This is a summary of the discussion on Day 1. This is the fifth class organized by MOE Singapore for local kindergarten teachers. MCI offers early childhood courses with emphasis on mathematics and science.
ECM101 Development of Early Childhood NumeracyJimmy Keng
This course is offered to pre-school teachers by Pre-School Unit, Ministry of Education Singapore. This is Day 1 of the 12-hour course. Forty participants enrolled for the class which is the 4th Cohort.
This short course is part of a module participants for Specialist Certificate in Mathematics Teaching (Primary) is offering. This module focuses on whole numbers and using everyday things to teach.
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 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 outlines an October 2012 mathematics professional development workshop led by Dr. Yeap Ban Har on effective assessment strategies, including discussing the concept of assessment, designing assessment tasks, and examples of formal paper-and-pencil assessment. The workshop also covered reviewing assessment tools like anchor tasks, student journals, and a six-item homework format.
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.
ECM101 Development of Early Childhood NumeracyJimmy Keng
This course is offered to pre-school teachers by Pre-School Unit, Ministry of Education Singapore. This is Day 1 of the 12-hour course. Forty participants enrolled for the class which is the 4th Cohort.
This short course is part of a module participants for Specialist Certificate in Mathematics Teaching (Primary) is offering. This module focuses on whole numbers and using everyday things to teach.
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 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 outlines an October 2012 mathematics professional development workshop led by Dr. Yeap Ban Har on effective assessment strategies, including discussing the concept of assessment, designing assessment tasks, and examples of formal paper-and-pencil assessment. The workshop also covered reviewing assessment tools like anchor tasks, student journals, and a six-item homework format.
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.
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.
This document provides examples of how to teach Singapore Math concepts using the textbook both as written and with modifications. It demonstrates lessons on shapes, fractions, word problems, and equations being taught through worked examples, guided practice, and differentiation for varying skill levels. Supplemental materials like bar modeling techniques are also presented as ways to explain mathematical concepts.
The document discusses Singapore Math and its emphasis on visualization and multi-step word problems involving fractions. It provides examples from primary level textbooks showing how visuals are used to teach concepts like the distributive property without using formal terms. The examples illustrate multi-step fraction word problems and how they are visually represented and solved step-by-step to find the total number of coins or durians originally involved.
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.
MCI Worchester State University Singapore Math InstituteJimmy Keng
Register at www.si.mcinstitute.com.sg
This exciting institute features a line-up of Singapore and US experts on Singapore Math, led by Dr. Yeap Ban Har and Dr. Richard Bisk.
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.
The document announces a Singapore Math Symposium exclusively for Missouri school administrators to take place on November 7, 2012 at the Chase Park Plaza Hotel in St. Louis. The event will explore how applying Singapore's research and curriculum approaches have led to strong math achievement results. It will focus on teaching fewer topics in greater depth and equipping students with visual-spatial problem solving skills. The keynote speaker is Dr. Yeap Ban Har, an expert in Singapore Math, who will present in the morning and after lunch.
NCTM Math Intervention in the Middle School Using Singapore MathJimmy Keng
The document summarizes a presentation about using Singapore Math to provide math intervention for middle school students struggling with mathematics. It discusses how Singapore schools differentiate instruction through both curriculum and teaching strategies to help build students' confidence in math. It also outlines typical intervention models and resources used in Singapore from grades 1-8.
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.
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.
This document summarizes the key points from a 3-day professional development session on teaching Singapore Math for upper grades. On day 3, sessions included a video study on a problem-solving approach using addition, problem solving and drill practice techniques, and using bar modeling to represent quantities. The document also provides examples of homework solutions and further examples of how the Singapore Math approach emphasizes teaching multiplication in a spiral curriculum across grades 1 through 4.
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.
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.
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.
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.
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 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.
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.
Here are the steps:
1. Think of two digits, e.g. 3 and 5
2. Make the largest number: 53
3. Make the smallest number: 35
4. Find the difference: 53 - 35 = 18
I notice that the difference is always 18 no matter what two digits are chosen. This is because when forming the largest and smallest numbers from two digits, the ones digit remains the same while the tens digit changes. So the difference is always 10 * (tens digit of largest number - tens digit of smallest number) = 10 * (1 - 0) = 18.
Development of Numeracy in Early Childhood EducationJimmy Keng
Here are the steps:
1. Think of two digits, e.g. 3 and 5
2. Make the largest number: 53
3. Make the smallest number: 35
4. Find the difference: 53 - 35 = 18
I notice that the difference is always 18 no matter what two digits are chosen. This is because when forming the largest and smallest numbers from two digits, the ones digit remains the same while the tens digit changes. So the difference is always 10 * (tens digit of largest number - tens digit of smallest number) = 10 * (1 - 0) = 18.
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.
This document provides examples of how to teach Singapore Math concepts using the textbook both as written and with modifications. It demonstrates lessons on shapes, fractions, word problems, and equations being taught through worked examples, guided practice, and differentiation for varying skill levels. Supplemental materials like bar modeling techniques are also presented as ways to explain mathematical concepts.
The document discusses Singapore Math and its emphasis on visualization and multi-step word problems involving fractions. It provides examples from primary level textbooks showing how visuals are used to teach concepts like the distributive property without using formal terms. The examples illustrate multi-step fraction word problems and how they are visually represented and solved step-by-step to find the total number of coins or durians originally involved.
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.
MCI Worchester State University Singapore Math InstituteJimmy Keng
Register at www.si.mcinstitute.com.sg
This exciting institute features a line-up of Singapore and US experts on Singapore Math, led by Dr. Yeap Ban Har and Dr. Richard Bisk.
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.
The document announces a Singapore Math Symposium exclusively for Missouri school administrators to take place on November 7, 2012 at the Chase Park Plaza Hotel in St. Louis. The event will explore how applying Singapore's research and curriculum approaches have led to strong math achievement results. It will focus on teaching fewer topics in greater depth and equipping students with visual-spatial problem solving skills. The keynote speaker is Dr. Yeap Ban Har, an expert in Singapore Math, who will present in the morning and after lunch.
NCTM Math Intervention in the Middle School Using Singapore MathJimmy Keng
The document summarizes a presentation about using Singapore Math to provide math intervention for middle school students struggling with mathematics. It discusses how Singapore schools differentiate instruction through both curriculum and teaching strategies to help build students' confidence in math. It also outlines typical intervention models and resources used in Singapore from grades 1-8.
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.
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.
This document summarizes the key points from a 3-day professional development session on teaching Singapore Math for upper grades. On day 3, sessions included a video study on a problem-solving approach using addition, problem solving and drill practice techniques, and using bar modeling to represent quantities. The document also provides examples of homework solutions and further examples of how the Singapore Math approach emphasizes teaching multiplication in a spiral curriculum across grades 1 through 4.
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.
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.
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.
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.
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 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.
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.
Here are the steps:
1. Think of two digits, e.g. 3 and 5
2. Make the largest number: 53
3. Make the smallest number: 35
4. Find the difference: 53 - 35 = 18
I notice that the difference is always 18 no matter what two digits are chosen. This is because when forming the largest and smallest numbers from two digits, the ones digit remains the same while the tens digit changes. So the difference is always 10 * (tens digit of largest number - tens digit of smallest number) = 10 * (1 - 0) = 18.
Development of Numeracy in Early Childhood EducationJimmy Keng
Here are the steps:
1. Think of two digits, e.g. 3 and 5
2. Make the largest number: 53
3. Make the smallest number: 35
4. Find the difference: 53 - 35 = 18
I notice that the difference is always 18 no matter what two digits are chosen. This is because when forming the largest and smallest numbers from two digits, the ones digit remains the same while the tens digit changes. So the difference is always 10 * (tens digit of largest number - tens digit of smallest number) = 10 * (1 - 0) = 18.
1. The document discusses curriculum documents and frameworks related to teaching counting concepts and addition/subtraction in early years education.
2. It provides examples of strategies, activities, and resources to help children develop understanding of counting, cardinality, addition, and subtraction.
3. The frameworks emphasize developing rich learning experiences using concrete experiences, language, visuals, and symbols to build number sense in young children.
This document provides an overview of the aims and framework of Singapore's mathematics education system. The key points are:
- The aims of Singapore math education are to develop skills in number, measurement, problem solving, logical reasoning, and positive attitudes towards math.
- The mathematical framework emphasizes mathematical problem solving and its five interrelated components: concepts, skills, processes, attitudes and metacognition.
- Singapore's approach emphasizes number bonds and word problems from an early age using concrete, pictorial, and abstract representations to build a strong conceptual foundation. Model drawing is a key problem solving strategy taught.
- Textbooks and instruction use varied tasks, a spiral approach, and focus on developing understanding rather than ro
This document provides a Stage 1 Understanding by Design template for a 2nd grade mathematics unit on multiplication titled "Marvelous Multiplication". The 3-week unit focuses on helping students understand multiplication as repeated addition and using arrays, skip counting, and multiplication tables to find products. The template identifies the relevant content standards and divides the unit into understandings, essential questions, and knowledge and skills that students will gain. It provides examples of each to guide instruction and assesses student learning.
The document outlines the learning outcomes, assessment strategies, instructional plan, and assessment of student learning for a math lesson on addition of whole numbers up to 1000. It describes representing addition strategies concretely, pictorially, and symbolically, as well as estimating sums. The plan involves using place value cards, ten frames, and a tens-ones mat to build numbers and add with regrouping. Student understanding will be assessed through observation, problem solving, and explaining strategies.
Your Math Students: Engaging and Understanding Every DayDreamBox Learning
The most important and challenging aspect of daily planning is to regularly—and yes, that means every day—create, adapt, locate, and consider mathematical tasks that are appropriate to the developmental learning needs of each student. A concern Francis (Skip) Fennell often shares with teachers is that many of us can find or create a lot of “fun” tasks that are, for the most part, worthless in regards to learning mathematics. Mathematical
tasks should provide a level of demand on the part of the student that ensures a focus on understanding and involves them in actually doing mathematics.
1. The document outlines various methods for engaging students in mathematics education, including hands-on activity-based learning, problem solving, modeling, experimentation and demonstration, self-learning, peer collaboration, and use of online resources.
2. Key aspects of the vision for school mathematics are for children to enjoy rather than fear math, learn important concepts beyond formulas, communicate about math, and see it as meaningful.
3. The teacher's role is to engage every student, help them develop a positive attitude, enjoy math over fearing it, and use more ICT tools for teaching.
The document discusses principles and methods for teaching mathematics. It covers:
1) The spiral progression approach which revisits math basics each grade level with increasing depth and breadth.
2) Principles like balancing standard-based and integrated approaches, using problem-solving, and assessment-driven instruction.
3) Bruner's three-tiered learning theory of enactive, iconic, and symbolic representation.
4) Teaching methods like problem-solving, concept attainment strategies, concept formation strategies, direct instruction, and experiential/constructivist approaches.
The document discusses the importance of developing conceptual understanding in mathematics teaching and learning. It provides examples of activities and problems that promote conceptual understanding over rote memorization of procedures. Teachers are encouraged to assess for conceptual understanding and recognize its presence or absence. Conceptual knowledge allows students to make connections and think flexibly rather than just follow recipes to solve problems.
This is part of the professional development for the team that translate My Pals Are Here into Dutch and also people who are going to provide professionald evelopment for teachers using Singapore textbooks in the future.
This document provides an overview of Numicon, a math teaching program that uses structured images to represent numbers. It discusses that Numicon helps children develop an understanding of mathematical concepts through multi-sensory and hands-on learning. Children enjoy using Numicon as it plays to their strong sense of pattern recognition and helps increase their confidence in math. The document outlines the different Numicon kits for different grade levels and provides guidance on activities to use based on the specific math skills needing development.
Creating opportunities to develop algebraic thinking and enhancing conceptual understanding of mathematics is essential at every grade level. In this webinar, Math/Technology Curriculum Specialist Aubree Short explored the use of problem solving methods and hands-on manipulatives to guide students in the discovery of algebraic concepts at all levels of learning.
The document outlines an instructional goal analysis for a 90-minute math lesson on decomposing and composing numbers for 19 early childhood students. The lesson will use manipulatives like farm and bear counters, as well as a smart board, laptop, and document camera. About half the students struggle with one-to-one correspondence and composing/decomposing numbers. The goal is for students to demonstrate an understanding of numbers and operations through play and activities by showing different ways a set of up to five objects can be decomposed or composed.
This document provides an overview and agenda for a webinar on the Common Core Georgia Performance Standards (CCGPS) Mathematics for second grade, unit 1 on extending base ten understanding. The webinar will begin at 3:15 pm and participants are instructed to configure their audio and download any documents. The session will focus on the specific grade level and unit, discuss the big ideas and enduring understandings, and provide resources and strategies for teaching the content. A list of resources will be shared and feedback from participants is requested to help improve future unit-by-unit webinars.
The document discusses approaches to teaching mathematics at the foundational stage. It focuses on developing both higher-order skills like problem-solving and content-specific skills. Teachers should emphasize real-world connections, use concrete examples initially and move to more abstract concepts over time. A four-block approach is recommended: 1) oral math talk, 2) skills teaching, 3) skills practice, and 4) math games. The gradual release of responsibility model shifts responsibility from teacher to students. A variety of pedagogical tools can aid learning, including toys, games, stories and spending time in nature.
The workshop will provide middle level mathematics teachers with ideas for engaging students in the understanding of math concepts and the creative aspects of mathematics topics in the 6-8 curriculum. The workshop will be hands-on and based upon a constructivist approach to learning and teaching. Handouts will be provided.
Presenter(s): Shirley Disseler
The document describes the Direct Instruction model of teaching. It is a teacher-directed approach where the teacher introduces new content to all students in a systematic way. It uses the "I do, we do, you do" approach of gradual release of responsibility. Key aspects include behavioral modeling by the teacher, whole and small group instruction, and individualizing for each student. The steps involve introduction, presentation by the teacher, guided practice with students participating, and independent practice. Benefits include developing thinking skills, automaticity of skills, fostering independent learning, and promoting self-knowledge. Technology tools and differentiation strategies can be used to meet individual student needs. An example for teaching time telling to 1st graders is provided.
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.
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
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
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.)
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
7. “Mathematics is an excellent
vehicle for the development
and improvement of a person’s
intellectual competencies”
Singapore Ministry of Education 2006
19. Development of
Geometric Thinking
van Hiele Model of Geometric Thinking
There are 5 levels:
• Level 0: Visualisation
• Level 1: Analysis
• Level 2: Informal Deduction
• Level 3: Deduction
• Level 4: Rigour
The levels are sequential – must start at the basic
level.
20. Level 0: Visualisation
• Recognise the appearance of the
shapes (look sort of alike)
• Properties are incidental to the shape
(implicit)
“A square is a square because it looks
like a square.”
21. Implications for Instruction
Level 0: Visualisation
• Provide concrete materials that can be
manipulated
• Include different and varied examples of
shapes
• Involve lots of sorting, identifying, and
describing of various shapes
• Provide opportunities to build, make, draw,
put together and take apart shapes
22. Level 1: Analysis
• More aware of the properties of a
shape than to its appearance
• Use properties to define categories of
shapes (able to list the properties but
not the relationships among the
properties)
23. Implications for Instruction
Level 1: Informal Deduction
• Engage in the same activities as level 0 but
the focus of the activities should be on the
properties of the shapes, not identification
• Classify shapes by properties
• Derive generalisation by studying examples
• Use appropriate vocabulary
24. Level 2: Informal Deduction
• Understand the relation of properties
within and among figures
“A square is a rectangle, a rectangle is
parallelogram which is also a
quadrilateral.”
25. Level 3: Formal Deduction
• Construct proofs to determine the
truth of a mathematic statements
Level 4: Rigour
• Highly abstract form of geometric
thought
26. Summary
Understand the importance of visualisation
and geometric thinking (van Hiele model of
geometric thinking )
Use activities to reinforce visualisation skills
• Tangram activity
• Grandfather Tang’s story
• Create your own picture
42. Number Bonds
Core Concepts
- Whole
- Parts
Can students figure out that a given number (up to ten)
comprises of two numbers?
Convention
Do students understand a convention used
to represent number bonds?
The common convention used in Singapore
primary school textbooks is shown