Developing a Learning Trajectory on Fraction Topics by Using Realistic Mathem...iosrjce
This research and development was purposed at (1) developing a learning trajectory on fraction
topics by using Realistic Mathematics Education approach in Primary School; and (2) determining the validity,
practicality, and the effectiveness of the learning trajectory. The results of this research were (1) a learning
trajectory on fraction topics in the form of Teacher’s Guide Book and Student’s Book. (2) Teachers’ Guide Book
and the Student’s Book of learning trajectory were considered valid, practical and effective after being judged
by experts in Mathematics Educators, Language Educators, Experienced Teachers and an Educationalist.
Based on the research results, it can be concluded that the learning trajectory on Fraction Topics by using
Realistic Mathematics Education Approach can be effectively used to improve the learning effectiveness on
Fraction Topics in Primary School.
JURNAL: An Action Research The Effect of Computer-based Mathematics on Proble...Zuzan Michael Japang
This document provides an overview of an action research project examining the effects of computer-based mathematics instruction on problem solving and student attitudes. The researcher plans to have their 3rd grade students use the Edutest computer program for math instruction in addition to their regular curriculum. Students will take pre- and post-tests to measure achievement and an attitudes survey. The goal is to see if computer-based math improves problem solving and influences student attitudes towards math.
An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...AJHSSR Journal
This article is about an analysis of teachers’ Pedagogical Content Knowledge (PCK) during
teaching the concept of number for early childhood. Research subjects were three kindergarten teachers in
Depok area, West Java, Indonesia. This type of research is qualitative that analyzed the phenomenon of PCK
when teaching the concept of numbers to children aged 5-6 years. Researchers conducted two observations,
interviews and documentation studies. The results showed that the three respondents did not understand the
concept of numbers as a whole. Respondents also did not comprehend the definition of the concept of numbers
and the appropriate stages associated with the concept of numbers. In addition, the three teachers did not
understand the overall curriculum of early childhood education. However, with their sufficient teaching
experience, they were considered to have good teaching skills and good evaluation of learning process. The
obstacle faced by them was quite the same in which they still found it difficult to teach the concept of numbers
with different characteristics of children. It required a particular strategy for the teachers to overcome these
obstacles. The results of this study is expected to be a consideration to hold a professional workshop
development program in order to improve the professionalism of early childhood teachers particularly in
teaching mathematics.
This study was done to analyze the effect of Polyatype problem solving learning oriented toward realistic mathematics on the ability to solve mathematical word problems. This study belongs to an experimental research with the Posttest Only Control Group Design. The population used in this study was the students of grade 4 at Gugus VIII SukawatiGianyarelementary schools with the total number of 138. The sample was selected through random sampling. The result of selection by lottery assigned Grade 4 students of SDN 4 SingapaduKaler to the control class and Grade 4 students of SDN 1 SingapaduKaler to the experiment class. The data were collected through an essay test that had been validated. The data that had been collected were analyzed through a difference test (t-test). Based on the result of data analysis it can be concluded that the use of Polya type problem solving teaching model oriented toward realistic mathematics gave a positive effect to the ability to solve word problems among the Grade 4 students in Gugus VIII Sukawati Gianyar.
Project based science-learning_and_pre-service_teachersGraceLangcoy
This study examined the effectiveness of project-based science learning on pre-service teachers' science literacy skills and creative thinking abilities in wave and optical materials. 115 pre-service teachers participated in the study. Students were divided into two groups - an experimental group that used project-based learning and a control group that used conventional learning.
The results showed that project-based learning was more effective at improving students' science literacy skills and creative thinking abilities compared to conventional learning. Students' science literacy skills such as analyzing and interpreting data improved to a moderate degree with project-based learning, while conventional learning led to low improvements. Students were also more likely to search scientific journals and proceedings for references after project-based learning. However, some
The effectiveness of direct learning in academic writing referred to students...Alexander Decker
(1) The study examined the effectiveness of three teaching methods (Direct Learning, Inquiry Learning, and Problem Based Learning) on academic writing skills and the influence of reading habits (high vs. low).
(2) It found that Direct Learning was the most effective method for improving academic writing, while Inquiry Learning and Problem Based Learning had similar effectiveness. High reading habits also had more influence on academic writing skills.
(3) Additionally, there was an interaction between the teaching methods and reading habits - the method's effectiveness depended on whether students had high or low reading habits.
The application of reciprocal teaching on the subject of straight line equati...Alexander Decker
This document summarizes a study on applying reciprocal teaching to teach straight line equations in secondary school mathematics. The study found that:
1) Students who learned using reciprocal teaching had better learning outcomes than those taught through conventional methods.
2) Reciprocal teaching was an effective model for teaching straight line equations. Both students and teachers responded positively to this approach.
3) Reciprocal teaching helped students communicate knowledge through discussion, ask questions, and summarize what they learned. It trained them to be more independent learners.
This literature review discusses how group work can impact student attitude in an English classroom. It describes that while lectures, whole-class discussions, group work, and individual work all have a place in English instruction, research shows that small group work specifically allows students to learn from each other and arrive at a deeper understanding of texts. When working in groups, students can analyze their own responses to readings as well as their peers' responses, drawing on different experiences and perspectives to comprehend the literature. The review cites several theorists who argue that dialogue-focused small group work helps students consider both the text and their classmates' knowledge, leading to fuller understanding.
Developing a Learning Trajectory on Fraction Topics by Using Realistic Mathem...iosrjce
This research and development was purposed at (1) developing a learning trajectory on fraction
topics by using Realistic Mathematics Education approach in Primary School; and (2) determining the validity,
practicality, and the effectiveness of the learning trajectory. The results of this research were (1) a learning
trajectory on fraction topics in the form of Teacher’s Guide Book and Student’s Book. (2) Teachers’ Guide Book
and the Student’s Book of learning trajectory were considered valid, practical and effective after being judged
by experts in Mathematics Educators, Language Educators, Experienced Teachers and an Educationalist.
Based on the research results, it can be concluded that the learning trajectory on Fraction Topics by using
Realistic Mathematics Education Approach can be effectively used to improve the learning effectiveness on
Fraction Topics in Primary School.
JURNAL: An Action Research The Effect of Computer-based Mathematics on Proble...Zuzan Michael Japang
This document provides an overview of an action research project examining the effects of computer-based mathematics instruction on problem solving and student attitudes. The researcher plans to have their 3rd grade students use the Edutest computer program for math instruction in addition to their regular curriculum. Students will take pre- and post-tests to measure achievement and an attitudes survey. The goal is to see if computer-based math improves problem solving and influences student attitudes towards math.
An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...AJHSSR Journal
This article is about an analysis of teachers’ Pedagogical Content Knowledge (PCK) during
teaching the concept of number for early childhood. Research subjects were three kindergarten teachers in
Depok area, West Java, Indonesia. This type of research is qualitative that analyzed the phenomenon of PCK
when teaching the concept of numbers to children aged 5-6 years. Researchers conducted two observations,
interviews and documentation studies. The results showed that the three respondents did not understand the
concept of numbers as a whole. Respondents also did not comprehend the definition of the concept of numbers
and the appropriate stages associated with the concept of numbers. In addition, the three teachers did not
understand the overall curriculum of early childhood education. However, with their sufficient teaching
experience, they were considered to have good teaching skills and good evaluation of learning process. The
obstacle faced by them was quite the same in which they still found it difficult to teach the concept of numbers
with different characteristics of children. It required a particular strategy for the teachers to overcome these
obstacles. The results of this study is expected to be a consideration to hold a professional workshop
development program in order to improve the professionalism of early childhood teachers particularly in
teaching mathematics.
This study was done to analyze the effect of Polyatype problem solving learning oriented toward realistic mathematics on the ability to solve mathematical word problems. This study belongs to an experimental research with the Posttest Only Control Group Design. The population used in this study was the students of grade 4 at Gugus VIII SukawatiGianyarelementary schools with the total number of 138. The sample was selected through random sampling. The result of selection by lottery assigned Grade 4 students of SDN 4 SingapaduKaler to the control class and Grade 4 students of SDN 1 SingapaduKaler to the experiment class. The data were collected through an essay test that had been validated. The data that had been collected were analyzed through a difference test (t-test). Based on the result of data analysis it can be concluded that the use of Polya type problem solving teaching model oriented toward realistic mathematics gave a positive effect to the ability to solve word problems among the Grade 4 students in Gugus VIII Sukawati Gianyar.
Project based science-learning_and_pre-service_teachersGraceLangcoy
This study examined the effectiveness of project-based science learning on pre-service teachers' science literacy skills and creative thinking abilities in wave and optical materials. 115 pre-service teachers participated in the study. Students were divided into two groups - an experimental group that used project-based learning and a control group that used conventional learning.
The results showed that project-based learning was more effective at improving students' science literacy skills and creative thinking abilities compared to conventional learning. Students' science literacy skills such as analyzing and interpreting data improved to a moderate degree with project-based learning, while conventional learning led to low improvements. Students were also more likely to search scientific journals and proceedings for references after project-based learning. However, some
The effectiveness of direct learning in academic writing referred to students...Alexander Decker
(1) The study examined the effectiveness of three teaching methods (Direct Learning, Inquiry Learning, and Problem Based Learning) on academic writing skills and the influence of reading habits (high vs. low).
(2) It found that Direct Learning was the most effective method for improving academic writing, while Inquiry Learning and Problem Based Learning had similar effectiveness. High reading habits also had more influence on academic writing skills.
(3) Additionally, there was an interaction between the teaching methods and reading habits - the method's effectiveness depended on whether students had high or low reading habits.
The application of reciprocal teaching on the subject of straight line equati...Alexander Decker
This document summarizes a study on applying reciprocal teaching to teach straight line equations in secondary school mathematics. The study found that:
1) Students who learned using reciprocal teaching had better learning outcomes than those taught through conventional methods.
2) Reciprocal teaching was an effective model for teaching straight line equations. Both students and teachers responded positively to this approach.
3) Reciprocal teaching helped students communicate knowledge through discussion, ask questions, and summarize what they learned. It trained them to be more independent learners.
This literature review discusses how group work can impact student attitude in an English classroom. It describes that while lectures, whole-class discussions, group work, and individual work all have a place in English instruction, research shows that small group work specifically allows students to learn from each other and arrive at a deeper understanding of texts. When working in groups, students can analyze their own responses to readings as well as their peers' responses, drawing on different experiences and perspectives to comprehend the literature. The review cites several theorists who argue that dialogue-focused small group work helps students consider both the text and their classmates' knowledge, leading to fuller understanding.
Searching for the relationship between secondary schools students' motivation...inventionjournals
This study aims to search students' science learning motivation in relation with some variables (such as having a separate study room at home and a personal computer) and the effect of motivational factors on students' science achievement. In the study, descriptive corelational survey model has been used to examine students' motivation in relation with some variables and to search the relationship between students' science learning motivation and their TEOG exam scores. The sample of the study consisted of 232 8th grade students attending 3 state secondary schools in Kahramanmaraş during 2013-2014 academic year. Students' motivation level has been determined by administering SMTSL. Students' average scores of the TEOG exam have been considered as their science achievement. The findings show that female students’ motivation level is higher than the male students. In addition, it has been observed that female students’ motivation is higher in sub-categories of active learning strategies, science learning value and achievement goal. There is a direct relationship between the students’ motivation and their TEOG scores. This shows that students with higher levels of motivation have higher success in TEOG.
Efforts to Improve Indonesian Language Learning Outcomes Students in Writing ...M. Ifaldi Sidik
This study aims to obtain information and find out about Efforts to Improve Student Learning Outcomes of Students in Writing Creative Drama Texts in One Chapter by Paying Attention to the Authenticity of Ideas through the Two Stay Two Stray Model in Class VIII.3 SMPN 1 Batang Anai, Padang Pariaman District. This type of research is classroom action research with 34 students. This research uses a qualitative approach. Research procedures include planning, implementing, observing, and reflecting. This research is carried out in two cycles and is carried out collaboratively between researcher and observer. The technique used in gathering Data are observations, tests, field notes and documentation with the research subjects being the teacher and students. The results of this study indicate that student learning outcomes in the learning process by using the Two Stay Two Stray learning model experienced an increase starting from pre-cycle, Cycle I and Cycle II.
The document discusses several perspectives on effective teaching and learning strategies:
- Humor can promote positive student-teacher relationships (Gorhan and Christophel)
- Teachers must understand students and equip themselves with effective skills and materials to motivate students and ensure academic success (Almario)
- Teaching is a responsibility that requires teachers to reflect on improving education quality (Gonzales)
- Effective teaching depends on a teacher's understanding of students and the learning process (Bustos and Espiritu)
- Identifying student weaknesses and achievement levels is key to teaching study skills effectively (Aquino)
- Providing adequate instructional resources and training teachers on their use is important for math teaching (A
It is necessary to develop metacognitive skills-based teaching materials to foster mathematical problem-solving abilities. This research is a research and development. Method used for development using four phases: Design, Construction, Testing, Evaluation and Revision. The criteria used to assess the quality of the learning device refer to the material quality criteria namely: validity, practicality, effectiveness. Subject of trials in this research are 25 students of XI IPA-4 and 25 students of XI IPA-2. Two indicators of this study are metacognitive skills and problem solving. Metacognitive skills are: prediction skills, planning skills, monitoring skills, and evaluation skills. Indicators of problem solving are: understanding the problem, devising a plan, carrying out the plan, and looking back. The data are collected by giving Tests and questionnaires, and through observations. The research instruments are: questionnaire of validation for teaching materials, student questionnaire responses to instructional materials, observation sheet activities of learners, observation sheets of learning implementation and learning management observation sheet. The result of this research is metacognitive skills-based teaching materials are succeeded (fulfilling the criteria of valid, practical, and effective) to emerge students mathematical problem-solving.
1) The document discusses students' beliefs about mathematics, including their beliefs about the characteristics of mathematics, mathematical content, processes, cognitive processes, and usefulness of mathematics. It also examines students' self-beliefs and relationship to mathematics anxiety.
2) Research findings show that students identify mathematical content as numbers, operations, and problem-solving using formulas. Some see mathematics as exploring topics. Others view it as understanding concepts or thinking processes.
3) Students believe mathematics is useful for daily life, overcoming problems, and careers. Their self-confidence and views of teachers also impact their relationship to mathematics.
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.
This study aims to investigate whether student anxiety about the subject of mathematics has any effect on the achievement of middle-school students in Amman, Jordan. It also aims to investigate whether student gender plays a role. The study sample consists of 180 seventh grade students enrolled in Amman public schools during the 2018/2019 academic year. These are distributed into three levels of anxiety as displayed by the students: low, middle, and high. Then, math anxiety measurements are collected, the validity and reliability for which are verified. The results reveal that there are statistically-significant differences in achievement between the middle level of math anxiety and the two other extremes. It is found that middle anxiety level have a positive effect on achievement, whereas for low and high math anxiety levels, no differences in achievement are perceived. In addition, no statistically significant differences (α≤0.01) were found between males and females with regards to math anxiety; and there is no interaction between the level of math anxiety and gender in achievement.
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 purpose of this research is to analyze the improvement of students' mathematical literacy ability through the use of mathematics teaching materials with metacognitive approach guidance. This research will be held in the city of Kendari to the subject of this research target is students who are at grade 5 Land in Junior High VIIID Kendari years lessons 2017/2018 with many limited scale trial class is only required as much as 1 class. To know the significance of the increase in the literacy abilities of students using paired t-test. Data processing using the SPSS program with criteria if α=0,05 then there is an increased of student's mathematical literacy ability. The results of the analysis on the stages of the evaluation shows the learning materials with metacognitive approach guidance can provide better against an increase in student learning. The ability of the early mathematical literacy against students is very less because of learning during this time students have not been directed with the ability of mathematical literacy. After the students get learning by using learning materials through metacognitive approach guidance, the ability of mathematical literacy students’ level 3 and level 4 underwent significant improvement.
1) The document discusses students' beliefs about mathematics, including their beliefs about the characteristics of mathematics, mathematical content, processes, cognitive processes, and usefulness of mathematics. It also discusses factors influencing students' self-concept, anxiety levels, and perceptions of mathematics teachers.
2) Research findings show that mathematics anxiety is a major contributor to students' achievement in mathematics. Students' relationships with their teachers also significantly impact their motivation and success.
3) Students view ideal mathematics teachers as having qualities like patience, clear explanations, ensuring students understand concepts, and being approachable. Both personal characteristics and instructional skills are important for effective teaching.
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 several studies on factors that influence student achievement and performance in mathematics. It describes research finding that teacher classroom management skills, teaching strategies, use of instructional materials, and student motivation and interest are important factors. Additionally, it discusses how teacher experience and competencies, as well as environmental school factors can impact student learning outcomes.
This document discusses a study on the differences in self-efficacy levels between male and female students based on their science literacy skills and learning outcomes. The study found that male students had higher levels of self-efficacy than female students across three dimensions: magnitude, strength, and generality. Male students also had superior science learning outcome scores compared to female students. However, the differences in scores between genders were not large. The study suggests developing students' self-confidence to improve their self-efficacy levels and academic performance.
Enhancing Pupils’ Knowledge of Mathematical Concepts through Game and Poemiosrjce
The study investigated the effects of game and poem enhanced instruction on pupils’ knowledge of
mathematics concepts in mathematics (Fractions and decimals, Volume of, cylinder; triangular prisms and
sphere; Capacity and Weight). A total of 344 pupils from twelve (12) public primary schools of Ogbia and
Yenagoa Local Government Areas of Bayelsa State, Nigeria were involved in the study. A pretest-posttest
control group quasi-experimental design was adopted in the research. The moderating effects of gender were
also examined on the independent and dependent variables. Using ANCOVA statistics, the results revealed that
pupils exposed to game and poem enhanced instruction have better mean score in knowledge of mathematics
concepts than the control groups. Poem was found to be more effective in improving pupils’ knowledge of
mathematics concepts than game and a non-significant gender difference existed in the mean scores in
knowledge of mathematics concepts. There was no significant interaction effect of gender on pupils’ knowledge
of mathematics concepts. The implication of the findings was discussed and appropriate recommendations were
made.
Melinda Eichhorn - Exploring the use of a screening tool to investigate stude...Melinda Eichhorn
This document discusses a study that investigated the use of a mathematical screening tool with second grade students in Kolkata, India. The screening tool was designed to identify students' grade-level math skills, number sense, and common error patterns. The study found that the screening tool provided teachers with valuable information about their students' mathematical understanding and misconceptions. This allowed teachers to better target instruction and interventions to support students who were struggling. The screening tool empowered teachers to identify issues and begin interventions earlier than waiting for a formal diagnosis. Overall, the screening tool was an effective way for teachers to assess their students' math abilities and tailor instruction accordingly.
This research is aimed at finding out: 1) the influence of discovery learning model with RME approach on Mathematics learning achievement; 2) the influence of interpersonal intelligence on Mathematics learning achievement; 3) the interaction between discovery learning model with RME approach and interpersonal intelligence on Mathematics learning achievement. The research was conducted at one of the state Elementary Schools in Banjarsari sub-district, Surakarta. The method used in this research was quasiexperimental method with 2x3 factorial design. Hypothesis test was done by two-way variance ANOVA test with different cells. It can be concluded that the discovery learning model with RME approach gives better influence on the Mathematics learning achievement than the direct learning model. Students having high interpersonal intelligence category get better Mathematics learning achievement than those having medium and low category. The students having medium interpersonal intelligence get better Mathematics achievement than those having low category. There is no interaction between learning model and interpersonal intelligence on Mathematics learning achievement.
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.
Exploring Teachers Practices of Classroom Assessment in Secondary Science Cla...Md. Mehadi Rahman
The study investigates teachers’ classroom assessment practices of secondary schools in Bangladesh. The study is mainly quantitative with some integration of qualitative approach. Secondary science teachers and their science classrooms were main data source of the study, which were selected randomly. Data sources were secondary science teachers and their science classrooms. The study used a lesson observation protocol to understand their classroom assessment practice, and pre-lesson and post-lesson observation interview protocols as main sources of data collection. Qualitative data from interview were used to triangulate the quantitative data from observation. A total of thirty teachers (twenty male and ten female) were chosen randomly from six secondary schools in Dhaka. The study explored that teachers’ current practice of classroom assessment was to only assess students learning achievement and they followed traditional methods to assess students. The dominated assessment activity was oral questioning and very few students take part in the assessment activities by answering the questions. The classroom questions are basically focused very specific responses and encouraged rote learning; even students’ didn’t get enough time for thinking and answering the questions. Therefore the study suggests changing current practices by using different assessment strategies like self and peer assessment and focus on assessment for learning to ensure effective teaching-learning and quality education. These findings can inform the classroom teachers as well as o relevant stakeholders in making necessary changes in the present classroom assessment practices in Bangladesh.
The effect of project based learning model with kwl worksheet on student crea...Alexander Decker
This document summarizes a study that analyzed the effect of project-based learning (PjBL) with KWL worksheets on student creative thinking in physics problem solving. The study involved randomly assigning undergraduate physics students to either an experiment group that used PjBL and KWL worksheets or a control group that used traditional cooperative learning. Assessment results showed that students in the PjBL group had higher creative thinking scores than the control group, indicating PjBL is an effective way to develop student creative thinking and engagement in physics learning. The document also provides background on PjBL principles and benefits, defining it as a student-centered approach that uses authentic projects to help students construct knowledge and demonstrate understanding through hands-on
The document provides background information on factors that affect students' mathematics performance. It discusses how positive attitudes and understanding the real-world applications of math can improve performance. The conceptual framework outlines how student-related factors like interest and study habits, and teacher-related factors like personality, teaching skills, and instructional materials influence mathematics performance. The study aims to determine the extent of these factors and their relationship to performance among high school students.
The document discusses several studies and perspectives on effective teaching strategies and factors that influence student achievement and performance. Specifically, it discusses:
1) The importance of providing adequate instructional resources and materials to support effective mathematics teaching.
2) The need for teachers to practice effective study skills and receive training on using instructional materials.
3) Factors found to influence student performance including gender, interest in mathematics, teaching competencies, strategies, library setting, and classroom setting.
4) The role of teachers in classroom management, facilitating learning, and evaluating students, and ensuring a conducive learning environment.
Professionalism in teaching mathematics demographic profiling of secondary sc...Alexander Decker
1) The document profiles secondary school mathematics teachers in Taraba State, Nigeria based on their teaching experience, university subject studied, and academic qualifications.
2) It surveyed 327 secondary school mathematics teachers and found that they come from diverse backgrounds and less than 40% have teacher certification in mathematics education.
3) The study aimed to examine teachers' conceptions of problem solving and how they relate to professionalism in teaching mathematics, in order to help address poor student performance in the subject.
Searching for the relationship between secondary schools students' motivation...inventionjournals
This study aims to search students' science learning motivation in relation with some variables (such as having a separate study room at home and a personal computer) and the effect of motivational factors on students' science achievement. In the study, descriptive corelational survey model has been used to examine students' motivation in relation with some variables and to search the relationship between students' science learning motivation and their TEOG exam scores. The sample of the study consisted of 232 8th grade students attending 3 state secondary schools in Kahramanmaraş during 2013-2014 academic year. Students' motivation level has been determined by administering SMTSL. Students' average scores of the TEOG exam have been considered as their science achievement. The findings show that female students’ motivation level is higher than the male students. In addition, it has been observed that female students’ motivation is higher in sub-categories of active learning strategies, science learning value and achievement goal. There is a direct relationship between the students’ motivation and their TEOG scores. This shows that students with higher levels of motivation have higher success in TEOG.
Efforts to Improve Indonesian Language Learning Outcomes Students in Writing ...M. Ifaldi Sidik
This study aims to obtain information and find out about Efforts to Improve Student Learning Outcomes of Students in Writing Creative Drama Texts in One Chapter by Paying Attention to the Authenticity of Ideas through the Two Stay Two Stray Model in Class VIII.3 SMPN 1 Batang Anai, Padang Pariaman District. This type of research is classroom action research with 34 students. This research uses a qualitative approach. Research procedures include planning, implementing, observing, and reflecting. This research is carried out in two cycles and is carried out collaboratively between researcher and observer. The technique used in gathering Data are observations, tests, field notes and documentation with the research subjects being the teacher and students. The results of this study indicate that student learning outcomes in the learning process by using the Two Stay Two Stray learning model experienced an increase starting from pre-cycle, Cycle I and Cycle II.
The document discusses several perspectives on effective teaching and learning strategies:
- Humor can promote positive student-teacher relationships (Gorhan and Christophel)
- Teachers must understand students and equip themselves with effective skills and materials to motivate students and ensure academic success (Almario)
- Teaching is a responsibility that requires teachers to reflect on improving education quality (Gonzales)
- Effective teaching depends on a teacher's understanding of students and the learning process (Bustos and Espiritu)
- Identifying student weaknesses and achievement levels is key to teaching study skills effectively (Aquino)
- Providing adequate instructional resources and training teachers on their use is important for math teaching (A
It is necessary to develop metacognitive skills-based teaching materials to foster mathematical problem-solving abilities. This research is a research and development. Method used for development using four phases: Design, Construction, Testing, Evaluation and Revision. The criteria used to assess the quality of the learning device refer to the material quality criteria namely: validity, practicality, effectiveness. Subject of trials in this research are 25 students of XI IPA-4 and 25 students of XI IPA-2. Two indicators of this study are metacognitive skills and problem solving. Metacognitive skills are: prediction skills, planning skills, monitoring skills, and evaluation skills. Indicators of problem solving are: understanding the problem, devising a plan, carrying out the plan, and looking back. The data are collected by giving Tests and questionnaires, and through observations. The research instruments are: questionnaire of validation for teaching materials, student questionnaire responses to instructional materials, observation sheet activities of learners, observation sheets of learning implementation and learning management observation sheet. The result of this research is metacognitive skills-based teaching materials are succeeded (fulfilling the criteria of valid, practical, and effective) to emerge students mathematical problem-solving.
1) The document discusses students' beliefs about mathematics, including their beliefs about the characteristics of mathematics, mathematical content, processes, cognitive processes, and usefulness of mathematics. It also examines students' self-beliefs and relationship to mathematics anxiety.
2) Research findings show that students identify mathematical content as numbers, operations, and problem-solving using formulas. Some see mathematics as exploring topics. Others view it as understanding concepts or thinking processes.
3) Students believe mathematics is useful for daily life, overcoming problems, and careers. Their self-confidence and views of teachers also impact their relationship to mathematics.
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.
This study aims to investigate whether student anxiety about the subject of mathematics has any effect on the achievement of middle-school students in Amman, Jordan. It also aims to investigate whether student gender plays a role. The study sample consists of 180 seventh grade students enrolled in Amman public schools during the 2018/2019 academic year. These are distributed into three levels of anxiety as displayed by the students: low, middle, and high. Then, math anxiety measurements are collected, the validity and reliability for which are verified. The results reveal that there are statistically-significant differences in achievement between the middle level of math anxiety and the two other extremes. It is found that middle anxiety level have a positive effect on achievement, whereas for low and high math anxiety levels, no differences in achievement are perceived. In addition, no statistically significant differences (α≤0.01) were found between males and females with regards to math anxiety; and there is no interaction between the level of math anxiety and gender in achievement.
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 purpose of this research is to analyze the improvement of students' mathematical literacy ability through the use of mathematics teaching materials with metacognitive approach guidance. This research will be held in the city of Kendari to the subject of this research target is students who are at grade 5 Land in Junior High VIIID Kendari years lessons 2017/2018 with many limited scale trial class is only required as much as 1 class. To know the significance of the increase in the literacy abilities of students using paired t-test. Data processing using the SPSS program with criteria if α=0,05 then there is an increased of student's mathematical literacy ability. The results of the analysis on the stages of the evaluation shows the learning materials with metacognitive approach guidance can provide better against an increase in student learning. The ability of the early mathematical literacy against students is very less because of learning during this time students have not been directed with the ability of mathematical literacy. After the students get learning by using learning materials through metacognitive approach guidance, the ability of mathematical literacy students’ level 3 and level 4 underwent significant improvement.
1) The document discusses students' beliefs about mathematics, including their beliefs about the characteristics of mathematics, mathematical content, processes, cognitive processes, and usefulness of mathematics. It also discusses factors influencing students' self-concept, anxiety levels, and perceptions of mathematics teachers.
2) Research findings show that mathematics anxiety is a major contributor to students' achievement in mathematics. Students' relationships with their teachers also significantly impact their motivation and success.
3) Students view ideal mathematics teachers as having qualities like patience, clear explanations, ensuring students understand concepts, and being approachable. Both personal characteristics and instructional skills are important for effective teaching.
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 several studies on factors that influence student achievement and performance in mathematics. It describes research finding that teacher classroom management skills, teaching strategies, use of instructional materials, and student motivation and interest are important factors. Additionally, it discusses how teacher experience and competencies, as well as environmental school factors can impact student learning outcomes.
This document discusses a study on the differences in self-efficacy levels between male and female students based on their science literacy skills and learning outcomes. The study found that male students had higher levels of self-efficacy than female students across three dimensions: magnitude, strength, and generality. Male students also had superior science learning outcome scores compared to female students. However, the differences in scores between genders were not large. The study suggests developing students' self-confidence to improve their self-efficacy levels and academic performance.
Enhancing Pupils’ Knowledge of Mathematical Concepts through Game and Poemiosrjce
The study investigated the effects of game and poem enhanced instruction on pupils’ knowledge of
mathematics concepts in mathematics (Fractions and decimals, Volume of, cylinder; triangular prisms and
sphere; Capacity and Weight). A total of 344 pupils from twelve (12) public primary schools of Ogbia and
Yenagoa Local Government Areas of Bayelsa State, Nigeria were involved in the study. A pretest-posttest
control group quasi-experimental design was adopted in the research. The moderating effects of gender were
also examined on the independent and dependent variables. Using ANCOVA statistics, the results revealed that
pupils exposed to game and poem enhanced instruction have better mean score in knowledge of mathematics
concepts than the control groups. Poem was found to be more effective in improving pupils’ knowledge of
mathematics concepts than game and a non-significant gender difference existed in the mean scores in
knowledge of mathematics concepts. There was no significant interaction effect of gender on pupils’ knowledge
of mathematics concepts. The implication of the findings was discussed and appropriate recommendations were
made.
Melinda Eichhorn - Exploring the use of a screening tool to investigate stude...Melinda Eichhorn
This document discusses a study that investigated the use of a mathematical screening tool with second grade students in Kolkata, India. The screening tool was designed to identify students' grade-level math skills, number sense, and common error patterns. The study found that the screening tool provided teachers with valuable information about their students' mathematical understanding and misconceptions. This allowed teachers to better target instruction and interventions to support students who were struggling. The screening tool empowered teachers to identify issues and begin interventions earlier than waiting for a formal diagnosis. Overall, the screening tool was an effective way for teachers to assess their students' math abilities and tailor instruction accordingly.
This research is aimed at finding out: 1) the influence of discovery learning model with RME approach on Mathematics learning achievement; 2) the influence of interpersonal intelligence on Mathematics learning achievement; 3) the interaction between discovery learning model with RME approach and interpersonal intelligence on Mathematics learning achievement. The research was conducted at one of the state Elementary Schools in Banjarsari sub-district, Surakarta. The method used in this research was quasiexperimental method with 2x3 factorial design. Hypothesis test was done by two-way variance ANOVA test with different cells. It can be concluded that the discovery learning model with RME approach gives better influence on the Mathematics learning achievement than the direct learning model. Students having high interpersonal intelligence category get better Mathematics learning achievement than those having medium and low category. The students having medium interpersonal intelligence get better Mathematics achievement than those having low category. There is no interaction between learning model and interpersonal intelligence on Mathematics learning achievement.
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.
Exploring Teachers Practices of Classroom Assessment in Secondary Science Cla...Md. Mehadi Rahman
The study investigates teachers’ classroom assessment practices of secondary schools in Bangladesh. The study is mainly quantitative with some integration of qualitative approach. Secondary science teachers and their science classrooms were main data source of the study, which were selected randomly. Data sources were secondary science teachers and their science classrooms. The study used a lesson observation protocol to understand their classroom assessment practice, and pre-lesson and post-lesson observation interview protocols as main sources of data collection. Qualitative data from interview were used to triangulate the quantitative data from observation. A total of thirty teachers (twenty male and ten female) were chosen randomly from six secondary schools in Dhaka. The study explored that teachers’ current practice of classroom assessment was to only assess students learning achievement and they followed traditional methods to assess students. The dominated assessment activity was oral questioning and very few students take part in the assessment activities by answering the questions. The classroom questions are basically focused very specific responses and encouraged rote learning; even students’ didn’t get enough time for thinking and answering the questions. Therefore the study suggests changing current practices by using different assessment strategies like self and peer assessment and focus on assessment for learning to ensure effective teaching-learning and quality education. These findings can inform the classroom teachers as well as o relevant stakeholders in making necessary changes in the present classroom assessment practices in Bangladesh.
The effect of project based learning model with kwl worksheet on student crea...Alexander Decker
This document summarizes a study that analyzed the effect of project-based learning (PjBL) with KWL worksheets on student creative thinking in physics problem solving. The study involved randomly assigning undergraduate physics students to either an experiment group that used PjBL and KWL worksheets or a control group that used traditional cooperative learning. Assessment results showed that students in the PjBL group had higher creative thinking scores than the control group, indicating PjBL is an effective way to develop student creative thinking and engagement in physics learning. The document also provides background on PjBL principles and benefits, defining it as a student-centered approach that uses authentic projects to help students construct knowledge and demonstrate understanding through hands-on
The document provides background information on factors that affect students' mathematics performance. It discusses how positive attitudes and understanding the real-world applications of math can improve performance. The conceptual framework outlines how student-related factors like interest and study habits, and teacher-related factors like personality, teaching skills, and instructional materials influence mathematics performance. The study aims to determine the extent of these factors and their relationship to performance among high school students.
The document discusses several studies and perspectives on effective teaching strategies and factors that influence student achievement and performance. Specifically, it discusses:
1) The importance of providing adequate instructional resources and materials to support effective mathematics teaching.
2) The need for teachers to practice effective study skills and receive training on using instructional materials.
3) Factors found to influence student performance including gender, interest in mathematics, teaching competencies, strategies, library setting, and classroom setting.
4) The role of teachers in classroom management, facilitating learning, and evaluating students, and ensuring a conducive learning environment.
Professionalism in teaching mathematics demographic profiling of secondary sc...Alexander Decker
1) The document profiles secondary school mathematics teachers in Taraba State, Nigeria based on their teaching experience, university subject studied, and academic qualifications.
2) It surveyed 327 secondary school mathematics teachers and found that they come from diverse backgrounds and less than 40% have teacher certification in mathematics education.
3) The study aimed to examine teachers' conceptions of problem solving and how they relate to professionalism in teaching mathematics, in order to help address poor student performance in the subject.
The document summarizes two studies on the use of technology in education. The first study examined the impact of interactive whiteboards on student achievement in math and language arts, finding small increases in math scores. Teachers whose students scored above average used the whiteboards more frequently. The second study explored teachers' experiences using technology with at-risk students. It found that technology increased success rates but some students found online learning overwhelming, and identified strategies like choice, structure and customization that helped at-risk learners.
The document summarizes two research studies on the use of technology in education. The first study examined the impact of interactive whiteboards on student achievement in math and language arts, finding a small positive effect, especially in upper elementary grades. Teachers whose students scored above average were found to use the whiteboards more frequently. The second study explored teachers' experiences using technology with at-risk students, finding that teachers encountered difficulties but technology also provided opportunities for success when certain strategies were employed. Qualitative data analysis was used to identify themes in teachers' responses.
Influences of the pedagogical content knowledge of graduate social studies te...Alexander Decker
This document discusses a study that investigated how graduate social studies teachers' pedagogical content knowledge influences the questions they set for senior high school students in Ghana. A mixed methods approach was used, collecting data from questionnaires, interviews, and analyzing teacher-created exam questions. The study found that while teachers said they aimed to develop students' conceptual understanding and problem-solving skills, there were differences between their stated assessment goals and what was actually assessed. Most questions focused only on lower-level cognitive skills like recall, rather than higher-order thinking. The document provides background on effective assessment principles and the importance of teacher questioning skills in developing student thinking.
Using Action Research to Identify Data During Clinical Experience (main)Antwuan Stinson
Critical thinking is the focal point missed in many students’ education. Learning to ask appropriate questions and deduce information in order to build a deeper connection to the information is imperative. This paper discusses alternative master’s preservice teachers’ use of action research to serve as a guide during a 16-week clinical experience. Semi-structured interviews and reflection papers were conducted to create a comparative case study that analyzed the clinical experiences.
The attitude of students towards the teaching and learning of social studies ...Alexander Decker
This document summarizes a study on students' attitudes towards teaching and learning social studies concepts in colleges of education in Ghana. The study found that students had a positive overall attitude, as indicated by a mean of means of 2.66 on a 4-point scale. Specifically, students agreed that learning concepts facilitates understanding and supports attitudinal development. However, students disagreed that they show enthusiasm for concepts or find social studies uninteresting due to concepts. Factors like instructional materials and resource persons were found to enhance teaching and learning of concepts, while lack of funds, libraries and resource rooms hindered it.
The dissertation presentation chen lei GS55768.pptxalading
The document discusses a study on the effects of situational teaching, cooperative learning, and self-directed learning on mathematical learning ability among junior high school students in China. Specifically, it aims to 1) investigate the impact of situational teaching, cooperative learning, and self-directed learning on students' mathematical ability, and 2) explore differences in mathematical ability between genders. The study uses a quantitative research design and measures students' mathematical ability using scales assessing reasoning, argumentation, communication and other skills.
This document provides a summary of the key factors affecting mathematics performance identified in the related literature. It discusses several factors including student interest, study habits, teacher personality traits, teaching skills, and instructional materials. Effective study habits require practice and perfect practice. Instructional materials and teaching strategies are important determinants of math teaching methods. Students' beliefs about their ability and whether it can be improved also impact performance. A teacher's competence relies on possessing key personality traits and using varied teaching approaches helps student engagement. The literature shows relationships between these factors and mathematics achievement.
This document provides background information on factors affecting mathematics performance of students. It discusses how student-related factors like interest and study habits, and teacher-related factors like personality traits, teaching skills, and instructional materials can influence student performance in mathematics. The document reviews related literature on these factors and presents a conceptual framework and research questions to analyze the relationship between the factors and student performance. It aims to determine the extent of different factors and their impact on the mathematics performance of high school students.
This document summarizes research on incorporating reading strategies into math instruction. It discusses studies that found reading abilities impact student performance on math word problems and that teaching reading strategies can help students comprehend and solve problems. The document also notes challenges in communicating the importance of content area reading to math teachers and that simply exposing pre-service teachers to related research may not translate to strategy implementation in the classroom. The researcher intends to identify specific strategies and collaborate with a literacy coach to start applying reading instruction in their own math teaching.
This document provides background information on factors affecting mathematics performance of high school students. It discusses several key factors from previous studies, including student interest, study habits, teacher personality traits and teaching skills, and instructional materials. The conceptual framework outlines how these input factors may influence student mathematics performance outcomes. The study aims to determine the extent to which student-related factors and teacher-related factors impact mathematics performance of high school students at a particular university.
This chapter introduces the importance of mathematics in daily life and careers. It discusses how students often find mathematics boring and difficult to understand. The chapter also presents background information on factors that can influence students' mathematics performance, such as attitudes, engagement, instructional methods, and beliefs about intelligence. The theoretical framework outlines theories about fixed versus growth mindsets. The conceptual framework shows how student-related factors, teacher-related factors, and mathematics performance are related. The statement of the problem indicates the study aims to determine the relationship between these factors and performance for students at a particular university.
The document summarizes a literature review on teaching and learning processes to enhance teaching effectiveness. It discusses three key findings from the review:
1) Providing positive and developmental feedback as well as introducing role-playing activities have a profound positive impact on student confidence and self-esteem.
2) An active learning environment that promotes inclusivity can improve faculty and student academic performance.
3) Different learning styles must be accommodated, including visual, auditory, and kinesthetic learners, through a variety of teaching methods like lectures, group work, and hands-on activities.
Degree of creative teaching skills used by teachers practicing social studies...Alexander Decker
1) The document discusses a study that aimed to determine the degree to which social studies teachers in Jordan use creative teaching skills and how their qualifications, experience, and gender affect these skills.
2) The study found that social studies teachers had a large degree of creative teaching skills overall. It also found statistically significant differences based on qualifications, with masters degree holders having higher skills, and experience, with less experienced teachers having higher skills. No significant differences were found based on gender.
3) The study used a questionnaire to measure teachers' creative skills like lesson planning, content analysis, teaching methods, questioning techniques, and classroom management. It surveyed 145 teachers and analyzed results based on their qualifications, experience, and gender.
An Exploratory Study Of A Story Problem Assessment Understanding Children S ...Angie Miller
This study explored how students use their number sense when solving story problems by analyzing their strategies and reasoning. Researchers interviewed three 8- and 9-year-old students and had them solve story problems. Through qualitative coding, the researchers analyzed how the students' number sense was reflected in their problem-solving approaches and explanations. The results provided insights into how students coordinate different number sense constructs and showed flexibility in problem-solving. The study aimed to understand number sense in a holistic way rather than by assessing individual constructs in isolation.
This document discusses using action research as an instructional supervision approach to improve teaching practices in Ipil District. It found that some teachers were not engaging students or checking their understanding, resulting in low test scores. The research had teachers and school heads implement action research projects to address issues in their classrooms. It identified problems they encountered like time constraints and lack of support. To solve these challenges, teachers sought instructional support and applied lessons from supervisors. The research concluded that instructional supervision and collaboration on action research can strengthen teaching practices, especially for new teachers and school heads. It recommends continuing to use these approaches to promote best practices.
A Case Study Of Teachers Pedagogical Content Knowledge Of FunctionsJames Heller
This document summarizes a case study that explored three teachers' levels of pedagogical content knowledge (PCK) regarding functions. The study found that the teachers had mediocre PCK levels, with more experienced teachers having better knowledge. However, all teachers lacked some conceptual knowledge of functions and focused more on procedures than conceptual understanding when teaching. The study suggested providing teachers with additional resources on mathematics concepts and ongoing training to improve their PCK and ability to effectively teach functions.
An Investigation Of Teachers Questioning In The English Reading Classrooms ...Jeff Brooks
This document summarizes a study that examined teachers' questioning strategies in English reading classrooms. The study analyzed audio recordings and observations of three reading classes taught by one teacher in Vietnam. It categorized the teacher's questions into two main types: audience-oriented questions and content-oriented questions. The findings showed that audience-oriented questions were used three times more frequently than content-oriented questions. The questioning served three main functions: eliciting responses, focusing information, and checking comprehension. The study also found a relationship between the questioning functions and forms used by the teacher to engage students and guide them to higher-level thinking during reading activities.
Similar to Mathematics teachers’ ability to investigate students’ thinking processes about some algebraic concepts (20)
Abnormalities of hormones and inflammatory cytokines in women affected with p...Alexander Decker
Women with polycystic ovary syndrome (PCOS) have elevated levels of hormones like luteinizing hormone and testosterone, as well as higher levels of insulin and insulin resistance compared to healthy women. They also have increased levels of inflammatory markers like C-reactive protein, interleukin-6, and leptin. This study found these abnormalities in the hormones and inflammatory cytokines of women with PCOS ages 23-40, indicating that hormone imbalances associated with insulin resistance and elevated inflammatory markers may worsen infertility in women with PCOS.
A usability evaluation framework for b2 c e commerce websitesAlexander Decker
This document presents a framework for evaluating the usability of B2C e-commerce websites. It involves user testing methods like usability testing and interviews to identify usability problems in areas like navigation, design, purchasing processes, and customer service. The framework specifies goals for the evaluation, determines which website aspects to evaluate, and identifies target users. It then describes collecting data through user testing and analyzing the results to identify usability problems and suggest improvements.
A universal model for managing the marketing executives in nigerian banksAlexander Decker
This document discusses a study that aimed to synthesize motivation theories into a universal model for managing marketing executives in Nigerian banks. The study was guided by Maslow and McGregor's theories. A sample of 303 marketing executives was used. The results showed that managers will be most effective at motivating marketing executives if they consider individual needs and create challenging but attainable goals. The emerged model suggests managers should provide job satisfaction by tailoring assignments to abilities and monitoring performance with feedback. This addresses confusion faced by Nigerian bank managers in determining effective motivation strategies.
A unique common fixed point theorems in generalized dAlexander Decker
This document presents definitions and properties related to generalized D*-metric spaces and establishes some common fixed point theorems for contractive type mappings in these spaces. It begins by introducing D*-metric spaces and generalized D*-metric spaces, defines concepts like convergence and Cauchy sequences. It presents lemmas showing the uniqueness of limits in these spaces and the equivalence of different definitions of convergence. The goal of the paper is then stated as obtaining a unique common fixed point theorem for generalized D*-metric spaces.
A trends of salmonella and antibiotic resistanceAlexander Decker
This document provides a review of trends in Salmonella and antibiotic resistance. It begins with an introduction to Salmonella as a facultative anaerobe that causes nontyphoidal salmonellosis. The emergence of antimicrobial-resistant Salmonella is then discussed. The document proceeds to cover the historical perspective and classification of Salmonella, definitions of antimicrobials and antibiotic resistance, and mechanisms of antibiotic resistance in Salmonella including modification or destruction of antimicrobial agents, efflux pumps, modification of antibiotic targets, and decreased membrane permeability. Specific resistance mechanisms are discussed for several classes of antimicrobials.
A transformational generative approach towards understanding al-istifhamAlexander Decker
This document discusses a transformational-generative approach to understanding Al-Istifham, which refers to interrogative sentences in Arabic. It begins with an introduction to the origin and development of Arabic grammar. The paper then explains the theoretical framework of transformational-generative grammar that is used. Basic linguistic concepts and terms related to Arabic grammar are defined. The document analyzes how interrogative sentences in Arabic can be derived and transformed via tools from transformational-generative grammar, categorizing Al-Istifham into linguistic and literary questions.
A time series analysis of the determinants of savings in namibiaAlexander Decker
This document summarizes a study on the determinants of savings in Namibia from 1991 to 2012. It reviews previous literature on savings determinants in developing countries. The study uses time series analysis including unit root tests, cointegration, and error correction models to analyze the relationship between savings and variables like income, inflation, population growth, deposit rates, and financial deepening in Namibia. The results found inflation and income have a positive impact on savings, while population growth negatively impacts savings. Deposit rates and financial deepening were found to have no significant impact. The study reinforces previous work and emphasizes the importance of improving income levels to achieve higher savings rates in Namibia.
A therapy for physical and mental fitness of school childrenAlexander Decker
This document summarizes a study on the importance of exercise in maintaining physical and mental fitness for school children. It discusses how physical and mental fitness are developed through participation in regular physical exercises and cannot be achieved solely through classroom learning. The document outlines different types and components of fitness and argues that developing fitness should be a key objective of education systems. It recommends that schools ensure pupils engage in graded physical activities and exercises to support their overall development.
A theory of efficiency for managing the marketing executives in nigerian banksAlexander Decker
This document summarizes a study examining efficiency in managing marketing executives in Nigerian banks. The study was examined through the lenses of Kaizen theory (continuous improvement) and efficiency theory. A survey of 303 marketing executives from Nigerian banks found that management plays a key role in identifying and implementing efficiency improvements. The document recommends adopting a "3H grand strategy" to improve the heads, hearts, and hands of management and marketing executives by enhancing their knowledge, attitudes, and tools.
This document discusses evaluating the link budget for effective 900MHz GSM communication. It describes the basic parameters needed for a high-level link budget calculation, including transmitter power, antenna gains, path loss, and propagation models. Common propagation models for 900MHz that are described include Okumura model for urban areas and Hata model for urban, suburban, and open areas. Rain attenuation is also incorporated using the updated ITU model to improve communication during rainfall.
A synthetic review of contraceptive supplies in punjabAlexander Decker
This document discusses contraceptive use in Punjab, Pakistan. It begins by providing background on the benefits of family planning and contraceptive use for maternal and child health. It then analyzes contraceptive commodity data from Punjab, finding that use is still low despite efforts to improve access. The document concludes by emphasizing the need for strategies to bridge gaps and meet the unmet need for effective and affordable contraceptive methods and supplies in Punjab in order to improve health outcomes.
A synthesis of taylor’s and fayol’s management approaches for managing market...Alexander Decker
1) The document discusses synthesizing Taylor's scientific management approach and Fayol's process management approach to identify an effective way to manage marketing executives in Nigerian banks.
2) It reviews Taylor's emphasis on efficiency and breaking tasks into small parts, and Fayol's focus on developing general management principles.
3) The study administered a survey to 303 marketing executives in Nigerian banks to test if combining elements of Taylor and Fayol's approaches would help manage their performance through clear roles, accountability, and motivation. Statistical analysis supported combining the two approaches.
A survey paper on sequence pattern mining with incrementalAlexander Decker
This document summarizes four algorithms for sequential pattern mining: GSP, ISM, FreeSpan, and PrefixSpan. GSP is an Apriori-based algorithm that incorporates time constraints. ISM extends SPADE to incrementally update patterns after database changes. FreeSpan uses frequent items to recursively project databases and grow subsequences. PrefixSpan also uses projection but claims to not require candidate generation. It recursively projects databases based on short prefix patterns. The document concludes by stating the goal was to find an efficient scheme for extracting sequential patterns from transactional datasets.
A survey on live virtual machine migrations and its techniquesAlexander Decker
This document summarizes several techniques for live virtual machine migration in cloud computing. It discusses works that have proposed affinity-aware migration models to improve resource utilization, energy efficient migration approaches using storage migration and live VM migration, and a dynamic consolidation technique using migration control to avoid unnecessary migrations. The document also summarizes works that have designed methods to minimize migration downtime and network traffic, proposed a resource reservation framework for efficient migration of multiple VMs, and addressed real-time issues in live migration. Finally, it provides a table summarizing the techniques, tools used, and potential future work or gaps identified for each discussed work.
A survey on data mining and analysis in hadoop and mongo dbAlexander Decker
This document discusses data mining of big data using Hadoop and MongoDB. It provides an overview of Hadoop and MongoDB and their uses in big data analysis. Specifically, it proposes using Hadoop for distributed processing and MongoDB for data storage and input. The document reviews several related works that discuss big data analysis using these tools, as well as their capabilities for scalable data storage and mining. It aims to improve computational time and fault tolerance for big data analysis by mining data stored in Hadoop using MongoDB and MapReduce.
1. The document discusses several challenges for integrating media with cloud computing including media content convergence, scalability and expandability, finding appropriate applications, and reliability.
2. Media content convergence challenges include dealing with the heterogeneity of media types, services, networks, devices, and quality of service requirements as well as integrating technologies used by media providers and consumers.
3. Scalability and expandability challenges involve adapting to the increasing volume of media content and being able to support new media formats and outlets over time.
This document surveys trust architectures that leverage provenance in wireless sensor networks. It begins with background on provenance, which refers to the documented history or derivation of data. Provenance can be used to assess trust by providing metadata about how data was processed. The document then discusses challenges for using provenance to establish trust in wireless sensor networks, which have constraints on energy and computation. Finally, it provides background on trust, which is the subjective probability that a node will behave dependably. Trust architectures need to be lightweight to account for the constraints of wireless sensor networks.
This document discusses private equity investments in Kenya. It provides background on private equity and discusses trends in various regions. The objectives of the study discussed are to establish the extent of private equity adoption in Kenya, identify common forms of private equity utilized, and determine typical exit strategies. Private equity can involve venture capital, leveraged buyouts, or mezzanine financing. Exits allow recycling of capital into new opportunities. The document provides context on private equity globally and in developing markets like Africa to frame the goals of the study.
This document discusses a study that analyzes the financial health of the Indian logistics industry from 2005-2012 using Altman's Z-score model. The study finds that the average Z-score for selected logistics firms was in the healthy to very healthy range during the study period. The average Z-score increased from 2006 to 2010 when the Indian economy was hit by the global recession, indicating the overall performance of the Indian logistics industry was good. The document reviews previous literature on measuring financial performance and distress using ratios and Z-scores, and outlines the objectives and methodology used in the current study.
The APCO Geopolitical Radar - Q3 2024 The Global Operating Environment for Bu...APCO
The Radar reflects input from APCO’s teams located around the world. It distils a host of interconnected events and trends into insights to inform operational and strategic decisions. Issues covered in this edition include:
Top 10 Free Accounting and Bookkeeping Apps for Small BusinessesYourLegal Accounting
Maintaining a proper record of your money is important for any business whether it is small or large. It helps you stay one step ahead in the financial race and be aware of your earnings and any tax obligations.
However, managing finances without an entire accounting staff can be challenging for small businesses.
Accounting apps can help with that! They resemble your private money manager.
They organize all of your transactions automatically as soon as you link them to your corporate bank account. Additionally, they are compatible with your phone, allowing you to monitor your finances from anywhere. Cool, right?
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Brian Fitzsimmons on the Business Strategy and Content Flywheel of Barstool S...Neil Horowitz
On episode 272 of the Digital and Social Media Sports Podcast, Neil chatted with Brian Fitzsimmons, Director of Licensing and Business Development for Barstool Sports.
What follows is a collection of snippets from the podcast. To hear the full interview and more, check out the podcast on all podcast platforms and at www.dsmsports.net
The Genesis of BriansClub.cm Famous Dark WEb PlatformSabaaSudozai
BriansClub.cm, a famous platform on the dark web, has become one of the most infamous carding marketplaces, specializing in the sale of stolen credit card data.
Zodiac Signs and Food Preferences_ What Your Sign Says About Your Tastemy Pandit
Know what your zodiac sign says about your taste in food! Explore how the 12 zodiac signs influence your culinary preferences with insights from MyPandit. Dive into astrology and flavors!
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Top mailing list providers in the USA.pptxJeremyPeirce1
Discover the top mailing list providers in the USA, offering targeted lists, segmentation, and analytics to optimize your marketing campaigns and drive engagement.
How are Lilac French Bulldogs Beauty Charming the World and Capturing Hearts....Lacey Max
“After being the most listed dog breed in the United States for 31
years in a row, the Labrador Retriever has dropped to second place
in the American Kennel Club's annual survey of the country's most
popular canines. The French Bulldog is the new top dog in the
United States as of 2022. The stylish puppy has ascended the
rankings in rapid time despite having health concerns and limited
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[To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations]
This presentation is a curated compilation of PowerPoint diagrams and templates designed to illustrate 20 different digital transformation frameworks and models. These frameworks are based on recent industry trends and best practices, ensuring that the content remains relevant and up-to-date.
Key highlights include Microsoft's Digital Transformation Framework, which focuses on driving innovation and efficiency, and McKinsey's Ten Guiding Principles, which provide strategic insights for successful digital transformation. Additionally, Forrester's framework emphasizes enhancing customer experiences and modernizing IT infrastructure, while IDC's MaturityScape helps assess and develop organizational digital maturity. MIT's framework explores cutting-edge strategies for achieving digital success.
These materials are perfect for enhancing your business or classroom presentations, offering visual aids to supplement your insights. Please note that while comprehensive, these slides are intended as supplementary resources and may not be complete for standalone instructional purposes.
Frameworks/Models included:
Microsoft’s Digital Transformation Framework
McKinsey’s Ten Guiding Principles of Digital Transformation
Forrester’s Digital Transformation Framework
IDC’s Digital Transformation MaturityScape
MIT’s Digital Transformation Framework
Gartner’s Digital Transformation Framework
Accenture’s Digital Strategy & Enterprise Frameworks
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Mathematics teachers’ ability to investigate students’ thinking processes about some algebraic concepts
1. Journal of Education and Practice www.iiste.org
ISSN 2222-1735 (Paper) ISSN 2222-288X (Online)
Vol.5, No.25, 2014
Mathematics Teachers’ Ability to Investigate Students’ Thinking
Processes About Some Algebraic Concepts
Elisha Habila Zuya
Department of Science Education, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria
E-mail:elishazuya2@gmail.com
Abstract
The study investigated Mathematics teachers’ ability to evaluate students’ thinking process about some algebraic
concepts. The study involved 156 Mathematics teachers randomly selected from some Public Secondary Schools
in Bauchi State, Nigeria. Open ended questionnaire was used to collect data from the participants. The teachers
were required to respond in detail to the questions asked. The research design was a qualitative one and
expository method was used in the analysis of the data collected. It was revealed that, though the teachers
showed some success in understanding the students’ errors and misconceptions, great majority of them could not
assess students’ thinking process. The study also revealed that most of the teachers were unable to ask competent
questions that could help in evaluating the students’ thinking process. Another important finding was the
difficulty the teachers themselves had in understanding the problem situations, and hence asked irrelevant
questions or make irrelevant statements. It was suggested that training workshops be organized for the teachers
to improve their subject matter knowledge about the concepts studied.
Keywords: Ability, Thinking process, Algebraic concepts
1. Introduction
The mathematics teacher is a necessary component in the reform of teaching and learning mathematics. The
possession of various structures of knowledge by teachers indicates the kind of teachers they might be. And
talking about teachers’ knowledge brings to mind the concept of pedagogical content knowledge of teachers.
Tanisli and Kose (2013) asked, “What should teachers know?” They noted that the answer can be explained
through the concept of pedagogical content knowledge. According to them, pedagogical content knowledge is
defined as “the ways of representing and formulating the subject that makes it comprehensive to others”. They
maintained that pedagogical content knowledge is a kind of knowledge that reveals a teacher’s meaningful and
effective ways of teaching. Chick and Baker (2005) quoted Graeber as saying “an understanding of common
students’ misconceptions, and effective strategies to help students avoid them, are important aspects of
mathematics pedagogical content knowledge”.
Pedagogical content knowledge is the subject-matter knowledge that teachers have and it consists of
many components. According to Shulman (1987) pedagogical content knowledge has seven components, among
which include subject-matter knowledge, knowledge of students, knowledge of curriculum and knowledge of
educational purposes. Tamir (1988) categorized pedagogical content knowledge into four components:
knowledge of understanding students; knowledge of teaching methods, knowledge of measurement and
evaluation and knowledge of curriculum. Grossman (1990) also identified four components of pedagogical
content knowledge as: knowledge of strategies and representations for teaching particular topics; knowledge of
students’ understanding, conceptions and misconceptions of these topics; knowledge and beliefs about the
purposes of teaching particular topics; and knowledge of curriculum materials available for teaching. In the same
vein, Fennema and Franke (1992) categorized mathematics teachers’ pedagogical content knowledge under four
categories, and one of which is knowledge of students.
Shulman (1986) and Park and Oliver (2008) placed knowledge of students in the centre of pedagogical
content knowledge, and it is viewed as one of the key components. Knowledge of students is described as a
teacher’s knowledge of student’s procedural and conceptual knowledge, students’ thinking processes, learning
styles, difficulties and misconceptions in the process of learning a subject.
Several scholars in mathematics education (e.g. Carpenter, Fennema, Peterson & Carey, 1988; An,
Kulm & Wu, 2004; Chick & Baker, 2005; Chick, Baker, Pham & Cheng, 2006) have conducted studies about in-service
and pre-service teachers’ knowledge of students in many subject areas. The findings of these studies
indicated that mathematics teachers and pre-service mathematics teachers have incomplete and inadequate
knowledge of students in general. Carpenter, Fennema, Peterson and Carey (1988) pointed out that teachers’
knowledge of students is necessary for effective teaching. It goes without saying then that mathematics teachers’
knowledge of students is important in teacher education.
A study conducted by Tanisli and Kose (2013) revealed that students’ background knowledge, the
concepts which they have difficulty in understanding and their misconceptions are different from teachers’
expectations and predictions about them. Similarly, in a study carried out by Asquith, Stephens, Knuth and
Alibali (2007), the findings revealed that mathematics teachers’ knowledge of students about the concept of
117
2. Journal of Education and Practice www.iiste.org
ISSN 2222-1735 (Paper) ISSN 2222-288X (Online)
Vol.5, No.25, 2014
equal sign and variable was different from the students’ possible errors. They found out that the participating
teachers had difficulty in identifying and predicting students’ possible misconceptions and errors about equal
sign and variable. Tanisli and Kose (2013) noted that some studies about pre-service mathematics teachers’
ability to predict the errors and misconceptions of primary school pupils in relation to algebraic expressions and
manipulations indicated that the respondents generally made predictions about only one kind of errors and
misconceptions. They said the pre-service mathematics teachers predicted errors and misconceptions which
students didn’t have.
According to Boz (2002) and Stephens (2008), teachers’ predictions and expectations of students’
thinking processes fail to identify the ideas and errors behind students’ answers, and also fail to explain the
sources of students’ misconceptions. The studies also maintained that mathematics teachers could not come up
with good recommendations that would help eliminate students’ errors. Stephens (2008) pointed out that pre-service
mathematics teachers had limited knowledge of algebraic concepts as a part of subject-matter knowledge.
Boz (2002) noted in his study that though the pre-service mathematics teachers knew the rules for the letter
symbols, they could not demonstrate this same success in explaining the reasons for these rules.
Mathematics teachers’ ability to probe students’ thinking processes is important to effective teaching.
Mathematics teachers are expected to understand what students know and what they need to know. This can be
done effectively by the questioning skills of the teacher. This is because the quality of the questions asked by
teachers plays an important role in identifying students’ difficulties. Moyer and Milewicz (2002) said teachers
who are able to ask skillful questions can also analyze the depth of their students’ thought better. If a teacher
does not have an adequate understanding of the subject-matter, he/she will not be able to ask competent
questions that would reveal students’ errors and misconceptions.
This study sought to examine mathematics teachers’ ability to investigate students’ errors and
misconceptions in some algebraic concepts. The problem therefore is whether secondary mathematics teachers
are capable of evaluating students’ thinking processes and predicting students’ misconceptions in some algebraic
concepts.
2. Methodology
2.1 Research Design
The qualitative research approach was employed in this study. Qualitative approach emphasizes the process
rather than the product, and the study focused on mathematics teachers’ ability to identify, discuss and predict
students’ errors and misconceptions.
2.2 Participants
The participants to the study were mathematics teachers randomly selected from public secondary schools in
Bauchi State, Nigeria. The mathematics teachers who took part in the study were 156, and were of varying
qualifications and years of experience.
2.3 Instrument for the study
The instrument for the study was an open-ended questionnaire adopted from Tanisli and Kose (2013), with
changes in the names used in the problem statements only. The questionnaire consisted of three open-ended
items designed to evaluate mathematics teachers’ ability to identify, discuss and predict students’ errors and
misconceptions with regard to some algebraic concepts. The teachers were requested to answer the questions in
detail. The questionnaire is shown in Figure 1.
Question 1: The question “John is 4 cm taller than Joan. If Joan is n cm tall, how tall is John?”is being
discussed in class. The dialogue among three students is given below:
118
Adams: John’s height is 4n,
James: No. John’s height is 104 cm.,
Sarah: I think John’s height is x+4.
What kind of questions may be asked to each of these students to help them understand their errors?
Question 2: In the question “In the expression 4n+7, what does the symbol n represent?” Musa gives the
following answer “n does not mean anything here because there is no symbol “=” in the expression. For
example, in an expression such as 4n+7=11, n=1”.
Discuss the student’s idea.
Question 3:
“a) 4x-1=0 b) x+10=47 c) 3 5
2
+ =
x
d) -3x+6=2x+16”
What kind of incorrect answers may be given to the questions above by your students? Try and predict.
Figure 1: Teaching Mathematics Survey
3. Journal of Education and Practice www.iiste.org
ISSN 2222-1735 (Paper) ISSN 2222-288X (Online)
Vol.5, No.25, 2014
3. Results and Discussion
3.1 Results
The mathematics teachers’ ability to identify students’ errors, discuss students’ thinking process and predict
students’ errors was examined in this study. And the findings of the study are presented as follows:
3.1.1 Teachers’ ability to identify students’ errors about the concept of variable
The ability of teachers to ask skilful questions in order to help students recognize their errors and
misconceptions is a key component in the teaching and learning of mathematics. Mathematics teachers were
presented with hypothetical students’ solutions with regard to the concept of variable, and were required to ask
questions that would help the students recognize their mistakes. The problem situation and the incorrect
responses of the students are presented (“John is 4 cm taller than Joan. If Joan is n cm tall, how tall is John?”
Adams: John’s height is 4n, James: No. John’s height is 104 cm, Sarah: I think John’s height is x+4.). The
teachers were asked to identify the kind of questions they would ask each student to help them understand their
errors and misconceptions. The study revealed that majority of the questions the teachers asked were
instructional questions. An instructional question is teaching a student instead of assessing the student’s
knowledge about the concepts (Tanisli & Kose, 2013).
Examples of the questions the teachers asked to Adams who said that John’s height was 4n include:
“Do you know the difference between multiplication and addition? Aren’t you required to add?” “Is John 4 times
taller than Joan?” and “If john is 4n, it implies John is 4 times taller than Joan”. The questions the teachers asked
James who said that John’s height was 104 cm-“If John is 104 cm, does it mean Joan is 100 cm? but we’re told
that Joan is n cm.” and the questions the teachers asked to Sarah who said that John’s height was x+4- “Do you
not know that n is representing the height of Joan and not x?” and “x is not mentioned in the question, therefore,
is your x representing n?” The teachers emphasized their own thinking processes by revealing the answers
instead of assessing the students’ thinking process in this type of questions.
The study also revealed that a few of the questions asked by the teachers can be categorized as
investigative questions. Examples of these questions include: “What does 4n mean to you?”, “How do you know
Joan’s height is 100 cm?”, “How did you get 104 cm?” and “What does x stand for?” Regrettably, some of the
questions were either irrelevant or inadequate. Examples of such questions are: “What unit of length is used to
measure the height of John?” and “Is x the same as n? if so, x and n are unknown”.
3.1.2 Teachers’ ability to discuss students’ thinking process
The question asked to evaluate teachers’ ability to discuss students’ thinking process about the concept
of variable was: “What does n represent in the expression 4n+7?” The teachers’ responses to the students’
thinking processes revealed their inability to recognize students’ incorrect thinking process. Examples of
teachers’ statements such as, “The student’s idea is reasonable, in the sense that n should have a physical
quantity or a definition”, “The student may be right since 4n+7 is not equated to zero or any number. This means
the value of n cannot be found since the equation is not equated to anything”, and “4n+7 is not equated to
anything, therefore, it means nothing or is undefined” indicate that mathematics teachers were not able to
recognize students’ incorrect thinking process, and so could not discuss students’ errors and misconceptions.
Majority of the teachers who participated in this study were unable to analyze students’ thinking process.
Another finding of the study is that a few of the teachers made statements that revealed their
recognition of students’ incorrect thinking process about the question in which the variable n in the expression
4n+7 was asked. Examples of teachers’ statements about students’ thinking process such as, “Musa did not
understand the difference between an expression and an equation. He thinks that the unknown n in the
expression 4n+7 cannot be found since the expression is not equal to any number. Therefore, it means nothing to
him” and “He does not know the difference between an equation and an expression” indicate that the teachers
recognized the student’s errors and misconceptions in the interpretation of the variable n in the expression 4n+7.
It was also found that some teachers had difficulties themselves understanding the problems. This is
evident from the following questions asked by some of the teachers: “Do you know how to multiply numbers in
algebraic form?” and “Do you not know that unknown quantities are given in algebraic form?” This clearly
showed that such teachers could not understand the problems.
3.1.3 Teachers’ ability to predict students’ knowledge about the concept of equation
In order to evaluate teachers’ ability to predict students’ errors and misconceptions about equations,
the teachers were asked to predict students’ solutions to the equations: 4x-1=0, x+10=47, 3 5
119
2
+ =
x
and -
3x+6=2x+16. Studies have documented certain common types of errors and misconceptions that students make
(e.g. Moyer & Milewicz, 2002 & Hall,2002).
In this study the teachers predicted various types of errors and misconceptions that students make, some of
which are documented in the literature. The teachers’ predictions are presented in Table 1.
In the first equation, 4x-1=0, it is documented in the literature that students generally make the errors
4. Journal of Education and Practice www.iiste.org
ISSN 2222-1735 (Paper) ISSN 2222-288X (Online)
Vol.5, No.25, 2014
or misconceptions of 4x=1, x=1-4, x=-3, which is called “The Other Inverse Error”. In this study 49% of the
teachers predicted these errors or misconceptions. Majority of the teachers predicted that their students would
− , which Kieran referred to as “Switching Addends Error”. Other errors and
x
+3=5, 66% of the teachers predicted the common errors and misconceptions
22
120
make the error of x=
1
4
misconceptions predicted by the teachers were the “Omission of Error”: x=0, and “Absence of Structure Error”:
x=1. Also 16% predicted the error: x=4, as against 17% of the participants in Tanisli and Kose’s study. There
were other predictions which have not been documented in the literature.
In the second equation, x+10=47, 66% of the teachers predicted the common errors and
misconceptions reported in the literature (Table 1). Also the errors x=47 and x=-37 were each predicted by 33%
of the teachers.
In the third equation,
2
documented in the literature (see Table 1). According to Kieran (1992), most students tend to reach x+3=10, x=7,
because they do not take the symmetry of the equation into consideration when multiplying both sides by two.
Also, 33% predicted x=4, and this error was predicted by 36% of the participants in Tanisli and Kose’s study.
The fourth equation given to the teachers was -3x+6=2x+16,and only 16% predicted the errors
mentioned in the literature (see Table 1). The error: x=
5
was predicted by 33% of the teachers, and this error
was predicted by just 14% of the participants in Tanisli and Kose (2013). Many other errors analyzed in this
study have not been reported in previous studies.
Table 1: Errors and misconceptions predicted by the teachers.
Equation C o m m o n errors and
misconceptions in the
literature
Number of
teachers who
predicted
Other predicted
errors or
misconceptions
Number of
teachers who
predicted
4x -1=0 4x=1, x +4=1
x=1 - 4, x=-3
77 (49.34%) x=-1/4
x=5
x=0
x=4
x=1
130(83%)
26(16.6%)
77(49.3%)
26(16.6%)
26(16.6%)
x + 10=47 x=47 +10, x=57 104(66.6) x=4.7
10x=47
x=37
52(33.3%)
26(16.6%)
52(33.3%)
x
2
+ 3=5
x + 3=10, x=7 104(66.6%) x=4
x=1
x=5.5
x=14
x=10/3
x=13
52(33.3%)
20(12.82%)
32(20.51%)
26(16.66%)
29(18.59%)
23(14.24%)
-3x +
6=2x + 16
x+ 6=16, x=10 26(16.6%) -3x + 2x=16 + 6
(x+16)/2=5
x=-1
x=2
x=22/5
20(12.82%)
23(14.74%)
30(19.23%)
31(19.87%)
52(33.3%)
3.2. Discussion
The importance of teachers’ ability to identify, discuss and predict students’ errors, misconceptions and thinking
process cannot be overemphasized, if learning is to be effective and meaningful in mathematics. An important
finding in this study is the success of the teachers in understanding students’ thinking process with respect to
variable and equations. This is in line with the findings of Boz (2004), Stephens (2006), Asquith, Stephens,
Knuth and Alibali (2007) and Tanisli and Kose (2012).
Another key finding of the study is the inability of most of the teachers to evaluate the students’
thinking process through effective questioning. The teachers generally asked instructional questions instead of
investigative questions in their effort to identify students’ errors and to evaluate their thinking process. This
finding agrees with the findings by Moyer and Milewicz (2002) and Tanisli and Kose (2013). According to
Moyer and Milewicz (2002) teachers who are able to ask skilful questions can also analyze the depth of their
students’ thought better. This finding therefore implies that such teachers will not be able to teach mathematics
effectively, as they are not able to evaluate the thinking process of their students in depth.
5. Journal of Education and Practice www.iiste.org
ISSN 2222-1735 (Paper) ISSN 2222-288X (Online)
Vol.5, No.25, 2014
The study also revealed that more than half of the teachers were successful in predicting the common
errors and misconceptions reported in the literature with regards to the second and third equations (see Table 1).
In Tanisli and Kose’s study, more than half of the participants predicted the common errors reported in the
literature with respect to the second equation, while only 20% predicted the common errors in the literature with
respect to the third equation. On the other hand, only 16% of the teachers predicted the common errors and
misconceptions reported in the literature with respect to the fourth equation in this study, while 36% of the
participants in Tanisli and Kose’ study predicted these common errors and misconceptions. Furthermore, some
other errors and misconceptions predicted by the teachers in this study were not predicted in previous studies
(see Table 1).
Another important finding of the study was that the teachers themselves had difficulties in
understanding the problem situations and also the students’ solutions. For instance, in response to the problem
situation involving 4n+7, the teachers made statements such as: The student’s idea is reasonable, in the sense
that n should have a physical quantity or should have a definition and The student may be right since 4n+7 is not
equated to zero or any number. This is implies that the teachers matched the variable n with only a particular
number, and hence had difficulty understanding the various uses of the variable concept. Similarly, some of the
teachers’ questions were irrelevant. Examples, with respect to the question concerning the height of John and
Joan, questions such as: What unit of length is used to measure John’s height?, Is x the same as n? If so, x and n
are unknown. This is a revelation of the teachers’ failure to understand the problem. And it shows the teachers’
need for improvement in their subject-matter knowledge.
4. Conclusion
The inability of the teachers to discuss students’ thinking process is regrettable, as this is an indicator to problem
in the teaching and learning of mathematics. There can be no effective teaching when teachers lack the necessary
knowledge required of them. Generally, the teachers displayed inadequate skills of asking questions that are
investigative in nature. Instructional questions, the type which the teachers asked most, cannot identify students’
errors and misconceptions or assess students’ thinking process. The need for teachers to ask competent questions
that would help in identifying students’ errors and misconceptions is necessary. The failure of the teachers
themselves to have difficulty in understanding the problem, even though the problems were elementary in nature,
calls for serious concern. There is therefore, the need for training workshops and seminars to help improve the
subject-matter knowledge of the teachers, as this would improve their art of questioning too.
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