October 2016 - Infinite Math Ideas

Feedback is everything when teaching Math

In my 18 years of teaching, I often look back at how I taught then and how different a teacher I am now. Getting better feedback from students has been the biggest game changer for me. One of the first things I warn new teachers that I mentor about it the trap of gauging feedback by watching nodding heads. It’s very easy to say things like “does anyone have any questions?” and assume that silence and shaking heads means they got it.

In this article I’d like to share some very concrete practices (above and beyond the traditional) that were game changers for me. I’d love to hear more ideas from other teachers. Continue reading

Do you speak Geometry?

I had 3 of my own children go through the public school system in my town. Great schools overall. But two things drove me absolutely crazy about their Math education.

Two things that drove me crazy when I was a parent who had kids in high school.

Students were not allowed to keep their tests. As a math teacher this was particularly frustrating because I so wanted to go over my child’s test with them to see what kind of mistakes they were making. I also wanted to help them go over the problems they got wrong. If parents ask me what was most important thing they could do with their child to help them with math, I would say it was to go over their mistakes with them (or have a teacher/tutor do it) so they can learn from their mistakes. I often assign test corrections (for big tests) as an extra assignment because it is so critical to do this for a subject like math that builds upon prior knowledge.
My children’s Geometry teacher (we had the same teacher for 2 of my children) was sloppy about her Geometry notation. I diligently prepped my children how to properly write line segment names, angle names, congruency statements, etc. when they started Geometry. But when I reviewed her worksheets, handouts, and notes that they brought home – she was inconsistent with notations. Math is difficult enough to begin with. If you are sloppy about how you write things for students, it makes it that much more difficult for them to follow. You are teaching them to speak a language called Math.

Pattern learning and why it hurts students

I work with a lot of students after school, many of who are struggling. I always say it’s the best place to learn about issues students are having. Students are more open to discussing their frustrations and you can watch a particular student work for much longer periods of time. I hear this from students (and parents) all the time: “My son seemed to understand it even when I went over the problems with him but he gets it wrong on the test. I can’t understand it”. So what is going on?

One of the first things I learned years ago is that students learn to solve problems by (smartly) recognizing patterns. It’s tough at his age to have a real desire to understand “why something works the way it does” (I didn’t have it at 15 years old). But the problem with pattern learning is that it falls apart as soon as a problem looks a little different.

Example of common mistakes with distributive property

Let me give my first example that I see very frequently that involves the distributive property (of multiplication).

On the left is how students are typically are shown how to distribute. All of the problems they practice look like this so they learn to distribute whenever they see a number next to a parenthesis – without a thought as to why they should do it. But when they number appears on the right side of the parenthesis, they don’t know what to do (even though it is still multiplication and the 2 should be distributed).

pattern1

Using your Seating Chart as a GPS for teaching Math

Math class seating chart with markups about each student.

One of the first tips I give new teachers I mentor is to create a seating chart for all of your classes. The next tip is to get new ink for your printer because you’ll be printing new versions often! On day 1 of classes, my students walk in and the seating chart is on the Smartboard with their names on a desk. Here is what I use my seating chart for:

To learn student names quickly.
To know at a glance who has a low average (so I can call on them or visit their desks more often).
To be able to identify relevant special learning accommodations such as who struggles with attention disorders or who needs written instruction over verbal.

Here is a (fictitious) sample of one of my seating charts. I slip it into a plastic protective cover and carry it around with me during class. Note I do not actually write the key I included here (it is in my head). Here is how organize my codes: Continue reading

Infinite Math Ideas

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