order and convergent or divergent. High order questions require deeper thinking while divergent questions have open-ended answers. Research shows that most teacher questions are low-level convergent, focusing on recall. The document outlines techniques for crafting higher-order, divergent questions like wait time and probing responses. When these techniques are used, students provide more thoughtful answers and teachers ask a greater variety of questions.
The document describes the development of a construct map for teacher attentiveness based on responses to open-ended assessment items. It involved the following steps:
1. The researchers reviewed literature to identify potential levels of attentiveness and coded responses from teachers and teacher candidates to assessment items.
2. The coded responses were organized into qualitative categories that were hierarchically ordered to show increasing levels of attentiveness.
3. The ordered categories were organized into a construct map diagram to operationalize the attentiveness construct and show how it is measured by the assessment. The goal was to provide an example of developing a construct map for a complex teaching skill based on open-ended response data.
This document provides a guide for writing educational cases. It outlines a 6-step case writing process: 1) identifying needs, 2) establishing needs, 3) initial contact, 4) data collection, 5) writing process, and 6) release. The writing process involves planning, organizing, drafting, and revising. Planning involves identifying the purpose and intended learners. Organizing arranges ideas in a narrative structure. Drafting develops the ideas and materials. Revising improves the case through evaluation. The goal is to present a problem-based learning experience that engages students and leads to intended outcomes.
This research is aimed to know students‟ concept understanding profile on heat and temperature. This research is descriptive research using a qualitative approach. Subjects of this research are 10th-grade students in Surakarta in the academic year of 2016/ 2017. They represent high, medium, and low categorized school. Subject selection is based on the average score of physics at the latest four years. This research uses the question of extended response test through essay question. Before having given to the subjects, essay questions are validated by the experts. Based on the research result and the data analysis, students‟ concept understanding on heat and temperature as follows: (1) The average percentage of students‟ concept understanding at high categorized school is 60,66%, at medium categorized school is 51,47%, and at low categorized school is 48,83%, (2) Most students have misconception on basic concept of heat and temperature such as heat capacity, thermal conductivity, and expansion concept.
The document discusses revisions that were made to Bloom's Taxonomy of Learning. The original taxonomy classified learning objectives into six levels from simple to complex. It was revised in 1999 to address criticisms and broaden its applicability. The revised version distinguishes between factual, procedural, conceptual, and metacognitive knowledge. It also changes the names of the categories from nouns to verbs to better reflect thinking as an active process. The revision emphasizes higher-order thinking and has been widely adopted to improve curriculum, instruction, and assessment.
The purpose of this study is to determine the mathematics teacher performance category in building high order thinking skills (HOTS) of students. The study was conducted on 560 students taken randomly from ten junior high schools and eight high schools from eight districts in North Sumatra Province. Data collection techniques and instruments are carried out by giving questionnaires to students which contain a number of questions about students' assessment of the mathematics teacher's performance in constructing the HOTS indicator. Based on descriptive analysis, it was found that the performance of mathematics teachers built HOTS indicators, namely (1) understanding of concepts, (2) mathematical communication, (3) creativity, (4) problem solving, and (5) reasoning is enough category. The results of analysis of variance show that teacher performance builds (1) understanding of concepts, (2) mathematical communication, (3) creativity, (4) problem solving, and (5) reasoning significantly influences students' abilities.
OCAS Assessments adopted Bloom's Taxonomy to help students develop higher-order cognitive abilities and improve their thinking skills. Bloom's Taxonomy is a framework for categorizing levels of thinking skills, from basic recall to more complex skills, like evaluation and synthesis. It was developed by Benjamin Bloom in 1956 to classify intellectual behaviors important for learning. The taxonomy includes six cognitive levels - knowledge, comprehension, application, analysis, synthesis, and evaluation - which represent increasing sophistication in students' skills, advancing from memory to creative abilities.
This study aims to develop the teacher's perceptions of critical thinking in science learning in elementary schools. The samples in this study were 50 elementary school teachers in Central Java. Selection of samples employed convenience sampling. The instruments in this study used a modified Likert Scale. The validity tests used in this research were content validity and construct validity. Content validity was measured using CVR (Content Validity Ratio) and construct validity was measured using EFA (Exploratory Factor Analysis). By using SPSS, reliability estimation was obtained with the Cronbach Alpha formula 0.83 and it can be stated that the instruments for evaluating teacher perceptions of critical thinking in science learning are reliable.
Despite its central place in the mathematics curriculum the notion of mathematical proof has failed to permeate the curriculum at all scholastic levels. While the concept of mathematical proof can serve as a vehicle for inculcating mathematical thinking, studies have revealed that students experience serious difficulties with proving that include (a) not knowing how to begin the proving process, (b) the proclivity to use empirical verifications for tasks that call for axiomatic methods of proving, and (c) resorting to rote memorization of uncoordinated fragments of proof facts. While several studies have been conducted with the aim of addressing students’ fragile grasp of mathematical proof the majority of such studies have been based on activities that involve students reflecting and expressing their level of convincement in arguments supplied by the researchers, thereby compromising the voice of the informants. Further, research focus has been on the front instead of the back of mathematics. Hence, there is a dearth in research studies into students’ thinking processes around mathematical proof that are grounded in students’ own proof attempts. Therefore current investigations should aim at identifying critical elements of students’ knowledge of the notion of proof that are informed by students’ actual individual proof construction attempts.
One of the most fundamental subjects of primary school mathematics, the
concept of fraction plays a key role in students' educational background.
Students experience difficulties and misconceptions regarding this concept.
Therefore, it is of great importance to understand this subject well and to use
different teaching methods and techniques. Various methods can be used in
learning mathematics, such as invention method, computer-assisted
teaching, problem solving, creative drama and discussion. Argumentation
method is a scientific discussion of a claim on a subject by providing data,
warrant and backing, and by revealing the rebuttal and the invalidity of the
claim. Students gain more skills by interacting with teachers or collaborating
with their peers, and that they possess skills that have not been obtained
before or that are too difficult to achieve on their own. Therefore, the
argumentation method was chosen for its effect on the development of
primary school students’ fraction calculation strategies. Having a case study
design, this study was conducted with 28 primary school fourth-grade
students and 10 open-ended questions prepared by the researchers were used
during interviews. The results suggested that primary school students were
able to develop fraction calculation strategies through the argumentation
method. In general, inventing strategies, using representations, number
sense, addition and subtraction, using unit fractions and proportional
reasoning were used as fraction calculation strategies. It recommended to
use the argumentation method in other critical subjects of mathematics as
well.
The purpose of this study is to find out the critical thinking skills indicators and aspects of prospective elementary school teachers in mathematics-science integration lectures on electrical circuits and mathematical logic lesson. This research uses random sampling technique in which 30 first semester students were chosen randomly from one of university in Padang region West Sumatera Indonesia. This research uses Research and Development (R & D). The critical thinking skills are seen from processes, observations, and tests. The process of critical thinking skills of prospective elementary school teachers on the average of critical thinking skills indicator is 84% in strategies and tactics, 80% in advanced clarification and 83% in elementary clarification, basic support, and inference. The result of observing the critical thinking skills of prospective elementary school teachers on the average of each lectures is significantly increased to be 81.9%. The results of pre-test and post-test were increased significantly. It is shown from N-gain of 0.7 to be medium category.
Proving a proposition is emphasized in undergraduate mathematics learning. There are three strategies in proving or proof-production, i.e.: proceduralproof, syntactic-proof, and semantic-proof production. Students‟ difficulties in proving can occur in constructing a proof. In this article, we focused on students‟ thinking when proving using semantic-proof production. This research is qualitative research that conducted on students majored in mathematics education in public university in Banten province, Indonesia. Data was obtained through asking students to solve proving-task using thinkaloud and then following by interview based task. Results show that characterization of students‟ thinking using semantic-proof production can be classified into three categories, i.e.: (1) false-semantic, (2) proof-semantic for clarification of proposition, (3) proof-semantic for remembering concept. Both category (1) and (2) occurred before students proven formally in Representation System Proof (RSP). Nevertheless, category (3) occurred when students have proven the task in RSP then step out from RSP while proving. Based on the results, some suitable learning activities should be designed to support the construction of these mental categories.
Assessing Problem-Solving Strategy Use By Engineering UndergraduatesHeather Strinden
This document summarizes a research study that assessed problem-solving strategies used by engineering undergraduates. The study examined which strategies students reported using, whether certain strategies clustered together, and if frequent strategy use correlated with better course performance. It also looked at how confidence, familiarity with course material, and interest affected performance. The researchers identified three types of strategies - Execution, Planning and Looking Back, and Low Confidence in Ability. Frequent use of strategies and higher confidence predicted better grades, while low confidence hindered performance. Strategy use differed between physics and thermodynamics courses.
This research is aimed at developing a learning model that encourages the skills of analytical thinking in science. The method used is research and development. The result is the ICAE (Incubation, Collection of data, Analysis, and Evaluation) model that promotes analytical thinking skills. Results of normalized gain tests show that the gain score is 0.28, which indicates that the ICAE learning model positively affects students’ analytical thinking, even though still within the lower category. The ICAE model also promotes the skills of analytical thinking in science and it has gained positive response from students.
1) The document discusses the concept of "chunking" which involves breaking down reading material into more digestible sections to improve comprehension. It contrasts this with a "folk psychology" view of learning as simply acquiring knowledge.
2) Jigsaws are described as an instructional strategy that uses chunking and allows students to construct their own understanding through discussion and comparison of different ideas.
3) Using jigsaws supports higher-order thinking skills like analysis, synthesis and evaluation, which are necessary for high-level work, by having students make connections across different chunks of knowledge.
“Social science inquiry method is based on the belief that providing a reflective and enquiry frame of reference to social issues helps to improve the personal and social life”.
Main developers: Byron Massialas, Benjamin Cox.
Massialas and Cox (1966) believed that school fosters development and inculcation of values in children and plays a crucial role in ‘creative reconstruction of culture’. Social inquiry method is helpful in identifying the social issues and dealing with them effectively.
Cox experimented with inquiry methods in teaching Junior High U.S. History, while Massialas focused on the use of inquiry instruction in teaching High School World History.
Algebraic Thinking A Problem Solving ApproachCheryl Brown
This document discusses developing algebraic thinking through a problem solving approach in mathematics education. It argues that solving mathematical problems can help students develop a deeper understanding of algebraic concepts by encouraging them to consider the generalities and relationships within problems. The document outlines several key aspects of algebraic thinking, such as reasoning about patterns, generalizing, and thinking about mathematical relations. It advocates facilitating student discourse and communication of mathematical ideas to promote algebraic reasoning. Finally, it suggests students progress through stages of developing algebraic thinking, starting with describing generalities verbally and moving to using diagrams, symbols, and formal algebraic notation.
This document discusses the use of case studies in foreign policy analysis courses. It explains that case studies recount real events and problems to give students experience dealing with complex situations. There are two main types: retrospective cases present a complete history for analysis, while decision-forcing cases omit outcomes to require students identify options. Case teaching grounds instruction in reality by engaging students in discussions of specific situations. It helps students learn content and critical thinking skills. Foreign policy cases explore the articulation, formulation, implementation, and evaluation phases of the policy process.
This document provides an overview of the conceptual framework for mathematics education. It discusses how students learn mathematics through the experiences provided by teachers. The twin goals of mathematics in basic education are developing critical thinking and problem solving skills. It outlines five content areas - numbers and number sense, measurement, geometry, patterns and algebra, and probability and statistics. The document also discusses learning theories that support the framework, including experiential learning, reflective learning, constructivism, cooperative learning, discovery learning, and inquiry-based learning.
This document discusses higher order thinking skills (HOTS) and Bloom's Taxonomy of learning. It defines HOTS as skills involving critical, logical, reflective thinking that are activated when individuals encounter unfamiliar problems. Bloom's Taxonomy categorizes different levels of thinking from basic recall/remembering to higher order skills like analysis, evaluation, and creation. The document also discusses the difference between lower order skills like memorization versus higher order skills like critical thinking. It emphasizes the importance of developing students' HOTS through teaching strategies that go beyond basic factual recall.
Authentic Tasks And Mathematical Problem SolvingJim Webb
This document discusses authentic tasks in mathematical problem solving and their role in developing mathematical literacy. It describes four key dimensions of authentic tasks: thinking and reasoning, discourse, mathematical tools, and attitudes and dispositions. Each of these dimensions supports meaningful learning and prepares students to solve everyday problems. The document provides examples of lessons and programs that incorporate these dimensions through real-world, problem-based activities.
This document discusses higher order thinking skills (HOTS) and their importance in education. It defines HOTS as skills involving analysis, evaluation and synthesis which require different teaching methods than memorizing facts. The document outlines Bloom's Taxonomy of cognitive skills and differentiates between lower and higher order thinking. It argues that while schools teach lower order skills well, the job market demands higher order skills like problem solving. Reform efforts emphasize teaching HOTS through inquiry, problem-solving and open-response assessments.
Assessing Knowledge, Process, Understanding, Performance/ProductCarlo Magno
The document provides a guide on assessing students based on four domains: knowledge, process, understanding, and performance/product. It describes each domain and provides examples of questions to assess each one. Knowledge refers to basic facts and information, while process refers to cognitive operations and thinking skills. Understanding involves making connections and has six facets. Performance/product assesses what students can do by having them complete authentic tasks. The guide aims to help teachers properly assess students under the Philippines' K to 12 education reform.
Monitoring The Status Of Students' Journey Towards Science And Mathematics Li...noblex1
A major focus of the current mathematics and science education reforms is on developing "literacy;" that is, helping students to understand and use the languages and ideas of mathematics and science in reasoning, communicating, and solving problems. In many ways, these standards documents are far more voluminous and complex than any scope and sequence in place in school systems today. But these documents are meant to be used as frameworks which provide guidance in education reform - they are not the definitive sources articulating to teachers how education reform must occur in their classrooms.
Our plan in this discussion is to lay out the components of mathematics and science literacy as set down in the major reform documents and then, using selected how-to articles, to show how strategies and activities tried by math and science teachers have been used, or can be used, to promote math and science literacy among students. For pragmatic reasons only, our discussions often focus either on mathematics or science reform recommendations and examples. In doing this, we do not mean to imply that the elements of literacy in these disciplines are somehow separate or different. In fact, the separate discussions show how both the mathematics and science education communities, coming from different directions at different points in time, independently arrived at similar positions and many of the same recommendations regarding the ideas of literacy.
In support of this discussion of the components of literacy, we also provide samples of resources, materials, and services that teachers might find useful in promoting mathematics and science literacy in their classrooms. The how-to articles are meant to be quick-reads that can be applied or adapted to classrooms directly. These articles are included to make it easier to decide which ones might be of special interest. Other articles and documents are intended as sources of a more general background. These documents provide some of the research bases and rationales behind some of the reform recommendations. Finally, we have included other references and information on databases which are not directly cited in the discussion but might prove valuable as additional sources of classroom ideas.
During the last decade, the mathematics education community appeared to lack clear focus and a sense of direction. Although many conferences were held, papers written, and reports produced, there was not a general consensus regarding which direction mathematics education should head.
The Standards offer an organization of important mathematical topics and abilities by grade-level groups (Kindergarten - grade 4, grades 5 - 8, and grades 9 - 12). Throughout the Standards the emphasis is: "knowing" mathematics is "doing" mathematics.
Source: https://ebookschoice.com/monitoring-the-status-of-students-journey-towards-science-and-mathematics-literacy/
how to develop students to perform internation assessment SamerYaqoob
The document discusses different types of assessments used in PISA:
1. Proficiency tests assess reading, math, and science literacy through scales measuring students' abilities to complete tasks. For reading, scales evaluate information retrieval, interpretation, and reflection.
2. Diagnostic science tests consider scales based on scientific competencies or separating knowledge into concepts and methodology.
3. Discrete and integrative tests for problem-solving and financial literacy use overall proficiency scales due to limited data.
This document discusses various teaching strategies and methods for teaching science. It defines science as involving logical thinking and testing of hypotheses based on observations. It also discusses the goals of science education as developing students' knowledge, process skills, and scientific attitudes. The document then outlines several teaching strategies for science education, including enhancing context strategies, collaborative grouping strategies, questioning strategies, inquiry strategies, and assessment strategies. It also discusses two approaches to teaching science: inquiry-based learning and problem/issue-based learning. Finally, it discusses several methods for teaching science, such as lecturing, demonstrating, collaborating, debriefing, and using laboratories.
This document discusses higher order thinking skills and Bloom's taxonomy. It defines higher order thinking as skills involving analysis, evaluation and synthesis which require different teaching methods than memorizing facts. Bloom's taxonomy categorizes questions and thinking skills from lower order skills like recalling information to higher order skills like analysis, evaluation and design. The document provides examples of how technology applications can be used for lower order skills like presentations or higher order skills like databases which allow analysis and problem solving. It argues education should focus more on developing students' higher order thinking abilities.
This document defines and describes thinking, reasoning and working mathematically (t, r, w m) and how it can be promoted in mathematics learning. T, r, w m involves making decisions about what mathematical knowledge to use, incorporates communication skills, and is developed through engaging investigations. It promotes higher-order thinking and confidence in doing math. The document outlines how t, r, w m can be encouraged in three phases of investigations: identifying problems, understanding concepts, and justifying solutions. Teachers can support t, r, w m through discussion, challenging problems, and reflection. The curriculum promotes these skills through real-world problems, investigative approaches, and connections between topics.
Similar to The process of thinking by prospective teachers of mathematics in making arguments (20)
The role of entrepreneurship in addressing the issue of educated unemployment is well acknowledged, while its specific implications for health professions students remain inadequately explored. This study's main objective is to investigate entrepreneurship education's effect on entrepreneurial intention by considering entrepreneurial self-efficacy as a mediator in students majoring in medical laboratory technology. This quantitative research uses an exploratory approach involving 300 respondents determined through simple random sampling techniques and analyzed using partial least square structural equation model (PLS-SEM). The analysis revealed that entrepreneurship education directly impacts self-efficacy and entrepreneurial intention. Furthermore, entrepreneurial self-efficacy was identified to exert a positive mediating effect between these variables. However, the effect size between the relationships of the research variables is low. Nevertheless, higher education offering health majors can optimize entrepreneurship education by implementing practical learning and field experience to increase confidence and intention in entrepreneurial activities.
Recent studies claimed that the absence of a paradigm is a challenge to developing education for sustainable development and soft skills competencies. This integrative study examines stimulating these transferable and transversal competencies through constructivist approaches to teaching from the cognitive, social, radical, and critical perspectives. The study argues that the use of constructivist approaches to teaching can contribute to the achievement of education for sustainable development and soft skills competencies through the delegation of power from teachers/lecturers to students. This, in active and interactive classrooms, empowers students and builds their confidence to develop on the personal, academic, and professional levels. The use of the cognitive constructivist approach assists in developing competencies based on a clear understanding of the cognitive structures of students in a vibrant classroom environment. The use of the social constructivist approach assists in constructing individualized learning environment based on predetermined zones of proximal development in sociocultural contexts. The radical and critical constructivist approaches to teaching, through the rejection of conventional epistemologies, allow students the freedom to creatively address issues related to environmental, economic, and social sustainability. This becomes effective through the fostering of self and social awareness, challenging existing ideas, and provoking innovative thoughts that are necessary to shape a sustainable future.
The research aimed to describe the development of solar electric cars as a prop in energy conversion learning using the analyze, design, develop, implement, and evaluate (ADDIE) model and to ascertain the effectiveness of an electric car as a prop in energy conversion learning. Utilization of prop in the learning process is one way to support the development of knowledge, skills, and basic needs for delivering material, concepts, and physics information. This research is a descriptive study involving media and pedagogical experts and 40 students of the university in Tasikmalaya. Data collection techniques were carried out through the study of literature, expert validation, and student perception questionnaires. Expert validation and student perception were obtained by using a Likert scale. The expert judgment results were processed using the V value equation developed by Aiken. The results showed a value of 1, meeting the minimum validation requirements. The students also had positive responses to a prop. They have new experience learning in energy conversion and have good media to help their comprehension. It has a significant impact on helping students to achieve their learning goals.
The rise and growing prevalence of juvenile delinquency is a matter of concern for many parties. This study aims to establish a research instrument in the form of a questionnaire that can be deployed to assess the learning environment perceived by high school students. This research endeavor constitutes a developmental study, wherein the outcomes are a single survey instrument encompassing six variables, nineteen indicators, and forty questions. The data-collecting process involved the utilization of a Google Form across five schools in five districts, containing a total of 1615 participants. The analysis of expert data was conducted utilizing V. Aiken and field trials employing confirmatory factor analysis (CFA) Second Order. The findings of this study indicate that the diagnostic survey instrument used to assess the learning environment's impact on the mental health of high school students demonstrated validity, as evidenced by loading factor values exceeding the established minimal threshold. The reliability of the instrument remains insufficient. This survey can be utilized to detect adolescent persistent tendencies carried out by students or other school members that interfere with mental health: the emergence and significant raising of juvenile delinquency.
Marinyo is a culture left by the Portuguese around the 15th century in Maluku. The purpose of this study was to find out to what extent students' misconceptions about the concept of sound in the Marinyo case in the Kepuluan Tanimbar Regency. The method used was a qualitative study in ethnography in ten villages in two sub-districts. In addition, they conducted a survey in the form of a diagnostic test in the form of questions related to the Marinyo case on 300 elementary school students. The findings in the field show that students experience relatively high misconceptions. It was because teachers did not accustom students to learn from natural phenomena around them and were given scientific questions to seek, find and provide answers and solutions related to these natural phenomena. The teacher was more pursuing the conditions and problems of physics in textbooks and less exploring contextual matters. Future researchers are suggested to develop physics or science teaching materials based on regional local advantages that are oriented towards understanding concepts, mental models, critical thinking, problem-solving, creativity and innovative thinking so that teachers and students can learn well so that knowledge of science becomes better.
Online learning is a growing trend in education during the corona virus disease (COVID-19) pandemic. The purpose of this study is to ascertain the difficulties that online majors in non-English languages have when attempting to acquire English. The subject of this study involved using the questionnaire method for as many as 412 students and interviewing 15 students with a total of 17 questions. The results of this study indicate that there are several challenges faced by students during online learning; i) less familiarity with online learning as shown by 31% of students agreeing that online learning is a new learning method, ii) psychologically 30% of students choose strongly agree that they have limited opportunities to interact directly and freely with lecturers as well as with students, iii) limited facilities and infrastructure as much as 28% agree that the budget is limited to get quota or internet credit, and iv) limited internet access as many as 35% of students do not have good internet coverage to take online lectures. The findings of this study should be a reference for English lecturers to continue learning to innovate in providing online English learning by considering the existing challenges.
English for young learners (EYL) teachers have practiced some creative activities to maintain their pupils’ learning with natural exposure to the target language amidst the pandemic. One activity practiced by Indonesian and Korean teachers was an international collaboration to perform a virtual drama of each country’s folktale. This phenomenological research aimed at tapping the teachers’ perceptions regarding interculturality and world Englishes (WE) in the virtual dramatic play collaboratively conducted and delving into their commitments in honing interculturality and WE. Two Indonesian and Korean teachers were involved in three sessions of in-depth interviews using pre-prepared interview questions. The trustworthiness of the data was achieved by the group discussions allowing the participants to comment on and revise the transcribed data, as well as triangulation by two international collaborators. Thematic analysis was performed to identify emerging themes and to provide novel insights into EYL teachers' encounters with interculturality and WE. The Indonesian and Korean teachers admitted the compatibility between language and culture, the urgency of introducing varieties of English, and the merits of conducting international collaboration to promote interculturality and WE. The teachers are committed to integrate interculturality and WE in their instructions despite some differences in the stipulated curricula.
The fear of failure stops students from thinking logically and processing information in mathematics. Creating an appropriate classroom climate based on every student's ability is crucial to overcoming the prejudices associated with mathematics. In this regard, this study aims to create the best classroom climate approach that will increase interest in mathematics and ensure academic success. For this purpose, mathematicians' views on the classroom climate approach and how they create them were discussed by using qualitative techniques. It was considered that teachers participating in this research are working in 9th grade in state high schools affiliated with the Turkish Republic of North Cyprus Ministry of Education, accepting students through examination. The researchers collected teacher views through a semistructured interview form and analyzed them using context analysis. The findings showed that teachers were in a hurry to teach and generally paid attention to creating a comfortable classroom climate in which students could express their thoughts and opinions. This situation also revealed a lack of adequate classroom climate approach skills among teachers. Therefore, the classroom climate approaches discussed in this study are expected to make a significant contribution to this field by offering solutions to teachers in creating a supportive classroom climate.
The article is devoted to the study of the issue of training future police officers to use unmanned aerial vehicles (UAVs) in their professional activities. Based on the results of the theoretical analysis of scientific and applied works, modern trends in the development of drones in the activities of law enforcement agencies were identified, and the problem of their implementation in practical activities was outlined. An online survey was conducted in order to study the opinion of scientific, scientific and pedagogical workers and graduates of higher education institutions with specific learning conditions that train police officers about the need to train future police officers in the control of UAVs. The need to introduce into the system of primary professional training the training of service skills using drones is substantiated. On the basis of the study of the content of the training program for unmanned aircraft systems of the first class according to the basic qualification level of the first level, it is proposed to introduce the general professional educational unit “formation of skills and skills of controlling an UAV” into the training program of the primary professional training of police officers in the specified specialty.
English language teaching (ELT) in Islamic boarding schools in Indonesia, commonly known as pesantren, presents a unique context that requires a tailored pedagogical approach. This study aimed to explore the application of context-responsive pedagogy in ELT within the unique context of Islamic boarding schools in Indonesia. This qualitative study employed semistructured interviews and classroom observation as data generation methods to gain insights into the experiences and perspectives of English language teachers regarding the implementation of context-responsive pedagogy in English language instruction. The findings revealed the importance of understanding learner needs, incorporating authentic materials, promoting cultural sensitivity, and effective use of technology in ELT practices in Islamic boarding school contexts. This study delves into how English language teachers navigated and negotiated their practices with the socio-cultural and religious values entrenched in this institution. It also highlighted the challenges English language teachers in this school context faced in the implementation of context-responsive pedagogy. Eventually, this research provides valuable insights for ELT practitioners, policymakers, and researchers interested in incorporating context-specific pedagogy to optimize ELT in Islamic boarding schools and similar educational contexts.
This study aimed to develop and evaluate a training curriculum intended to enhance the quality of life for the elderly. As Thailand witnesses a demographic shift with increasing numbers of older adults, driven by declining birth rates and extended life expectancies, the importance of ensuring quality elderly care becomes paramount. The devised curriculum encompasses eight principal elements focusing on the elderly, defined as those aged 60 and above, addressing their physical and mental changes, well-being, health, and overall satisfaction. The content is holistic, integrating components of music, art, health care, and exercise. Delivered over a two-day period, the curriculum employs a structured approach featuring lectures, discussions, and knowledge exchanges, supported by a range of media and materials. Initial assessments revealed a moderate quality of life among the elderly, but post-training evaluations indicated enhanced knowledge, understanding, and positive attitudes towards the activities, pointing to an overall high level of effectiveness of the curriculum.
The study of the role of the pedagogy of partnership (PoP) in building the professional competence of future primary school teachers is relevant in the context of modern educational and pedagogical transformations, which require the preparation of teachers for new challenges and creating a favourable learning environment. Therefore, the aim of our study was to check the effect of observing the pedagogical partnership principles in the educational process on the development of the communicative competence of future primary school teachers. The study employed the following psychodiagnostic methods: the Thomas-Kilmann conflict mode instrument (TKI), Myers-Briggs type indicator (MBTI), Snyder’s self-control in communication. The implementation of the PoP programme in higher education institutions (HEIs) has a positive effect on the development of the communicative competence of future teachers, in particular, on developing the ability for self-control and increasing the scope of psychological knowledge. The study revealed some important correlations. Our results indicate that cooperation and the ability to make compromises are directly related to the communicative abilities of future teachers. Further research can be focused on studying the impact of pedagogical partnership on other aspects of future teacher training, such as methodical mastery, motivation for learning and development.
This study examined the relationship between students’ academic performance, teachers’ commitment, and leadership behavior of school administrators. Teachers’ commitment was measured in two areas– commitment to job and commitment to organization and the leadership behavior of school administrators were evaluated in terms of consideration and initiating structure. Eighty-one teachers, 11 school heads, and 470 students served as respondents. The descriptive survey research technique, correlation analysis, and the following statistical methods were used: frequency, mean, standard deviation, and correlation coefficient. The study revealed that the initiating structure and consideration dimensions of leadership behavior affect teachers’ commitment to job (CTJ) and teacher’s commitment to organization (CTO). The correlation between CTJ and CTO and leadership behavior-initiating structure is positive and with leadership behavior-consideration negative. CTJ and CTO is correlated with the students’ academic performance in math, but not in Science and English. The correlation is negative. Students’ academic performance in all subject areas is negatively correlated with leadership behavior-initiating structure and has no significant relationship with leadership behavior-consideration. The leadership behavior-initiating structure is positively correlated with teachers’ commitment to both job and organization but has negative correlation with students’ academic performance in math, science, and English.
This study aims to describe preservice mathematics teacher knowledge of higher order thinking skills in terms of definition, Bloom's taxonomy level, curriculum, learning, and evaluation. This research is quantitative research with a survey method. and sample consisted of 248 preservice mathematics teachers in semesters VI - VIII of the Department of Mathematics Education, Nusa Cendana University, Timor University, and Wira Wacana Sumba University. The instrument used was a questionnaire about high order thinking skill (HOTS) which consisted of 105 statements. Data analysis used Likert's summeted rating, one sample test, Mann Whitney, Kruskall-Wallis tests, multiple linear regression test, and multivariate analyisis of variance (MANOVA) test. The results showed that the knowledge level of preservice mathematics teacher was in the good category. Based on gender differences, there was no significant difference in the average knowledge of preservice mathematics teacher about HOTS, there was a significant difference in the average knowledge of preservice mathematics teacher about HOTS which is significant based on differences in academic ability and gender differences do not significantly affect knowledge about HOTS levels in Bloom's taxonomy, curriculum, and pedagogy while academic knowledge has a significant effect on HOTS knowledge of preservice teachers in almost all aspects except for pedagogy.
Formative assessment is an evaluative practice developed in the classroom for the improvement of learning using evidence on student progression. The objective of this research is to compare sample groups from multigrade and single-grade classrooms on the theme of formative assessment based on the students' opinion of the teacher's performance. The method used was a comparative quantitative method. The sample type is a probability sample of 683 students from 5th to 8th grade from urban and rural schools in the commune of Longaví, located in the Maule Region of Chile. A validated Likert scale questionnaire with a high level of reliability (α = 0.93) was used. The results of the research showed that, in the six dimensions, the best teacher performance concerning formative assessment is found in multi-grade schools and not in single-grade schools. This can be explained on the basis of several reasons, among them the level of adaptability that teachers have in this type of classroom, the heterogeneous characteristics of the classroom (different ages and learning goals) and the need for teachers to monitor the learning progression of students with different classroom characteristics.
Financial literacy, as a fundamental skill in the 21st century, has become a life skill that is urgently needed to be improved. Globally, the drive to enhance financial literacy involves integrating it into the education curriculum, necessitating educators’ comprehensive grasp of financial literacy education before imparting it to students. This research aims to outline a conceptual model of financial literacy professional development to improve teachers’ professional competence, employing a narrative review that synthesizes 28 relevant literatures retrieved from Scopus databases. The results of the study show that an effective training model for teacher professional development (TPD) in financial literacy education should focus on essential financial literacy content consisting of planning and budgeting, banking services, income and careers, insurance, investment, savings, also spending and credit. Furthermore, the main characteristics of TPD regarding financial literacy education should encompass content focus, coherence, ownership, active learning, duration, and collective participation.
The objective of this research is to examine teachers' competence in designing activities after engaging in professional development activities aimed at enhancing teaching design in order to develop students' thinking abilities that are contextually appropriate. The participants consist of 5 elementary school science teachers from schools. The research employed semi-structured interviews and classroom observation as research instruments. The findings reveal that teachers engaged in self-development through observation and learning from their peers within the community of practice (CoP). They receive advice and feedback from fellow teachers and apply these insights to improve their activities. Consequently, teachers are able to continuously refine and develop their teaching approaches to align with students' contexts. This approach facilitate diversification in thinking and learning management, as well as collaborative teamwork to enhance teaching methods. As a result, engaging and interesting thinking development activities are incorporated into student learning, along with the creation of a seamless learning-promoting environment. Collaborative teamwork in instructional design and problem-solving further afford teachers the opportunity for additional self-learning and personal development. This collaborative approach also contributes to fostering cognitive diversity and relieved the need for individual teachers to undertake all tasks independently.
Adaptive online learning can be realized through the evaluation of the learning process. Monitoring and supervising learners’ cognitive levels and adjusting learning strategies can increasingly improve the quality of online learning. This analysis is made possible by real-time measurement of learners’ cognitive levels during the online learning process. However, most of the currently used techniques for evaluating cognitive levels rely on labour-intensive and time-consuming manual coding. In this study, we explore the machine learning (ML) algorithms and taxonomy of Bloom’s cognitive levels to explore features that affect learner’s cognitive level in online assessments and the ability to automatically predict learner’s cognitive level and thus, come up with a recommendation or pedagogical intervention to improve learner’s acquisition. The analysis of 15,182 learners’ assessments of a specific learning concept affirms the effectiveness of our approach. We attain an accuracy of 82.21% using ML algorithms. These results are very encouraging and have implications for how automated cognitive-level analysis tools for online learning will be developed in the future.
This systematic literature review (SLR) aimed to investigate the potential of digital online game-based learning (DOGBL) to enhance motivation in English as a foreign language (EFL). Online gaming has grown in popularity among students, opening up the possibility of using games as powerful instructional resources. Academic achievement depends on motivation, and this study, led by self-determination theory (SDT), explored how external rules, like rewards and recognition, could increase motivation in EFL utilizing DOGBL. The study used the SLR method, examining databases and choosing articles based on predetermined criteria. The chosen publications were examined in-depth, and a preferred reporting items for systematic reviews and meta-analyses (PRISMA) diagram was employed for analysis. For results, DOGBL could enhance teaching EFL by providing flexible and interesting learning environments. Key elements in motivating in DOGBL included game design, personalization, social engagement, curricular integration, and instructor assistance. As a promising method to improve EFL instruction, game-based learning, especially DOGBL, saw considerable developments between 2018 and 2023. Thus, these ground-breaking techniques transformed the way people learn English vocabulary and provided a fun and engaging way to learn the language. For educators and students, the potential for DOGBL to change EFL education is still exciting as technology develops.
The development of postmodern-era technology in the world of education is increasingly sophisticated, thus impacting the character of students and their social environment. Technological progress negatively affects the lives of today's generation. When misuse of technology is widespread, it is imperative to strengthen cultural and religious filtration. So that the influence of globalization on technological development can be minimized. So as not to damage the cultural values and morality of students as the next generation of the nation. This study aims to explain the importance of transforming the values of Bima's local wisdom "Nggusu Waru" through the media of social studies e-books. The results and conclusions of this study are efforts to develop students' social character that require teacher collaboration, supervision, and optimal parental attention so that their interest in learning is higher and minimizes deviant behavior. This research method uses research and development design. At the stage of preliminary studies with models developed by Borg and Gall. Through several stages of research, information gathering, development of initial forms of products, and initial field testing. In this step, data is collected through interviews, observation and documentation. The data is analyzed to find out some of its weaknesses and shortcomings.
More from Journal of Education and Learning (EduLearn) (20)
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
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it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
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reasonable solution for problem solving. Improving the competence of making arguments is necessary for
students to make them capable to describe some reasons of whether strengthening or refusing a perspective,
view, or idea. Having such competence, students may leave any hesitancy and vacillation behind, and thus,
solve the problem. They may also be free to choose and propose a reasonable solution.
The process of an individual making arguments should be analyzed using a more fruitful format so
that he/she might not solely distinguish the premises and conclusions [18]. Therefore Toulmin proposed a
layout of argument known as Toulmin’s Scheme. It consists of Data (D), claim (C), Warrant (W), Backing
(B), Rebuttal ( R), and Qualifier (Q). Data refers to some facts to support the claim proposed. Claim is a
proposition with supporting data. Data and Claim derive from a condition in which “if D, then C”. Warrant is
an assurance for data to support the claim. It has Backing as its supporter. Backing provides further legal-
based evidence as the basis of warrant. Rebuttal is an exceptional condition for arguments, and Qualifier may
reveal the strength level of the data proposed for the claim by warrant. Toulmin’s Scheme to analyze
arguments is presented in Figure 1.
Figure 1. Toulmin’s scheme for analyzing arguments
Warrant types include inductive, structural-intuitive, and deductive [19, 20] and so on. Inductive
warrant is a base derived from the process of evaluating one or more specific cases. Structural-intuitive
warrant is a base derived from the result of intuition (i.e., intuitive thinking) on the structure of an
individual’s internal representation. Deductive warrant is a base derived from the process of formal
mathematics justification in order to assure the general conclusion made. Again, deductive warrant is a
formal mathematics justification to assure a general conclusion [19]. The justification is through several
ways, such as axial cuts, algebraic manipulation, or the examples of denying. Deductive was a thought
derived from general things implemented and led to more specific ones [21]. Deductive was a process of
thinking derived from an existing proposition led to the new one in the form of conclusion [22]. With such
deductive thinking, individuals may start their departure from a theory, principle or conclusion they think it is
right and general in nature. at student-level, it is expected to use deductive warrant in the process of logically
explaining, justifying, and reasoning their arguments in order to ensure, strengthen, or refuse other
arguments, perspectives, or ideas. Therefore, this study focused on the process of thinking of prospective
teachers of mathematics in making arguments with deductive warrant initiated by inductive one.
The utilization of Toulmin’s Scheme for analyzing arguments in education of mathematics was seen
in [23] study which formulated the profile of students’ arguments to solve mathematical problems. That
profile is helpful for teachers to have better understanding on students’ approaches in solving problems. [24]
described the concept of evidence by prospective teachers to justify their arguments in class. Another study
using Toulmin’s Scheme was [25] that evaluated the position of rebuttal. It shows that the previous studies
tended to focus on individuals’ arguments in class discussion (i.e., argument in dialogue) rather than
argument not-in-dialogue. Thus, this present study would specifically discuss the second one; argument not-
in-dialogue. It is important as individuals try to reveal and ensure the right perspective using arguments led to
themselves. They try to ensure themselves. With this competence (i.e., argument not-in-dialogue), they may
get ready for any argument in-dialogue.
The students of mathematics education program were selected as the subject of this study, as they
would be the prospective teachers of mathematics and might contribute to the development of students’
thinking in mathematical argumentation. Students’ arguments depended on the construction of theorem habit
in class, the characteristics of tasks, and the kinds of particular reasoning by teachers [26]. Teachers’
encouragement for students to explain, note, and justify their arguments in a class discussion aimed to
improve students’ capability on argumentation [27]. The concept of evidence by the teachers of mathematics
in junior high schools may affect their teaching practices in assisting students to make arguments [24].
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19
Following the previous theory and studies on the process of thinking and mathematical
argumentation, this present study aimed to describe the process of students’ thinking in making arguments. It
would be analyzed using the framework of Toulmin’s Scheme, that each of the components within would be
further analyzed with Swatz’s theory.
2. RESEARCH METHOD
The sixth-semester students of mathematics education program in STKIP PGRI Jombang participated as
the subject of this study. They are the prospective teachers of mathematics for junior and high school levels. They
were selected as they had learned the concept of relation, indicating that they were capable to solve the given
problems. The selected students were those making arguments with deductive and inductive warrants.
First, the students were given a mathematical problem to be solved by optimally expressing their thought
during the process of problem solving (i.e, think aloud). Second, a task-based semi-structural interview was
conducted. In broadly speaking, this interview aimed to see what kind of thought the subject was thinking of while
inferring something and taking a step. The question might be in the form of “How do you think of this?” or
“what are you thinking of right now?” The questions also aimed to see their reason in taking some steps to solve
the given problem.
The data collection was through test and semi-cultural interview. Thus, the instrument of this study
was a task of mathematics and interview manual. The task was aimed to describe the subject’s arguments
based on the kinds of warrant, as seen in Figure 2. It was adapted from [20]. Some information along with
statements the subject needed to investigate was provided within the instrument. Furthermore, they were
asked to express their thought aloud during the process of completing the given task. Video recording was
conducted to see the subjects’ activities during the process of problem-solving.
Figure 2. Mathematical task
3. RESULTS AND ANALYSIS
260 undergraduate students of mathematics education program of STKIP PGRI Jombang participated in
this study. The kinds of warrant they used were presented in Table 1.
Table 1. Categorization of Students’ Warrant-Based Arguments
Kind of Warrant The Quantity of Student
Inductive 56
Structural-intuitive 15
Deductive 5
Structural inductive and deductive 21
Inductive and deductive 163
Table 1 showed that 62.69% of the prospective teachers of mathematics made their arguments using
inductive and deductive warrant. The following described the process of their thinking in making arguments
with inductive and deductive warrant.
3.1. Constructing the First Idea
The process of thinking by the subject in making arguments to investigate the truth of a given statement
had already started since they mentioned the information provided, including: “P is not chain”. That information
was data for making conclusion that “P is antichain”. The following showed the subject’s think aloud.
Dedefinition 1. Given that S is a partially ordered set of binary relation R on S, and A is the subset of S.
A is called chain if each of two distinctive elements; a , b; on A meets one of either a R b or
b R a.
Definition 2. S is a partially ordered set of binary relation R on S, and B is the subset of S. B is called
antichain, if each of two distinctive elements; a, b; on B meets bot a R b and b R a.
Investigate the truth of the statement “If P is not chain, then P is antichain”!
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Subject: “P is not chain, then P does not meet the condition in which ‘if each of two distinctive elements;
a , b; is on A, then P would be qualified’. However, P does not meet the condition either a R b or
b R a. may it be called antichain?”
The subject’s constructed idea to investigate the mathematical statement was by making the
examples of partially ordered set S and identifying those examples using the definition of chain and
antichain. They had such idea from the previous experience with identic task.
The process of explaining the idea by the subject started from providing the example of set S ={1, 2,
3, 4, 5, 6, 7} and binary relation R = {(a, b)| a is the factor of b, a, b S}. Subsequently, they made and
identified the subset of S using the definition of chain and antichain, respectively. The identification aimed to
show that the example successfully met one of two possibilities: (i) if P is not chain, then P is antichain; or
(ii) if P is chain, then P is antichain. Thus, the subject’s argument used inductive warrant. Figure 3 presented
the subject’s written answer showing argument with inductive warrant.
Figure 3. The subject’s written result
Following [28] perspective, the process of thinking by the subject was on basic level, in which they
used their logical reasoning through multiplication, division, or addition. Following the way of the subject’s
experiment was classified into naïve empiricism, in which they asserted the truth of their result in making
conclusion after verifying some cases [29]. However, that argument was classified into informal argument as
the warrant was based on the concrete interpretation of mathematical concepts [30]. The concrete
representation by group 1 was making specific examples.
3.2. Evaluating the Fairness of the First Idea
At the stage of evaluating the fairness of their idea, the subject expressed the legal basis (i.e.,
backing) of their idea. They claimed that the backing was in the form of a subset not classified into chain, and
thus indeed classified into antichain, as well as the vice versa.
The subject concluded that if P was not chain, then P was antichain. The level of trust (i.e., qualifier)
for that conclusion was still probable, in which if P was most likely not chain, then P would be antichain. It
was because the subject still saw S as a set consisting of 7 members. Another possibility was that, for
instance, S was a set of complex and real numbers.
The conformity between qualifier and the kind of warrant in the subject’s argument was consistent
with [20] that inductive warrant aimed to alleviate the uncertainty of conclusion. The following presented the
subject’s statement on an interview.
Subject : I thought that there might be an exception as the conclusion remained likely true, Mam.
The subject’s exploration showed that there was likely a rebuttal on the conclusion. However, they
did not specifically describe what such rebuttal was.
Identifying the specific evidence 1
Identifying the specific evidence 2
Identifying the specific evidence 3
Qualifier Rebuttal
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The process of thinking by prospective teachers of mathematics in making arguments (Lia Budi Tristanti)
21
3.3. Constructing the Second Idea
The second idea constructed by the subject was to investigate the truth of formally mathematical
statement. The process of explaining this idea started since they negated the definition of chain. The negation
of the definition of chain was the definition of “non-chain”. The subject compared definitions between “non-
chain” and “antichain”. They realized that the definition of “non-chain” is not similar to the definition of
“antichain”. Hence, they argued that if P was not chain, it was still in the air that P was antichain. Therefore,
they made some examples of denying for the statement “if P was not chain, then P was antichain”. The
examples of denying by the subject was set A = {2, 3, 4} and himpunan B = {4, 9, 16} with binary relation R
= {(a, b)| a the factor of b, a, b S}. Thus, the argument used deductive warrant. They concluded that the
statement “of P was not chain, then P was antichain” was wrong. Figure 4 presented the subject’s written
result showing the argument with deductive warrant.
Figure 4. The subject’s written result
That argument was classified into formal one as the warrant was based on the definition, axiom, and
theorem [30]. The subject used the formal argument to eliminate any hesitancy, and thus ensure the truth of
the statement.
3.4. Clarifying the Ideas
At this stage, the subject did not combine those constructed ideas to ensure the conclusion in case of
comparing the definition of non-chain and antichain as well as the counterexample. The reason not
combining those ideas was because they revealed different conclusions. Thus, the subject put aside those
which had different conclusions. Nevertheless, the ideas were used as the conclusion’s rebuttal. It was
consistent with [31] that inductive frame was constructed at the initial phase of deductive frame. In addition,
deductive frame might be useful to either support or rebut inductive warrant.
3.5. Evaluating the Fairness of the Ideas
The subject re-read their written result and adjusted each of their ideas with the given information.
Those ideas were justified based on the applied rule. The basic rule (i.e., backing) was in the form of
negation of both quantor and plural statements. The subject inferred that if P was not chain, then it was still
in the air that P was antichain. They defined that the statement was wrong as not all non-chain were
antichain. They found a rebuttal on their ideas, in which the conclusion would not be applicable if each of
the elements of A was not interrelated. The subject revealed the qualifier from their conclusion in the form of
certain. The conformity between the qualifier and the kinds of warrant in the argument did exist. It was
consistent with [20] that deductive warrant was used to alleviate any hesitancy and uncertainty on the
conclusion. The following showed the result of the subject’s think aloud. Table 2 interpreted the thinking
path of such argument, as follow.
The piece of the definition of chain
Making the definition on non-chain
Making the counter example 1
Making the counter example 2
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Subject : If P is not chain, then P is antichain, and thus, the inconformity disappears, oh wait,.. rather
than disappeared, it is used as a rebuttal in which each of the elements of P is not interrelated,
and thus, it would meet the statement ‘if P is not chain, then P is antichain. Thus, it is clear
that the statement ‘if P is not chain, then P is antichain is wrong.
Table 2. The Stage of Thinking and the Scheme of the Subject’s Argument
The Stage of
Thinking
The Scheme of Mathematical Argumentation Explanation
Constructing
the first idea
The subject defined the data (D) and claim (C) based on the
given information on task, and then identified some specific
cases to make a general conclusion. Therefore, they used
inductive warrant (Wi) to ensure the data for the claim.
Evaluating the
fairness of the
first idea
The subject revealed the backing (Bi) ensuring the truth of
the first idea. The qualifier (Qi) from the conclusion was
probable. They found an exceptional condition (rebuttal)
(Ri) in that conclusion. Nevertheless, they did not
specifically describe what such rebuttal was.
Constructing
the second idea
Constructing the second idea was aimed to strengthen the
conclusion of the first idea. It was to verify the conclusion
derived from a theory or principle that they considered true,
and thus, they used deductive warrant (Wd) on their
argument.
Clarifying the
first and the
second ideas
At this stage, the subject combined between inductive (Wi)
and deductive (Wd) warrants to ensure the data for the claim
(C). Those two warrants, however, might reveal different
conclusions, and thus, it made deductive warrant act against
the conclusion derived from inductive warrant.
Evaluating the
fairness of the
ideas
The subject revealed the backing (Bd) to ensure the truth of
deductive warrant (Wd). In addition to backing, the subject
also revealed a rebuttal (Rd), indicating that no exceptional
condition existed on the conclusion. The Qualifier (Qd) of
the conclusion derived from deductive warrant was certain.
Thus, the qualifier and conclusion derived from deductive
warrant may against the qualifier and conclusion derived
from inductive warrant.
4. CONCLUSION
The process of thinking by undergraduate students in making arguments started from the stage of
constructing the first idea, in which they expressed the components of arguments, including Data, Claim, and
Warrant. The idea was by taking some objects in order to make conclusion. At the stage of evaluating the
first idea, they showed the components of Qualifier, Backing, and Rebuttal. The level of trust (i.e., qualifier)
of the conclusion derived from inductive warrant was probable. Furthermore, they found an exceptional
condition (i.e., rebuttal) on the conclusion. However, they did not specifically describe what the rebuttal was.
At the stage of constructing the second idea, the students verified and formulated a conclusion using
D Ci
Wi
D Qi, Ci
Wi
Bi
Ri
D
Wd
Cd
D
Wi
Bi
Ri
Qi, Ci
Wd
Cd
Conclusion Qualifier
Rebuttal
D
Wi
Bi
Ri
Qi, Ci
Wd
Bd
Rd
Qd, Cd
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deductive warrant. Their current argument with this second idea was derived from a theory, principle, and/or
conclusion they considered true or general in nature. The justification was from some axial cuts, algebraic
manipulation, and counterexample. At the stage of clarifying the ideas, the students connected inductive
warrant to deductive warrant. These two warrants were connected when they had similar conclusion.
Inductive warrant would be put aside when the conclusion revealed was different from deductive warrant. At
the stage of evaluating the fairness of the second idea, the students showed the components of Backing,
Qualifier, and Rebuttal. They eliminated any possible rebuttal as the qualifier of the conclusion was
certain. Thus, deductive warrant might improve the assurance of the conclusion revealed; from being
probable to certain. Overall, deductive warrant might either strengthen or weaken the conclusion derived
from inductive warrant.
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BIOGRAPHIES OF AUTHORS
Lia Budi Tristanti She graduated from elementary to junior high school in Jombang, namely MI
Raden Fattah Ngusikan Jombang (graduated in 2000), MTsN Bakalan Rayung Ngusikan
Jombang (graduated in 2003), SMKN 1 Jombang (graduated in 2006). Education Mathematics
S1 at STKIP PGRI Jombang (graduated in 2010) with degree S.Pd. The next education she took
at the State University of Surabaya with the ongoing BPPS scholarship from Dikti. In 2012, she
holds a Masters Degree in Mathematics Education. She continued her education in Mathematics
Doctoral Program at State University of Malang in 2013 with BPPDN scholarship from Dikti.
Career as a lecturer at STKIP PGRI Jombang from 2010 until now.