## Monday, May 16, 2016

### Manchester, England | 16.17.18 May 2016

Day 1 focuses on lesson structure. Day 2 on differentiation for advanced learners and Day 3 on assessment and bar models.

This is a summary of some ideas on how learners are supported during lessons put forth by participants.

1. Peer Disucssion. By working with friends and talking through things, students get to see models of how people think and articulate their thinking. They also get help from friends. This concurs with Vygotsky's idea of learning through interaction.

2. Use of Manipulative. The use of manipulative makes ideas accessible. Example making ten is obvious because of the ten frames. This is based on Bruner's ideas of representations.

3. Spiralling of Lessons. In the second lesson on formal long division method, students get to revisit the number bonds method.

4. Informal Learning. Long division is first learnt informally using number bonds. This is Dienes ideas on stages of learning.

5. Context. All calculations are learnt through context and stories.

6. Multiple Methods. Some methods are more literal and accessible to beginners.

## Thursday, May 5, 2016

### Easton, USA | 5 May 2016

Helen Keller Middle School

I did an open lesson on solving a challenging problem involving percent and fractions for grade seven for teachers to have a professional conversation around anchor task.

I presented the word problem in my trademark style - word by word and students guessing the words - I am just having fun but what are the pedagogical advantages of this?

A group comprises 75 children and some adults. 15% of the group are males and. Of the males, 2-thirds are adults and the remaining 6 are females.

Our problem was to help Spiky show the information on a bar model and to decide if we can determine the number of boys, men, girls and women in the group | Easton School District

## Monday, May 2, 2016

### New Rochelle, USA | 2.3 May 2016

In the introduction, I provided some data to show that it is possible for the average learners to perform at a high level and struggling learners to continue to have subsequent opportunities. The rest of the two days is to work out how.

In Session 1, we looked at how even computation can be taught as problem solving. We look at word problem lesson (grade five), long division (grade three and beyond) and addition within twenty (grade one) are taught in the problem solving approach.
Lessons begin with exploration followed by structured learning. At some point, students journal.

We also examined ways to develop visualization.

In Session 2, we looked at bar models. In Session 3, we consolidated our learning about ways to develop visualization.

In the making ten lesson, ten frames and counters were used to help students visualize how 8 + 6 becomes 10 + 4.