Interpretation construction (icon) design modelThiyagu K
One major and popular instructional model based the constructivist approach is Interpretation Construction Model or ICON model which emphasizes on learners’ encounter with authentic issues in pair or groups, on constructing interpretation by the learners in groups, searching for information about the problems in groups and facing different interpretations about the problems in groups. In other words, it is group-based teaching-learning co-operative as well as collaborative approach which, as it is evident, lays emphasis and importance on the inclusive and all round socio-academic growth of the learners and also in way has drawn insights from the concept of Multiple Intelligences as propounded by the eminent cognitive scientist Gardner (1993). ICON Model, as Tsai, Chin-Chung. 2011 and other scholars in educational psychology argue, mainly rests on the principles such as observation in authentic activities (Understanding Zone), contextualizing prior knowledge and interpretation construction (Understanding Zone), cognitive conflict and apprenticeship (Understanding Zone), collaboration (Application Zone), multiple interpretations (Higher Order Thinking Skill zone), and multiple manifestations (Higher Order Thinking Skill zone).
The concentric circles approach to organizing content involves introducing a subject matter over multiple years, with elementary knowledge provided in introductory years and more advanced knowledge added each subsequent year. A topic is broken into sub-topics that are allotted to different classes based on difficulty. This allows steady, gradual coverage of a topic from basic to full knowledge. It is considered a psychologically sound approach that maintains student interest through revision and presentation of small portions over time to create lasting impressions. Teachers must take care that topics are neither too long nor too short each year.
This document discusses principles and rationale for developing mathematics curriculum. It provides definitions of curriculum and aims such as stimulating pupil interest and developing mathematical concepts. Principles for curriculum development like disciplinary value and utility are outlined. The existing mathematics curriculum is then critically analyzed, noting shortcomings like lack of conformity with aims, emphasis on examinations, and lack of practical work. Suggestions for improvement include considering cognitive/affective domains, practical work, and organizing content logically from simple to complex.
This presentation will help understand how to frame specific objectives for teaching any subject in general and Mathematics in particular under cognitive, affective and psychomotor domain.
TNTEU - B.Ed New Syllabus - Pedagogy of Mathematics - Semester 1 - Code BD1MA - Unit III Approaches for teaching - Bigge and Hunt Steps - Reflective Level of Teaching Advantages and Disadvantages - Conclusion
Inductive method:a psychological method of developing formulas and principles
Deductive method:A speedy method of deduction and application.
best method is to develop formuias and then apply in examples therefore -inducto -deductive method
This document discusses the concept of correlation in education. It defines correlation as the relationship between different subjects in the curriculum. Correlation can be direct or reciprocal. There are three types of correlation: within a subject, between subjects, and between subjects and life/environment. Correlation between science and other subjects can be incidental or systematic. Incidental correlation occurs naturally through broad subject treatment, while systematic correlation requires careful curriculum organization and teacher cooperation. Examples are provided to illustrate incidental correlation in physics, chemistry, and biology lessons.
The document discusses the importance and functions of a mathematics library. It states that a mathematics library is an important source for acquiring mathematical knowledge and skills through promoting self-study habits. It provides access to a variety of books and materials that can help students develop problem-solving abilities. A well-stocked mathematics library can help supplement classroom teaching by filling gaps in knowledge and clarifying doubts. It should contain different categories of books and materials organized systematically to best serve students and teachers.
Interpretation construction (icon) design modelThiyagu K
One major and popular instructional model based the constructivist approach is Interpretation Construction Model or ICON model which emphasizes on learners’ encounter with authentic issues in pair or groups, on constructing interpretation by the learners in groups, searching for information about the problems in groups and facing different interpretations about the problems in groups. In other words, it is group-based teaching-learning co-operative as well as collaborative approach which, as it is evident, lays emphasis and importance on the inclusive and all round socio-academic growth of the learners and also in way has drawn insights from the concept of Multiple Intelligences as propounded by the eminent cognitive scientist Gardner (1993). ICON Model, as Tsai, Chin-Chung. 2011 and other scholars in educational psychology argue, mainly rests on the principles such as observation in authentic activities (Understanding Zone), contextualizing prior knowledge and interpretation construction (Understanding Zone), cognitive conflict and apprenticeship (Understanding Zone), collaboration (Application Zone), multiple interpretations (Higher Order Thinking Skill zone), and multiple manifestations (Higher Order Thinking Skill zone).
The concentric circles approach to organizing content involves introducing a subject matter over multiple years, with elementary knowledge provided in introductory years and more advanced knowledge added each subsequent year. A topic is broken into sub-topics that are allotted to different classes based on difficulty. This allows steady, gradual coverage of a topic from basic to full knowledge. It is considered a psychologically sound approach that maintains student interest through revision and presentation of small portions over time to create lasting impressions. Teachers must take care that topics are neither too long nor too short each year.
This document discusses principles and rationale for developing mathematics curriculum. It provides definitions of curriculum and aims such as stimulating pupil interest and developing mathematical concepts. Principles for curriculum development like disciplinary value and utility are outlined. The existing mathematics curriculum is then critically analyzed, noting shortcomings like lack of conformity with aims, emphasis on examinations, and lack of practical work. Suggestions for improvement include considering cognitive/affective domains, practical work, and organizing content logically from simple to complex.
This presentation will help understand how to frame specific objectives for teaching any subject in general and Mathematics in particular under cognitive, affective and psychomotor domain.
TNTEU - B.Ed New Syllabus - Pedagogy of Mathematics - Semester 1 - Code BD1MA - Unit III Approaches for teaching - Bigge and Hunt Steps - Reflective Level of Teaching Advantages and Disadvantages - Conclusion
Inductive method:a psychological method of developing formulas and principles
Deductive method:A speedy method of deduction and application.
best method is to develop formuias and then apply in examples therefore -inducto -deductive method
This document discusses the concept of correlation in education. It defines correlation as the relationship between different subjects in the curriculum. Correlation can be direct or reciprocal. There are three types of correlation: within a subject, between subjects, and between subjects and life/environment. Correlation between science and other subjects can be incidental or systematic. Incidental correlation occurs naturally through broad subject treatment, while systematic correlation requires careful curriculum organization and teacher cooperation. Examples are provided to illustrate incidental correlation in physics, chemistry, and biology lessons.
The document discusses the importance and functions of a mathematics library. It states that a mathematics library is an important source for acquiring mathematical knowledge and skills through promoting self-study habits. It provides access to a variety of books and materials that can help students develop problem-solving abilities. A well-stocked mathematics library can help supplement classroom teaching by filling gaps in knowledge and clarifying doubts. It should contain different categories of books and materials organized systematically to best serve students and teachers.
This document discusses teacher competencies, which are defined as the set of knowledge, skills, and experience necessary to be an effective teacher. It identifies three main types of teacher competencies: subject competencies which refer to strong knowledge of content areas; pedagogical competencies which involve teaching skills and understanding how students learn; and technological competencies which include the ability to use technology appropriately in the classroom. The document provides details on each type of competency and their importance for quality teaching. It emphasizes that competent teachers have both in-depth content knowledge as well as skills for effectively imparting that knowledge to students.
The recomendations of ncf 2005 and 2009jakeerhusain1
This document discusses the National Curriculum Frameworks (NCF) of 2005 and 2009 in India. It provides a brief history of NCFs since 1975. The NCF of 2005 recommended softening subject boundaries, incorporating local knowledge into textbooks, and creating a stimulating school environment. The NCF of 2009 emphasized changing trainee teachers' negative approaches, moving beyond an examination-focused curriculum, and providing flexible training for in-service teachers. The conclusion states that NCFs aim to help teachers play a significant role in national development, as envisioned by the Education Commission.
Nature ,Scope,Meaning and Definition of Mathematics AngelSophia2
This document provides an overview of mathematics as a subject. It discusses how mathematics plays an important role in social and economic development. It also examines definitions of mathematics from different sources, describing it as a systematic, organized science that deals with quantities, measurements, and spatial relationships. The document outlines key characteristics of mathematics, including that it is a science of discovery, an intellectual game, and a tool subject. It also discusses the abstract nature of mathematical concepts and how mathematics requires logical sequencing and applying concepts to new situations.
This document discusses the correlation of mathematics with various domains:
1) Mathematics is correlated with life activities through concepts like percentages, interest rates, and ratios that are useful in everyday life.
2) Different branches of mathematics like arithmetic, algebra, geometry are interrelated through concepts like functions and mathematical structures.
3) Topics within the same branch of mathematics are also correlated, for example concepts in algebra relate to equations, and areas of shapes relate in geometry.
4) Mathematics is also correlated with other subjects like physical sciences through expression of laws as mathematical equations, with biology through use of higher math methods, and with engineering as mathematics forms the basis of engineering courses.
Core curriculum is a set of basic courses considered essential for a well-rounded education. It includes compulsory subjects like social science, geography, biology, and history. Core curriculum also includes optional subjects like fine arts, home economics, languages, and music. Characteristics of a core curriculum include emphasizing discussion, group problem solving, integrating learning across disciplines, focusing on original source materials, and weaving common elements to encourage reflection and development of social skills.
The document discusses different modalities of teaching: conditioning, training, instruction, and indoctrination. It provides definitions and comparisons of each:
1) Conditioning is the lowest level and involves establishing automatic responses through reinforcement. It is not considered teaching.
2) Training focuses on developing skills through practice and is a higher level than conditioning. It can overlap with teaching when developing understanding.
3) Instruction imparts knowledge but only affects the cognitive domain, while teaching aims to develop the whole person. Instruction is part of teaching.
4) Indoctrination uncritically teaches a fixed set of beliefs through repetition without questioning. It aims to promote actions rather than independent thought, unlike educ
This document discusses principles of curriculum construction. It begins by defining curriculum as the sum total of experiences a student receives through activities at school, including the classroom, library, laboratories, playgrounds, and interactions with teachers. It then provides definitions of curriculum from various scholars. The main body outlines 14 principles that should guide curriculum construction, such as ensuring it reflects the aims of education and the needs, interests, and abilities of students (child-centric principle), considers civic and social needs, conserves cultural heritage while allowing for creativity, prepares students for the future and living, integrates subjects logically, accommodates individual differences, and considers the time available.
Deficit theory - Language Across the CurriculumSuresh Babu
The deficit theory suggests that students from lower socioeconomic environments enter school without the necessary linguistic resources for success. It explains that disadvantaged students often show high failure rates because they come from homes lacking verbal stimulation. The deficit theory is problematic because teachers' expectations, which can be influenced by this theory, have a large impact on how students perform. If teachers believe only certain types of students can succeed, they will teach in a way that self-fulfills that belief. Believing in the deficit theory can lead to poor student performance, increased delinquency, feelings of helplessness, and lack of interest in school.
CONTINUOUS AND COMPREHENSIVE EVALUATION(CCE)Sani Prince
CCE was made mandatory in National Policy on Education,1986 (NPE 1986) to introduce Continuous and Comprehensive Evaluation in schools as an important step of examination reform and for the qualitative improvement in the education system.
This document outlines the aims, objectives, and scope of teaching mathematics. It discusses the differences between aims, which are general long-term goals, versus objectives, which are specific and measurable. The document then lists several general aims of teaching mathematics, such as developing logical reasoning and problem solving skills. It also provides examples of objectives at different educational stages, from primary to secondary. Finally, the document discusses the wide scope and career applications of mathematics, such as actuary, teacher, engineer, and more.
curriculum : meaning and concept, principles of curriculum, curriculum construction and curriculum organisation, bases of curriculum, types of curriculum, method of organisation of curriculum ppt
The document discusses several teaching methods:
1. The inductive method proceeds from specific examples to generalizations. It involves presenting examples, making observations, and deriving general rules or formulas.
2. The deductive method proceeds from general rules to specific cases. The rule or formula is given first and then applied to solve problems.
3. The analytic method breaks down problems into known and unknown parts to derive solutions. It proceeds from unknown to known.
4. The synthetic method combines known elements to derive unknown parts. It proceeds from known to unknown.
5. The heuristic method emphasizes experimentation and discovery learning with the teacher as a facilitator rather than instructor. Students take an active role
Aims and objectives of teaching in physical scienceJIPSA MOHAN
The document discusses the aims and objectives of teaching physical science in secondary school. It states that the main purpose is to provide students with basic knowledge of physical science needed for further study in modern science and technology. It also aims to develop students' experimental skills, ability to think, and use of mathematics to solve problems. The study of physical science can benefit fields like industry, defense, and agriculture. Objectives should control classroom instruction and be written in measurable terms for each instructional unit in order to effectively teach students physical science concepts and theories.
Pedagogical analysis in teaching mathematicsAnju Gandhi
This presentation helps the learners to develop an understanding of the concept of Pedagogical analysis and its process. It is specifically for B.Ed students.
Analysis of syllabus and textbook class 8 th scienceSalman Zahid
This document provides an analysis of an 8th grade science textbook published by NCERT in India. It examines details of the book such as authorship, number of pages, alignment with national curriculum frameworks. The analysis finds that the textbook covers a variety of genres, uses illustrations to support concepts, and presents local contexts. It also notes that the language is simple, tasks give scope for engagement, and themes are related to students' lived experiences. Some suggestions for improvement include adding learning outcomes, improving physical aspects like binding, and including more higher-level cognitive questions.
Role of Education in National integrationASHUTOSH JENA
Education plays an important role in promoting national integration in India. The government has taken several steps to emphasize this, such as establishing the Education Commission to promote education's role in national development. Curriculums and educational institutions also contribute by teaching subjects from a national perspective, celebrating national days, and encouraging co-curricular activities. Teachers are seen as central to this effort through the way they teach, by sharing stories of national heroes, and by not discriminating against students.
This presentation is about techniques of teaching mathematics-Drill Work, Dalton Plan. It includes the definition of each technique, advantages, disadvantages, role of teacher etc.
Role of MHRD, UGC, NCTE and AICTE in Higher EducationPoojaWalia6
The document discusses the roles of various regulatory bodies in higher education in India. The Ministry of Human Resource Development oversees education at both the school and higher education levels through two departments. The University Grants Commission regulates and coordinates university education, while the National Council for Teacher Education and All India Council for Technical Education regulate teacher education and technical education, respectively. They are responsible for planning, maintaining standards, providing grants, and ensuring quality across higher education institutions in India.
This document discusses different techniques for teaching mathematics, including oral work, written work, and assignment work. It explains that oral work involves solving problems mentally without writing and helps build a foundation for later written work. Both oral and written work are important, with the ultimate aim being proficiency in written work. Assignments allow students to study independently and supplement classroom teaching. The document provides guidelines for creating effective assignments and examples of how assignments and oral/written work can be used in teaching mathematics.
Algebraic Thinking A Problem Solving ApproachCheryl Brown
This document discusses developing algebraic thinking through a problem solving approach in mathematics education. It argues that solving mathematical problems can help students develop a deeper understanding of algebraic concepts by encouraging them to consider the generalities and relationships within problems. The document outlines several key aspects of algebraic thinking, such as reasoning about patterns, generalizing, and thinking about mathematical relations. It advocates facilitating student discourse and communication of mathematical ideas to promote algebraic reasoning. Finally, it suggests students progress through stages of developing algebraic thinking, starting with describing generalities verbally and moving to using diagrams, symbols, and formal algebraic notation.
The document discusses key topics in mathematics pedagogy for CTET exams, including:
- Defining pedagogy and mathematics.
- The nature of mathematics as both a science of discovery and logical processes.
- Guiding principles and vision for mathematics in the NCF-2005 curriculum.
- Strategies for teaching mathematics like written work, oral work, group work and homework.
- Reasons for keeping mathematics in school curriculums like its basis in other sciences and role in developing logical thinking.
- The language of mathematics including concepts, terminology, symbols and algorithms.
- Approaches like community mathematics and mathematical communication to engage students.
This document discusses teacher competencies, which are defined as the set of knowledge, skills, and experience necessary to be an effective teacher. It identifies three main types of teacher competencies: subject competencies which refer to strong knowledge of content areas; pedagogical competencies which involve teaching skills and understanding how students learn; and technological competencies which include the ability to use technology appropriately in the classroom. The document provides details on each type of competency and their importance for quality teaching. It emphasizes that competent teachers have both in-depth content knowledge as well as skills for effectively imparting that knowledge to students.
The recomendations of ncf 2005 and 2009jakeerhusain1
This document discusses the National Curriculum Frameworks (NCF) of 2005 and 2009 in India. It provides a brief history of NCFs since 1975. The NCF of 2005 recommended softening subject boundaries, incorporating local knowledge into textbooks, and creating a stimulating school environment. The NCF of 2009 emphasized changing trainee teachers' negative approaches, moving beyond an examination-focused curriculum, and providing flexible training for in-service teachers. The conclusion states that NCFs aim to help teachers play a significant role in national development, as envisioned by the Education Commission.
Nature ,Scope,Meaning and Definition of Mathematics AngelSophia2
This document provides an overview of mathematics as a subject. It discusses how mathematics plays an important role in social and economic development. It also examines definitions of mathematics from different sources, describing it as a systematic, organized science that deals with quantities, measurements, and spatial relationships. The document outlines key characteristics of mathematics, including that it is a science of discovery, an intellectual game, and a tool subject. It also discusses the abstract nature of mathematical concepts and how mathematics requires logical sequencing and applying concepts to new situations.
This document discusses the correlation of mathematics with various domains:
1) Mathematics is correlated with life activities through concepts like percentages, interest rates, and ratios that are useful in everyday life.
2) Different branches of mathematics like arithmetic, algebra, geometry are interrelated through concepts like functions and mathematical structures.
3) Topics within the same branch of mathematics are also correlated, for example concepts in algebra relate to equations, and areas of shapes relate in geometry.
4) Mathematics is also correlated with other subjects like physical sciences through expression of laws as mathematical equations, with biology through use of higher math methods, and with engineering as mathematics forms the basis of engineering courses.
Core curriculum is a set of basic courses considered essential for a well-rounded education. It includes compulsory subjects like social science, geography, biology, and history. Core curriculum also includes optional subjects like fine arts, home economics, languages, and music. Characteristics of a core curriculum include emphasizing discussion, group problem solving, integrating learning across disciplines, focusing on original source materials, and weaving common elements to encourage reflection and development of social skills.
The document discusses different modalities of teaching: conditioning, training, instruction, and indoctrination. It provides definitions and comparisons of each:
1) Conditioning is the lowest level and involves establishing automatic responses through reinforcement. It is not considered teaching.
2) Training focuses on developing skills through practice and is a higher level than conditioning. It can overlap with teaching when developing understanding.
3) Instruction imparts knowledge but only affects the cognitive domain, while teaching aims to develop the whole person. Instruction is part of teaching.
4) Indoctrination uncritically teaches a fixed set of beliefs through repetition without questioning. It aims to promote actions rather than independent thought, unlike educ
This document discusses principles of curriculum construction. It begins by defining curriculum as the sum total of experiences a student receives through activities at school, including the classroom, library, laboratories, playgrounds, and interactions with teachers. It then provides definitions of curriculum from various scholars. The main body outlines 14 principles that should guide curriculum construction, such as ensuring it reflects the aims of education and the needs, interests, and abilities of students (child-centric principle), considers civic and social needs, conserves cultural heritage while allowing for creativity, prepares students for the future and living, integrates subjects logically, accommodates individual differences, and considers the time available.
Deficit theory - Language Across the CurriculumSuresh Babu
The deficit theory suggests that students from lower socioeconomic environments enter school without the necessary linguistic resources for success. It explains that disadvantaged students often show high failure rates because they come from homes lacking verbal stimulation. The deficit theory is problematic because teachers' expectations, which can be influenced by this theory, have a large impact on how students perform. If teachers believe only certain types of students can succeed, they will teach in a way that self-fulfills that belief. Believing in the deficit theory can lead to poor student performance, increased delinquency, feelings of helplessness, and lack of interest in school.
CONTINUOUS AND COMPREHENSIVE EVALUATION(CCE)Sani Prince
CCE was made mandatory in National Policy on Education,1986 (NPE 1986) to introduce Continuous and Comprehensive Evaluation in schools as an important step of examination reform and for the qualitative improvement in the education system.
This document outlines the aims, objectives, and scope of teaching mathematics. It discusses the differences between aims, which are general long-term goals, versus objectives, which are specific and measurable. The document then lists several general aims of teaching mathematics, such as developing logical reasoning and problem solving skills. It also provides examples of objectives at different educational stages, from primary to secondary. Finally, the document discusses the wide scope and career applications of mathematics, such as actuary, teacher, engineer, and more.
curriculum : meaning and concept, principles of curriculum, curriculum construction and curriculum organisation, bases of curriculum, types of curriculum, method of organisation of curriculum ppt
The document discusses several teaching methods:
1. The inductive method proceeds from specific examples to generalizations. It involves presenting examples, making observations, and deriving general rules or formulas.
2. The deductive method proceeds from general rules to specific cases. The rule or formula is given first and then applied to solve problems.
3. The analytic method breaks down problems into known and unknown parts to derive solutions. It proceeds from unknown to known.
4. The synthetic method combines known elements to derive unknown parts. It proceeds from known to unknown.
5. The heuristic method emphasizes experimentation and discovery learning with the teacher as a facilitator rather than instructor. Students take an active role
Aims and objectives of teaching in physical scienceJIPSA MOHAN
The document discusses the aims and objectives of teaching physical science in secondary school. It states that the main purpose is to provide students with basic knowledge of physical science needed for further study in modern science and technology. It also aims to develop students' experimental skills, ability to think, and use of mathematics to solve problems. The study of physical science can benefit fields like industry, defense, and agriculture. Objectives should control classroom instruction and be written in measurable terms for each instructional unit in order to effectively teach students physical science concepts and theories.
Pedagogical analysis in teaching mathematicsAnju Gandhi
This presentation helps the learners to develop an understanding of the concept of Pedagogical analysis and its process. It is specifically for B.Ed students.
Analysis of syllabus and textbook class 8 th scienceSalman Zahid
This document provides an analysis of an 8th grade science textbook published by NCERT in India. It examines details of the book such as authorship, number of pages, alignment with national curriculum frameworks. The analysis finds that the textbook covers a variety of genres, uses illustrations to support concepts, and presents local contexts. It also notes that the language is simple, tasks give scope for engagement, and themes are related to students' lived experiences. Some suggestions for improvement include adding learning outcomes, improving physical aspects like binding, and including more higher-level cognitive questions.
Role of Education in National integrationASHUTOSH JENA
Education plays an important role in promoting national integration in India. The government has taken several steps to emphasize this, such as establishing the Education Commission to promote education's role in national development. Curriculums and educational institutions also contribute by teaching subjects from a national perspective, celebrating national days, and encouraging co-curricular activities. Teachers are seen as central to this effort through the way they teach, by sharing stories of national heroes, and by not discriminating against students.
This presentation is about techniques of teaching mathematics-Drill Work, Dalton Plan. It includes the definition of each technique, advantages, disadvantages, role of teacher etc.
Role of MHRD, UGC, NCTE and AICTE in Higher EducationPoojaWalia6
The document discusses the roles of various regulatory bodies in higher education in India. The Ministry of Human Resource Development oversees education at both the school and higher education levels through two departments. The University Grants Commission regulates and coordinates university education, while the National Council for Teacher Education and All India Council for Technical Education regulate teacher education and technical education, respectively. They are responsible for planning, maintaining standards, providing grants, and ensuring quality across higher education institutions in India.
This document discusses different techniques for teaching mathematics, including oral work, written work, and assignment work. It explains that oral work involves solving problems mentally without writing and helps build a foundation for later written work. Both oral and written work are important, with the ultimate aim being proficiency in written work. Assignments allow students to study independently and supplement classroom teaching. The document provides guidelines for creating effective assignments and examples of how assignments and oral/written work can be used in teaching mathematics.
Algebraic Thinking A Problem Solving ApproachCheryl Brown
This document discusses developing algebraic thinking through a problem solving approach in mathematics education. It argues that solving mathematical problems can help students develop a deeper understanding of algebraic concepts by encouraging them to consider the generalities and relationships within problems. The document outlines several key aspects of algebraic thinking, such as reasoning about patterns, generalizing, and thinking about mathematical relations. It advocates facilitating student discourse and communication of mathematical ideas to promote algebraic reasoning. Finally, it suggests students progress through stages of developing algebraic thinking, starting with describing generalities verbally and moving to using diagrams, symbols, and formal algebraic notation.
The document discusses key topics in mathematics pedagogy for CTET exams, including:
- Defining pedagogy and mathematics.
- The nature of mathematics as both a science of discovery and logical processes.
- Guiding principles and vision for mathematics in the NCF-2005 curriculum.
- Strategies for teaching mathematics like written work, oral work, group work and homework.
- Reasons for keeping mathematics in school curriculums like its basis in other sciences and role in developing logical thinking.
- The language of mathematics including concepts, terminology, symbols and algorithms.
- Approaches like community mathematics and mathematical communication to engage students.
The document discusses key topics in mathematics pedagogy for CTET exams, including:
- Defining pedagogy and mathematics.
- The nature of mathematics as both a science of discovery and logical processes.
- Guiding principles and vision for mathematics in the NCF-2005 curriculum.
- Strategies for teaching mathematics like written work, oral work, group work and homework.
- Reasons for keeping mathematics in school curriculums like its basis in other sciences and role in developing logical thinking.
- The language of mathematics including concepts, terminology, symbols and algorithms.
- Approaches like community mathematics and mathematical communication to engage students.
The document discusses the challenges in determining what information to include in math tournaments. It notes that students have varying levels of understanding due to differences in school curriculums, teaching styles, and how students perceive math. This makes it difficult to create tournaments that are both challenging and fair. The document suggests standardizing curriculums, focusing more on conceptual understanding than memorization, and including individual, group, and testing components in tournaments to accommodate different learning preferences.
This document discusses integrating mathematics with other subjects and effective teaching strategies for mathematics. It describes how math can be integrated into subjects like science, social studies, literacy, and arts. Six teaching strategies for math are outlined: making conceptual understanding a priority, setting meaningful homework, using cooperative learning, strategic questioning, focusing on real problem-solving and reasoning, and using mixed modes of assessment. The conclusion emphasizes that integrating math into other subjects helps students understand math concepts better and see real-world applications. Effective teaching approaches can improve math learning outcomes.
EFFECTIVENESS OF SINGAPORE MATH STRATEGIES IN LEARNING MATHEMATICS AMONG FOUR...Thiyagu K
The Singapore math method is child-focused, and seeks to make sure that the student gains a full and complete understanding of the fundamental mathematical concepts, rather than merely memorizes a rote collection of facts. This approach not merely enhances mathematical learning; it also offers a firm foundation from which broader mathematical principles can be extrapolated. The present study tries to find out the effectiveness of Singapore math strategies in learning mathematics among fourth standard students. Two equivalent group experimental-designs are employed for this study. The investigator has chosen 64 Fourth standard students for the study. According to the scoring of pre-test, 32 students were chosen as control group and 32 students were chosen as experimental group. Finally the investigator concludes; (a) the experimental group student is better than control group students in their gain scores. (b) There is no significant difference between control group and experimental group students in their pre test scores and post test. (c)There is significant difference between control group and experimental group students in the scores of posttest attainment of knowledge, understanding and application objectives.
Nature and Development of Mathematics.pptxaleena568026
This document discusses the nature and development of mathematics. It begins by defining mathematics as both an art and a science that involves learning, numbers, space, and measurement. Several experts provide definitions of mathematics emphasizing its role in science, order, reasoning, and discovery. The document outlines the nature and scope of mathematics, including that it is an abstract, precise, logical science of structures, generalizations, and inductive and deductive reasoning. It concludes by discussing the inductive and deductive methods of teaching mathematics and their respective merits and demerits.
Research in mathematics education primarily focuses on improving teaching and learning approaches in mathematics. The objectives of mathematics education research include teaching basic numeracy skills, practical mathematics applications, abstract concepts, problem solving strategies, and deductive reasoning. Continuing research is important to develop useful tools and concepts, train abstract thinking, and improve teacher understanding of how students learn. Current areas of focus include conceptual understanding, formative assessment, homework, helping struggling students, and algebraic reasoning. New areas of research thrusts relate to teacher education, using resources, language and communication, contextualized learning, reasoning skills, and integrating technology into mathematics instruction.
Nature and principles of teaching and learning mathJunarie Ramirez
This document discusses effective teaching of mathematics. It outlines three phases of mathematical inquiry: (1) abstraction and symbolic representation, (2) manipulating mathematical statements, and (3) application. It also discusses the nature and principles of teaching mathematics, including that mathematics relies on both logic and creativity. Effective teaching requires understanding what students know and challenging them, as well as using worthwhile tasks to engage them intellectually. Teachers must have mathematical knowledge and commit to students' understanding.
This document discusses approaches to mathematics curriculum as suggested by the National Curriculum Framework (NCF) and Kerala Curriculum Framework (KCF). It outlines three levels of mathematics taught in schools: daily life calculations, concepts for higher education, and more complex theoretical ideas. The document also examines why students find mathematics difficult and why it is important to learn. It proposes teaching mathematics in a way that makes it enjoyable and helps students think logically and communicate numerically. The goal is for students to understand fundamental concepts and have confidence in their mathematical abilities.
This document contains information about fostering mathematical reasoning in the classroom. It discusses the importance of having students explore concepts, make conjectures, justify their thinking, and engage in mathematical discussions. Open-ended questions and tasks are recommended as they allow for multiple solutions and require students to explain their reasoning. The document provides several examples of classroom activities and formative assessments that can help develop students' reasoning abilities, such as the "Always, Sometimes, Never" activity where students determine if statements are always, sometimes, or never true and justify their answers. Overall, the document emphasizes the importance of reasoning in learning and doing mathematics.
The document discusses using simulations in mathematics education. It begins by defining instructional simulations and how they can bridge the gap between classroom and real-world learning. It then provides examples of simulations used in different disciplines like economics and various types of simulations from simple to complex. The document emphasizes that simulations can engage students in deep learning and understanding over simple memorization. It also provides guidance on how to effectively teach with simulations, including instructor preparation, active student participation, and post-simulation discussion.
Improving Communication about Limit Concept in Mathematics through Inquisitio...IOSR Journals
In this action research study, where the subjects are our undergraduate grade mathematics students,
w e try to investigate the impact of direct ‘inquisition’ instruction on their communication and achievement.
We will strategically implement the addition of ‘replication’ study into each concept of limit over a four-month
time period and thus conclusion can be making for the rest of the Mathemat ics . The students practiced using
inquiry in verbal discussions, review activities, and in mathematical problem explanations. We discovered
that a majority of students improved their overall understanding of mathematical concepts based on an analysis
of the data we collected. We also found that in general, students felt that knowing the definition of
mathematical words are important and that it increased their achievement when they understood the concept as a
whole. In addition, students will be more exact in their communication after receiving inquiry instructions. As
a result of this research, we plan to continue to implement inquisition into daily lessons and keep replication
communication as a focus of the mathematics class
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This document outlines 9 strategies for engaging math lessons:
1. Explicit instruction involves directly teaching math concepts and using examples.
2. Conceptual understanding focuses on helping students understand why concepts are important through activities like number talks.
3. Using math vocabulary in games and activities helps build fluency and engagement.
4. Cooperative learning organizes classroom activities into academic and social experiences like jigsaw math problems.
5. Meaningful homework involves assigning real-world math problems to apply skills.
The document discusses programmed instruction, which is a systematic, self-paced method of instruction designed to ensure learning. It breaks content into small steps with built-in feedback. There are different types, including linear, branched, and mathetics programming. Programmed instruction aims to place the learner at the center and allow them to construct knowledge through active participation, as opposed to passive absorption of information. While it shows promise, programmed instruction has seen limited application in Indian classrooms.
MATD611 Mathematics Education In Perspective.docxstirlingvwriters
The document discusses four views of mathematics:
1) Logicism view - Mathematics is a continuation of logic and can be reduced to logic.
2) Intuitionist view - Mathematics is a product of human imagination and must be mentally constructed.
3) Instrumentalist view - Mathematics is a collection of unrelated rules and facts that serve practical purposes.
4) The document also discusses teachers' views on the nature of mathematics, the benefits of teaching history of mathematics, and ways to implement student-centered learning in mathematics classrooms.
Monitoring The Status Of Students' Journey Towards Science And Mathematics Li...noblex1
A major focus of the current mathematics and science education reforms is on developing "literacy;" that is, helping students to understand and use the languages and ideas of mathematics and science in reasoning, communicating, and solving problems. In many ways, these standards documents are far more voluminous and complex than any scope and sequence in place in school systems today. But these documents are meant to be used as frameworks which provide guidance in education reform - they are not the definitive sources articulating to teachers how education reform must occur in their classrooms.
Our plan in this discussion is to lay out the components of mathematics and science literacy as set down in the major reform documents and then, using selected how-to articles, to show how strategies and activities tried by math and science teachers have been used, or can be used, to promote math and science literacy among students. For pragmatic reasons only, our discussions often focus either on mathematics or science reform recommendations and examples. In doing this, we do not mean to imply that the elements of literacy in these disciplines are somehow separate or different. In fact, the separate discussions show how both the mathematics and science education communities, coming from different directions at different points in time, independently arrived at similar positions and many of the same recommendations regarding the ideas of literacy.
In support of this discussion of the components of literacy, we also provide samples of resources, materials, and services that teachers might find useful in promoting mathematics and science literacy in their classrooms. The how-to articles are meant to be quick-reads that can be applied or adapted to classrooms directly. These articles are included to make it easier to decide which ones might be of special interest. Other articles and documents are intended as sources of a more general background. These documents provide some of the research bases and rationales behind some of the reform recommendations. Finally, we have included other references and information on databases which are not directly cited in the discussion but might prove valuable as additional sources of classroom ideas.
During the last decade, the mathematics education community appeared to lack clear focus and a sense of direction. Although many conferences were held, papers written, and reports produced, there was not a general consensus regarding which direction mathematics education should head.
The Standards offer an organization of important mathematical topics and abilities by grade-level groups (Kindergarten - grade 4, grades 5 - 8, and grades 9 - 12). Throughout the Standards the emphasis is: "knowing" mathematics is "doing" mathematics.
Source: https://ebookschoice.com/monitoring-the-status-of-students-journey-towards-science-and-mathematics-literacy/
This document provides an overview of the 5th grade mathematics standards for North Carolina related to the Common Core. It is intended to help educators understand what students are expected to know and be able to do under the new standards. The document explains that the standards describe the essential knowledge and skills students should master in order to be prepared for 6th grade. It also provides examples for how the standards can be unpacked to clarify their meaning and intent. Educators are encouraged to provide feedback to help improve the usefulness of the document.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
3. “
”
A lesson without the opportunity for
learners to generalise is not a
mathematics lesson.
- J Mason, 1996
4. MATHEMATICAL GENERALIZATION
• In mathematics, generalization can be both a process and a
product.
• When one looks at specific instances, notices a pattern, and uses
inductive reasoning to conjecture a statement about all such
patterns, one is generalizing. The symbolic, verbal, or visual
representation of the pattern in your conjecture might be called a
generalization.
5. • What is generalization?
• There are three meanings attached to generalization from
the literature. The first is as a synonym for abstraction. That
is, the process of generalization is the process of “finding and
singling out [of properties] in a whole class of similar objects.
In this sense it is a synonym for abstraction.
• The second meaning includes extension (empirical or
mathematical) of existing concept or a mathematical
invention.
• The third meaning defines generalization in terms of its
product. If the product of abstraction is a concept, the
product of generalization is a statement relating the
concepts, that is, a theorem.
6. By defining examples such as:
• a2 × a3 = (a × a) × (a × a × a) = a5
• a3 × a4 = (a × a × a) × (a × a × a × a) = a7 and so on
• One can conclude that:
• am × an = am+n
• …thus generalizing to all cases for a specific domain for the base “a” and
the exponents “m” and “n.”
7. One more example-
• When a student notices that the sum of an even and an odd
integer always results in an odd integer, that student is
generalizing.
Generalizations such as this allow students to think about
computations independently of the particular numbers that are
used. Without this, and many other generalizations made in
mathematics from the early grades, all work in mathematics would
be cumbersome and inefficient.
8. Role of generalization in advanced
mathematical thinking
• Generalization and abstraction both play an important role in the
minds of mathematics students as they study higher-level
concepts.generalization as the derivation or induction from
something particular to something general by looking at the
common things and expanding their domains of validity. As we
teach our own math courses, we can look out for opportunities to
introduce generalization and abstraction in order to help our
students better understand the pattern behind what they are
learning.
9. Importance of mathematical generalization
in teaching mathematics
There are several advantages to applying
generalization in our math classes, and its positive
effect on teaching and learning is a fundamental
way to provide our students with the tools needed
for successful advanced thinking in mathematics.
10. “
”
Generalizing is the process of "seeing through
the particular" by not dwelling in the
particularities but rather stressing
relationships… whenever we stress some
features we consequently ignore others, and
this is how generalizing comes about.
- Mason