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Math Matters

Getting To Deeper Thinking

Math MattersGetting To Deeper Thinking
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Process over Product

As a young teacher, I often used a lot of direct teaching in my classroom to "throw" content at my students in hopes that they were thinking and learning. I was naive to think that they were as interested as I was lol.


I soon learned that like the "wacky wall walkers" I played with as a child, this content was not sticking and I needed to reinvent how my students were interacting with the content. I want students to really engage in the classroom so they can think about processes they are using, why they work, when they don't, and get beyond just answer finding.


In this newsletter, I'm going to share just a few thoughts on how to get students to do more engaging and more thinking about your math content, rather than always focusing on direct teach and worksheet practice.

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Correct/Incorrect or True/False?

Analysis of other student work is powerful for getting students to really focus on the process rather than just the answer. Instead of giving students a sheet of problems to solve, give them problems that are already worked and have them find the ones that are incorrrect or false statements. Then extend by having them make corrections and talk about common errors. They are less likely to make the common mistakes with that heightened awareness of them.
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Who is Right?

Taking it one step further, instead of giving one answer, either right or wrong for each problem, have them explore two processes. In the example shown they compare two solution processes and choose the correct one. You could also present two correct solutions that are different just to throw in a chance to talk about multiple paths to the same answer.

Use this structure as a chance to talk about reasonableness. Role play with is happening in the situation and discuss if the answer should be larger or smaller than the numbers in the problem, and WHY!

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What's the Process?

Matching problems/answers on cards definitely makes typical "worksheet math" more engaging. And knowing that you can match an answer to each question can help build confidence in struggling students before committing work to paper. But sometimes they don't really understand how they got from problem to solution. Try first matching problems to a process card. This opens the door to a discussion about multiple paths to the same answer. Extend by having students create process cards that describe the way they might solve it. After that you can match answer cards to complete the process.

Always, Sometimes, Never True

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I just LOVE this structure. It is versatile enough to be used as a pre-assessment, an instructional activity, or a formative assessment, but it really helps students get to thinking deeply about what they understand on a topic. I have 5 different versions so far and there are endless topics you can incorporate.

In the activity, give students statements to analyze about a topic. They decide if the statement is always true, sometimes true, or never true. So much thinking goes on! You can extend by having students talk about how to change statements to move them to another category, or even have them create a statement of their own for each heading.

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Current Reading

I love a good book that actually describes changes I can incorporate that make a positive impact on student learning. I'm reading Hacking Mathematics: 10 Problems that Need Solving by Denis Sheeran currently. This would make an awesome book study for a campus team because you could try out the strategies he suggests together as a team, support each other, and gain support of your admin as a team of teachers working on your craft.
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How can I serve you?

I would love to help you. I specialize in turning tedious work into hands-on fun. I serve teachers through learning opportunities and creating & pre-printing materials to give you time back for other things that are important to you.

If you like what you see here, visit my website or email me anytime.

Kelli

Email: integralmathematics@gmail.com
Website: www.mathcutups.com
Phone: 214-471-5760
Facebook: https://www.facebook.com/MathCutUps/
Twitter: @Mathcutups

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Professional Learning

Ideas from this newsletter are a part of a larger presentation, and can be easily applied to any grade level and content. If you need more ideas, I would love to learn with you. Reach out to me if you are interested in professional learning on your campus.


Here's where I'll be presenting next in case you can come:

DFW Mini-CAST in HEB = February 8

Dallas ISD (8th grade) = February 14

Pan-STEM conference, Lubbock = June 30-July 1

CAMT, Ft Worth = July 8-10