Edited by Megan Schmidt (@veganmathbeagle)
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This Week at Global Math

Math Fights and Middle Bits

Presented by Rick Barlow and Shira Helft

Pushing students to think, write and talk clearly about their mathematical ideas is challenging. In our experience, structures are key to supporting all students to communicate and justify their thinking well. In this session we will share two participation structures we have used to scaffold students’ mathematical communication & the thinking behind it. Teachers will also brainstorm how to integrate and implement participation structures like these in their classroom.

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Last Week: What is the MTBoS and How Do I Join?  View recording here.  

Four Pillars of Homework

Once again, I read something on Elizabeth Statmore’s blog (“Cheesemonkey Wonders”) that made me fairly jump out of my seat. It’s getting to be something of a routine. Exhausting, but wonderful.

This time, Elizabeth described her four pillars of homework that she will implement next year. They all sound easy to do, and highly impactful. As a matter of fact, one of them reminded me of what some math teachers who flip their classes do, that is, have students spend the first ten minutes working together to review and discuss their learning. 

The other practices are lagging the homework behind the classwork by about a week, changing the role of the teacher, and collecting all homework every two weeks. The one about lagging homework is the one that made me jump out of my seat – what a simple idea, brilliantly described and justified by Henri Picciotto on his blog to which Elizabeth of course refers in her post. 

The most incredible thing to me is that I never would have heard about any of it if I hadn’t been on Twitter, so that I could see Fawn Nguyen’s tweet about Elizabeth’s blogpost about Henri’s idea. How do I love thee Twitter? Let #MTBoS count the ways.

(Written by Audrey McLaren - @a_mcsquared)


Increase the Use of Number Lines

Following our theme of repeatable classroom structures, I wanted to share an older post from @tracyzager. In Building Number Lines in Kindergarten, Tracy demonstrates the power in physically modeling, but even more important, the use of number lines. Number lines hold so much power in showing what students know and understand about numerous concepts. Yet, they are widely underused.

Through questioning, Zager and the classroom teacher were able to get these kindergarteners to order given numbers and consider the intervals between each number.  The use of the number lines naturally prompted students to use SMP 5 Use appropriate tools strategically, which led to SMP 2 Reason abstractly and quantitatively and SMP 3 Construct viable arguments and critique the reasoning of others.

This post will inspire you to get the conversation started to increase the use of numbers lines in your classroom.  This will aid in determining more ways to incorporate number lines in your classroom.  I’m definitely inspired.

Written by:  Jenise Sexton (@MrsJeniseSexton)

Hints In the Classroom

One of the strategies my math department has been using this year to scaffold lessons has been to offer hint cards to students that seem to be struggling on a given task. Unfortunately, I have found that many of my hint cards are either are too vague like, "create a table" and don't help students any further or my hint cards become: "Fine, I'll practically give you the answer" card -- my cards give too much away of my thinking and limit the thinking of my students.  In his ShadowCon talk, Michael Pershan says, "Hints are a lost art for most teachers".  He offers four problems with our reasonings, which he calls pedagogical sins.

1) Our hints are too vague. Been there.
2) Our hints kill thinking. Done that.
3) Our hints don't have reasons. Just do it. Right?
4) We improvise too much.  All day. Every day. I do it for a living.

His suggestion: Add context, add reasons, and be specific enough. 

In response to the talk, Anna Blinstein shares that she isn't comfortable with hints because she finds they generally "funnel student thinking in a predetermined direction" and remove most of the exploration a student would do on his or her own.  She offers a broader view of hint to include questions that push students to think and develop strategies on their own.  She provides with some great questions that can be used as guiding questions (or hints if you prefer): (What information would be helpful to get unstuck? What things do you think that you know? What don't you know?)

While Henri Picciotto finds these may be helpful for some students, they may not benefit a student who has considerably lacks confidence in his or her abilities and needs more than just these general questions to begin. He makes the argument that even in a student-centered classroom there is interaction between teachers and students and the role of the teacher is to provide support. Sometimes, this support comes in the form of standing back and observing, other times in the form of the questions provided by Blinstein, and other times it comes in the form of a more specific hint.  

Make sure to check out these blog posts and listen to Michael Pershan's entire short talk and share your own thoughts on this issue!  What do hints look like in your classroom?

(Written by Umussahar Khatri - @KhatriMath)
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