Community of Adult Math Instructors (CAMI)
teachers learning math together
In another edition of revisiting problems from the CAMI vaults, at this month’s meeting we went back to further explore a number pattern we first looked at in January 2017 (Carl’s Basketball Problem).
We started off discussing WHAT IS SIMILAR? WHAT IS DIFFERENT? looking at these four expressions:
2024 marks the 10th anniversary of CAMI (!) and to honor all we have learned and all the ways we have grown as a group, we are going into the vaults for a few CAMI meeting, to reopen and revisit some of our early explorations together. This month’s meeting was a new take on a problem we explored in June 2016 at Making and Testing Conjectures: The Diagonal Problem.
We started with a Which One Doesn’t Belong?
In the December evening meeting, Amy Vickers led us through a new exploration that was loosely inspired by last month’s meeting on some circles.
As a warm-up, Amy presented us with this question: Why might a manhole cover (or, in the gender-neutral, maintenance cover) be round? One of the central ideas that came up in the resulting discussion was that a circle won’t fall through its own hole, no matter which way you turn it. It has a constant diameter, or constant width.
In CAMI Meetings and in class with students, we often want a prompt to get students generating their own mathematical questions to answer, rather than giving them a predetermined math problem that everyone needs to solve. In the November evening meeting, we started off by considering some prompts and sentence starters to get students asking questions that will lead to math explorations.
Here are a sentence-starters that we came up with:
And a few questions we can ask to get students thinking mathematically:
What questions do you ask students to get them thinking? What kinds of questions do you want them to ask themselves?
Whole Group
We started this meeting with a Which One Doesn’t Belong which also included talking about what the four pictures have in common:
Annie Perkins is a middle school/high school math teacher in Minneapolis, MN and she has been sharing a daily math art challenge every day since the governor’s made the call for everyone to stay at home. As I write this, we are going on Day 19.
Continue reading “Math Art Challenges”We learned how to draw interlocking knots and investigated mathematical questions related to counting features of the knots.
We started by looking at a few Celtic knots and thinking about what we noticed and wondered.
Maybe you’ll take a few notes before you move to the next page…
Continue reading “Celtic Knots”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.
Continue reading “Exploring Algebraic Thinking in a Math Teachers’ Circle”
Draw a rectangle on grid paper and draw a diagonal. Is there a way to predict the number of squares the diagonal will pass through?
I have been thinking about MP3 from the Common Core, specifically about how to get students to make conjectures, to test those conjectures and to refine their conjectures when it turned out they were not always true. I was also thinking about student perseverance and helping them not get too frustrated. I’ve done some activities like Marilyn Burns’ consecutive sums problem (see additional resources below), but I want something that feels messier and a little more unwieldy. Continue reading “Making and Testing Conjectures: The Diagonal Problem”
Facilitating a meeting in Dallas, while live-tweeting with teachers in NYC, we explored a visual pattern to model what our teachers’ circle is all about.
This CAMI Roadshow involved about 35 teachers in a ballroom at the Sheraton at the 2016 COABE conference and 3 additional teachers who were back in NYC, participating through Twitter.
We wanted to maximize teachers’ time working on the problem but we also wanted to convey some important norms about how we run CAMI meetings, so we began with an ice breaker. The instructions were simple. First, everyone sat down (including the facilitators). After that, the only goal was that there be 5 people standing and the only rule was we had to do it without talking. Continue reading “CAMI Roadshow: COABE 2016”
