Teaching Algebra Archives - Infinite Math Ideas

8 things to consider as I start my new year.

My top 8 list for 2017-2018…

At the start of each year I try to set some goals (and reflect on things that worked well the previous years). I thought I’d share them here.

Math class seating chart

Code your seating chart.

My laminated seating chart has all kind of information about each student – especially learning needs. See this article for more about this.
Try something new.

This year I’m going to do a lot more with our new edulastic.com web service. It’s going to allow us to quickly create small assessments (such as a 3 question exit ticket) to get better and instant feedback as to where the class is. Try using desmos for graphing or perhaps socrative for getting quick feedback. Don’t simply do the same thing as last year – it’s an easy rut to fall into. Continue reading

You CAN teach a new dog old tricks!

Even Chloe knows to go to infinitemathideas.com for Math help!

Welcome Chloe fans! I want to throw Chloe a bone (literally) for providing the first external link to our Math blog! Although she has thousands of subscratchers and this blog only has 12 (counting my mother…), we feel it’s a fair exchange. Here is the email exchange that started Chloe’s love of math! Chloe fans who have children in school may want to read this article.

So on the topics of old tricks for new dogs, I want to talk about a better (in my opinion) way to teach (and learn) logs (think really large sticks Chloe…). Specifically converting to and from exponential forms.

Bacon and Eggs go Vegan.

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

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

Tip for getting nice function graphs onto your Smart Board

Desmos graph pasted into Smart Notebook. No way my handwriting is that neat!

If you use a smart board and you graph/discuss functions as much as I do, I think you’ll love this tip. Even some of the veteran teachers in my dept. loved this and didn’t know how easy it was.

September means PEMDAS season.

I give this substitution problem every year in my summer Algebra I refresher class. The mistake they almost all make, is a classic PEMDAS problem. So I teach order of operations rather strictly as illustrated in the example below. Here are 2 things essential things I teach them:

Do only ONE level per line (M/D and A/S are the same level). Put the letter(s) you are doing next to each line.
Do NOT drop parenthesis until the M/D line (i.e. leave them in the

Here is a typical PEMDAS mistake students make:

Matter, Anti-matter and “Cancels out”

explosion Matter and anti-matter cancels out (violently I might add). The airlines can cancel your flight. You can’t cancel out in Math (instead you “reduce” or “divide”). If you do try to cancel out, bad things can happen. Let me explain.

Our Department abolished the phrase “Cancels out” a long time ago, and now we use phrases such as “reduces to 1“, “divides to 1 over 1“, etc. which demonstrates the math operation not some magic. We also always replace numbers and variables that reduce with a number even if it’s one (see below right).

Infinite Math Ideas

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8 things to consider as I start my new year.

My top 8 list for 2017-2018…

Code your seating chart.

Try something new.

You CAN teach a new dog old tricks!

Bacon and Eggs go Vegan.

Feedback is everything when teaching Math

Pattern learning and why it hurts students

Example of common mistakes with distributive property

Using your Seating Chart as a GPS for teaching Math

Tip for getting nice function graphs onto your Smart Board

September means PEMDAS season.

Here is a typical PEMDAS mistake students make:

Matter, Anti-matter and “Cancels out”

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Show articles for:

More Categories:

Archives

My top 8 list for 2017-2018…

Code your seating chart.

Try something new.

Bacon and Eggs go Vegan.

Example of common mistakes with distributive property

Here is a typical PEMDAS mistake students make:

Welcome!

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