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The document discusses the importance and relevance of mathematical investigations, particularly during the pandemic. It defines mathematical investigations as investigations involving collections of mathematical and problem-solving issues. Mathematical investigations give students opportunities to make discoveries they will remember longer than teacher-told concepts. They encourage higher-order thinking skills. A complete investigation requires finding patterns, seeking logical proofs, and coherent organization. Research shows student-discovered ideas lead to stronger conceptual understanding of mathematical connections. Mathematical investigations also improve student mathematical learning and develop their mathematical power.

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Nature and Development of Mathematics.pptx

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.

Sierpinska

The document discusses the distinction between theoretical and practical thinking in mathematics. It presents a model that defines theoretical thinking as focusing on conceptual connections, logical reasoning, and developing consistent theories, while practical thinking focuses on solving particular problems and understanding factual relationships. The author argues that successful mathematics students demonstrate a "practical understanding of theory" by applying theoretical knowledge flexibly to efficiently solve problems. Examples of student work show the importance of both theoretical and practical thinking skills for high achievement in university mathematics.

MATD611 Mathematics Education In Perspective.docx

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.

Nature and principles of teaching and learning math

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.

An Exploration Of Strategies Used By Students To Solve Problems With Multiple...

This document summarizes a study that analyzed how 35 students solved math problems that could be solved in multiple ways. It reviewed relevant literature on problem solving approaches and frameworks. Specifically, it discussed Perkins and Simmons' model of four knowledge frames - content, problem-solving, epistemic, and inquiry - that characterize different types of knowledge used in problem solving. The purpose of the study was to understand the strategies and difficulties students experience when approaching problems with multiple solutions.

Arithmetic skills

The document discusses mathematical skills and higher order thinking skills (HOTS) in mathematics. It begins by defining key arithmetic skills like number sense, measurement, and patterns that are important for students to learn. It then discusses different types of graphs and charts used to visualize data. The document outlines the five fundamental HOTS: problem solving, inquiring, reasoning, communicating, and conceptualizing skills. It notes that developing HOTS better prepares students for challenges in work and life. The document provides examples of how to incorporate HOTS into mathematics teaching and assessments in order to improve student performance.

Arithmetic skills

The document discusses mathematical skills and higher order thinking skills (HOTS) in mathematics. It defines arithmetic skills such as addition, subtraction, multiplication and division. It also discusses geometric skills and interpreting graphs and charts. The document then defines HOTS as including skills such as problem solving, reasoning, communication and conceptualizing. It provides examples of each skill and discusses the importance of incorporating HOTS into mathematics teaching to better prepare students. The document concludes by providing suggestions for how to improve students' HOTS through revising textbooks and using open-ended testing.

Meaning and definition of mathematics

Mathematics is defined in multiple ways throughout the document. It is summarized as the science of quantity, measurement, and spatial relationships. It involves both inductive and deductive reasoning. Inductive reasoning involves making general conclusions from specific observations, while deductive reasoning involves drawing logical conclusions from initial assumptions or axioms. Teaching mathematics effectively uses both inductive and deductive methods, moving from specific examples to broader conclusions or from general principles to specific applications.

Nature and Development of Mathematics.pptx

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.

Sierpinska

The document discusses the distinction between theoretical and practical thinking in mathematics. It presents a model that defines theoretical thinking as focusing on conceptual connections, logical reasoning, and developing consistent theories, while practical thinking focuses on solving particular problems and understanding factual relationships. The author argues that successful mathematics students demonstrate a "practical understanding of theory" by applying theoretical knowledge flexibly to efficiently solve problems. Examples of student work show the importance of both theoretical and practical thinking skills for high achievement in university mathematics.

MATD611 Mathematics Education In Perspective.docx

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.

Nature and principles of teaching and learning math

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.

An Exploration Of Strategies Used By Students To Solve Problems With Multiple...

This document summarizes a study that analyzed how 35 students solved math problems that could be solved in multiple ways. It reviewed relevant literature on problem solving approaches and frameworks. Specifically, it discussed Perkins and Simmons' model of four knowledge frames - content, problem-solving, epistemic, and inquiry - that characterize different types of knowledge used in problem solving. The purpose of the study was to understand the strategies and difficulties students experience when approaching problems with multiple solutions.

Arithmetic skills

The document discusses mathematical skills and higher order thinking skills (HOTS) in mathematics. It begins by defining key arithmetic skills like number sense, measurement, and patterns that are important for students to learn. It then discusses different types of graphs and charts used to visualize data. The document outlines the five fundamental HOTS: problem solving, inquiring, reasoning, communicating, and conceptualizing skills. It notes that developing HOTS better prepares students for challenges in work and life. The document provides examples of how to incorporate HOTS into mathematics teaching and assessments in order to improve student performance.

Arithmetic skills

The document discusses mathematical skills and higher order thinking skills (HOTS) in mathematics. It defines arithmetic skills such as addition, subtraction, multiplication and division. It also discusses geometric skills and interpreting graphs and charts. The document then defines HOTS as including skills such as problem solving, reasoning, communication and conceptualizing. It provides examples of each skill and discusses the importance of incorporating HOTS into mathematics teaching to better prepare students. The document concludes by providing suggestions for how to improve students' HOTS through revising textbooks and using open-ended testing.

Meaning and definition of mathematics

Mathematics is defined in multiple ways throughout the document. It is summarized as the science of quantity, measurement, and spatial relationships. It involves both inductive and deductive reasoning. Inductive reasoning involves making general conclusions from specific observations, while deductive reasoning involves drawing logical conclusions from initial assumptions or axioms. Teaching mathematics effectively uses both inductive and deductive methods, moving from specific examples to broader conclusions or from general principles to specific applications.

Mathematical skills

Mathematical skills such as arithmetic, geometry, and graphing are important foundations for students. Key skills include number sense, measurement, patterns, problem-solving, and computational fluency. Higher-order thinking skills (HOTS) like problem-solving, reasoning, and conceptualizing are valued as they better prepare students for challenges. HOTS involve skills like critical thinking, creativity, and systems thinking. Teachers should focus on developing students' HOTS through open-ended learning activities.

MATH_INVESTIGATION_CG.pdf

The document provides information on a K-12 Special Science Program Research Curriculum Guide for grades 7-10. It outlines the content standards, performance standards, and learning competencies for research courses in each grade level. The courses introduce concepts of mathematical investigation and guide students through the process of conducting their own research projects, from formulating questions to revising drafts to the final presentation. The goal is for students to gain experience in mathematical investigation and eventually submit their work for publication.

Solving Exponential Equations: Learning from the Students We Teach

The purpose of this paper is to share with the mathematics community what I discovered from analyzingone of myGrade 11 students’ approach to solving exponential equations of the form a a k x p x q , where a and k are positive integers greater than 1, and p , q . The student got a correct answer using a procedure which does not conform with the known exponential laws, thereby making it difficult to evaluate the student’s work. I gave the student’s script to fellow mathematics educators and they marked the student wrong, arguing that laws of exponents cannot be extended to a sum or difference of exponentials with the same base. Ithen decided to present the student’s solution method to other mathematics experts (through the Math Forum)for further evaluation. The responses and comments I received were far from being conclusive. It was suggested that there was need to use mathematical proof to verify whether the student’s approach was valid or not. I then set out to investigate why what looked like invalid reasoning on the surface gave the right answer in the end.After a careful analysis of the student’s approach, coupled with some kind of empirical investigations and mathematical proof, I eventually discovered that there was some logic in the student’s approach, only that it was not supported by the known theory of exponents. I therefore recommend that mathematics educators should not take students’ solution methods for granted. We might be marking some of the students’ solution methods wrong when they are valid, and robbing them of their precious marks. It is possible for students to come up with new and valid methods of solving mathematics problems which are not known to the educators.Good mathematics educators should therefore be on the lookout for new unanticipated approaches to solving mathematical problems that students of exceptional abilities may use in class. The famous German mathematician and astronomer, Carl Friedrich Gauss (1777-1855)amazed his teachers when he discovered a quick way of summing the integers from 1 to 100, at the age of seven. Such exceptional intellectual abilities still existeven in school children of today.

Mathematical

This document reports on a study that examined the effects of a historical approach, problem-based calculus course on Taiwanese college students' views of mathematical thinking. The study involved three stages: 1) Initial assessment of students' pre-instruction views via questionnaire and interviews, 2) An 18-week course integrating historical problems and concepts, 3) Post-instruction assessment of students' views using the same questionnaire and interviews to identify shifts. The findings showed that after the course, students were more likely to value logical thinking, creativity, and imagination in mathematics, took a more conservative view of mathematical certainty, and shifted from seeing mathematics as a set of procedures to a process.

CTET / TET Mathematics Preparation :Important key words

while practicing for ctet I came across some word which i didn't find in syllabus. so in this PPT I am discussing all those key words. wish it will help you in your studies. if you find any other words which I this PPt doesn't contain then plz let me know I will definitely try to find out.

10.1007%2 f978 3-319-62597-3-73

This document summarizes the proceedings of Topic Study Group No. 46, which focused on conceptualizing and measuring knowledge for teaching mathematics at the secondary level. The study group consisted of four sessions that addressed: 1) conceptual frameworks for understanding teacher knowledge, 2) methods for measuring teacher knowledge, 3) connections between teacher knowledge and classroom practice, and 4) reflections on the previous discussions. Presentations in each session explored topics like different conceptualizations of teacher knowledge, valid ways to measure knowledge, and the relationship between advanced mathematics training and secondary teaching. Overall, the study group reflected on progress in the field over the past 30 years while also identifying open questions around developing a comprehensive framework and ensuring generalizability of teacher knowledge measures.

Constructivist Approach Vs Expository Teaching: Exponential Functions

This document summarizes a study that compared the effects of expository teaching and constructivist teaching approaches on students' understanding of exponential functions. The study involved 50 10th grade students split into two classes, one taught using expository methods and one taught using constructivist activities. An assessment given after found that both groups struggled with conceptual questions about exponential functions, such as writing the domain and range or determining if an exponential function is one-to-one. The constructivist approach was intended to support active learning but students may have preferred rote memorization due to testing pressures. Overall, neither approach significantly improved students' conceptual grasp of exponential functions.

Instrumentation 1

The document discusses the development of teaching and learning mathematics globally and locally through history. It covers theories and principles of mathematics education like constructivism and cooperative learning. It also profiles various mathematicians and educators who contributed to advancing mathematics education, such as Euclid, Pólya, Freudenthal, and 10 famous Filipino mathematicians including Raymundo Favila, Bienvenido Nebres, and Jose Marasigan.

inclusive science.pptx

Inclusive science teaching involves three main concepts: differentiated learning to accommodate different needs, scientific reasoning and problem solving, and allowing students to explore and develop their own understanding of scientific knowledge and processes. It provides opportunities for all students to discover and engage with scientific phenomena in different practical and theoretical ways. Effective inclusive science lessons consider how to support varied learning needs and styles, incorporate scientific practices, and help students understand the nature and development of scientific knowledge.

Rickard, anthony teaching prospective teachers about mathematical reasoning n...

William Allan Kritsonis, PhD - Editor-in-Chief, NATIONAL FORUM JOURNALS (Founded 1982). Article published by NATIONAL FORUM JOURNALS

Philip Siaw Kissi

This study investigated the effects of using a graphical calculator (Microsoft Math Tool) on students' performance in linear functions. Ninety-eight students from two schools participated, with one group receiving instruction using the graphical calculator (experimental group) and the other receiving traditional lecture-based instruction (control group). Pre-tests showed no significant difference between the groups. Post-test results revealed significantly higher scores for the experimental group compared to the control group, suggesting that using graphical calculators can improve students' understanding of linear functions and performance on related tasks. The study recommends integrating graphical calculators into mathematics instruction.

Assessing Multiplicative Thinking Using Rich Tasks

The document describes the development of a learning and assessment framework to evaluate students' multiplicative thinking skills in Years 4 to 8. Researchers designed rich assessment tasks and administered them to nearly 3,500 students. The tasks were based on an initial hypothetical learning trajectory identified from the literature. Student response data were used to refine the tasks, scoring rubrics, and a final learning and assessment framework consisting of nine levels of increasing complexity in multiplicative thinking. Sample assessment tasks, such as a multi-part "Butterfly House" problem, and corresponding scoring rubrics are provided as illustrations.

The process of thinking by prospective teachers of mathematics in making argu...

The process of thinking by prospective teachers of mathematics in making argu...Journal of Education and Learning (EduLearn)

This study aimed to describe the process of thinking by prospective teachers of mathematics in making arguments. It was a qualitative research involving the mathematics students of STKIP PGRI Jombang as the subject of the study. Test and task-based semi structural interview were conducted for data collection. The result showed that 163 of 260 mathematics students argued using inductive and deductive warrants. The process of thinking by the prospective teachers of mathematics in making arguments had begun since they constructed their very first idea by figuring out some objects to make a conclusion. However, they also found a rebuttal from that conclusion, though they did not further describe what such rebuttal was. Therefore, they decided to construct the second ideas in order to verify the first ones through some pieces of definition.curriculum theory.pdf

This document discusses different theories of curriculum. It begins by explaining the different views of scientific theory, including the received view which sees theory as deductively connected laws. For curriculum theory, the received view takes basic concepts and defines others in terms of them through axioms and definitions. The document then discusses criticisms of the received view and alternatives like instrumentalism and realism. It provides definitions of curriculum theory and describes the common functions of theories as description, prediction, explanation, and guidance. The rest of the document outlines different ways of classifying curriculum theories, such as focusing on structure, values, content, or processes, and examines some major theorists within those classifications.

Curriculum theory

This document discusses different theories of curriculum. It begins by explaining the concept of theory in general and debates around the "received view" of scientific theory. It then examines different approaches to curriculum theory, including their functions of description, prediction, explanation and guidance. The document also analyzes different frameworks for classifying curriculum theories, such as focusing on their structure, values, content or processes. Specific theorists are discussed, such as Macdonald who viewed curriculum as a social system, and Apple who analyzed the relationship between society and schools through the concept of hegemony.

Authentic Tasks And Mathematical Problem Solving

This document discusses authentic tasks in mathematical problem solving and their role in developing mathematical literacy. It describes four key dimensions of authentic tasks: thinking and reasoning, discourse, mathematical tools, and attitudes and dispositions. Each of these dimensions supports meaningful learning and prepares students to solve everyday problems. The document provides examples of lessons and programs that incorporate these dimensions through real-world, problem-based activities.

Modelling presentation

This document describes a study that aims to monitor biology students' progression in mathematical competencies through engaging modelling tasks. The study will introduce biologically-themed modelling sessions in a freshman mathematics course. It will assess students' competencies before and after using a three-dimensional framework, and analyze any progression over the sessions. The document outlines the research questions, strategies, design, tasks and data collection methods. It also describes frameworks for understanding competence and a coding system to identify competencies demonstrated in students' work. The goal is to determine if modelling can help students develop mathematical competencies.

teaching algebra revised

This document discusses principles of teaching algebra. It describes a 3-part structure of algebra involving representing elements algebraically, transforming symbolic expressions, and interpreting new forms. Perspectives on algebra's usefulness in fields like science are provided. Principles for school mathematics emphasize patterns, quantitative relationships, and analyzing change. Models for teaching algebra include demonstrating worked examples, conceptual attainment, inductive thinking, advance organizers, and inquiry training. Each model involves multiple phases like confronting problems, gathering data, formulating explanations, and analyzing thinking processes.

The logic of informal proofs

The document discusses the logic of informal proofs in mathematics. It makes 5 key claims:
1) Understanding informal proofs is important because most mathematical proofs are informal.
2) Informal proofs rely on both logical form and content.
3) Properly understanding informal proofs requires seeing logic as the study of inferential actions, where content plays a role.
4) This conception accommodates proofs involving actions on objects other than propositions.
5) It explains why mathematics relies on external representations, since representations can be manipulated.
The document argues this view connects logical questions about rigor to the cultural study of mathematical practices.

Applying Learning Principles based on Cognitive Science to Improve Training ...

The document discusses applying cognitive science principles to improve training performance. It defines learning science and its relationship to cognitive science. Six cognitive strategies are described to enhance training: spaced practice, interleaving, retrieval practice, elaboration, dual coding, and concrete examples. The document recommends incorporating these strategies into learning design through effective organization, coherence, stories, and multiple examples. It also suggests offering learning environments that promote cognitive disequilibrium and flexibility to enhance performance.

MATHEMACAL INVESTIGATION IN GRADE 5.pptx

This document discusses fractions and their properties. It defines a fraction as a numerical value that represents part of a whole, evaluated by dividing the whole into parts. It notes that fractions with the same denominator are similar fractions, while those with different denominators are dissimilar fractions. It provides instructions for adding similar fractions by adding the numerators and writing the sum over the denominator, and for adding dissimilar fractions by renaming them to have a common denominator before adding the numerators and writing the sum over the denominator.

class orientation.pptx

Mrs. Jelly Joy Rosario Fernandez will be the class adviser for Grade V-A for the 2023-2024 school year. The agenda discusses the subjects, which include ESP, English, Araling Panlipunan, Filipino, Mathematics, Science, EPP, and MAPEH. It also outlines the class schedule, grading system where written works and performance tasks make up 50% of grades and the quarterly exam makes up 20%, and the classroom rules of being prompt, honest, prepared, participative, respectful, and responsible.

Mathematical skills

Mathematical skills such as arithmetic, geometry, and graphing are important foundations for students. Key skills include number sense, measurement, patterns, problem-solving, and computational fluency. Higher-order thinking skills (HOTS) like problem-solving, reasoning, and conceptualizing are valued as they better prepare students for challenges. HOTS involve skills like critical thinking, creativity, and systems thinking. Teachers should focus on developing students' HOTS through open-ended learning activities.

MATH_INVESTIGATION_CG.pdf

The document provides information on a K-12 Special Science Program Research Curriculum Guide for grades 7-10. It outlines the content standards, performance standards, and learning competencies for research courses in each grade level. The courses introduce concepts of mathematical investigation and guide students through the process of conducting their own research projects, from formulating questions to revising drafts to the final presentation. The goal is for students to gain experience in mathematical investigation and eventually submit their work for publication.

Solving Exponential Equations: Learning from the Students We Teach

The purpose of this paper is to share with the mathematics community what I discovered from analyzingone of myGrade 11 students’ approach to solving exponential equations of the form a a k x p x q , where a and k are positive integers greater than 1, and p , q . The student got a correct answer using a procedure which does not conform with the known exponential laws, thereby making it difficult to evaluate the student’s work. I gave the student’s script to fellow mathematics educators and they marked the student wrong, arguing that laws of exponents cannot be extended to a sum or difference of exponentials with the same base. Ithen decided to present the student’s solution method to other mathematics experts (through the Math Forum)for further evaluation. The responses and comments I received were far from being conclusive. It was suggested that there was need to use mathematical proof to verify whether the student’s approach was valid or not. I then set out to investigate why what looked like invalid reasoning on the surface gave the right answer in the end.After a careful analysis of the student’s approach, coupled with some kind of empirical investigations and mathematical proof, I eventually discovered that there was some logic in the student’s approach, only that it was not supported by the known theory of exponents. I therefore recommend that mathematics educators should not take students’ solution methods for granted. We might be marking some of the students’ solution methods wrong when they are valid, and robbing them of their precious marks. It is possible for students to come up with new and valid methods of solving mathematics problems which are not known to the educators.Good mathematics educators should therefore be on the lookout for new unanticipated approaches to solving mathematical problems that students of exceptional abilities may use in class. The famous German mathematician and astronomer, Carl Friedrich Gauss (1777-1855)amazed his teachers when he discovered a quick way of summing the integers from 1 to 100, at the age of seven. Such exceptional intellectual abilities still existeven in school children of today.

Mathematical

This document reports on a study that examined the effects of a historical approach, problem-based calculus course on Taiwanese college students' views of mathematical thinking. The study involved three stages: 1) Initial assessment of students' pre-instruction views via questionnaire and interviews, 2) An 18-week course integrating historical problems and concepts, 3) Post-instruction assessment of students' views using the same questionnaire and interviews to identify shifts. The findings showed that after the course, students were more likely to value logical thinking, creativity, and imagination in mathematics, took a more conservative view of mathematical certainty, and shifted from seeing mathematics as a set of procedures to a process.

CTET / TET Mathematics Preparation :Important key words

while practicing for ctet I came across some word which i didn't find in syllabus. so in this PPT I am discussing all those key words. wish it will help you in your studies. if you find any other words which I this PPt doesn't contain then plz let me know I will definitely try to find out.

10.1007%2 f978 3-319-62597-3-73

This document summarizes the proceedings of Topic Study Group No. 46, which focused on conceptualizing and measuring knowledge for teaching mathematics at the secondary level. The study group consisted of four sessions that addressed: 1) conceptual frameworks for understanding teacher knowledge, 2) methods for measuring teacher knowledge, 3) connections between teacher knowledge and classroom practice, and 4) reflections on the previous discussions. Presentations in each session explored topics like different conceptualizations of teacher knowledge, valid ways to measure knowledge, and the relationship between advanced mathematics training and secondary teaching. Overall, the study group reflected on progress in the field over the past 30 years while also identifying open questions around developing a comprehensive framework and ensuring generalizability of teacher knowledge measures.

Constructivist Approach Vs Expository Teaching: Exponential Functions

This document summarizes a study that compared the effects of expository teaching and constructivist teaching approaches on students' understanding of exponential functions. The study involved 50 10th grade students split into two classes, one taught using expository methods and one taught using constructivist activities. An assessment given after found that both groups struggled with conceptual questions about exponential functions, such as writing the domain and range or determining if an exponential function is one-to-one. The constructivist approach was intended to support active learning but students may have preferred rote memorization due to testing pressures. Overall, neither approach significantly improved students' conceptual grasp of exponential functions.

Instrumentation 1

The document discusses the development of teaching and learning mathematics globally and locally through history. It covers theories and principles of mathematics education like constructivism and cooperative learning. It also profiles various mathematicians and educators who contributed to advancing mathematics education, such as Euclid, Pólya, Freudenthal, and 10 famous Filipino mathematicians including Raymundo Favila, Bienvenido Nebres, and Jose Marasigan.

inclusive science.pptx

Inclusive science teaching involves three main concepts: differentiated learning to accommodate different needs, scientific reasoning and problem solving, and allowing students to explore and develop their own understanding of scientific knowledge and processes. It provides opportunities for all students to discover and engage with scientific phenomena in different practical and theoretical ways. Effective inclusive science lessons consider how to support varied learning needs and styles, incorporate scientific practices, and help students understand the nature and development of scientific knowledge.

Rickard, anthony teaching prospective teachers about mathematical reasoning n...

William Allan Kritsonis, PhD - Editor-in-Chief, NATIONAL FORUM JOURNALS (Founded 1982). Article published by NATIONAL FORUM JOURNALS

Philip Siaw Kissi

This study investigated the effects of using a graphical calculator (Microsoft Math Tool) on students' performance in linear functions. Ninety-eight students from two schools participated, with one group receiving instruction using the graphical calculator (experimental group) and the other receiving traditional lecture-based instruction (control group). Pre-tests showed no significant difference between the groups. Post-test results revealed significantly higher scores for the experimental group compared to the control group, suggesting that using graphical calculators can improve students' understanding of linear functions and performance on related tasks. The study recommends integrating graphical calculators into mathematics instruction.

Assessing Multiplicative Thinking Using Rich Tasks

The document describes the development of a learning and assessment framework to evaluate students' multiplicative thinking skills in Years 4 to 8. Researchers designed rich assessment tasks and administered them to nearly 3,500 students. The tasks were based on an initial hypothetical learning trajectory identified from the literature. Student response data were used to refine the tasks, scoring rubrics, and a final learning and assessment framework consisting of nine levels of increasing complexity in multiplicative thinking. Sample assessment tasks, such as a multi-part "Butterfly House" problem, and corresponding scoring rubrics are provided as illustrations.

The process of thinking by prospective teachers of mathematics in making argu...

The process of thinking by prospective teachers of mathematics in making argu...Journal of Education and Learning (EduLearn)

This study aimed to describe the process of thinking by prospective teachers of mathematics in making arguments. It was a qualitative research involving the mathematics students of STKIP PGRI Jombang as the subject of the study. Test and task-based semi structural interview were conducted for data collection. The result showed that 163 of 260 mathematics students argued using inductive and deductive warrants. The process of thinking by the prospective teachers of mathematics in making arguments had begun since they constructed their very first idea by figuring out some objects to make a conclusion. However, they also found a rebuttal from that conclusion, though they did not further describe what such rebuttal was. Therefore, they decided to construct the second ideas in order to verify the first ones through some pieces of definition.curriculum theory.pdf

This document discusses different theories of curriculum. It begins by explaining the different views of scientific theory, including the received view which sees theory as deductively connected laws. For curriculum theory, the received view takes basic concepts and defines others in terms of them through axioms and definitions. The document then discusses criticisms of the received view and alternatives like instrumentalism and realism. It provides definitions of curriculum theory and describes the common functions of theories as description, prediction, explanation, and guidance. The rest of the document outlines different ways of classifying curriculum theories, such as focusing on structure, values, content, or processes, and examines some major theorists within those classifications.

Curriculum theory

This document discusses different theories of curriculum. It begins by explaining the concept of theory in general and debates around the "received view" of scientific theory. It then examines different approaches to curriculum theory, including their functions of description, prediction, explanation and guidance. The document also analyzes different frameworks for classifying curriculum theories, such as focusing on their structure, values, content or processes. Specific theorists are discussed, such as Macdonald who viewed curriculum as a social system, and Apple who analyzed the relationship between society and schools through the concept of hegemony.

Authentic Tasks And Mathematical Problem Solving

This document discusses authentic tasks in mathematical problem solving and their role in developing mathematical literacy. It describes four key dimensions of authentic tasks: thinking and reasoning, discourse, mathematical tools, and attitudes and dispositions. Each of these dimensions supports meaningful learning and prepares students to solve everyday problems. The document provides examples of lessons and programs that incorporate these dimensions through real-world, problem-based activities.

Modelling presentation

This document describes a study that aims to monitor biology students' progression in mathematical competencies through engaging modelling tasks. The study will introduce biologically-themed modelling sessions in a freshman mathematics course. It will assess students' competencies before and after using a three-dimensional framework, and analyze any progression over the sessions. The document outlines the research questions, strategies, design, tasks and data collection methods. It also describes frameworks for understanding competence and a coding system to identify competencies demonstrated in students' work. The goal is to determine if modelling can help students develop mathematical competencies.

teaching algebra revised

This document discusses principles of teaching algebra. It describes a 3-part structure of algebra involving representing elements algebraically, transforming symbolic expressions, and interpreting new forms. Perspectives on algebra's usefulness in fields like science are provided. Principles for school mathematics emphasize patterns, quantitative relationships, and analyzing change. Models for teaching algebra include demonstrating worked examples, conceptual attainment, inductive thinking, advance organizers, and inquiry training. Each model involves multiple phases like confronting problems, gathering data, formulating explanations, and analyzing thinking processes.

The logic of informal proofs

The document discusses the logic of informal proofs in mathematics. It makes 5 key claims:
1) Understanding informal proofs is important because most mathematical proofs are informal.
2) Informal proofs rely on both logical form and content.
3) Properly understanding informal proofs requires seeing logic as the study of inferential actions, where content plays a role.
4) This conception accommodates proofs involving actions on objects other than propositions.
5) It explains why mathematics relies on external representations, since representations can be manipulated.
The document argues this view connects logical questions about rigor to the cultural study of mathematical practices.

Applying Learning Principles based on Cognitive Science to Improve Training ...

The document discusses applying cognitive science principles to improve training performance. It defines learning science and its relationship to cognitive science. Six cognitive strategies are described to enhance training: spaced practice, interleaving, retrieval practice, elaboration, dual coding, and concrete examples. The document recommends incorporating these strategies into learning design through effective organization, coherence, stories, and multiple examples. It also suggests offering learning environments that promote cognitive disequilibrium and flexibility to enhance performance.

Mathematical skills

Mathematical skills

MATH_INVESTIGATION_CG.pdf

MATH_INVESTIGATION_CG.pdf

Solving Exponential Equations: Learning from the Students We Teach

Solving Exponential Equations: Learning from the Students We Teach

Mathematical

Mathematical

CTET / TET Mathematics Preparation :Important key words

CTET / TET Mathematics Preparation :Important key words

10.1007%2 f978 3-319-62597-3-73

10.1007%2 f978 3-319-62597-3-73

Constructivist Approach Vs Expository Teaching: Exponential Functions

Constructivist Approach Vs Expository Teaching: Exponential Functions

Instrumentation 1

Instrumentation 1

inclusive science.pptx

inclusive science.pptx

Rickard, anthony teaching prospective teachers about mathematical reasoning n...

Rickard, anthony teaching prospective teachers about mathematical reasoning n...

Philip Siaw Kissi

Philip Siaw Kissi

Assessing Multiplicative Thinking Using Rich Tasks

Assessing Multiplicative Thinking Using Rich Tasks

The process of thinking by prospective teachers of mathematics in making argu...

The process of thinking by prospective teachers of mathematics in making argu...

curriculum theory.pdf

curriculum theory.pdf

Curriculum theory

Curriculum theory

Authentic Tasks And Mathematical Problem Solving

Authentic Tasks And Mathematical Problem Solving

Modelling presentation

Modelling presentation

teaching algebra revised

teaching algebra revised

The logic of informal proofs

The logic of informal proofs

Applying Learning Principles based on Cognitive Science to Improve Training ...

Applying Learning Principles based on Cognitive Science to Improve Training ...

MATHEMACAL INVESTIGATION IN GRADE 5.pptx

This document discusses fractions and their properties. It defines a fraction as a numerical value that represents part of a whole, evaluated by dividing the whole into parts. It notes that fractions with the same denominator are similar fractions, while those with different denominators are dissimilar fractions. It provides instructions for adding similar fractions by adding the numerators and writing the sum over the denominator, and for adding dissimilar fractions by renaming them to have a common denominator before adding the numerators and writing the sum over the denominator.

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The document discusses the 5Rs of waste management: reduce, reuse, recycle, repair, and recover. It defines each of the 5Rs. Reduce means lessening unnecessary use of materials. Reuse means using items again, either by yourself or others. Recycle means processing waste materials to make new products. Repair means fixing broken items to reuse them. Recover means extracting energy or materials from waste that can no longer be used. The 5Rs approach promotes a clean environment by transforming waste into useful materials through these methods.

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- 1. THE RELEVANCE OF MATHEMATICAL INVESTIGATION DURING PANDEMIC RHODALYN F. LATINA Teacher III, Aliwekwek ES
- 2. MATHEMATICAL INVESTIGATION -is typically defined as an investigation that involves a collection of mathematical and problem solving based issues.
- 4. MATHEMATICAL INVESTIGATION Investigate polygons with area 5x^2 units on an x by x unit grid.
- 5. MATHEMATICAL INVESTIGATION What shapes and how many are there if I only consider polygons made up of squares?
- 6. Gives the students the opportunity to make important mathematical explorations or discoveries that they will remember much longer than if they had been simply told what to do by the teacher. MATHEMATICAL INVESTIGATION
- 7. It encourages students to use higher order thinking skills, which are far more important than the concept involved. MATHEMATICAL INVESTIGATION
- 8. A complete mathematical investigation requires at least three steps: (1) finding a pattern or other conjecture, (2) seeking the logical interconnections that constitute proof, and (3) organizing the results in a way that can be presented coherently. MATHEMATICAL INVESTIGATION
- 9. WHY ARE MATHEMATICAL INVESTIGATIONS IMPORTANT? Research studies show that when students discover mathematical ideas and invent mathematical procedures, they have a stronger conceptual understanding of connections between mathematical ideas. MARK GREGORY V. BATO, Division Seminar-Workshop on Mathematical Investigation August 11-13, 2021
- 10. WHY ARE MATHEMATICAL INVESTIGATIONS IMPORTANT? Mathematical Investigations improve the mathematical learning of the students and develop their mathematical power.
- 11. WHAT IS THE RELEVANCE OF MATHEMATICAL INVESTIGATION DURING PANDEMIC?
- 13. REFERENCES • Mocles, A. (2012). Mathematical Investigation and Mathematical Modelling. https://www.scribd.com/doc/78285752/Mathematical-Investigation-and-Mathematical- Modeling • Quinnell, L. (2010). Why are mathematical investigations important?. Australian Mathematics Teacher, The, 66(3), 35-40. • Ramon, M. (2010). Stages of Math Investigation. https://www.scribd.com/doc/31102633/Stages-of-Math-Investigation