Contexts for Puzzling and Math Discourse

Wouldn’t it be great to have lots of  instructional materials that help us develop contexts to engage students in puzzling through math problems.  I’ve found that Cathy Fosnot’s Contexts for Learning Mathematics units do just that. http://www.contextsforlearning.com/

For those of you not familiar with these materials, they include units for K – 6, each taking about 2 – 3 weeks, and using activities, games, and mini-lessons to develop grade level concepts and skills.

Discourse is an essential component of each of these units.  As students investigate a unit’s context and questions, they share their findings and reason together in pairs and in whole class discussions.  Each unit guides teachers in facilitating the discourse, referred to as “Math Congress”, suggesting questions and representations that engage students  in making sense of the math. Discourse is also an important part of the wonderful number string work in these materials.  In these number strings students work together to make sense of related problems that designed to strengthen students’ mental computation skills.

I’ve particularly enjoyed working with teachers and students with the following units (for descriptions click here ):

Bunk Beds and Apple Boxes in K

Organizing and Collecting in 1st grade

The Double Decker Bus also in 1st grade

Ages and Timelines in 2nd grade

The Big Dinner in 3rd grade

Muffles’ Truffles also in 3rd grade

Field Trips and Fund-Raisers in 4th and 5th grades

The California Frog-Jumping Contest in 5th grade

It was actually work in these units in a first grade that led me to write my Use Your Math Power books demonstrating students engaging in productive math discourse.

A Good Next Move?

Discussing strategy with games is a great way to engage students in talking about their reasoning.  We often use games in math class. We can engage our students in  productive discussions if we have students work together to consider next best moves.

Nancy Anderson recently taught this simple but flexible game at an ATMIM  meeting in January.  Once we understood the game she had us think about the next best move for a particular scenario.

I am calling the game “Guess My Problem”.  It’s like Hangman, only it’s about making math equations.

Here is an example of how you could play it with 2 digit + 2 digit addition equations.

“Guess My Problem” (Like “Hangman”)

Try to use as few moves as you can.

Player 1 writes down the equation with blanks and the list of digits.

Ex. __ __ + __ __ = __ __

Player 1 records the equations with numbers in a hidden place.

As Player 2 guesses digits, player 1 fills in the blanks guessed correctly and keeps track of the numbers tried and the numbers eliminated.

So here is where we can start thinking about strategy:

After 3 moves, one game looked like this with two digits left to be placed:

__+­ ­­­­__ 1 = ­­­ ­44      Correct Guesses             Numbers Eliminated

1,  4                                           7

What is the best digit to guess next? Why?

 Challenge students to reason as a class about best moves.  Play it with larger numbers or different operations.  I’d love to see parents playing this with their children as they wait in a restaurant or for an appointment!

Thanks to Nancy Anderson, co-author of Classroom Discussions in Math,  for teaching this at ATMIM in January.

Kids Discuss Using Math Power!

I had a lovely visit in a Boston Public School 1st grade today.  Several weeks ago the teacher read Monkeys for the Zoo to the class, and they discussed the story.  Today I reread most of the book to them, and we discussed how students can use their power in math!

Before rereading the book, I asked them to think about what Ms. Green means when she says, “Use Your Math Power”.  After listening to the story, the students shared ideas about:

  • What it means to”Use Your Math Power”
  • How the characters in the book use their math power
  • How each of them use their math power, especially when something is new

These first graders talked a lot about the importance of thinking and learning from each others’ thinking.  They discussed the importance of listening and sharing ideas with classmates.     Many talked about how they can use their math power to try different ways, an important component in Monkeys for the Zoo.  Then they each got to write about how they can use their math power.

Here are some of their reflections.

“I can use my math power by thinking and sharing ideas and by trying different ways.”
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“I can use my math power by thinking and listening.”
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“I can use my math power by using thinking and talking to my partner and looking back in the book.”
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“I can use my math power by if you get a new problem and if some one else does not know how to do it you can talk with your partner and share your ideas.”

We talked a lot about how nervous Mia was when she took a risk and shared her answer.  The class said Mia worried that she might be wrong.  We all acknowledged having similar experiences.  We talked about how Ms. Green helped her feel okay about taking a risk.

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“I can use my math power by thinking and trying different ideas and risking myself.” Thought bubble:”OK”.

It was lovely hearing the students thinking about how they can engage in math.  I think conversations like this stimulate students to engage more productively in math class.