Types of Mistakes

  After discovering what the four types of mistakes are, I went looking for more information.  In the process, I stumbled across a website devoted to looking at student math mistakes.  The site "Math Mistakes" is a place where teachers can submit student errors to share with others.

I like that there are two indexes associated with this site.  The first is listed according to subject and the other is broken down by grades and are aligned to the Common Core Standard.

The latest example shows a circle with the following questions.
c. How many lines of symmetry.    Answer  - 1000
d. Explain why each line of symmetry cuts a circle in half?  Answer - I don't really know
e. Explain why each line of symmetry must go through the center.  Answer - Because it wouldn't all match up.

The owner of the site asks two questions about this.
1. How do kids come to see lines as having no thickness at all?
2. What experiences would support that change?

Questions that really  have me thinking about it.  I'll be teaching this in a couple of months, so this is important for me to think about before then.  It also alerts me to possible problems on this topic.

I checked out the trig problems and the first one was on using the law of sines.
the problem was set up correctly but when the student began solving it, he or she replaced the x in sin x with the value of 10 rather than making it 10 sin x.

He talks about three categories of mistakes that most students make.

1. Mistakes Due To Limited Applicability of Models
2. Mistakes Due To Applying Properties of a Familiar Model in an Less Familiar Situation
3. Mistakes Due to Quickly Associating Something In Place Of Another

He went on to classify this as a mistake of the third type.  Its not that the child did not know the material, just went a bit fast.

I plan to check out more of this site as I prepare to teach binomial multiplication.  I already know most of my students will multiply the first two terms and the last two terms and forget the middle term.