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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.
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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).
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Does your child ever say to you “I’m just not good at math”?
Does this sound familiar to you? Your child in high school cannot seem to get higher than an 80 (or low C) average in a non-honors level Math class. You feel like he/she is trying but get frustrated easily and they often give up quickly. They might get “careless mistake” comments on assessments. They tell you they hate math class. You might feel that the teacher can’t connect or reach your child. Your child will tell you they don’t like the teacher’s style and they can’t understand how they present information on the board. They do well or average in other subjects except math (and perhaps Science). You may have even tried private tutors. The tutor will tell you they seem to understand what they went over but they still get poor grades on assessments. Continue reading
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:
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 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).
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I can’t stress enough how important extra help is to being successful in Math. Some of the highest average students in my Honors sections got there because they came regularly to extra help. Another benefit is that a teacher that you might feel is not very approachable, is usually a lot more so at extra help where they aren’t trying to manage a large class.
The problem sometimes is that students don’t know how to get the most out of extra help.
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 A place to record problems you struggled with One of the tricks I suggest to all my students is to create a page filled with all the problems you struggled with or got wrong during the past unit. (I call it the “I got pwned page” – pwned is teen-speak for getting destroyed by something). I suggest students use the last page of your notebook because it’s always easy to find. They should record either a reference to the problem (problem #, worksheet, etc.) or simply copy the problem down.
The night before the test (or a couple of nights before the test!) they should do all of these problems first as part of their practice. Hopefully they have solutions to these problems in their notes. They then check the solution v. their work. If they get it right, just cross it off! If they don’t, come back to it after doing all of the other problems and try again.
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Contrary to popular opinion, I feel that students should be doing math more often than taking notes. A binder (3 ring) should be used for the technique described below. Note taking should be minimal (better to watch the teacher more and then eventually do problems yourself!) and here is how I teach all my students to do it.
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Welcome! My name is Scott Campbell and I am a High School Math teacher. Welcome to my math blog. Find out moreIt’s all Free! Please copy and use anything you find on this blog with your classes.
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