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?

# Mathematics Teacher Education: Singapore Approach

This blog is about teacher professional development courses that I conduct in Singapore and other countries.

## Saturday, November 22, 2014

## 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

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

## Friday, November 7, 2014

## 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.

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

OOO

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.").

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.").

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