Let's Give Them Something To Talk About! Aliens, Piles of Books, Magic Words, A Bad Engineer, and Bonnie Raitt

 Hi All,

 

Math Talk

Last week a video, this week an article! This blog continues to evolve. :) I originally wrote this piece for https://www.weareteachers.com Which is a very cool website run by some friends. You might want to check it out. 

The suggestions below focus on helping kids to express their mathematical thinking. Ways to get into some serious "Math Talk."

The Bad Engineer

I used to always tell my classes a story about the bad engineer who went to a town council meeting. The council was looking for proposals to build a new bridge for the town. This engineer comes in and shows the council a drawing and a model for his proposed bridge design. They look it over and then ask him why his design is the best. He answers, “Because it just is.”  I would then ask my class, “Would you consider this a satisfactory answer if you were on the council?” There is always a unanimous “No!” in response. I then ask why not, and they usually say something along the lines of “Because he didn’t explain it,” or “He didn’t prove his was the best.” No? Then when you tell me 6 x 8 = 48. Why should I accept your explanation of “Because it just is?”

 

Bonnie Raitt Said It

Being able to explain your thinking is a life skill that is valuable in most any profession and certainly in anything math related. The Common Core State Standards for Mathematical Practice (2000) include Standard 3: Construct viable arguments and critique the reasoning of others. And it makes sense. Students who cannot explain how they arrived at an answer or why it is reasonable are signaling that they don’t really understand what they are doing well enough to articulate it or be confident in it. They may have memorized a procedure or even gotten lucky, but they mostly likely lack understanding.

 

How do we help support students become proficient in explaining their reasoning and develop deeper understanding? Provide them opportunities to do so regularly. Make it an expectation. There was a refrain in a song by Bonnie Raitt where she would sing, “Let’s give them something to talk about.” It probably wasn’t math she was referring to, but the lyric applies to math class.

 

All the prompts and strategies for stimulating discussion in math class, will not be very helpful if we “don’t give them something to talk about.” This argues for rich, interesting, problems. Yes, we need to learn the times tables, and yes, we need to learn procedures for finding the lowest common denominator, but these are just “things.” They are tools for solving problems. So, very simply, math should be learned in a problem-solving context and beginning any lesson with a question or problem helps do this.

 

Piles of Books

For example, rather than saying, “Today we are going to learn about multiplying by fives,” put 8 groups of books out on the floor. Make sure there are 5 books in each group, fanned out so that the number is apparent. Then ask students to sit down in a circle around the books and ask, “How many books are there?” That’s the problem. Now ask for answers and make sure they tell you how they know, what strategy they used, and if one strategy is more efficient (quick and accurate) than another. In this problem, you could count by 1's, count by 5's, or you might recognize that there are 8 groups of 5 so 8 x 5 = 40. All are valid strategies, but some are more efficient than others.

 

The Magic Word is....Because!

In the beginning when students solve a problem and share an answer, you most likely will have to prompt and ask questions like, “Why do you say that?” and “How do you know?” The magic word we are always looking to hear from students is “because.” For example, “I know there are 40 books on the floor because…” Allow students time to think and also to use pictures, diagrams, number lines and other materials to help demonstrate their thinking. In fact, a good way to get at student thinking is to ask very directly, “How did you solve it?” or “Can you prove with a picture, a diagram, or materials, that what you’re saying is correct?”

 

Through regular use of this process, students should come to understand that it is an expectation that they be able to explain their answer to others, telling how it was done and why it is correct. The teacher should not become too directive of the discussion, but should be ready to prompt as needed to get to effective, understandable, reasonable explanations. Students should work with the assumption that whenever they provide an answer, they will be ready to explain how and why they arrived at that answer, unlike our unfortunate friend, the bridge engineer.

 

The Aliens Arrive!

One format my students have always enjoyed in explaining their thinking is when I ask them to imagine that a new student (or even better, an alien!) has just arrived for the first day in their math class. I ask, “How would you suggest the aliens approach this problem? And why?” or “Tell our new friends how you got your answer and why it is correct.” Even when you play a math game together it is reasonable to ask, “What are strategies that worked well in this game that a new player should know?”

Providing opportunities and time for talking about math in class yields big dividends in student thinking and understanding and it’s more fun and engaging too. Especially when those aliens show up. 

 

Math Vocabulary Bulletin Board

To support all learners in their math discussions, but especially ELL students, create a math vocabulary board or chart. As new math terms are encountered throughout the year, add them to the chart. Have students create definitions and illustrations to accompany each new term. This can serve as a handy reference during discussions, writing, and problem solving.

All the best!

Your friend in math,

Bob