The MasterClass on Fundamentals of Singapore Mathematics Curriculum was attended by about 70 educators. It was held at Stadskasteel Oudaen in beautiful Utrecht.
First New Teachers' Conference, Manila, 10 September 2011Jimmy Keng
ย
This document contains summaries from presentations given at various schools around the world on teaching mathematics. It discusses lessons from Chile, Japan, and the Philippines on public lessons, as well as a LEAP program in Manila. Participants at Keys Grade School in Manila provided methods for finding the difference between two numbers. At De Tweemaster in the Netherlands, participants demonstrated methods for finding the area of polygons by counting dots. The document outlines three main points about teaching mathematics through visualization, generalization, and communication. It provides further examples and solutions for percentage and angle problems.
This document provides an overview of the bar model method for teaching mathematics. It discusses using bar models to develop visualization, number sense, and problem-solving abilities. It provides examples of using part-whole and comparison bar models to represent word problems involving fractions, percentages, multi-step word problems, algebra, and real-world scenarios. It also discusses how bar models can be used to differentiate instruction for different levels of learners.
This document summarizes a presentation on Singapore Math. It discusses how Singapore Math focuses on thinking, visualization using bar models, patterns and generalization, problem solving, and applying knowledge through problem solving. It provides examples of how concepts like fractions division and place value are taught using hands-on approaches like paper folding rather than solely drill-and-practice.
This is a one-day course on Essentials of Singapore Maths which is equivalent to MAP101 Fundamentals of Singapore Mathematics. About 60 participants attended this session.
This document summarizes the key points from a 3-day professional development session on teaching Singapore Math for upper grades. On day 3, sessions included a video study on a problem-solving approach using addition, problem solving and drill practice techniques, and using bar modeling to represent quantities. The document also provides examples of homework solutions and further examples of how the Singapore Math approach emphasizes teaching multiplication in a spiral curriculum across grades 1 through 4.
The document discusses key aspects of teaching fractions according to the Singapore Math approach, including a problem-solving approach and CPA (Concrete-Pictorial-Abstract) approach. It covers topics like equal parts, equivalent fractions, fraction operations, and includes examples of tasks and methods. The goal is to meet the needs of all learners using this approach.
LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011Jimmy Keng
ย
This plenary lecture on elementary school mathematics was given at the conference which marks the end of the three-year Leaders and Educators in Asia Programme.
First New Teachers' Conference, Manila, 10 September 2011Jimmy Keng
ย
This document contains summaries from presentations given at various schools around the world on teaching mathematics. It discusses lessons from Chile, Japan, and the Philippines on public lessons, as well as a LEAP program in Manila. Participants at Keys Grade School in Manila provided methods for finding the difference between two numbers. At De Tweemaster in the Netherlands, participants demonstrated methods for finding the area of polygons by counting dots. The document outlines three main points about teaching mathematics through visualization, generalization, and communication. It provides further examples and solutions for percentage and angle problems.
This document provides an overview of the bar model method for teaching mathematics. It discusses using bar models to develop visualization, number sense, and problem-solving abilities. It provides examples of using part-whole and comparison bar models to represent word problems involving fractions, percentages, multi-step word problems, algebra, and real-world scenarios. It also discusses how bar models can be used to differentiate instruction for different levels of learners.
This document summarizes a presentation on Singapore Math. It discusses how Singapore Math focuses on thinking, visualization using bar models, patterns and generalization, problem solving, and applying knowledge through problem solving. It provides examples of how concepts like fractions division and place value are taught using hands-on approaches like paper folding rather than solely drill-and-practice.
This is a one-day course on Essentials of Singapore Maths which is equivalent to MAP101 Fundamentals of Singapore Mathematics. About 60 participants attended this session.
This document summarizes the key points from a 3-day professional development session on teaching Singapore Math for upper grades. On day 3, sessions included a video study on a problem-solving approach using addition, problem solving and drill practice techniques, and using bar modeling to represent quantities. The document also provides examples of homework solutions and further examples of how the Singapore Math approach emphasizes teaching multiplication in a spiral curriculum across grades 1 through 4.
The document discusses key aspects of teaching fractions according to the Singapore Math approach, including a problem-solving approach and CPA (Concrete-Pictorial-Abstract) approach. It covers topics like equal parts, equivalent fractions, fraction operations, and includes examples of tasks and methods. The goal is to meet the needs of all learners using this approach.
LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011Jimmy Keng
ย
This plenary lecture on elementary school mathematics was given at the conference which marks the end of the three-year Leaders and Educators in Asia Programme.
This document discusses how mathematics lessons in Singapore textbooks can be used to develop mathematical practices in students. It explains that lessons are designed to develop, consolidate, and apply concepts. The focus is on how the choice and unfolding of problems in lessons can facilitate developing practices like problem-solving. Examples of anchor tasks and key questions are provided, such as a task involving square tiles and questions about fractions of groups, to illustrate this approach.
The document discusses several mathematics word problems from Singaporean schools. It includes problems about sharing money equally, identifying patterns in number sequences, determining the minimum number of sweets one possesses, calculating wire length used based on different wire lengths, solving simple equations, and determining the sum of the first 100 positive integers. The problems cover a range of core mathematical concepts and skills practiced in problem-solving classrooms.
This document provides information about numeracy and the New Zealand Mathematics Curriculum. It discusses the components of the curriculum, including number and algebra, statistics, geometry, and measurement. It then describes the New Zealand Numeracy Framework and the key stages of numeracy development. These stages progress from emergent counting to advanced proportional reasoning. The document concludes by offering tips parents can use to help children build numeracy knowledge and strategies, such as counting objects, recognizing numbers, and ordering numbers.
Math on the Move:Combining Like Terms and Distributive Propertycwallace1214
ย
Students complete 5 math problems placed around the classroom independently and then check their work against answer keys in a central location. The practice problems include solving for the variable x in equations such as 15x + 12 = 25x - 8. A teacher thanks various teachers who created math products to help students succeed on standardized tests, noting this product should only be used in one classroom.
Pearl City Hawaii Lower Grades 12 AugustJimmy Keng
ย
This is the second and final day of the professional development for teachers in K-2. This event held in Pearl City Hawaii was made possible by Kamehameha Schools, Nanakuli Elementary School and State of Hawaii Department of Education.
Thi is Day 1 of a three-day professional development for teachers in Hawaii. Today, we focus on the fundamenatals - thinking and learning theories basic to Singapore Math. There was also an Open Lesson with Grade 4 students.
This document outlines different mental math strategies and provides examples of how they can be used to solve word problems. It discusses counting on or back, rounding and adjusting, partitioning, re-ordering, inverse operations, and factors. It then describes how students in different year levels demonstrate these strategies. For example, year 2 students use counting on, year 3 uses re-ordering, and year 6 solves a word problem using a strategy and the RUCSAC procedure to show their work.
This document summarizes a parent information evening about numeracy and mathematics teaching at St Joseph's School. It discusses how mathematics is now taught using multiple strategies and developmental stages. Parents are encouraged to ask their children questions about how they solve problems and to discuss mathematics at home. A variety of games that can be played at home with dice, cards and dominoes are suggested to support children's numeracy learning.
This document summarizes the math curriculum at the school from years 0-8. It is divided into 4 levels that cover different stages of strategic thinking. Level 1 covers years 0-2 and focuses on counting skills. Level 2 covers years 3-4 and introduces addition, subtraction and place value concepts. Level 3 covers years 5-6 and involves more advanced additive and early multiplicative strategies. Level 4 covers years 7-8 and focuses on proportional reasoning with multi-digit numbers and decimals. The document also outlines basic fact stages and how math is taught with a focus on place value, real-world problems, and the use of technology.
These were the materials covered in last year's professional development. This year's session is a follow-up with revisiting of core ideas and extension of others.
This document summarizes Singapore's approach to mathematics education. It discusses how Singapore Math emphasizes conceptual understanding through concrete experiences and visual representations. It highlights Singapore's high performance on international assessments like TIMSS and PISA. It also outlines recent developments in Singapore's mathematics curriculum, pedagogy, textbooks, and use of technology and learning support strategies to help all students succeed.
This document provides an overview of a math lesson on multiplying and dividing by 9. The lesson includes fluency practice with dividing by 8 and decomposing multiples of 9. The concept development teaches patterns for multiplying by 9, such as the digit in the tens place being one less than the number of groups and the ones place being 10 minus the number of groups. Students apply these patterns to solve nines facts from 1 to 10. An application problem has students use nines facts to check their work. A problem set, debrief, exit ticket and homework assignment conclude the lesson.
The document outlines a schedule for four sessions occurring between 08:30-04:00 with a forum period from 03:30-04:00. It then discusses using a lesson on the Common Core to understand critical areas for Grade 1, including number bonds, comparison of numbers, and conservation of numbers. Various methods for developing visualization like the CPA approach, bar models, and teacher questioning are listed. The document goes on to discuss elements of effective math lessons including exploration, structure, journaling, reflection, and guided/independent practice using addition and subtraction strategies like counting all, making 10, subtracting from ten, and renaming before subtracting with examples provided.
The document discusses the theoretical underpinnings of the Singapore Math approach. It describes three key theories that influenced the development of Singapore Math:
1. Bruner's theory of the concrete-pictorial-abstract approach to help students develop a strong mathematical foundation.
2. Skemp's theory of conceptual understanding versus procedural understanding, with Singapore Math emphasizing the former.
3. Dienes' theory of variation in mathematics education through perceptual and mathematical variability in tasks.
The document provides examples of how these theories are applied in Singapore Math teaching materials, lessons, and instructional models.
Bendermeer Primary School Seminar for ParentsJimmy Keng
ย
This document provides an overview of a presentation on helping children with primary mathematics. It discusses how mathematics can develop intellectual competence and reflects on shifts in test questions to require more conceptual understanding and real-world problem solving over rote algorithms. Examples of math questions and lessons from various primary grades in Singapore, the US, UK, Netherlands and Japan are presented, covering topics like number sense, patterns, problem solving and visual models. Key competencies and strategies for problem solving are discussed.
National Singapore Math Summer Institute Denver 2011Jimmy Keng
ย
This document discusses lesson study, a form of professional development for teachers. It provides details about a lesson study program in Singapore, including an overview of the lesson study process. The key steps in lesson study are to identify a professional learning goal, plan a research lesson to address that goal, conduct the lesson with students, and have a post-lesson discussion where teachers analyze student understanding and refine the lesson. The document also gives examples of different schools in Singapore that have implemented lesson study and the professional learning goals they focused on.
This document provides an overview of a middle school mathematics institute that will take place on Saturday. It discusses the basic lesson format, which includes an anchor task, guided practice, and independent practice. It also references Bruner's idea of using concrete experiences and pictorial representations to help students understand abstract ideas. The document then provides several case studies as examples of lessons that could be used to develop, apply, and practice various mathematical concepts involving fractions, algebra, geometry, and more.
The document discusses using math journals in elementary school classrooms to teach mathematical concepts. It describes a framework for teaching mastery that involves anchor tasks, guided practice, and independent practice. Journaling is presented as one part of this process where students explore concepts, structure their understanding, and reflect on their learning. Examples are provided of kindergarteners recording number bonds in their journals to master basic counting and addition. The journal entries allow teachers to assess understanding and provide differentiated instruction.
This document discusses how mathematics lessons in Singapore textbooks can be used to develop mathematical practices in students. It explains that lessons are designed to develop, consolidate, and apply concepts. The focus is on how the choice and unfolding of problems in lessons can facilitate developing practices like problem-solving. Examples of anchor tasks and key questions are provided, such as a task involving square tiles and questions about fractions of groups, to illustrate this approach.
The document discusses several mathematics word problems from Singaporean schools. It includes problems about sharing money equally, identifying patterns in number sequences, determining the minimum number of sweets one possesses, calculating wire length used based on different wire lengths, solving simple equations, and determining the sum of the first 100 positive integers. The problems cover a range of core mathematical concepts and skills practiced in problem-solving classrooms.
This document provides information about numeracy and the New Zealand Mathematics Curriculum. It discusses the components of the curriculum, including number and algebra, statistics, geometry, and measurement. It then describes the New Zealand Numeracy Framework and the key stages of numeracy development. These stages progress from emergent counting to advanced proportional reasoning. The document concludes by offering tips parents can use to help children build numeracy knowledge and strategies, such as counting objects, recognizing numbers, and ordering numbers.
Math on the Move:Combining Like Terms and Distributive Propertycwallace1214
ย
Students complete 5 math problems placed around the classroom independently and then check their work against answer keys in a central location. The practice problems include solving for the variable x in equations such as 15x + 12 = 25x - 8. A teacher thanks various teachers who created math products to help students succeed on standardized tests, noting this product should only be used in one classroom.
Pearl City Hawaii Lower Grades 12 AugustJimmy Keng
ย
This is the second and final day of the professional development for teachers in K-2. This event held in Pearl City Hawaii was made possible by Kamehameha Schools, Nanakuli Elementary School and State of Hawaii Department of Education.
Thi is Day 1 of a three-day professional development for teachers in Hawaii. Today, we focus on the fundamenatals - thinking and learning theories basic to Singapore Math. There was also an Open Lesson with Grade 4 students.
This document outlines different mental math strategies and provides examples of how they can be used to solve word problems. It discusses counting on or back, rounding and adjusting, partitioning, re-ordering, inverse operations, and factors. It then describes how students in different year levels demonstrate these strategies. For example, year 2 students use counting on, year 3 uses re-ordering, and year 6 solves a word problem using a strategy and the RUCSAC procedure to show their work.
This document summarizes a parent information evening about numeracy and mathematics teaching at St Joseph's School. It discusses how mathematics is now taught using multiple strategies and developmental stages. Parents are encouraged to ask their children questions about how they solve problems and to discuss mathematics at home. A variety of games that can be played at home with dice, cards and dominoes are suggested to support children's numeracy learning.
This document summarizes the math curriculum at the school from years 0-8. It is divided into 4 levels that cover different stages of strategic thinking. Level 1 covers years 0-2 and focuses on counting skills. Level 2 covers years 3-4 and introduces addition, subtraction and place value concepts. Level 3 covers years 5-6 and involves more advanced additive and early multiplicative strategies. Level 4 covers years 7-8 and focuses on proportional reasoning with multi-digit numbers and decimals. The document also outlines basic fact stages and how math is taught with a focus on place value, real-world problems, and the use of technology.
These were the materials covered in last year's professional development. This year's session is a follow-up with revisiting of core ideas and extension of others.
This document summarizes Singapore's approach to mathematics education. It discusses how Singapore Math emphasizes conceptual understanding through concrete experiences and visual representations. It highlights Singapore's high performance on international assessments like TIMSS and PISA. It also outlines recent developments in Singapore's mathematics curriculum, pedagogy, textbooks, and use of technology and learning support strategies to help all students succeed.
This document provides an overview of a math lesson on multiplying and dividing by 9. The lesson includes fluency practice with dividing by 8 and decomposing multiples of 9. The concept development teaches patterns for multiplying by 9, such as the digit in the tens place being one less than the number of groups and the ones place being 10 minus the number of groups. Students apply these patterns to solve nines facts from 1 to 10. An application problem has students use nines facts to check their work. A problem set, debrief, exit ticket and homework assignment conclude the lesson.
The document outlines a schedule for four sessions occurring between 08:30-04:00 with a forum period from 03:30-04:00. It then discusses using a lesson on the Common Core to understand critical areas for Grade 1, including number bonds, comparison of numbers, and conservation of numbers. Various methods for developing visualization like the CPA approach, bar models, and teacher questioning are listed. The document goes on to discuss elements of effective math lessons including exploration, structure, journaling, reflection, and guided/independent practice using addition and subtraction strategies like counting all, making 10, subtracting from ten, and renaming before subtracting with examples provided.
The document discusses the theoretical underpinnings of the Singapore Math approach. It describes three key theories that influenced the development of Singapore Math:
1. Bruner's theory of the concrete-pictorial-abstract approach to help students develop a strong mathematical foundation.
2. Skemp's theory of conceptual understanding versus procedural understanding, with Singapore Math emphasizing the former.
3. Dienes' theory of variation in mathematics education through perceptual and mathematical variability in tasks.
The document provides examples of how these theories are applied in Singapore Math teaching materials, lessons, and instructional models.
Bendermeer Primary School Seminar for ParentsJimmy Keng
ย
This document provides an overview of a presentation on helping children with primary mathematics. It discusses how mathematics can develop intellectual competence and reflects on shifts in test questions to require more conceptual understanding and real-world problem solving over rote algorithms. Examples of math questions and lessons from various primary grades in Singapore, the US, UK, Netherlands and Japan are presented, covering topics like number sense, patterns, problem solving and visual models. Key competencies and strategies for problem solving are discussed.
National Singapore Math Summer Institute Denver 2011Jimmy Keng
ย
This document discusses lesson study, a form of professional development for teachers. It provides details about a lesson study program in Singapore, including an overview of the lesson study process. The key steps in lesson study are to identify a professional learning goal, plan a research lesson to address that goal, conduct the lesson with students, and have a post-lesson discussion where teachers analyze student understanding and refine the lesson. The document also gives examples of different schools in Singapore that have implemented lesson study and the professional learning goals they focused on.
This document provides an overview of a middle school mathematics institute that will take place on Saturday. It discusses the basic lesson format, which includes an anchor task, guided practice, and independent practice. It also references Bruner's idea of using concrete experiences and pictorial representations to help students understand abstract ideas. The document then provides several case studies as examples of lessons that could be used to develop, apply, and practice various mathematical concepts involving fractions, algebra, geometry, and more.
The document discusses using math journals in elementary school classrooms to teach mathematical concepts. It describes a framework for teaching mastery that involves anchor tasks, guided practice, and independent practice. Journaling is presented as one part of this process where students explore concepts, structure their understanding, and reflect on their learning. Examples are provided of kindergarteners recording number bonds in their journals to master basic counting and addition. The journal entries allow teachers to assess understanding and provide differentiated instruction.
This document discusses differentiating instruction to challenge advanced learners. It provides examples of ways to assess basic subtraction skills through runway indicators. For advanced learners, it suggests having them solve problems in alternative ways, write stories for equations, or write notes applying math concepts to enrich their learning beyond basic skills.
This document summarizes a seminar on the Singapore Math approach. It discusses key concepts like conceptual understanding, variation theory, concrete-pictorial-abstract instruction, and assessment results that show Singapore student performance. Example word problems are provided to illustrate how Singapore Math teaches for understanding over rote memorization.
This document provides an overview of Singapore Math pedagogy and instructional practices for grades K-5. It discusses the C-P-A approach of moving from concrete to pictorial to abstract representations. It also references research supporting perceptual variability, relational understanding, and the Singapore Math instructional framework of math tasks, content standards, and mathematical practices. The document outlines typical math blocks and homework minutes for different grades. It concludes with resources for further learning about Singapore Math.
Seminar at Harvard Graduate School of Education 15 April 2010Jimmy Keng
ย
The document discusses several theories that underpin the approach to mathematics education in Singapore. It discusses Bruner's theory of moving from concrete to pictorial to abstract representations. It also discusses Skemp's theory of relational versus instrumental understanding. Dienes' theory of variation to aid conceptual understanding is also summarized. Examples are provided of how these theories are implemented in Singapore math textbooks and lessons through concrete models, pictorial representations, and variations in problems.
This document discusses strategies for helping struggling learners with math. It recommends using a concrete-pictorial-abstract approach where students first engage with hands-on materials, then visual representations, and finally abstract symbols. This allows students to review fundamentals as new topics are introduced. It also stresses the importance of ensuring students can read, comprehend, select the right strategy, and make sense of word problems involving math concepts. Sample word problems and their step-by-step solutions are provided as examples. The document shares experiences from various schools in Singapore and London that have implemented these approaches successfully.
Singapore Math Administrators Symposium, Chicago Jimmy Keng
ย
This national edition of the symposium was held in Chicago. This was Dr Yeap Ban Har's day-long presentation. Dr Duriya Aziz, Andy Clark, Dr Richard Bisk and Dr Steve Leinwand were among the other presenters.
MCI Worchester State University Lecture 1 YeapJimmy Keng
ย
Plenary Lecture 1 on Fundamentals of Singapore Math. This MCI-WSU Singapore Math Institute is a collaboration between the US university and Marshall Cavendish Institute. 76 participants spent three days with three presenters learning about teaching of whole numbers and fractions.
The document summarizes key aspects of Singapore's mathematics curriculum that has achieved high student performance and positive attitudes towards mathematics. It focuses on developing mathematical problem solving and thinking skills. The curriculum emphasizes concrete, pictorial, and abstract representations of concepts. Assessment is aligned with the curriculum and emphasizes higher-order thinking. As a result, over 40% of Singapore students demonstrate advanced understanding of mathematics compared to an international average of 5%. Students also have relatively high attitudes towards mathematics compared to other high-performing countries.
Education Summit Utrecht, The NetherlandsJimmy Keng
ย
The document discusses the Singapore approach to education, which emphasizes problem-solving, higher-order thinking skills, and using a concrete-pictorial-abstract approach to teaching mathematics. It provides examples of how schools in other countries have implemented aspects of the Singapore method, such as using visualization and extended discussion to engage students. The approach has been shown to lead to high achievement on international tests.
This session focuses on the use of the bar model to solve a range of problems. The presenter modelled a range of teacher behaviour to help students acquire the competencies that they are supposed to by engaging in word problems. It was presented at the Indianapolis conference. We hope not too many people were not able to get a seat at the session. If you were not able to gain entry to the session, please accept our apologies.
The document discusses Singapore's approach to mathematics education, with a focus on promoting critical and creative thinking. It provides examples of Singapore math lessons, textbooks, and assessments. It also discusses key aspects of Singapore math like the Concrete-Pictorial-Abstract approach, the spiral curriculum, and emphasis on relational understanding. The presentation highlights the importance of teacher preparation, development, and leadership to successful implementation of Singapore math.
This is part of the professional development for the team that translate My Pals Are Here into Dutch and also people who are going to provide professionald evelopment for teachers using Singapore textbooks in the future.
Professional Development Session for Teachers in California by singaporemath....Jimmy Keng
ย
The document discusses the theoretical underpinnings of the Singapore Math approach. It describes three key theories that influenced the development of Singapore Math:
1. Bruner's theory of concrete-pictorial-abstract learning, which emphasizes using concrete objects before moving to pictorial then abstract representations.
2. Skemp's theory of instrumental versus relational understanding, which stresses the importance of conceptual understanding over rote learning.
3. Dienes' theory of variation, which promotes using varied examples and representations to enhance conceptual understanding.
The document explains how these theories influenced the instructional models, curriculum design, and assessment in Singapore Math to develop students' conceptual understanding and mathematical thinking.
The document announces an international education seminar on January 4th 2012 in Singapore to introduce the Singapore method for teaching mathematics. The seminar will be led by Dr. Yeap Ban Har and will include presentations and workshops on the basic theories and models used in the Singapore approach, such as the bar model for problem solving. A schedule and contact information is provided for those interested in learning more about the Singapore math teaching method.
2nd Singapore Math Institute Plenary 2 Day 1Jimmy Keng
ย
The document discusses preparing children for a future driven by globalization and technological advancement through developing a range of competencies in the three-part lesson format of whole-class problem solving, guided practice, and independent practice. It also provides examples of math word problems and their solutions.
Seminar at Colegio Inmaculada Conception, Universidad Andres Bello &San Beni...Jimmy Keng
ย
Pensar sin Limites Seminars
This seminar was held at various places including Colegio Inmaculada in Conception, Universidad Andres Bello in Santiago & San Benito School in Santiago. The seminar explains the pedagogy behind the Spanish edition of My Pals Are Here! Mathematics.
This document provides an overview of a Grade 5 mathematics institute that will take place on a Friday. It outlines the basic lesson format, which includes an anchor task, guided practice, and independent practice. It also references several learning theories that provide a framework for the lesson, such as Bruner's idea of concrete, iconic, and symbolic representations. The document includes several math word problems from past PSLE exams in Singapore to use for practice. It concludes with key learning theories covered and strategies for challenging advanced learners.
1) The document discusses standards and instructional focus areas for Grade 4 mathematics, including multi-digit multiplication and division, fractions, and geometric shapes.
2) It provides examples of case studies to solve, including arranging fractions in order and word problems involving fractions of amounts.
3) Theories of learning and representation discussed include Bruner's CPA approach and Skemp's classifications of understanding in mathematics.
This document provides information about a grade 3 mathematics institute to be held on Wednesday. It discusses key theories in mathematics learning from Piaget, Bruner, Dienes, Vygotsky, and Skemp. The document also provides several case studies with examples of lesson plans and problems that assess different mathematical concepts like operations, fractions, problem solving, and place value.
The document discusses a Grade 2 math institute that will focus on place value using concrete and pictorial representations. It provides several case studies on topics like subtraction across zeros, fractions, and problem solving. The lessons follow a basic format of an anchor task, guided practice, and independent practice. Key learning theories that will be drawn from include those from Piaget, Bruner, Dienes, Vygotsky, and Skemp. Bruner's CPA approach and Skemp's classifications of understanding will be particularly relevant for using different representations to build conceptual and relational understanding.
This document contains instructions for cutting out numbers and mathematical symbols from a page. It includes numbers from 0 to 9, basic mathematical operators like + and -, and instructions to cut out the listed items. The document is repetitive, listing the same numbers and symbols twice.
The document summarizes discussions from breakout sessions at the 4th Singapore Math Institute on teaching mathematics using Singapore's approach. It provides tasks and problems from Singapore classrooms related to practicing skills through problem-solving, using anchor tasks to structure lessons, and teaching geometry in grades 4-6. The goals are to emulate Singapore's emphasis on problem-solving and multi-step word problems to develop students' mathematical thinking.
The document discusses strategies for developing and improving mathematical practices, such as using anchor tasks, collaborative structures, questioning techniques, journals, textbooks for reflection, and focusing on visualization, generalization, and number sense. It also discusses moving from concrete to pictorial to abstract representations, and using anchor tasks and challenging word problems to teach Singapore math concepts.
This document discusses using a problem-solving approach to teach mathematics. It focuses on practicing problem-solving lessons and breaking students into groups to work on problems. The document provides resources for lesson plans and contact information for the speaker who advocates for integrating problem-solving into mathematics education.
Se01 abc's of singapore math through whole numbersJimmy Keng
ย
The document discusses the Singapore approach to teaching mathematics, which was developed to help Singaporean students perform better in math. It is based on Bruner's ideas of a spiral curriculum and using representations. The document provides 15 sample math tasks that demonstrate fundamentals of Singapore Math instruction, such as the Concrete-Pictorial-Abstract approach. It also includes quotes from Bruner about revisiting basic ideas repeatedly to help students master structured bodies of knowledge.
This document contains an agenda for a staff development conference on Singapore Math strategies with a focus on visualization. It includes 4 sample math tasks: 1) finding the area of a 4-sided polygon on a geoboard; 2) calculating leftover wire used to make a figure of 6 equilateral triangles; 3) dividing numbers by 3, 4, and 6; and 4) a word problem about Peter and Nancy exchanging coins to determine how many Peter originally had. The tasks are meant to illustrate ways to get students to visualize math concepts.
The document discusses strategies for differentiated instruction for advanced learners. It focuses on enrichment rather than acceleration. It provides 6 case studies as examples of anchor tasks that can challenge advanced learners in lessons, including problems about number sequences, geometry of rooms and chairs, properties of triangles, and finding sums of hexagon angles. The goal of the session is to explore general strategies for differentiating instruction to meet the needs of advanced students.
This document contains a summary of fraction problems that will be covered in the "Let's Solve Them & Enjoy It: Fraction Problems" course at the Singapore Math Strategies National Conference. It outlines 7 fraction problems involving concepts like halves, adding fractions, finding percentages of amounts, and word problems about groups of children leaving a hall. The problems cover a range of skills from representing halves to multi-step word problems involving fractions.
This document contains information from a presentation on developing number sense and problem-solving skills for grades K-2. It includes example math tasks and problems involving counting, addition, subtraction, and comparing quantities. Strategies are provided for using objects, pictures and diagrams to model word problems and develop conceptual understanding of part-whole and comparison situations. The document also lists questions to guide effective lesson planning and Polya's four-step model for mathematical problem-solving.
This document contains information about a mathematics course taught by Dr. Yeap Ban Har in Singapore, including:
- Contact information for Dr. Yeap Ban Har and background on his experience teaching mathematics.
- An introduction to the Singapore approach to teaching mathematics, which uses Bruner's constructivist theory of a spiral curriculum and representations.
- Examples of lesson plans and case studies for teaching various mathematics topics like fractions, ratios, proportions and algebra.
- Discussion of instructional models, differentiated instruction, and holistic assessment approaches in mathematics.
The document provides an overview of the Singapore mathematics teaching methods and includes examples of lessons and assessments that could be used when teaching a variety of math topics.
This document contains information about a mathematics course taught by Dr. Yeap Ban Har in Singapore, including:
- Contact information for Dr. Yeap Ban Har and background on his experience teaching mathematics.
- An introduction to the Singapore approach to teaching mathematics, which uses Bruner's constructivist theory of a spiral curriculum and the Concrete-Pictorial-Abstract approach.
- Details and case studies for several sessions on topics like early numeracy, addition/subtraction, multiplication/division, fractions, ratio, proportion, and algebra.
- Information on differentiated instruction, assessment, and the use of games, journaling and modeling in mathematics lessons.
The document outlines an upcoming 5-day mathematics institute in Singapore led by Dr. Yeap Ban Har, providing his background and experience in mathematics education. It introduces the foundational CPA and spiral approaches used in Singapore mathematics teaching. Various case studies and sessions are described that will use these approaches to teach fractions, operations, and problem solving to teachers.
This document contains notes from a mathematics institute in Singapore led by Dr. Yeap Ban Har. It includes information about Dr. Har, introductions to teaching ratio and proportion, the advanced bar model method, algebra, and holistic assessment. Sample mathematics problems and lessons are provided to illustrate various concepts. The document appears to be notes that were given to participants of the institute on teaching approaches and content in Singapore mathematics.
This document summarizes a mathematics institute course held in Singapore by Dr. Yeap Ban Har. It provides an introduction to Dr. Har and his background, as well as an overview of the sessions to be covered in the course, including the Singapore approach to teaching mathematics, whole number operations, factors and multiples, lesson planning, word problem modeling and assessment. Case studies are presented in each section to illustrate the concepts.
This document contains notes from a mathematics training course led by Dr. Yeap Ban Har in Singapore. It discusses the Singapore approach to teaching mathematics, which was developed to improve student performance. It emphasizes Bruner's constructivist theory of a spiral curriculum and using concrete, iconic, and symbolic representations. The document provides examples of differentiated instruction for various math lessons and discusses using games and journal writing to engage students in math learning.
This document contains notes from a mathematics institute course with Dr. Yeap Ban Har in Singapore. It provides biographical information about Dr. Har and his background in education. It then outlines the key concepts to be covered in the course, including the Singapore approach to mathematics education, early numeracy, addition and subtraction strategies, lesson planning, and holistic assessment for young learners. Examples and case studies are provided to illustrate the various mathematical concepts and techniques.
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the bodyโs response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
ย
(๐๐๐ ๐๐๐) (๐๐๐ฌ๐ฌ๐จ๐ง ๐)-๐๐ซ๐๐ฅ๐ข๐ฆ๐ฌ
๐๐ข๐ฌ๐๐ฎ๐ฌ๐ฌ ๐ญ๐ก๐ ๐๐๐ ๐๐ฎ๐ซ๐ซ๐ข๐๐ฎ๐ฅ๐ฎ๐ฆ ๐ข๐ง ๐ญ๐ก๐ ๐๐ก๐ข๐ฅ๐ข๐ฉ๐ฉ๐ข๐ง๐๐ฌ:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
๐๐ฑ๐ฉ๐ฅ๐๐ข๐ง ๐ญ๐ก๐ ๐๐๐ญ๐ฎ๐ซ๐ ๐๐ง๐ ๐๐๐จ๐ฉ๐ ๐จ๐ ๐๐ง ๐๐ง๐ญ๐ซ๐๐ฉ๐ซ๐๐ง๐๐ฎ๐ซ:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
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Ivรกn Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
How to Make a Field Mandatory in Odoo 17Celine George
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In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
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The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
1. Welkom Master Class Singapore Math Dr.Yeap Ban Har (Marshall Cavendish Institute) 2011alt/ HCO R
2. Masterclass Singapore Rekenen Rotterdam ๏ฝ Utrecht DrYeap Ban Har banhar@sg.marshallcavendish.com Marshall Cavendish Institute Singapore Presentation slides are available at www.banhar.blogspot.com
3. Course MAP 101 Fundamentals of Singapore Mathematics Curriculum
8. Singapore Mathematics: Focus on Thinking an excellent vehicle for the development & improvement of a personโs intellectual competencies Ministry of Education Singapore 2006