Experiencing Singapore Math is an one-day executive program to give participants an overview of Singapore Math. It is based on MAP101 Fundamentals of Singapore Math that teachers do as part of their professional development in teaching Singapore Math. More than fifty Missouri educators participated in this one-day institute.
The document discusses Singapore's education system and experiences with Singapore Math. It provides statistics on students, teachers, schools and academic performance in Singapore. It traces the history and development of Singapore Math textbooks from 1982 to present. It emphasizes the importance of conceptual understanding, number sense, visualization and higher-order thinking in Singapore Math. Examples from Primary Mathematics textbooks show how visuals are used to teach concepts like distributive property without formal terms.
This document provides an overview of Singapore's education system and experiences with Singapore Math. It discusses Singapore's small land area but high GDP per capita. It notes there are around 500,000 students, 30,000 teachers, and 173 primary and 155 secondary schools. It also discusses Singapore's high performance on international math tests and how Singapore Math was introduced and revised over time with an emphasis on conceptual understanding and problem solving.
This document provides an overview of a professional development workshop on the Singapore Math method. It discusses key aspects of Singapore Math including its emphasis on visualization, problem solving, and pattern recognition. Examples are provided from Singapore math textbooks to illustrate how concepts like addition, multiplication, and calculating area are taught with a focus on visual models and representations. The document also shares information on the history and revisions of the Singapore math curriculum and textbooks over time.
The Singapore education approach emphasizes high achievement through problem-solving lessons and the concrete-pictorial-abstract teaching method. It has led to top scores in international tests. The approach uses extended discussions, multiple representations of concepts, and a focus on higher-order thinking skills like visualization. It has been successfully implemented in schools globally.
Education Summit Utrecht, The NetherlandsJimmy Keng
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.
MAP101 Fundamentals of Singapore Mathematics Curriculum Jimmy Keng
This document provides an overview of Singapore's education system and the use of Singapore Math. It notes that Singapore has about 500,000 students, 30,000 teachers, and 173 primary schools. It highlights Singapore's high performance on international tests in literacy, science and math since the 1960s. The document discusses the introduction and evolution of Singapore Math textbooks from 1982 to the present. It emphasizes the focus of Singapore Math on relational understanding, conceptual development, number sense, and visualization skills. Examples from Singapore, US, UK, Chile and the Philippines illustrate how these concepts are taught.
New Jersey Singapore Math Administrators Symposium East BrunswickJimmy Keng
The document provides an overview of Singapore's education system and approach to teaching mathematics. It notes that Singapore has around 500,000 students, 30,000 teachers, and 173 primary and 155 secondary schools. It describes how Singapore places a strong emphasis on problem solving in mathematics and uses a spiral curriculum approach with concrete, visual, and conceptual experiences to build understanding. Textbooks introduce concepts through visual representations before using formal terms.
The document discusses Singapore's education system and experiences with Singapore Math. It provides statistics on students, teachers, schools and academic performance in Singapore. It traces the history and development of Singapore Math textbooks from 1982 to present. It emphasizes the importance of conceptual understanding, number sense, visualization and higher-order thinking in Singapore Math. Examples from Primary Mathematics textbooks show how visuals are used to teach concepts like distributive property without formal terms.
This document provides an overview of Singapore's education system and experiences with Singapore Math. It discusses Singapore's small land area but high GDP per capita. It notes there are around 500,000 students, 30,000 teachers, and 173 primary and 155 secondary schools. It also discusses Singapore's high performance on international math tests and how Singapore Math was introduced and revised over time with an emphasis on conceptual understanding and problem solving.
This document provides an overview of a professional development workshop on the Singapore Math method. It discusses key aspects of Singapore Math including its emphasis on visualization, problem solving, and pattern recognition. Examples are provided from Singapore math textbooks to illustrate how concepts like addition, multiplication, and calculating area are taught with a focus on visual models and representations. The document also shares information on the history and revisions of the Singapore math curriculum and textbooks over time.
The Singapore education approach emphasizes high achievement through problem-solving lessons and the concrete-pictorial-abstract teaching method. It has led to top scores in international tests. The approach uses extended discussions, multiple representations of concepts, and a focus on higher-order thinking skills like visualization. It has been successfully implemented in schools globally.
Education Summit Utrecht, The NetherlandsJimmy Keng
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.
MAP101 Fundamentals of Singapore Mathematics Curriculum Jimmy Keng
This document provides an overview of Singapore's education system and the use of Singapore Math. It notes that Singapore has about 500,000 students, 30,000 teachers, and 173 primary schools. It highlights Singapore's high performance on international tests in literacy, science and math since the 1960s. The document discusses the introduction and evolution of Singapore Math textbooks from 1982 to the present. It emphasizes the focus of Singapore Math on relational understanding, conceptual development, number sense, and visualization skills. Examples from Singapore, US, UK, Chile and the Philippines illustrate how these concepts are taught.
New Jersey Singapore Math Administrators Symposium East BrunswickJimmy Keng
The document provides an overview of Singapore's education system and approach to teaching mathematics. It notes that Singapore has around 500,000 students, 30,000 teachers, and 173 primary and 155 secondary schools. It describes how Singapore places a strong emphasis on problem solving in mathematics and uses a spiral curriculum approach with concrete, visual, and conceptual experiences to build understanding. Textbooks introduce concepts through visual representations before using formal terms.
Math in Focus: Singapore Math Community Institute (updated) Jimmy Keng
The document discusses Singapore's approach to mathematics education. It provides background on Singapore as a country and details on its education system, including student and teacher numbers and types of schools. It then discusses the historical development and implementation of Singapore Math, focusing on its emphasis on problem solving and visualization. Several examples of math problems from Singapore textbooks are presented.
Singapore Math Administrators Symposium ScottsdaleJimmy Keng
The document discusses Singapore Math and how its approach to teaching mathematics concepts concretely first before building conceptual understanding has led to high performance on international tests. It provides examples of Singapore Math textbooks and curricula being used in schools in Singapore as well as other countries. The document emphasizes teaching mathematics visually and using variation and spiral progression to reinforce concepts.
Singapore Math Seminar at Minneapolis MNJimmy Keng
This seminar for about 400 teachers was held at Elk River High School. It is based on MAP101 Fundamentals of Singapore Math. A similar session was held in Chicago the next day. This is part of the Experiencing Singapore Math Program designed for administrators and teachers who are new to Singapore Math.
The document discusses the principles of a strong mathematics programme, including ensuring the weakest, average, and advanced students are appropriately challenged. It advocates focusing on intellectual abilities like visualization and number sense, as well as 21st century skills. Specific techniques mentioned that help achieve this include using visuals, making meaning, and providing careful variation. High achievement in Singapore's math programme has increased over time.
The document is a presentation about Singapore Mathematics. It provides an overview of Singapore's education system and curriculum. It then discusses key aspects of Singapore Math, including its focus on thinking, visualization, problem solving, conceptual understanding, learning new concepts through problem solving, and drill-and-practice through problem solving. Several examples of Singapore Math problems and methods are also presented.
This document discusses Singapore Math and its effectiveness in developing students' thinking skills. Singapore Math focuses on problem-solving, conceptual understanding, pattern recognition, and metacognition. It is implemented in classrooms through anchor tasks, guided practice, assessment, differentiation, and independent practice. The curriculum emphasizes number sense, visualization, and managing information to build students' thinking abilities.
New Syllabus Mathematics 7th Edition LaunchJimmy Keng
This lecture was given at the launch of the new edition of the New Syllabus Mathematics series. The Secondary 1 books for Express and Nornal (Academic) as well as the Additional Mathematics books will be used from 2013.
This document summarizes the keynote presentation "Connecting Singapore Math to Common Core State Standards" by Yeap Ban Har. The presentation focused on the alignment between Singapore mathematics and the Common Core State Standards in terms of big ideas and basic philosophy, while noting some differences in details. It provided examples from Singapore primary schools that illustrated key Singapore math concepts like conceptual understanding, problem solving thinking, part-whole situations, change situations, and comparison situations. The examples demonstrated how Singapore lessons begin with concrete examples and move towards more abstract representations.
Highline Session 3 at Parkside ElementaryJimmy Keng
The document summarizes key aspects of the Singapore Math approach used in Singaporean schools. It discusses the Concrete-Pictorial-Abstract (CPA) approach, the spiral curriculum, and emphasis on developing relational understanding. It provides examples of how these concepts are implemented in Singapore Math lessons and notes Singapore's high performance on international math assessments.
Seminar for Parents of Kindergarten Children Jimmy Keng
The document advertises mathematics courses conducted by the Marshall Cavendish Institute in Singapore for parents and tutors. The courses are held over four Saturdays in July through October for three different age groups (P1/2, P3/4, P5/6). Each course has a maximum of 40 participants and is held at the Civil Service College in Buona Vista. Contact details are provided for registration.
The document summarizes lessons from a workshop on the Singapore Math approach held at St Edward's School in Florida. It provides an overview of the Singapore education system and curriculum. It then summarizes 5 lessons that were observed which demonstrate the Singapore Math approach of using visual models and thinking strategies to teach basic math concepts and solve word problems. The lessons focused on multiplication facts, bar modeling techniques, and differentiated instruction strategies to help struggling students.
Houston Beyond the Basics Advanced Institute Day 1Jimmy Keng
This document summarizes key points from a presentation on Singapore Math. It discusses 7 lessons that focus on conceptual understanding, problem solving, and visual representations. The lessons cover topics like multiplication facts, multi-digit multiplication, setting up bar models, and using diagrams to solve equations. Singapore Math emphasizes thinking, visualization, and anchoring lessons around extended problems.
This course is in two parts. Today we focus on pre-fraction ideas i.e. ideas learnt in the early grades which are important in the learning of fraction as well as basic concept of fractions. We will also examine fraction topics typically taught in lower primary levels i.e. grades one to three.
Helping Lower Primary Children in MathematicsJimmy Keng
This document presents examples of learning math in a fun and effective way. It includes 7 examples of math word problems and activities involving ratios, number comparisons, story problems, visualization, and tangrams. The goal is to emphasize learning math through patterns, generalization, and hands-on activities. Schools from several countries are mentioned as places where these engaging math teaching methods can be applied.
Singapore Math Strategies for U.S. SchoolsJimmy Keng
The document provides an overview of Singapore Math strategies that could be used in U.S. schools. It discusses the fundamentals of Singapore Math which include a focus on problem solving, thinking, managing information, visualization, generalization, and number sense. It also discusses how Singapore students have demonstrated high achievement in international math assessments like TIMSS. The pedagogical approach of Singapore Math focuses on understanding over procedural skills. Differentiated instruction and assessment are also emphasized.
Yeap Ban Har gave the Opening Keynote and the Closing Keynote on the first day. He also taught one Core Elective on using bar models to solve challenging problems.
The document discusses Singapore's approach to mathematics education, known as the CPA Approach. It is based on Bruner's theory of enactive, iconic, and symbolic representations. The CPA Approach focuses on visualization, number sense, generalization, and seeing patterns and connections. It has helped students in Singapore and several other countries perform well in mathematics according to international test results. The approach views mathematics as an excellent way to develop intellectual competence.
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.
Math in Focus: Singapore Math Community Institute (updated) Jimmy Keng
The document discusses Singapore's approach to mathematics education. It provides background on Singapore as a country and details on its education system, including student and teacher numbers and types of schools. It then discusses the historical development and implementation of Singapore Math, focusing on its emphasis on problem solving and visualization. Several examples of math problems from Singapore textbooks are presented.
Singapore Math Administrators Symposium ScottsdaleJimmy Keng
The document discusses Singapore Math and how its approach to teaching mathematics concepts concretely first before building conceptual understanding has led to high performance on international tests. It provides examples of Singapore Math textbooks and curricula being used in schools in Singapore as well as other countries. The document emphasizes teaching mathematics visually and using variation and spiral progression to reinforce concepts.
Singapore Math Seminar at Minneapolis MNJimmy Keng
This seminar for about 400 teachers was held at Elk River High School. It is based on MAP101 Fundamentals of Singapore Math. A similar session was held in Chicago the next day. This is part of the Experiencing Singapore Math Program designed for administrators and teachers who are new to Singapore Math.
The document discusses the principles of a strong mathematics programme, including ensuring the weakest, average, and advanced students are appropriately challenged. It advocates focusing on intellectual abilities like visualization and number sense, as well as 21st century skills. Specific techniques mentioned that help achieve this include using visuals, making meaning, and providing careful variation. High achievement in Singapore's math programme has increased over time.
The document is a presentation about Singapore Mathematics. It provides an overview of Singapore's education system and curriculum. It then discusses key aspects of Singapore Math, including its focus on thinking, visualization, problem solving, conceptual understanding, learning new concepts through problem solving, and drill-and-practice through problem solving. Several examples of Singapore Math problems and methods are also presented.
This document discusses Singapore Math and its effectiveness in developing students' thinking skills. Singapore Math focuses on problem-solving, conceptual understanding, pattern recognition, and metacognition. It is implemented in classrooms through anchor tasks, guided practice, assessment, differentiation, and independent practice. The curriculum emphasizes number sense, visualization, and managing information to build students' thinking abilities.
New Syllabus Mathematics 7th Edition LaunchJimmy Keng
This lecture was given at the launch of the new edition of the New Syllabus Mathematics series. The Secondary 1 books for Express and Nornal (Academic) as well as the Additional Mathematics books will be used from 2013.
This document summarizes the keynote presentation "Connecting Singapore Math to Common Core State Standards" by Yeap Ban Har. The presentation focused on the alignment between Singapore mathematics and the Common Core State Standards in terms of big ideas and basic philosophy, while noting some differences in details. It provided examples from Singapore primary schools that illustrated key Singapore math concepts like conceptual understanding, problem solving thinking, part-whole situations, change situations, and comparison situations. The examples demonstrated how Singapore lessons begin with concrete examples and move towards more abstract representations.
Highline Session 3 at Parkside ElementaryJimmy Keng
The document summarizes key aspects of the Singapore Math approach used in Singaporean schools. It discusses the Concrete-Pictorial-Abstract (CPA) approach, the spiral curriculum, and emphasis on developing relational understanding. It provides examples of how these concepts are implemented in Singapore Math lessons and notes Singapore's high performance on international math assessments.
Seminar for Parents of Kindergarten Children Jimmy Keng
The document advertises mathematics courses conducted by the Marshall Cavendish Institute in Singapore for parents and tutors. The courses are held over four Saturdays in July through October for three different age groups (P1/2, P3/4, P5/6). Each course has a maximum of 40 participants and is held at the Civil Service College in Buona Vista. Contact details are provided for registration.
The document summarizes lessons from a workshop on the Singapore Math approach held at St Edward's School in Florida. It provides an overview of the Singapore education system and curriculum. It then summarizes 5 lessons that were observed which demonstrate the Singapore Math approach of using visual models and thinking strategies to teach basic math concepts and solve word problems. The lessons focused on multiplication facts, bar modeling techniques, and differentiated instruction strategies to help struggling students.
Houston Beyond the Basics Advanced Institute Day 1Jimmy Keng
This document summarizes key points from a presentation on Singapore Math. It discusses 7 lessons that focus on conceptual understanding, problem solving, and visual representations. The lessons cover topics like multiplication facts, multi-digit multiplication, setting up bar models, and using diagrams to solve equations. Singapore Math emphasizes thinking, visualization, and anchoring lessons around extended problems.
This course is in two parts. Today we focus on pre-fraction ideas i.e. ideas learnt in the early grades which are important in the learning of fraction as well as basic concept of fractions. We will also examine fraction topics typically taught in lower primary levels i.e. grades one to three.
Helping Lower Primary Children in MathematicsJimmy Keng
This document presents examples of learning math in a fun and effective way. It includes 7 examples of math word problems and activities involving ratios, number comparisons, story problems, visualization, and tangrams. The goal is to emphasize learning math through patterns, generalization, and hands-on activities. Schools from several countries are mentioned as places where these engaging math teaching methods can be applied.
Singapore Math Strategies for U.S. SchoolsJimmy Keng
The document provides an overview of Singapore Math strategies that could be used in U.S. schools. It discusses the fundamentals of Singapore Math which include a focus on problem solving, thinking, managing information, visualization, generalization, and number sense. It also discusses how Singapore students have demonstrated high achievement in international math assessments like TIMSS. The pedagogical approach of Singapore Math focuses on understanding over procedural skills. Differentiated instruction and assessment are also emphasized.
Yeap Ban Har gave the Opening Keynote and the Closing Keynote on the first day. He also taught one Core Elective on using bar models to solve challenging problems.
The document discusses Singapore's approach to mathematics education, known as the CPA Approach. It is based on Bruner's theory of enactive, iconic, and symbolic representations. The CPA Approach focuses on visualization, number sense, generalization, and seeing patterns and connections. It has helped students in Singapore and several other countries perform well in mathematics according to international test results. The approach views mathematics as an excellent way to develop intellectual competence.
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.
The document outlines strategies for teaching mathematics successfully, including key competencies like generalization, visualization, and problem-solving. It presents sample word problems and asks teachers to consider strategies for developing skills in students, such as using bar models. The document provides worked examples of math problems and prompts reflection on teaching approaches.
The document announces a seminar for parents on coaching children in primary 1-2 mathematics, providing details on dates, location, and contact information. It also advertises Yeap Ban Har's course on primary mathematics at the Marshall Cavendish Institute and directs readers to his blog for slides. The seminar aims to provide parents with strategies for helping their children learn key mathematical concepts in the early primary grades.
King of Prussia 1 | Lecture on VisualizationJimmy Keng
Singapore developed its approach to math, known as Singapore math, in response to low student achievement and economic struggles in the 1960s. The approach focuses on visualization and uses a concrete-pictorial-abstract method. It was influenced by both economic needs for problem solving skills and considerations of how children learn best. Lessons involve both problem solving and building basic skills.
This document discusses Singapore Math and its origins in Singapore. It summarizes that Singapore developed Singapore Math in response to low student achievement and a poor economy in the 1960s. The key aspects of Singapore Math are its focus on fundamental math concepts and pattern observation. It is presented as a way to improve math education and outcomes.
The document discusses Singapore's history and development of its mathematics education system. Upon gaining independence in 1965, Singapore faced high unemployment, poverty, and illiteracy. In the 1970s, Singapore developed an approach based on Bruner's work and other learning theories to help students learn mathematics better, which became known as Singapore Math. The document also announces a summer institute on fundamentals of Singapore Math to be held in Philadelphia.
Weston 2013 Session 1 Fundamentals of Singapore Math Jimmy Keng
This document outlines an upcoming professional development workshop for Weston Public Schools teachers on the fundamentals of Singapore Math. The workshop will cover case studies and examples for teaching equivalent fractions to grade 3 students, integer multiplication to grade 7 students, finding the area of polygons in grade 4, the Pythagorean theorem in grade 8, and general modeling techniques. It will provide an overview of the Singapore Math approach including the concrete-pictorial-abstract methodology and an emphasis on problem solving.
Progressive Classroom Designs: Common Core State Standards Math - The Singapo...Jimmy Keng
This document discusses Singapore's approach to mathematics education. It begins with an introduction and data showing Singapore students outperforming peers internationally in mathematics. Singapore focused on conceptual understanding and developed its approach in response to low student achievement and economic challenges in the 1960s-1970s. Key aspects of the Singapore approach include visualizing concepts, flexibility with numbers, seeing patterns, and relational understanding. Subsequent slides cover topics like counting, basic operations, and the bar model method.
Here are some tips for improving problem solving skills in PSLE Mathematics:
- Take time to understand the question fully before attempting to solve it. Re-read if needed.
- Look for key information like numbers, operations, shapes etc and think about how they might be related.
- Draw diagrams or make lists when working with multiple steps, relationships or parts. This helps organize your thinking.
- Estimate answers before calculating to check if your working makes sense.
- Check your work - go back and ensure steps are correct and you have not made computational errors.
- Practice explaining your reasoning and showing your working, as this helps develop logical thinking skills.
- Review incorrect or challenging questions again later
This document outlines a professional development seminar on Singapore Math presented by Dr. Yeap Ban Har from the Marshall Cavendish Institute in Singapore. The seminar focuses on issues of pacing, differentiated instruction, assessment through problem solving. It is equivalent to a course on differentiated instruction and enrichment/remediation in primary mathematics. Slides and additional information are available online.
Hawaii Department of Education - Professional Development in Oahu Jimmy Keng
This document provides information about a course on helping students learn mathematics based on the Singapore Math approach. The course focuses on teaching basic skills and concepts for various grade levels, including addition, multiplication, division, and fractions. It will include one example of a practice lesson from a textbook. The document also provides contact information for the course instructor.
The document discusses the bar model method for teaching primary mathematics. It begins with an introduction to the presenter and includes links to additional resources. It then provides examples of using bar models to represent and solve word problems involving ratios, equations, and systems of equations. The examples are from primary classrooms in Singapore, New York, Chile, and Guatemala. The document demonstrates how bar models can help students learn abstract mathematical concepts through concrete, visual representations.
The document is a slide presentation on mathematics learning in Singapore given by Yeap Ban Har from the Marshall Cavendish Institute in Singapore. It discusses Singapore's history of improving mathematics education over time, from achieving low passing rates on early exams to consistently high performance on international tests. It also describes Singapore's focus on visual and concrete learning approaches, as well as the country's emphasis on developing intellectual competence through mathematics.
This document summarizes the Concrete-Pictorial-Abstract (CPA) approach to teaching primary mathematics. It discusses how the CPA approach is based on Bruner's work on using enactive, iconic, and symbolic representations. Examples are provided of how the CPA approach can be applied to teaching fractions, division, addition, area of a circle, and other math concepts from Primary 1 through 6. The approach aims to develop students' intellectual competence through mathematics according to Singapore's Ministry of Education.
This document provides information about Singapore Math, a mathematics program used in Singapore schools. It discusses the introduction and evolution of Singapore Math textbooks and curricula from 1982 to 1997. It also notes that Singapore places an emphasis on mathematics as a way to develop intellectual competence. The document outlines some key features of a Singapore Math lesson, including prolonged engagement with anchor tasks, using Bruner's spiral approach, working in groups based on Vygotsky's theories, and applying Polya's problem-solving methods. Charts show that Singapore students significantly outperform international averages on mathematics assessments. The summary concludes that Singapore Math focuses on visuals, concrete experiences, and understanding concepts rather than just procedures.
Singapore Math Administrators Symposium NewarkJimmy Keng
The document discusses Singapore's education system and approach to teaching mathematics, known as Singapore Math. It provides background on Singapore's population, economy, and education statistics. The key aspects of Singapore Math are its emphasis on conceptual understanding, concrete experiences, number sense, and visual representation to build proficiency in problem solving.
The document discusses Singapore's approach to improving math instruction and performance. It outlines Singapore's curriculum framework which is revised every six years and emphasizes mathematical modeling. It also discusses strategies used like aligning textbooks to the curriculum, providing leadership support, and utilizing research-backed pedagogies in professional development programs for teachers that focus on developing skills as a learner, observer, and reflective practitioner. International test results show Singapore and other Asian countries achieving top scores in mathematics over several decades.
The document summarizes key aspects of the Singapore Math approach used in Singapore and some schools in the United States. It discusses the Concrete-Pictorial-Abstract approach, the spiral curriculum, three-part lesson structure, emphasis on relational understanding, and data showing Singapore students outperforming peers internationally and enjoying math more.
This document discusses mathematics teacher preparation and professional development in Singapore. It outlines Singapore's approach which includes selecting top students to become teachers, emphasizing pedagogical and content knowledge in pre-service teacher education programs, and providing ongoing professional development for in-service teachers through professional learning communities and 100 hours of training per year. The goal is to develop teachers' capacity to continuously improve their practice and enhance student learning.
Singapore Math at Edgemont School District New YorkJimmy Keng
This document provides an overview of a professional development day for the Edgemont Union Free School District on the fundamentals of Singapore Math. The day included presentations and workshops on key aspects of the Singapore Math approach like the Concrete-Pictorial-Abstract method and its emphasis on problem solving, thinking, and visualization. Sessions also demonstrated how to incorporate differentiated instruction and anchor tasks, guided practice, and independent practice. The document shares international assessment data showing Singapore students performing highly in mathematics compared to other countries.
NCTM Differentiated Instruction Using Singapore Math Jimmy Keng
This document summarizes a workshop on differentiated instruction using Singapore Math. The workshop is presented by Dr. Yeap Ban Har and teaches how to differentiate math tasks to cater to mixed-ability classes. It explains how Singapore Math is designed to enable all learners to learn mathematics well through adequate scaffolding for struggling learners and extending tasks to engage advanced learners. The workshop also provides examples of differentiating word problems and using the Singapore Math approach of solving one math problem during a lesson.
The document is a seminar for parents about helping children learn mathematics. It discusses how Singapore math focuses on using visuals and concrete experiences to teach mathematical concepts and problem solving. It provides examples of how Singapore math techniques are being used in classrooms around the world.
The document discusses Singapore Math, which focuses on developing conceptual understanding using a concrete-pictorial-abstract approach. It emphasizes problem solving, the spiral curriculum where topics are revisited at increasing levels of difficulty, and three-part lesson structures involving exploration, concept introduction, and guided practice. International test data shows Singapore students performing highly in mathematics compared to other countries.
Singapore Math focuses on using visuals and concrete experiences to teach mathematics. It emphasizes understanding why procedures work, not just knowing how. The approach was introduced in Singapore in the 1980s and has since spread internationally. Research shows Singapore students performing at the top levels in international math assessments from the 1960s to present. They also report higher enjoyment and preference for mathematics compared to international averages.
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 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 an agenda and slides for a workshop on teaching fractions based on the Singapore mathematics approach. The workshop covers fundamental fraction concepts, operations like division and multiplication of fractions, and the bar model method. It discusses how the Singapore approach teaches for meaning and understanding through a concrete-pictorial-abstract sequence. The approach emphasizes developing thinking skills and 21st century competencies in students.
The plenary panel discussion includes discussants from Korea, Hong Kong, the Philippines and Singapore. It is moderated by Japan. In my segment, I spoke about what is considered to be excellent classroom practice in mathematics teaching by examining various policies related to mathematics education in the system.
PISA is an international assessment of the skills and knowledge of 15-year olds. It is a project of the Organisation for Economic Co-operation and Development (OECD) and takes place at three-year intervals.
This document discusses Singapore Math and teacher preparation. It focuses on the approach of Singapore Math, which emphasizes problem solving, conceptual understanding, and thinking. It outlines the framework for preparing teachers to teach mathematics in this way, which includes having teachers learn content conceptually and the corresponding pedagogical knowledge. Courses in Singapore help teachers develop as learners and observers by giving opportunities to study math lessons.
Spiral Approach For Mathematics Teaching Manila Jan2010Jimmy Keng
The document discusses Singapore's approach to teaching mathematics which focuses on developing students' conceptual understanding through problem solving. It uses a spiral curriculum where concepts are revisited at increasing levels of difficulty. This helps students extend their knowledge over time based on Piaget's theories of learning. The approach aims to develop students' mathematical thinking skills for the 21st century workplace. International test results show Singapore students outperforming their peers in other countries.
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.
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.
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.
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.
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
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.
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Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
South African Journal of Science: Writing with integrity workshop (2024)
Singapore Math at Saint Louis
1. St LouisMissouri
Experiencing Singapore Math
an institute for administrators
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
3. Experiencing
Singapore Math
Land
270 sq miles
700 sq km
introduction People
5.3 million
GDP per capita
1965 USD500
2011 USD50 000
Junyuan Secondary School, Singapore in current USD
5. General Overview of Singapore and its
Education System
Students
500 000
Teachers
30 000
Principals & Vice-Principals
900
Schools
173 Primary Schools (Primary 1 – 6)
155 Secondary Schools (Secondary 1 – 4)
13 Junior Colleges (JC 1 – 2) Canossa Convent Primary School, Singapore
15 Mixed-Level Schools
The data refers to 1-12 school system. Pre-school is not part of the formal education
system. The data excludes post-secondary education system which includes institutes
of technical education, polytechnics and universities.
6. High achievement was not a given. In 1960,
among 30 615 candidates who sat for the
first Primary School Leaving Examination,
45% of the candidates passed.
Today, about the
same proportion
achieve the
highest grade in
each of the four
subjects tested.
Keon Ming Public School, Singapore
7. Experiencing
Singapore Math
All major international tests (literacy, science and mathematics) between 1964
and 2003 were placed on a common scale. Selected countries shown in the table.
Score 1960-1970s 1980s 1990s 2000s
500 Japan Japan Japan Japan
Korea Korea Korea
Hong Kong Singapore Hong Kong
Hong Kong Singapore
400 Thailand Singapore Malaysia Malaysia
Thailand Thailand Thailand
The Philippines
300 Indonesia Indonesia
The Philippines The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
8.
9. Experiencing
Singapore Math
Mathematics is “an excellent
vehicle for the development and
improvement of a person’s
intellectual competence”.
1982 Ministry of Education Singapore 2006
Introduction of Singapore mathematics
textbooks as they are known today. 2001
Introduction of textbooks published by
1992 private publishers and approved by
Introduction of Problem- Ministry of Education.
Solving Curriculum 2007
New editions of textbooks are
1997 published with the introduction of the
Thinking Schools revised curriculum.
Learning Nation
2013
New editions of textbooks are
published with the revision of the
curriculum.
Page 1
11. Experiencing
Singapore Math
Achievement
Attitude
Singapore 71 41
Hong Kong 67 40
Taiwan 50 24
Grade 4
Japan 62 23
Kazakhstan 89 19
England 62 16
Russia 80 16
International 72 5
12. Experiencing
Singapore Math
Achievement
Attitude
Taiwan 37 45
S Korea 33 40
Singapore 60 40
Grade 8
Hong Kong 47 31
Japan 30 26
Hungary 30 10
England 40 8
International 54 2
13.
14. Experiencing
Singapore Math
Mean
Shanghai 600
Singapore 562
Hong Kong 555
15 year-olds
S Korea 546
Taiwan 543
Finland 541
Liechtenstein 536
International 496
26. 3
A number is of a second number.
Experiencing
Singapore Math
5
The sum of the two numbers is 120.
King Solomon Academy, London UK
27. Box B contains twice as many
books as Box A. Box C
contains 20 more books than
Box A. Together, the three
boxes contains 116 books.
Edgewood Elementary School, New York
Singapore Math
Experiencing
28. In the learning of basic concepts such as
those in fractions, the emphasis is on
visualization, generalization and number
sense. There is also an emphasis on 21st
Century Competencies such as creativity,
critical thinking, communication, metacognition
and so on.
29. Experiencing
Singapore Math
Relational
Understanding
R Skemp
what & how Concrete
Introduction
J Bruner
Junyuan Secondary School, Singapore
Page 08
Page 13
42. Long division and the learning of
multiplication facts emphasis that it is not
necessary to learn a procedural blindly and
it is not necessary to do rote memorization in
order to remember.
59. Experiencing
Singapore Math
Da Qiao Primary School, Singapore
60. Experiencing
Singapore Math
Primary Mathematics (Third Edition)
See Ho, S. Y. & Yeap, B. H. (2011). Development of Visualization Skills in Singapore Primary
School Mathematics Textbooks. Paper presented at PME-35 Angkara, Turkey.
See also Yeap, B. H. (2011). The Emphasis of Primary-Level Textbooks in Singapore on
Higher-Order Thinking Skills. Paper presented at International Conference on School
Mathematics Textbooks Shanghai, China.
61. Experiencing
Singapore Math
Visuals are used to teach
concepts – distributive
property of multiplication
– without using formal
terms.
Primary Mathematics (Third Edition)