If you just heft two objects in your hands, like in this picture, it is easy enough to describe the objects as either lighter than, the same mass as or heavier than each other.
But is becomes a more challenging task when you look at a diagram and need to read something important in it. For example, in the diagram below, you need to see that the object on the left pan balances the 5 objects on the right pan. That tells you something. That tells you that 5 tomatoes have the same mass as one bottle. Or it may even tell you that one tomato has the same mass as one fifth of the bottle.
If you analyse what you see in the two diagrams below, this time you see that 5 small yellow balls are heavier than a large yellow cube. But the second diagram tells you that those same 5 small yellow balls are actually lighter than the large yellow sphere. Both diagrams need to be looked at to work out which object is the heaviest – the large cube? The large sphere? Or the 5 small balls?
In a recent numeracy test, 70% of Year 3 students were correctly able to identify the least heavy mass from a sequence of diagrams. Yet last year, in 2016, only 67% of Year 5 students could correctly identify the heaviest mass from a similar diagram. After two more years of school. ARRGGGHHH!
Does this mean the Year 3 students are dramatically improving their understandings? It’s so difficult to know how to respond to these results.
The test diagrams show a set of balance pans with one only object in each pan. Some show the objects as equal in mass. Some show the objects as lighter or heavier than each other. You need to use your mass logic to look at each diagram, understand which object is heavier and then transfer this realisation to the second or third diagram. In other words. You need to go beyond your first response, your first diagram.
In this year’s test 11% of Year 3 incorrectly selected their first response. What they selected was correct if there was not a second diagram giving you new information. In other words it was their problem-solving skills that let them down. For these one in 10 students, they need to practice perseverence, rereading the question, making time for the problem to become real, making time for them to use their correct understandings of balance pan diagrams. They do NOT need to be taught how to read a balance pan. Their mass thinking is correct but they just didn’t carry it on far enough.
In last year’s test 27% of Year 5 incorrectly selected their first response. Again, it was their problem-solving skills that let them down, not their ability to read meaning into a mass diagram. This is reinforced by the very small number of students who selected totally incorrect answers from the multiple choice. So 67 + 27 = 94. That’s potentially 94% of Year 5 students who could have been correct – a much more reasonable expectation for Year 5.
So, as teachers, we need to think carefully about what test results actually reveal. We should place more emphasis on developing problem-solving skills than reteaching known mass concepts. All students need time to solve a multi-step problem (of course not in a test situation …). They need to reread the question to see that they need to go further than their initial reaction. They need to use logic when they think about their answers. They need to develop pride in being an effective problem-solver.