Day 1 Plenary Lecture on a selection of learning theories that underpin Singapore Math. The focus is on Bruner's theories with mentions of Dienes and Skemp.
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.
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.
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.
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.
This document provides an introduction to the Singapore Math approach. It discusses Jerome Bruner's model of concrete, pictorial, and abstract representations in learning. It presents examples of how Singapore textbooks and lessons move from hands-on activities to visual representations to symbolic expressions. The document shares photos of students in Singapore and Indonesia using concrete materials to understand mathematical concepts like volume. It provides word problems and worked examples demonstrating the concrete-pictorial-abstract approach.
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.
This document contains information from a presentation on Singapore Math given by Dr. Yeap Ban Har. It includes 6 lessons on various math topics taught using the Singapore Math approach such as multiplication, problem solving, bar modeling, and area of polygons. It emphasizes concepts like visualization, problem solving, conceptual understanding, and differentiated instruction. Contact and biography information is provided for Dr. Yeap Ban Har.
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.
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.
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.
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.
This document provides an introduction to the Singapore Math approach. It discusses Jerome Bruner's model of concrete, pictorial, and abstract representations in learning. It presents examples of how Singapore textbooks and lessons move from hands-on activities to visual representations to symbolic expressions. The document shares photos of students in Singapore and Indonesia using concrete materials to understand mathematical concepts like volume. It provides word problems and worked examples demonstrating the concrete-pictorial-abstract approach.
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.
This document contains information from a presentation on Singapore Math given by Dr. Yeap Ban Har. It includes 6 lessons on various math topics taught using the Singapore Math approach such as multiplication, problem solving, bar modeling, and area of polygons. It emphasizes concepts like visualization, problem solving, conceptual understanding, and differentiated instruction. Contact and biography information is provided for Dr. Yeap Ban Har.
Balancing Higher-order Thinking and Basic Skills - Video StudyJimmy Keng
This 3-sentence summary provides the high-level information from the document:
The document discusses a closing session from Day 2 of a conference that focused on balancing higher-order thinking with basic skills in mathematics lessons. Videos were shown from Singapore classrooms demonstrating lessons that emphasized problem-solving, conceptual understanding, and breaking down multi-digit division problems. The document notes observations made about the Singapore lessons and questions posed about how often students learn tricks and strategies in math.
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.
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.
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.
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.
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.
This document provides an overview of a seminar for parents on what children learn in mathematics. It begins with background on Singapore's economic growth and education system. Graphs show Singapore and other Asian countries scoring highly on international math tests. The introduction of the Singapore math textbooks in 1982 and a problem-solving curriculum in 1992 are noted as factors in its success. Data shows Singapore students outperforming peers on PISA exams. The seminar highlights how Singapore Math focuses on using visuals and concrete experiences to teach concepts. It provides examples from schools in different countries of how they use Singapore Math approaches to teach fractions, word problems, and other topics.
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.
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.
This document provides information about a course on pre-numeracy skills taught by Dr. Yeap Ban Har from Marshall Cavendish Institute. It includes his contact information, as well as slides and resources available on his blog and Facebook page. The document discusses different types of numbers, counting, features of the Singapore Math approach, and number bonds, with a focus on introducing foundational numerical concepts to young children before they learn addition.
The document announces a new syllabus for a mathematics professional development workshop in Jakarta on October 6th, 2012. The workshop will be led by Dr. Yeap Ban Har and will cover fundamentals of Singapore math, difficulties with word problems, and strategies for teaching word problems. It will also include a forum for discussing mathematics teaching.
The document discusses the Model Method, an instructional approach for upper primary students. It provides examples of word problems modeled with bars or arrays to represent the relationships and operations in the problems. The examples demonstrate modeling problems for up to 8 days to help average students, and using algebra to model problems for 3-4 days for advanced students. It also discusses using differentiated instructional strategies and modeling techniques for struggling learners.
The document provides information about an algebra workshop presented by Dr. Yeap Ban Har from Marshall Cavendish Institute in Singapore. It lists his contact information and links to resources on the Marshall Cavendish website and blog. It also contains sample slides about algebraic thinking and modeling using bar models and word problems. The slides demonstrate strategies for visualizing problems, developing number sense, and differentiating instruction for struggling, average, and advanced learners.
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.
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.
EdCrisch Kindergarten Mathematics ECM101Jimmy Keng
This course focuses on making early childhood mathematics lessons interesting and easy to learn. It teaches the importance of visualization, generalization, number sense, and soft skills like communication and metacognition. Students will learn strategies and theories to help young children recognize rectangles, count to 5, and understand different types of numbers. The course is taught by Dr. Yeap Ban Har from Marshall Cavendish Institute and focuses on what and how to approach numeracy programs in early childhood education.
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 document discusses teaching mathematics through problem solving using the Singapore method. It emphasizes using concrete, pictorial, and abstract representations to help students develop conceptual understanding and problem solving skills. Sample math problems and teaching strategies are presented to illustrate dividing shapes into equal parts, fractions, ratios, and comparing methods for solving problems. The key focus is on developing thinking and problem solving abilities.
The document discusses teaching fundamental fraction concepts using a problem solving approach, where students solve word problems to learn concepts like halves, quarters, and equivalency rather than through direct instruction. It provides examples of problems where students determine which of two students is correct about fractional amounts, explore equivalent fractions, and work with mixed numbers involving fractional parts of multiple whole cakes.
Balancing Higher-order Thinking and Basic Skills - Video StudyJimmy Keng
This 3-sentence summary provides the high-level information from the document:
The document discusses a closing session from Day 2 of a conference that focused on balancing higher-order thinking with basic skills in mathematics lessons. Videos were shown from Singapore classrooms demonstrating lessons that emphasized problem-solving, conceptual understanding, and breaking down multi-digit division problems. The document notes observations made about the Singapore lessons and questions posed about how often students learn tricks and strategies in math.
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.
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.
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.
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.
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.
This document provides an overview of a seminar for parents on what children learn in mathematics. It begins with background on Singapore's economic growth and education system. Graphs show Singapore and other Asian countries scoring highly on international math tests. The introduction of the Singapore math textbooks in 1982 and a problem-solving curriculum in 1992 are noted as factors in its success. Data shows Singapore students outperforming peers on PISA exams. The seminar highlights how Singapore Math focuses on using visuals and concrete experiences to teach concepts. It provides examples from schools in different countries of how they use Singapore Math approaches to teach fractions, word problems, and other topics.
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.
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.
This document provides information about a course on pre-numeracy skills taught by Dr. Yeap Ban Har from Marshall Cavendish Institute. It includes his contact information, as well as slides and resources available on his blog and Facebook page. The document discusses different types of numbers, counting, features of the Singapore Math approach, and number bonds, with a focus on introducing foundational numerical concepts to young children before they learn addition.
The document announces a new syllabus for a mathematics professional development workshop in Jakarta on October 6th, 2012. The workshop will be led by Dr. Yeap Ban Har and will cover fundamentals of Singapore math, difficulties with word problems, and strategies for teaching word problems. It will also include a forum for discussing mathematics teaching.
The document discusses the Model Method, an instructional approach for upper primary students. It provides examples of word problems modeled with bars or arrays to represent the relationships and operations in the problems. The examples demonstrate modeling problems for up to 8 days to help average students, and using algebra to model problems for 3-4 days for advanced students. It also discusses using differentiated instructional strategies and modeling techniques for struggling learners.
The document provides information about an algebra workshop presented by Dr. Yeap Ban Har from Marshall Cavendish Institute in Singapore. It lists his contact information and links to resources on the Marshall Cavendish website and blog. It also contains sample slides about algebraic thinking and modeling using bar models and word problems. The slides demonstrate strategies for visualizing problems, developing number sense, and differentiating instruction for struggling, average, and advanced learners.
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.
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.
EdCrisch Kindergarten Mathematics ECM101Jimmy Keng
This course focuses on making early childhood mathematics lessons interesting and easy to learn. It teaches the importance of visualization, generalization, number sense, and soft skills like communication and metacognition. Students will learn strategies and theories to help young children recognize rectangles, count to 5, and understand different types of numbers. The course is taught by Dr. Yeap Ban Har from Marshall Cavendish Institute and focuses on what and how to approach numeracy programs in early childhood education.
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 document discusses teaching mathematics through problem solving using the Singapore method. It emphasizes using concrete, pictorial, and abstract representations to help students develop conceptual understanding and problem solving skills. Sample math problems and teaching strategies are presented to illustrate dividing shapes into equal parts, fractions, ratios, and comparing methods for solving problems. The key focus is on developing thinking and problem solving abilities.
The document discusses teaching fundamental fraction concepts using a problem solving approach, where students solve word problems to learn concepts like halves, quarters, and equivalency rather than through direct instruction. It provides examples of problems where students determine which of two students is correct about fractional amounts, explore equivalent fractions, and work with mixed numbers involving fractional parts of multiple whole cakes.
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.
W8 Whole Number Division and MultiplicationJimmy Keng
This is classroom session taught by Yeap Ban Har on Day 1 of WSU Singapore Math Summer Institute. More than 70 participants took part in this institute - the second one in this university.
This document discusses strategies for teaching advanced mathematics learners. It mentions using the concrete-pictorial-abstract approach to represent mathematical concepts at different levels. Advanced learners are challenged through problem-solving, problem-posing, guided practice, and journaling activities. Differentiation strategies get advanced learners to practice and learn new skills, deepen their thinking, generalize concepts, and evaluate multiple solutions. Open lessons and journaling provide opportunities for differentiation.
This document discusses using visual representations to teach fractions, including concrete objects like fraction discs and pictorial models. It recommends first building conceptual understanding before teaching procedural skills like computation. Key concepts covered include part-whole relationships, mixed numbers and improper fractions, multiplication and division of fractions using concrete examples, and word problems.
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 session focuses on studying students' responses. We did the responses of Grade 5 students in using bar models. There are materials for further study involving Grade 3 students doing Singapore Math outside Singapore.
The document discusses bar models, a method for representing word problems pictorially using bars or diagrams. It was developed in the 1980s to help students in primary school who struggle with word problems. Bar models use pictures to represent quantities and relationships, making problems more visual and intuitive. They are particularly effective for younger students. The document outlines different types of bar models, including part-whole, comparison, and change models. It provides guidelines for constructing bar models and examples of using models to solve a variety of word problems.
NSMI Core Elective on Challenging ProblemsJimmy Keng
This document contains sample math word problems from Singapore schools as well as slides related to teaching bar modeling techniques. It discusses key focuses of Singapore mathematics including problem solving, conceptual understanding, and learning standards. Several examples are provided to illustrate bar modeling approaches to solving word problems involving variables, ratios, time, percentages and more.
This document discusses number bonds and strategies for addition and subtraction using number bonds. Number bonds show the different combinations of numbers that make up a given number. They help build foundations for efficiently learning addition and subtraction. The document outlines activities and strategies like near-10, doubles, and near-100 that use number bonds to develop number sense and mental math skills before learning formal algorithms.
Singapore Math Institute First AnnouncementJimmy Keng
This institute will be held in Singapore in November 2012. Ministry of Education (Singapore) teachers will register through their schools. International participants, please contact geraldynsng@sg.marshallcavendish.com for registration details.
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.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
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
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.