Tuesday, July 14, 2015

Intentional Talk Book Study- Chapter 4 "Why? Let's Justify

This summer I am participating in the Summer Book Study on Twitter hosted by @BridgetDunbar

I joined this book study because I really want to learn "how to structure and lead productive mathematical discussions" in my 7th grade math classes this coming school year.  I use the workshop model of delivery and students already do a wonderful job of working collaboratively.  I would like to improve the mathematical discourse during group work time and during whole class discussions.
We use a lot of Disciplinary Literacy Strategies in our 7th grade math classes.  Below is an example of one of those strategies, called the "Do/What" Strategy.  We use this with our students to get them to give a good and complete justification of a problem they solve.  We start using this strategy right away with our first chapter.

Question 1:  What are some math rules or tricks your students use that you would want them to better make sense of and justify?  When we are dividing fractions and we need to make the divisor a whole number I make sure they explain that moving the decimal the same number of spaces to the right to make the divisor a whole number, we are multiplying the divisor and dividend by 10, 100, etc.  I always make them explain that the decimal moves right or left because of multiplication or division.

Question 2:  What classroom routines or structures do you incorporate that encourage students to notice patterns in which to justify? We are constantly looking for patterns in our math class.  An example is when multiplying integers.  Multiplication is like repeated addition. Ex) -3 x -4 Means "the opposite of three groups of -4", " the opposite of -4 + -4 + -4" which would be 12.  

Another way is to have students extend the pattern:
-5 x 5 = -25
-5 x 4 = -20
-5 x 3 = -15
-5 x 2 = -10
-5 x 1 = -5
-5 x 0 = 0
-5 x -1 = 5
-5 x -2 = 10
-5 x -3 = 15

Question 3:  What is the most common form of justification you hear/see from students?  Why do you think they justify that way?  I think I really have to move students beyond just showing their work/procedures when solving problems, to a deeper level of reasoning mathematically.  I want them to have a conceptual understanding, not just procedural fluency.

Question 4:  Reflecting on the Why? Let's Justify Template, How do you support student thinking during justification?  If they say _____ I may ask _____.  
I tend to ask questions like:
How do you know that?
Can you explain that with more detail?
Can you give me another example of what that would look like? 
I think it is really important to make sure students focus on using correct mathematical language. They need to use correct vocabulary in the context of the problems.  Students often have to be pushed to specify thinking with strong math terms instead of vague language.

Question 5:  What next steps would you like to take in facilitating discussions that incorporate justification?  
I think it's really important for me to model what a good justification answer sounds like.  I want them to justify reasoning and their mathematical thinking, not just the procedural steps in solving a problem.

I really enjoyed this chapter.  We focus quite a bit on justification in our math classes, as it is one of our three report card standard we use with Standards Based Grading.  I really like the strategies presented for encouraging better justification during class discussions.

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