Monday, June 24, 2013

Progressive Classroom Designs Institute at Danburry, Connecticut

Photographs at my Facebook.

Day 1 Presentation is available here

We saw (1) CPA Approach (2) Spiral Approach (subtle variation from day to day lessons).

We heard Bruner, Dienes, Vygotsky and Skemp.

We spoke of several ways to challenge advanced learners in basic skills lessons

Can-You-Explain / Write-a-Note-to-Absent-Friend Strategy
Write-A-Story Strategy
What-Is-The-Mistake Strategy
Taking-Perspective Strategy

Photographs of the lessons including solutions to Homework tasks are available here

Day 2 Presentation is available here

Thursday, June 20, 2013

M4thodology Institute - Workshop on Challenging Word Problem

Problem Set is available here.

The solutions to the Challenging Problems are here.

The solutions to the Homework will be available later.

Problem 1 Emma and Farid Problem

Problem 2 Chairs and Tables

Problem 3 Apples

Warm Up Problem for Textbook

Review of Problem from Lecture on Assessment

Wednesday, June 19, 2013

M4thodology Institute at The Bolles School (Grades 3-6 Session)

Photographs of the board and charts are available here.

Day 1

Opening Lecture on Role of Mathematics

Breakout Session 1 on Anchor Task (see notes below)

Breakout Session on Anchor Task
Notes on Anchor Task Breakout Session

Day 2

General Session on Assessment

General Session on Challenging Word Problems - Problems used in the session is available. See for solutions to the eight problems for the session including the three homework problems.

General Session on Generalization and Links to Algebra

Breakout Sessions on Fraction, Ratio and Percent

The discussion on Fractions is here.

Problem for Ratio

Problem for Percentage Change
Day 3

General Session on Visualization

General Session on Questioning Strategies
There are also additional summary notes in the blog entry for the K-2 Institute.

Breakout Session on Multiplication and Division (see below)

Breakout Session on Measurement and Area where we did one word problem lesson, one basic concept lesson (area of triangle) and one drill-and-practice lesson (based on Pick's Theorem on the geoboard grid).

In the Closing Forum, we look at the Japanese features of effective mathematics lesson (Shimizu, 2013). The slide is available in another blog entry.
Lesson to Develop Formula for Area of Triangle

Lesson to Apply (Measurement)

Lesson to Consolidate (Area)


Monday, June 17, 2013

Bar Model Session at The Bolles School (K-2 Session)

In this class we discussed four problems and what if versions to challenge advanced learners.

See the problems here.


Solution to Problem 1 - this is grade three problem and a grade two version can be crafted from this. Ali had 17 more coins in the end.

Without drawing, some students ended up with 13 more coins. Model drawing allows students to capture complexities of situations (in this case that Billy's number of coins is reduced by 4 in the process).

A Grade 2 version - At first, Ali had 9 more coins than Billy. Billy had 7 coins and he then gave Ali 4 coins.
Problem 2: Grade 2 Problem

Problem 2 is a typical two-step word problem in Grade 2. A what if version for advanced learners - What if together Cindy and David has 15 candies (instead of Cindy has 15 candies.). The class decided that it was probably not possible because candies do no come in fractional parts but the problem is okay if it was about Hersey bars or cupcakes.

Problem 2 Extension: What if .. total number is 15? Is it possible?
Problem 3

What if she ended up with five times as much money as him?

Problem 5 Solution

In Problem 3, which requires advanced techniques of cutting and moving the bars, we did a problem extension. What if .... After Feliz gave Ginny $12, Ginny had 5 times as much money as Feliz (instead of the same amount)?

A Grade 2 version that is accessible even by average and struggling learners: Feliz had three times as much money as Ginny. After Feliz gave Ginny $12, they both had the same amount of money.

In Problem 4, we talked about what by Saturday meant. The class could not decide, so we tried both scenario of the fact that by Saturday meant she had folded 50 paper cranes on Monday to Friday as well as she had folded 50 cranes on Monday to Friday (but 50 is not a possible total given that cranes do not come in fractions).

The class continues on Day 2. These classes is a two-hour course on advanced skills in bar model drawing for K-2 teachers. Typically, bar models are used in Grade 2 onwards. Younger students model with pictures or unit diagrams.

Sunday, June 16, 2013

M4thodology Institute at The Bolles School K-2 Session 17-19 June 2013

Opening Lecture by Ban Har

Photographs of the board and flipcharts are available for downloads and reference.

General Session on Visualization

Classroom Session 1 by Ban Har: Questioning Technique

Classroom Session 2 by Ban Har: Bar Model Method. This class continues on Day 2.

Images of the board are available in a separate blog entry as well as on Ban Har's Facebook Photo Album.

Day 2

General Session on Anchor Tasks

General Session on Assessment

Classroom Session on Differentiated Instruction

Classroom Session on Advanced Bar Model

Day 3

General Session on Generalization

Classroom Session on Math Trail and Use of Literature

This is a two-and-a-half day institute.

Friday, June 14, 2013

Earlybird Kindergarten Mathematics - Planning Lesson, Providing Concrete Experience

This is based on a discussion I have with teachers at The Blake School on planning lesson for a kindergarten lesson. I used Lesson 1.1 in Book A on Sorting and Matching.

See the slides here.

The Blake School, Hopkins, MN

Thursday, June 13, 2013

Singapore Math at The Blake School, Hopkins MN

This week I visit The Blake School which was established in 1900.

History of Singapore Math slides are available here.

Grade 3 Lesson was on subtraction with multiple regrouping. That was a basic skill lesson. Grade 4 Lesson was on looking for a pattern while calculating areas of polygons. That was a drill-and-practice lesson. Both are taught in a problem-solving approach.

- Lesson Structure, Three-Part Lesson Format, Anchor Task
- Planning Lesson - identifying essential understanding for lessons and learning to assess (runway-taking off-cruising analogy)
- Problem-Solving Approach
- Constructivism and other theories CPA Approach
- Visualization, Number Sense and Patterns

Photographs are available on my Facebook.

In the three-part lesson format, the lesson begins with the presentation of an anchor task (in Math in Focus it is the task in the Learn box; in Primary Mathematics, it is the un-numbered task; in My Pals Are Here! Maths, it is the one solved completely).

Features of Anchor Task
(1) Less is More - students are not solving a lot of problems. They are focused on only one (or a small number of related tasks). Student engagement with one task for an extended period of time allows ample learning opportunities for all (struggling learners get the time they need while advanced learners are made to go deeper and presented from going faster).
(2) Multiple Strategies - hopefully the book you use suggest multiple strategies. In any case, an essential step in planning lesson is to anticipate students' responses. Try to provide strategies that can support struggling students (more literal methods) and also challenge able students (more abstract, elegant(?) methods).
(3) Key Question - anchor task allows students to go back to key question again and again ... in the Grade 2 fraction lesson the key question is Are the parts equal? How can you tell?. In the Earlybird lesson, it was Are the things the same? Why do you say so?. In the Grade 4 open lesson, it was What's the area? Are you sure? Do you see a pattern?

Monday, June 10, 2013

Math in Focus 3A - Planning Lesson, Choosing Anchor Tasks

One key step in planning lesson is the choice of anchor task - the one used for teaching. A good starting point is to look at the textbook and ask if the given task is a good one. Good tasks allow the attainment of learning outcomes and allow teachers to challenge advanced learners even as he takes care of the rest of the students.

Today we look at Math in Focus 3A Lesson 4.3 Subtraction with Regrouping. I was planning for a lesson I will be teaching to third graders at The Blake School in Hopkins, MN.

The main method (which is in the textbook) is to develop an understanding of the standard algorithm, which is essentially about regrouping / renaming a numbers to facilitate subtraction.

The alternate method (which is not in the book) is to get students to see 2,598 as 2,500 + 98 ... which make subtraction from 5,000 + 100 + (46) fairly straight forward. 46 can be put aside.

The choice of numbers in this anchor task allows for the alternate method (which teachers may get advanced students to think about) while letting the other students have ample time to master the main method.

The choice of numbers allows emphasis on doubles facts (4,000 - 2,000, 1,000 - 500 and 16 - 8).

It is important for teachers, in the lesson planning process to think about the choice of examples selected.

Grade 4 Lesson