## Wednesday, April 20, 2016

### Measuring Up

I was in a grade 6 class yesterday and a couple of quick questions really made me understand why students might have some measurement misconceptions: they see something like length as a count and not a measure
This was the first question:

We were expecting some answers of 15cm but in actual fact, there were very few of these. The most common answer was 9cm. They weren't measuring, they were counting. But they started the count "1" at the '7' mark, then "2" at the 8 mark and so on. Now, both myself and the class teacher were pretty sure that if we gave the students a proper ruler, they would have been more successful, but is this because they are actually measuring or merely reading a number?
The second question revealed the extent of this misconception though:
The majority of the students circled the correct answer, c. We then asked the students to explain how they got their answer. Some gave this:
It was the same mistake seen in the first question! These students were counting dots, not measuring length. It was clear that they knew how to calculate area of the two shapes, but were using the wrong values.
Others gave this answer:
These students were again counting to get the length/base and width/height, but this time were counting the dots inside the shape to do so!
It is perhaps not surprising why students should have this misconception. All their measurement experience from primary years is based on using a count to get a measure. So they have developed this misconception that measurement is discrete not continuous.
So how do we change this? Well, we started by using the response to the first question to create a contradiction: