Thirteen Ways of Looking at Multiplication Tables

Looking for the surprising in the familiar, we see what happens when you look, really look, at the multiplication table and tumble through the looking glass.

I once taught a poem by Wallace Stevens called “Thirteen Ways of Looking at a Blackbird” to a class of adult literacy students. Before I gave out the poem I put the title on the board and asked students what they thought the poem was going to be about. They had all kinds of ideas about looking at blackbirds. Then I asked them, “What about the first part? What does that mean Thirteen ways of looking at a blackbird?”And they said things like:

• “Thirteen ways to understand the bird is better than one… but you have to take time to see the bird.”
• “If you look at the bird you will find all the different things it does, but you have to look closely.”
• “We don’t pay attention to these things and he wants us to focus.”
• “He stopped to pay attention to something so maybe we will too.”

Multiple Factors

Several engaging activities for exploring factors. Which would you use for HSE math classes and how would you use them?

I puzzled over what to bring to today’s meeting for days. I have a couple unfinished problems that I’ve been thinking to bring to a CAMI meeting, but in the end I chose to go with a few activities on factors, mostly from Fostering Algebraic Thinking, by Mark Driscoll. A group of us read the book last summer and loved the problems. There were so many good ones that we weren’t able to solve them all while reading the book. I went into this meeting hoping that the surprise of the central problem wouldn’t be ruined. Continue reading “Multiple Factors”

Exploring Algebraic Thinking in a Math Teachers’ Circle

How to use an inquiry-based exploration of visual thinking to develop algebraic thinking in our adult numeracy and hse classes.

Eric, Solange and Mark led a webinar called “Exploring Algebraic Thinking in a Math Teachers’ Circle”, revisiting a workshop that we gave at the 2015 National COABE Conference. This webinar focuses on an inquiry-based process of algebraic thinking through use of visual patterns and multiple strategies for problem solving, including drawing, different ways of seeing, making charts/tables, and making predictions using rules. Facilitators model an open approach, having students generate their own problems and also discuss how to help students analyze and connect different solution methods and how to bridge visual thinking into algebraic thinking.

Exploration of Consecutive Numbers

In this meeting, Usha returned to lead an exploration of consecutive numbers through a low-entry, high-ceiling problem she recommends as an introduction to functions/algebra.

For our June meeting, we were lucky to have Usha Kotelawala, Director of Math Education for CUNY’s LINCT to Success, as a guest presenter. Usha started the meeting by talking a little about her thought process in choosing today’s problem. In discussing CAMI with Usha, Eric had raised the issue of how to order problems through a semester, so that the mathematics is sequenced and scaffolded for students and students learn through problem-solving. In response to this question, Usha brought us a problem she recommends as the first in a sequence on algebraic reasoning. Continue reading “Exploration of Consecutive Numbers”

CAMI Roadshow: 2017 COABE and NYC Adult Basic Education Conferences

CAMI did a few workshops in April, sharing our teaching circle’s work on exploring real-life math through three-act math tasks.

Eric and Mark did a workshop at the 2017 COABE Conference in Orlando called Mathematical Modeling: Questions from a Math Teachers’ Circle. A few weeks later at the NYC ABE Conference, Brian took the lead and together with Mark and Eric did a similar workshop called 3-Act Math Tasks: Let Students Build the Problem. Continue reading “CAMI Roadshow: 2017 COABE and NYC Adult Basic Education Conferences”

Making Trains from Cuisenaire Rods

Inspired by Mathematical Mindsets, by Jo Boaler, we explored questions related to “trains” made out of Cuisenaire rods.

A few of us are reading Mathematical Mindsets, by Jo Boaler, as part of a book group on LINCS that will start this coming Monday, April 17th. The book is similar to Boaler’s other writing in that it cites evidence of recent work in brain science to show that everyone can learn, that the brain is plastic and grows like a muscle when used, and there is no such thing as math people and non-math people. Boaler also argues for an approach to developing growth mindsets that is rooted in mathematics. The book  includes examples of low-entry, high ceiling problems that can be used to develop mathematical mindsets. Continue reading “Making Trains from Cuisenaire Rods”

Multiple Ways of Multiplying

We explored multiplication through a number talk and alternative algorithms for calculating products.

Before the meeting, Davida showed Rachel and me a multiplication method a student had showed her earlier in the day. The student said that she only knew how to do multiplication using the method on the right and wanted to learn the method on the left. What a coincidence! This is exactly what I was planning to explore today.

Carl’s Basketball Problem

With a simple set up, CAMI enters a rabbit hole of notice/wonder and number patterns.

At our meeting, we worked on two tasks that I got last summer at a gathering of teachers from the K-12 system called NYC Twitter Math Camp.

The first is an activity teachers can use to develop group problem-solving norms with students. Continue reading “Carl’s Basketball Problem”

Keep it in the Family (with Pythagorean Triples)

Many of us are familiar with the 3, 4, 5 right triangle, and maybe the 5, 12, 13. Do you know any others? Is there a pattern to these triples?

As we came in the room, Eric asked us to place a post-it with our name on a voting spectrum he’d drawn on the board, ranging from “Never” to “This morning” under the statement, “The last time I thought about multiplication”.

As we settled in, Eric shared his goals for the meeting. He’s been working on a lesson for students combining some work he’s been doing on area models with a problem that has been consuming him for weeks. Continue reading “Keep it in the Family (with Pythagorean Triples)”

Signed Number Pyramids

Using number pyramids to practice adding signed numbers leads to a surprising discovery.

Jane started the meeting by telling us that her class has been studying signed numbers recently. She has been looking for creative ways for them to understand adding and subtracting signed numbers. One example was to imagine taking away negativity as the same thing as making someone happier.