What’s going on?

In 2016 a large cohort of Year 5 students had lots of trouble correctly identifying how long a length measure was when the cm tape measure didn’t start at 0. Only 42% of students surveyed answered correctly (5 cm). This year, in 2017, Year 3 students are overwhelmingly successful at correctly identifying a similar measure using informal units. Too many swings and roundabouts for me.

When you analyse the incorrect responses, 46% of these Year 5 students selected the answer which was just one more than the correct answer (6 cm). In other words, they counted the 6 marks on the ruler, counting up from the first mark as 1 rather than 0. What on earth do they think length is about? The ruler measures off units of length and the marks in themselves are not the units. Perhaps too many Year 5 students have experienced pen and paper experiences? Or had too strong a focus on the ruler or tape measure marks rather than the actual length of a unit.

So what do we discover when we analyse the Year 3 response to a similar question? This year’s question was open-ended rather than multiple choice. But in itself this doesn’t explain why so many more students were correct. In fact this year’s question was more difficult as it involved far more units (13 units and last year there were only 5 units). We don’t know how many students answered 14 units, but 81% of Year 3 students answered correctly anyway. This is a dramatic change in behaviour and understanding with the 2016 Year 5 cohort.

I believe that there is a glaring explanation. This year’s question talks about measuring with blocks placed end-to-end. In other words, students are virtually told how to interpret the ruler in the diagram. They are told to see it as blocks in a line. So of course they don”t focus on counting up the marks (which would include the mark at the start to get 14).

This explanation has major implications for how we discuss length units with all students. We need to continuously reinforce that length represents units like blocks. We need to talk about the misunderstanding that creates the blockage for the majority of older students.

Length is not just a measure of marks on a ruler. When your feet are together at the start of a number line you have not moved. You are at 0. It is only when you jump a unit of length that you record 1. This concept needs reinforcing with all primary age students. A ruler is conveniently marked to show where these length units reach. Whenever we begin to measure though, we always start at 0. Even if the ruler shows an object starting at 27, that starting point should now represent 0 in a new counting sequence. If an object starts at 108 on a ruler, 108 should now be seen as 0 in a new counting sequence. Even if an object starts at 389 on a tape measure, 389 should now be seen as 0 in a new counting sequence.

Let’s hope that we can make these length understandings part of all our student’s spatial visualisation skills.