Sunday, December 21, 2014

Friday, December 12, 2014

Greg Tang's Math Institute | Keynote Lectures 11.12 Dec 2014

Keynote on Anchor Tasks - What are anchor tasks? Why are they used? How can it be brought to life? Click Here

In this lecture we saw the original Singapore textbooks, where the three-part lesson format has already been established. Using a current textbook I showed how to bring an anchor task to life and how to use textbooks for reflection. I also showed how Guided Practice looks like.

Closing Keynote | Click Here

I presented for the first time a collection of my favourite list of fives - I have a set of seven lists.

Thursday, December 11, 2014

Greg Tang's Math Institute 3-5 Workshops | 11.12 December 2014

Day 1 Workshop on Making Connections using Multiplication and Division | Click Here for slides and photographs

We studied how multiplication facts are developed - counting, figuring out, remembering.
We saw how a practice lesson can be challenging for advanced learners yet support struggling learners with (a) a standard strategy (b) literal strategies such as doubling (c) extended time to work on a single idea - how to multiple two-digit numbers.

We looked at how division of fractions is connected to division of whole numbers.

Day 2 Workshop on Bar Models

We used four examples to learn basic and advanced ways to use bar models for complex word problems for topics in ratio, percent and so on.

We looked at teacher modeling reading, scaffolding visualizing and the emphasis on mental strategies. We saw examples of problem posing (Silver).

The last two problems are challenging. The last one is for 'homework'.

Greg Tang's Math Institute K-2 Workshops | Honolulu 11.12 December 2014

Workshop 1 | K-2 Click Here for Slides
This workshop focuses on the development of number sense.

We saw the fundamental of counting - same nouns, renaming when nouns are different.
We saw the use of ten frames in counting and also the difference between proportionate and non-proportionate materials. Participants offered the progression for counting - (1) real things before manipulative (2) single nouns before multiple nouns (3) proportionate before non-proportionate.

We saw the use of ten frames, number bonds and visual models to develop number sense.

For addition, we studied the case of single-digit addition and for subtraction, we saw multi-digit subtraction. We also saw an example of a lesson that focused on practice and how the advanced learners are challenged. Struggling learners get support from (1) concrete materials (2) time to figure out (3) working with friends.

Reflection Task | How does the make a shape using four tiles develop number sense?

Workshop 2 | slides are in the same Album as above.

The focus was on multiplicative structures for young children.

We looked at readiness for teen numbers as well as a strong concept in counting in single / two nouns. We also looked at comparing groups and making equal groups.

The main case study looked at variation of problems used in multiplication where we go from both factors represented using physical representations, to only one of the factors represented physically to both factors represented symbolically across four lessons.

Saturday, December 6, 2014

Anglo Singapore International School | Bangkok

Teachers Session | Click Here for a summary of the discussion on differentiated instruction using a common task.

We learn how to differentiate instruction using an open task as well as differentiated instruction using a basic skill practice tasks.

Make a list of strategies for advanced learners and a list of strategies to support struggling learners.

Three stages of a maths lesson. Four things teachers do to help acquisition and refinement of knowledge. Five things advanced children can do.

How does anchor task and guided practice promotes DI?
How does the use of a journal consistent with DI?
How is asking for more than one method a DI strategy?
How does concrete materials and visuals help?
How does the extended time with one task (anchor task) help?
How does collaborative learning help?

Parents Session | Click Here for two of my list of Big Fives.

Five things advanced children can do. Five core competencies in mathematics.

Wednesday, December 3, 2014

Northbridge International School Cambodia

Grade 6 Lesson on Ratio | Click Here

Learning Tree - Shinglee Professional Development | Bangkok

Anchor Task 2 | Secondary Case Click Here

Seminar for School Leaders - How to Increase Achievement Level and Cultivate Positive Attitude in Mathematics in Your School. During the seminar I did two anchor task demonstrations to illustrate the factors contributing to high achievement and positive attitude. The photographs show using an anchor task from New Syllabus Mathematics 1, a secondary level textbook series that is used by many secondary schools in Singapore (it was first developed in the 1980s and the 2013 Edition is now available for Book 1, 2 and 3 as well as Additional Mathematics). In this anchor task, students were asked to investigate the sum of angles in a polygon of n sides. We saw exploring, structuring, journaling and reflecting using the textbook. We also discussed how guided practice looks like using Worked Example 6. 

TIMSS Report 2011 Mathematics | Full Report

More to come ...

Friday, November 28, 2014

Alkem Professional Development

What are some core ideas in early numeracy ? | Slides

How to develop problem solving and critical thinking ? | Slides

Saturday, November 22, 2014

Taipei American School 2

This is my second entry. Colleagues at TAS, please Aldo look at the entry just before this to access the various sessions we did with the seven grade level teams.

One theme that surfaced throughout the week is how we challenge our advanced learners. I have put in things for us to observe during the week.

Did you see ...

some KA students were asked to count more than four tiles. At least one of them was asked to add three one-digit numbers. Those are examples of acceleration. But I did those in the context of common activities - everyone was playing with tiles, making stuff and later doing the same coloring activity.

Did you also see ...

Kindergarten students being asked to use 32 cubes to make three numbers, each greater than 10 and them to compare the numbers pairwise . Is that a challenge in itself? 

Did you see how groups that completed the job earlier were asked, the three numbers are the same now, can we make them different. Or the three numbers are different, can we make them the same.

Did you also see advanced learners 

investigating if there were any relationship between numver of ways to make the equation a + b = n and the value of n, while the class work on finding a and b. N = 12 for this lesson. Did you see students who are capable putting patterns they saw into words? Dud you see them learning to use what their friends did or said to construct their own understanding?

Are all these important?

Did you see advanced learners 

using 35 + 55 = 90 to generate equations that met the given conditions that the digits in the addends are different. Did you see the second graders doing things that you think are important for them to learn to do? Make a list of these things. These are your answers to parents who clam our for acceleration.

Not that you did not see acceleration. Did you see Grade 1 went on to do 99 + 3 in a lesson where the girl is to add 1, 2 or 3 to another one-digit numver.  The lesson started with 9 + 3. Did you see while other students merely counted on to get 102, advanced learners were saying things test made you proud they are your students? What are those things that they say. Write them down because these are the things you show parents of these kids when they say their children are not challenged enough.

Did you see I end lessons by asking what made you proud today? What challenged you today? What did you learn today?

Diid you see third graders solepce a challenging problem?

Jon folded paper stars. Each day he folded two more than the day before. In seven days, he folded 91 paper stars. The class found that he folded 7 on the first days. 

Did you hear 

a student suggested that the number in the first day cannot be an even number. 

Did you see another suggested doing 91 divided by 7 and use the quotient 13 to get the number folded on the first day. 

Did you see advanced learners not able to, initially anyway, not able to use the piece if paper to help them represent a linear equation. Did you see them posing more difficult equations in their design homework for your patents task? The rest were making up x + 1 = 12 while they wrote 2 x x = 12 and were told the xpconvention if leaving out multiplication sign in two times x.

Did you see the advanced learners from 5X learning to articulate their thinking and were pushed to say how a game is not fair and how to make it fair. Dud you see how advanced learners were challenged in the lesson although the whole class were working on the same task - playing a roll a dice game and the deciding where to place the digit in their _ _ _ _ _ 

Did you see advanced students having fun doing the lesson? Learning more content is fine but have they learn to enjoy what they do. If not that must be learnt before they are accelerated. Acceleration is fine. But let's do that after 'what counts' have been done well.

Did you see?

Monday, November 17, 2014

Taipei American School

Reflection | How giving students time to figure things out is important before discussing difficult ideas. We saw how some students in grade 1 were able to see that the number of equations for ? + ? = n is (n + 1) ways, We saw how students in grade 3 were able to solve this problem - Jon folded paper stars. Each day he folded two more than the day before. In seven days, he folded 91 paper stars. The class found that he folded 7 on the first days. Along the way a student suggested that the number in the first day cannot be an even number. Another suggested doing 91 divided by 7 and use the quotient 13 to get the number folded on the first day. All very high level thinking for grade 1 and grade 3 students. I encouraged teachers in the school to use anchor tasks to organize their mathematics lessons. 

Discussion Materials

Teaching Place Values 1 | Click Here

Grade 5 Lesson | Click Here We did comparing decimals and whole numbers.

Grade 4 Lesson | Click Here We did solving linear equations.

Grade 3 Lesson | Click Here and Here We did word problem solving.

Grade 2 Lesson |Click Here We did addition of two digit numbers using mental strategies.

Grade 1 Lesson | Click Here We did adding 1, 2 or 3 to another whole number.

Grade K Lesson | Click Here We did comparing three numbers.

Grade Kindergarten A Lesson | Click Here We did a play activity and a drawing activity while focusing on counting to four things in a set.

Singapore Standards for K | Click Here

Where to check out Ten Frames | Didax and EAI Education

Reference Materials

Struggles | Click Here

Another article on Struggles |Click Here

Monday, November 10, 2014

Raffles Girls' School | Singapore

I had a chance to meet with the mathematics department. | Slides

Wednesday, October 29, 2014

Lecture at ICSME 2014 at University of Philippines

Slides are available here | Slides

International Conference in Science and Mathematics Education is organized by UP NISMED.

Kindergarten Students in Bina bangsa School, Jakarta learning by solving a problem

Tuesday, October 21, 2014

History | Subitizing


How many O are there?

 Did you have to count to tell the number? Most likely you did not count. What you did was to subitize. To subitize is to tell how ,any without counting. In class, we discuss subitizing and counting. A little history. By hanging out at British Museum after work each day, I learnt that earliest humans were in Africa around 250,000 years ago. Notice the comma to help you subitize the zeros so you will not misread the numbers. Some people write it this way 200.000 others 200 000. I suppose you can do 200/000 or 200-000 but apparently those has not caught on! Anyway, we know little about these guys  because not much is left behind except for bits of fossils. Some writers speculate that the ability to subitize evolved in humans and otter primates as well as a couple of other animals to allow them to survive. Wolves are charging at you. If you have to count them to decide to fight or take flight, you are likely to be wolf food. It is likely you can tell how many wolves very quickly, at a glance by subitizing. Two wolves, maybe grab a stick and fight them and you get dinner Five wolves, then better climb that tree lest you become dinner (Wolves cannot climb trees, right? Oops!) | Subitize and History

Monday, October 20, 2014

Course 1 for UK Teachers | Clerkenwell Centre

Day 1 >> click on day 1 to access slides >>

Setting The Context - Data on student achievement over the years were presented.

Teaching through a Problem - What are the features of a mathematics lessons? What are the theoretical underpinnings and research basis for these features?
We did four basic concept lessons (equal parts, addition within forty, subtraction within 100 with regrouping, square) and one word problem lesson (division of three-digit number).

I often say 'Can you see with the eyes in your mind?' in my presentations. It is derived from the common phrase 'in my mind's eyes' which was given to use by Shakespeare (1602 in Hamlet when he write "In my mind's eyes, Horatio."). The concept of having mind's eyes is ancient, dating back to Chaucer (c.1390 when people still spelt funny, he wrote "It were with thilke eyen of his mynde, With whiche men seen, after that they been blynde."). 

Tuesday, October 14, 2014

Marshall Cavendish Education Conference 2014

Lecture 1 How Singapore Math Improves Student Achievement | Slides Here

Lecture 2 Using Assessment to Differentiate Instruction | Slides Here

Monday, August 4, 2014

Worcester State University Summer Institute

Click here for Slides used during the Presentations

Day 1 Slides | Day 2 Slides | Day 3 Slides | Complete Set of Handouts | CutOuts |




Monday, July 21, 2014

Blue Springs School District

On the first day, we talked about anchors tasks to introduce new topics, also anchor tasks for practice.
We saw the three part lesson format. We discussed variations in tasks across units.

Photographs are available here Photographs

Friday, July 18, 2014

Kaihe'e Elementary School

Photographs of the Sessions are available here.

Fort Zumwalt School District

Photographs for the Session are here. Photographs

Teachers from the entire district attended this one-day seminar that focused on the four operations.

Wednesday, July 9, 2014

SDE Singapore Math Strategies National Conference July 2014

The handouts used for the four sessions are available.

ABC's of Singapore Math


Fraction Problems 

Advanced Learners
Based on the participants' responses, we were able to say an truly advanced learner is able to do the math, in addition this student is also (a) do it in many ways (b) able to tell that s/he is correct or not (c) communicate his/her thinking to a friend and in writing. A truly advanced learner does not whine "Do I have to?" when asked to do something. If s/he does, that student is not advanced.

Ways to challenge advanced learners
(1) Can you explain it?
(2) Do it another way. Do it in an original way.
(3) What do you notice? Any patterns?
(4) Can you explain it to a friend? Can you write it in your journal?
(5) Go find someone who needs help. See what you can do.

(1) Use of concrete materials
(2) Use of visuals
(3) Use of questions - can you see?

Visualization includes seeing what is not there, not seeing what is there and moving things in one's head.

Photographs of the Session are also available at my Facebook

Sunday, June 15, 2014

USA Florida M4thodology Institute 16.17.18 June and 18.19.20 June


K-2 Institute | Day 1 | Day 2 | Day 3

3-6 Institute | Day 1 | Day 2 | Day 3

Course Notes | K-2 Class Day 1 and Day 2 & 3 | 3-6 Class

Achievement and Attitude in Math Learning Graph | click here

Monday, June 9, 2014

USA Minnesota @ Blake Institute, Hopkins, MN

Course Notes is available here |  Complete Course Notes for All Five Days

Photographs of White Board are available here | Day 1   Day 2   Day 3   Day 4   Day 5

Friday, May 30, 2014

EdCrisch Manila Professional Development for Adopting Schools

Elementary School - Anchor Task | Photographs

High School - Ancho Task

High School - Geometry

Wednesday, May 21, 2014

4-KKU Course on Qualitative Research In Mathematics Education

Article on Social Learning Theory to Research Teacher Learning | Watson

This is an overview on adult learning theories | Andragody

Finally, this is an overview on student learning theories. | University of Berkeley California

The fourth session focuses on the use of theory to frame research and how it influence research design, data collection, and data analysis.

PISA and TIMSS provide good frameworks to design instruments to measure student outcomes. tEDS-M for teacher outcomes. See PISA Report here.

3-Khon Kaen University Course on Qualitative Research Methods in Mathematics Education

We reviewed research problem and talked about delimiting a problem.
We also talked about literature review - major writers, unusual perspectives, recent research and local research.

In the third session, we focused on research design.

In the domain of teacher learning, we discussed the broad question of
1. What do teachers need to learn?
See D. Ball research. In particular, the "egg" diagram is taken from this article.

2. How do teachers learn?
I shared a possible framework and one of the students helped improve it.
By experiencing (e.g. In workshops where teachers become students doing mathematics), being told (e.g. lecture), seeing (e.g. observe a mentor), doing (e.g. practice teaching or micro teaching), discussing (e.g. lesson study if combined with seeing), reflecting (e.g. writng journal).

Exercise | Design a research on teacher learning during initial teacher preparation.
How are you delimiting the research problem? What are the research variables? What research data do you anticipate to collect and from whom?

We look at TEDS-M Study as an example of how research design impacts on the research findings.

TEDS-M and other IEA Studies are available here. | IEA Studies

Concepts discussed in the last few lessons included | classroom environment | opportunity to learn |

classroom environment - IEA Study on Classroom Environment look at the teacher aspect of classroom environment (management practice and instructional practices and the impact on student outcomes). Barry Fraser's work may also be of interest to those interested in classroom environment.

opportunity to learn - is essentially the idea of do students get learning opportunities on things that are being assessed. Sample articles on what is OTL are included below.

Article 1

Article 2

Tuesday, May 20, 2014

2-Khon Kaen University Course on Qualitative Research a Method in Mathematics Education

We reviewed how we identify research problem from a situation or a domain.

Based on the research problem, we write the initial research questions.
The answer to the initial research questions are located in the literature through the process of literature review.

The answers we get from the literature will tell us what else we need to answer. This leads to your final research questions that your research will answer.

And after you are done with the research, there are still parts of the questions not answered.

The parts of the research question that are not answered are your recommendations for future research.

The research proposal is your chapters on research problem, research questions and research design.

The third session is on research design.

Friday, May 16, 2014

1-Khon Kaen University Course on Qualitative Research Methods in Mathematics Education

This is a useful site for background reading by Harvard University.

0. Introduction

During the first session, you will be asked to state your research problems.

1. Crafting Research Problems

We talked about how research problem is derived from an Interesting and Important situation.

The selection of the research problem is based on economic / utility justification (the competencies under research is useful), is based on reasearch gaps justification (gaps found in international research in that domain), national curriculum justification (that it is a key aspect of the national curriculum or it is an important construct but not yet included in the national curriculum) and local context justification.

Students in this course are encouraged to write the chapter on Research Problem before they even embarked on their data collection. This together with literature review chapters should be ready before data collection.

Exercises are found here.

Statements of research problems shared on the first day:

Thiang's Research Problem | Mathematical communication is related to opportunities given to     students. The relationship is, however, unclear as most studies in mathematical communication     tended to focus on .... In this research, the relationship between students' mathematical communication and opportunities given to students, will be investigated through ... (Notice that the tense used in proposal and thesis are not the same).

What type of literature review do you expect Thiang to do?

What did we do in the other sessions? Session 2 | Session 3 | Session 4

Special Meeting with Masters students from Laos

Thursday, May 15, 2014

Workshop on Classroom Assessment | READ Conference

Samples of Marking Scheme for Source-Based Questions from MOE Singapore.
See Page 54 for the case discussed in the workshop. Click here.

Ministry of Education Singapore Website - see Syllabus

Singapore Examination and Assessment Board Website - for details in national examinations in Singapore.

Course Notes

Appendix - sample textbook pages for classroom assessment

Appendix - case study of holistic assessment in a Singapore school

Saturday, April 19, 2014

Keynote Lecture at Mt San Antonio College, 13th Developmental Education Conference

Keynote Lecture at 13th Parachutes and Ladders in California.

The slides used in the lecture are available here.

Friday, February 28, 2014

Presentation to Education Minister Brunei

This presentation was made to Education Minister Brunei.

Slides are available here.

Thursday, February 13, 2014

Presentation at Smithville, MO in USA

Morning Presentation - Teaching Math The Way It Should Be

Slides are available here

Afternoon Workshop - Teaching Middle School and High School Selected Topics

Singapore Schools

Friday, January 17, 2014

Wednesday, January 8, 2014

LSP102 Lesson Planning in Lesson Study

This is the basic materials for the session on 9 January 2014 at Punggol Primary School.