This session focuses on eight elements of early grade mathematics in Singapore that help develop a strong foundation for later mathematics learning. These include: 1) Sustained focus on thinking, 2) Focusing on a small number of topics taught in-depth, 3) Using concrete-pictorial-abstract approaches, 4) Having a spiral curriculum where topics are revisited over multiple years, 5) Utilizing non-specialist teachers with support materials, 6) Systematically varying tasks, 7) High aspirations among parents, and 8) Providing learning support and remediation. Concrete approaches, visual representations, and attention to disadvantaged students helps ensure all students learn well.
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 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.
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.
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 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.
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.
MCI Worchester State University Singapore Math Institute Jimmy 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 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.
Roxbury Township School District and Chester Township School District partnered together for a special parent engagement night for the Moms Club of Roxbury NJ on September 8, 2014.
Algebra Readiness: Equipping K-8 Students for SuccessDreamBox Learning
As the focus on standards-readiness grows, educators need reassurance that they’re not just teaching students how to pass a test, but also supporting their exploration, creativity, and deep understanding of applied knowledge. Joe Trahan, former middle school teacher, will discuss the pedagogical approach to preparing students for formal algebra. He'll share opportunities educators have to introduce the exploration of abstract concepts at an early age—at a time when students are more focused on concrete mathematical concepts.
Thi is Day 1 of a three-day professional development for teachers in Hawaii. Today, we focus on the fundamenatals - thinking and learning theories basic to Singapore Math. There was also an Open Lesson with Grade 4 students.
This 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.
Seminar at Colegio Inmaculada Conception, Universidad Andres Bello &San Beni...Jimmy Keng
Pensar sin Limites Seminars
This seminar was held at various places including Colegio Inmaculada in Conception, Universidad Andres Bello in Santiago & San Benito School in Santiago. The seminar explains the pedagogy behind the Spanish edition of My Pals Are Here! Mathematics.
MCI Worchester State University Singapore Math Institute Jimmy 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 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.
Roxbury Township School District and Chester Township School District partnered together for a special parent engagement night for the Moms Club of Roxbury NJ on September 8, 2014.
Algebra Readiness: Equipping K-8 Students for SuccessDreamBox Learning
As the focus on standards-readiness grows, educators need reassurance that they’re not just teaching students how to pass a test, but also supporting their exploration, creativity, and deep understanding of applied knowledge. Joe Trahan, former middle school teacher, will discuss the pedagogical approach to preparing students for formal algebra. He'll share opportunities educators have to introduce the exploration of abstract concepts at an early age—at a time when students are more focused on concrete mathematical concepts.
Thi is Day 1 of a three-day professional development for teachers in Hawaii. Today, we focus on the fundamenatals - thinking and learning theories basic to Singapore Math. There was also an Open Lesson with Grade 4 students.
This 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.
Seminar at Colegio Inmaculada Conception, Universidad Andres Bello &San Beni...Jimmy Keng
Pensar sin Limites Seminars
This seminar was held at various places including Colegio Inmaculada in Conception, Universidad Andres Bello in Santiago & San Benito School in Santiago. The seminar explains the pedagogy behind the Spanish edition of My Pals Are Here! Mathematics.
This presenttaion was made to a group of parnets, business leaders, administrators, teachers, school board members and university representatives in Cache School District in Logan, Utah. This group, The High School Renewal Committee, is keen to develop a world-class high school mathematics programmed. In this presentation, some recommendations were made on how to make the average high school student perform well in mathematics.
This session is on early grade mathematics. It focuses on key ideas in early grades mathematics. I have previously done a keynote lecture on this topic at Erikson Institute, Chicago (First International Symposium on Early Mathematics).
This was presented at the NCTM Annual Meeting and Exposition. It provides participants with features of math program that make mathematics accessible to average and struggling learners.
LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011Jimmy Keng
This plenary lecture on elementary school mathematics was given at the conference which marks the end of the three-year Leaders and Educators in Asia Programme.
This 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.
Developing a Learning Trajectory on Fraction Topics by Using Realistic Mathem...iosrjce
This research and development was purposed at (1) developing a learning trajectory on fraction
topics by using Realistic Mathematics Education approach in Primary School; and (2) determining the validity,
practicality, and the effectiveness of the learning trajectory. The results of this research were (1) a learning
trajectory on fraction topics in the form of Teacher’s Guide Book and Student’s Book. (2) Teachers’ Guide Book
and the Student’s Book of learning trajectory were considered valid, practical and effective after being judged
by experts in Mathematics Educators, Language Educators, Experienced Teachers and an Educationalist.
Based on the research results, it can be concluded that the learning trajectory on Fraction Topics by using
Realistic Mathematics Education Approach can be effectively used to improve the learning effectiveness on
Fraction Topics in Primary School.
Connect with Maths~ Maths Leadership Series-session 2-the right pedagogyRenee Hoareau
Connect with Maths ~ Maths Leadership Series
Session 2 - The right pedagogies
Presented by Rob Proffitt-White
Implementing curriculum intent requires a repertoire of pedagogies
Effective teaching of mathematics and numeracy capabilities require a range of pedagogical practices . This workshop is for teachers and school leaders who want to look at the processes involved in creating a common language around effective delivery of all mathematical proficiencies. It will focus heavily around
• Valuing teacher voice and building supportive and trusting culture for all
• Enacting the growth mindset in all classrooms
• Designing protocols and routines to support coaching/mentoring and reflecting.
Connect with Maths ~ supporting the teaching of Maths ONLINE
Connect with Maths Engaging All Students community ~ join at http://connectwith.engaging.aamt.edu.au
Similar to NCTM 2010 Regional Conferences & Expositions Denver 2 (20)
Model Attribute Check Company Auto PropertyCeline George
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Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
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1. NCTM Regional Conference & Exposition Denver Colorado 8 – 9 October 2010 Session 165 This session focuses on eight elements in early grades mathematics that help children develop a strong foundation for a demanding mathematics program in the upper grades. Concrete, visual approaches, coupled with special attention to economically disadvantaged children, systematic variation in representations and content help students learn well. Colorado Convention Center, 506 – 507 Denver, Colorado
2. Eight Things About Early Grades Mathematics in Singapore Session 165 DrYeap Ban Har Marshall Cavendish Institute Singapore banhar@sg.marshallcavendish.com slides are available at www.banhar.blogspot.com
3. Beliefs Interest Appreciation Confidence Perseverance Monitoring of one’s own thinking Self-regulation of learning Attitudes Metacognition Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Mathematical Problem Solving Reasoning, communication & connections Thinking skills & heuristics Application & modelling Skills Processes Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical The mathematical problem-solving curriculum framework was introduced in Singapore in 1992 in response to recommendations made in An Agenda for Action (in the US) and the Cockcroft Report (in the UK).
4. NCTM Regional Conference & Exposition Denver Colorado 8 – 9 October 2010 Session 165 This session focuses on eight elements in early grades mathematics that help children develop a strong foundation for a demanding mathematics program in the upper grades. Concrete, visual approaches, coupled with special attention to economically disadvantaged children, systematic variation in representations and content help students learn well. Colorado Convention Center, 506 – 507 Denver, Colorado
5. Students are expected to solve complex and, often, new problems in the program. The formal assessment such as school examination and national examination contains significant emphasis on problem solving. demanding program
6. A B F E Source: Singapore Examinations and Assessment Board PSLE Mathematics 2004 – 2008 and Specimen Paper 2009 D C
7. Grade 3 Examination Item (Raffles Girls’ Primary School 2009) Challenging Application Devi had some $2 notes and $5 notes. She had a total of $76. She had 4 more $5 notes than $2 notes. How many $2 notes did she have? Source Raffles Girls’ School, Singapore
8. Devi had some $2 notes and $5 notes. She had a total of $76. She had 4 more $5 notes than $2 notes. How many $2 notes did she have? $76 Number of $5 notes 4 $20 $56 8 Number of $2 notes $56 ÷ 7 = 8 8 She had eight $2 notes.
9. Grade 6 Examination Item (PSLE 2009) Challenging Application In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ. Find MPN Answer: 150o Source Singapore Examinations and Assessment Board PSLE Mathematics 2009
10. NCTM Regional Conference & Exposition Denver Colorado 8 – 9 October 2010 Session 165 This session focuses on eight elements in early grades mathematics that help children develop a strong foundation for a demanding mathematics program in the upper grades. Concrete, visual approaches, coupled with special attention to economically disadvantaged children, systematic variation in representations and content help students learn well. Colorado Convention Center, 506 – 507 Denver, Colorado
11. learning well Students who have learnt well in the early grades should do well in the upper grades. Also, the should find mathematics sufficiently challenging and within their grasp.
12. The majority of students in Singapore opt to study mathematics in Grades 11 and 12 when they are no longer required to. This is confirmed by the TIMSS data on attitude towards mathematics. The attitude index for Singapore students in TIMSS is also relatively high compared to other high-performing countries.
13. Attitude Achievement The figures refer to percentage of students with high PATM (for Attitude) and in the Advanced International Benchmark (for Achievement). Taiwan 37 45 Grade 8 S Korea 33 40 Singapore 60 40 Hong Kong 47 31 Japan 30 26 Hungary 30 10 England 40 8 International 54 2 Source TIMSS 2007 International Mathematics Report, Boston College
14. one: sustained focus on thinking One of the three stated rationales for teaching and learning mathematics is because mathematics is “an excellent vehicle for the development and improvement of a person’s intellectual competence” (Ministry of Education 2006)
15. Beliefs Interest Appreciation Confidence Perseverance Monitoring of one’s own thinking Self-regulation of learning Attitudes Metacognition Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Mathematical Problem Solving Reasoning, communication & connections Thinking skills & heuristics Application & modelling Skills Processes Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical The problem-solving framework has been in place since 1992. In 1997, Thinking Schools, Learning Nation philosophy was introduced to the entire education system. This is supported by the Teach Less, Learn More initiative in 2004.
16. For example, there is an emphasis on mental strategies. Mental strategies help students become flexible thinkers as they need to make decisions on the best strategy to use for a particular computation. In an earlier presentation (Session 106), I have discussed visualization, number sense, generalization and metacognition. Source Pensar sin Limites 2oBasico
17. Dagoberto Godoy School, Santago Princess Elizabeth Primary School, Singapore Keys Grade School, Manila Springhurst Elementary School, New York
18. There are some apples in a box. There are 5 different ways to put the apples into equal groups. Hint: The number is between 15 and 21. Keys Grade School, Manila
19. sustained focus on thinking Dagoberto Godoy School, Santiago, Chile
20. two: small number of topics This allows in-depth treatment of a few key ideas at the early grade levels. One core idea is number bonds.
21. Number Bonds is emphasized prior to the learning of addition. Children are given, say, 5 unifix cubes and guided to see that 1 and 4 make 5, for example. Others may say that 3 and 2 make 5 or 4 and 1 make 5. Yet others may say that 5 and 0 make 5. Source Earlybird Kindergarten Mathematics Book B
29. sustained focus on thinking focus on fewer topics Princess Elizabeth Primary School, Singapore
30. Circle Graphs are taught in Grade 6 in Singapore. Source TIMSS 2007 International Mathematics Report, Boston College
31. Based on Jerome Bruner’s ideas of enactive, iconic and symbolic representations, Singapore curriculum, textbooks and teacher education emphasized the importance of concrete materials and the progression to visual and symbolic representations. three: CPA approach Source Earlybird Kindergarten Mathematics – Kindergarten Textbook in Singapore
32. Is the rectangle cut into equal parts? illustration equal parts Source Professional Development Course for Singapore Teachers
33.
34.
35. bruner’s theory concrete Source mathz4kidz Learning Centre, Penang, Malaysia A Lesson from Earlybird Kindergarten Mathematics
36. concrete experiences Source mathz4kidz Learning Centre, Penang, Malaysia A Lesson from Earlybird Kindergarten Mathematics
37. The CPA Approach – the progression from concrete to pictures to abstract symbols is recommended for concept development. This is based on the work of Jerome Bruner. Source Fuchun Primary School, Singapore Research Lesson to Develop Formula for Circumference of Circles
40. Visuals are used extensively to develop conceptual understanding. In learning how to write mixed numbers as improper fractions in Grade 4, the visual approach is a common approach in the textbooks.
44. sustained focus on thinking focus on fewer topics the CPA approach Da Qiao Primary School, Singapore
45. four: spiral curriculum Students have many opportunities to learn a core idea. For example the concept of division takes five years to develop – in a systematic manner, with the goal of advancing students’ notion of the concept.
48. For example, students learn to do division of discrete quantities without the need to write division sentence in Grade 1. In Grade 2, the revisit this idea and use division sentences to represent the situations. In Grade 3, the idea is extended to include the idea of a remainder. They also learn to regroup before dividing for 2-digit and 3-digit numbers. The quantities used are limited to discrete quantities. Princess Elizabeth Primary School, Singapore My Pals Are Here! Mathematics Primary 1
49. In Grade 4, 4-digit numbers are used. In Grade 5, division of continuous quantities are dealt with where 13 ÷ 4 = 3.25 rather than 3 remainder 1. Keys Grade School, Manila
50. Up till 1992, there was no college graduates teaching in primary schools in Singapore. Today, half are college graduates. In pre-primary levels, many teachers hold only a Grade 10 certificate (with a teaching certificate), although increasingly more teachers completing the bachelor and graduate degrees. Compulsory education is Grade 1 to Grade 6. five: non-specialist teachers
55. Teachers received about 100 hours of courses in mathematics teaching and learning during pre-service training. National Institute of Education, Singapore
57. Teachers are expected to engage in professional development throughout their career. Princess Elizabeth Primary School, Singapore Marshall Cavendish Institute, Singapore
58. Some study for certification while others just for improvement. It is also an expectation. SEED Institute, Singapore
59. Tasks are presented in a systematic sequence to provide students with both mathematical as well as perceptual variability. six: systematic variation of tasks
63. Systematic Variation – students are presented with a variety of tasks in a systematic way. This is based on the idea of ZoltanDienes.
64. Source Primary Mathematics Grade 1 It is likely that a teacher will start this unit using the sticks. This is followed by the use of base ten blocks. Finally, non-proportionate materials such as coins are used. In each of these lessons, the teacher is likely to introduce the following five notations in turn – place value chart, expanded notation, number in numerals, number in words and the tens and ones notation. The question is what is an appropriate sequence? Should the place value chart be used first? Or the expanded notation? Give your reasons. Place Value Chart Expanded Notation Source Professional Development Materials Marshall Cavendish Institute, Singapore Words Numerals Tens and Ones Notation
65. It is likely that a teacher will start this unit using the sticks. This is followed by the use of base ten blocks. Finally, non-proportionate materials such as coins are used. In each of these lessons, the teacher is likely to introduce the following five notations in turn – place value chart, expanded notation, number in numerals, number in words and the tens and ones notation. The question is what is an appropriate sequence? Should the place value chart be used first? Or the expanded notation? Give your reasons. Place Value Chart Expanded Notation Words Numerals Tens and Ones Notation Primary Mathematics
66. non-specialist teachers sustained focus on thinking focus on fewer topics the CPA approach spiral curriculum Da Qiao Primary School, Singapore systematic variation
67. Through education, education level and consequently, social-economic status of families increase over one generation. Young parents have high aspirations for their children. Most send their young children to pre-schools and there number of school-age teenagers who are not in school is negligible although there is no compulsory education beyond Grades 1 – 6. seven: high aspirations among parents
68.
69. TelokKurau Primary School, Singapore “Sometimes my teacher gives me remedial classes. Some people go for Maths Olympiad training. My maths is not good. I don’t go for that.” Fifth Grader school support “In my school, we have a fixed day for remedial lessons. I get a group of students to attend this regularly.” Teacher
71. In grades one and two, students who did not attend pre-school, received a pull-out learning support for English and mathematics (LSP and LSM). They are taught in smaller groups of not more than ten while the regular class size is 30. Formal school hours end around 1:30 to free up time for a range of informal co-curricular and curricular activities. eight: learning support and remedial
72. safety nets and interventions non-specialist teachers Slides are available at www.banhar.blogspot.com sustained focus on thinking focus on fewer topics the CPA approach spiral curriculum systematic variation high parental expectations
73. Eight Things about Early Grades Mathematics in Singapore Slides are available at www.banhar.blogspot.com Da Qiao Primary School, Singapore