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# Summer School Insights: Week 4 Decimal operations

Craig Barton

Hello everyone,

This is the fourth post in our Eedi Summer School series, where I provide insights from the cohort of Year 6 students who are taking part in our seven week programme. My hope is that this may give you an indication of where our Year 7 students might struggle come September.

The subject of Week 4’s quiz is Decimal operations

Our group of 10 and 11 year olds did really well on this quiz, scoring an average of 82% across the 10 questions.

Here are the proportion of students getting each question correct in reverse order from the most poorly answered to the best answered:

We can see that Question 7 is the one that caused our group the most problems. What is Question 7, I hear you ask? It is this…

Take a moment to consider where you predict students might go wrong with this question.

Here are the results from our Summer School students:

Here we have something that doesn’t happen very often with a Diagnostic Question (and I am speaking as a man who spends a rather worryingly significant part of his life looking at data on Diagnostic Questions…) - we have hardly any students choosing two of the answers. Instead, answers B and C dominate, with 1 in 3 students opting for the incorrect answer of 0.29.

Why do they believe the correct answer is 0.29? Well, let’s have a read of some of their explanations:

Because you just do 23+6 which equals 29 then you add the decimal point back on which makes it 0.29

You line up the zero with the zero, the two with nothing and the three and six should be lined up and you then add them up

There were two distinct types of explanations given by students who chose answer B that I have tried to capture with these two examples. We had plenty of the first, which I would say is the classic misconception - treating this sum as the equivalent of 23 + 6 and then converting to a decimal at the end. But we probably had more of the latter, where students show an awareness that it is important to line something up when adding decimals, but something then goes wrong in the process.

As with all these misconceptions, I find it useful to ask myself two questions:

• Why are students going wrong?
• What am I going to do about it?

It seems clear that students first need to understand what decimal numbers are in order to answer this question correctly. Treating them as integers and then sticking a zero and a point in at the end is not going to cut it. Specifically, drawing their attention to the difference between 0.6 and 0.06 feels important.

Perhaps it is as simple as presenting the following problems next to each other:

• 0.23 + 0.6
• 0.23 + 0.06
• 0.23 + 0.60

Students could be challenged to consider what is the same and what is different about each sum, and what impact those differences will have on the answers.

A longer sequence of examples that develops this further can be found here.

But as we have seen from the second student’s explanation, this alone may not be enough. We need to also support students who know they need to line things up, but are not quite sure how to.

In situations like this I like to turn to examples and non-examples.

A question like this might prove useful:

This could be followed up by a series of questions where all students are asked to do is line up the digits for a variety of sums - not to then go ahead and work out the answer. Investing time focussing on this single “skill” until it is automated may really help students with questions like this going forward.

Let me show you the second and third worst answered questions from this quiz, together with the proportion of students opting for each answer:

Again, it might be useful to ask yourselves the questions:

• Why are students going wrong?
• What am I going to do about it?

You can access the whole quiz here, and the Insights page that will give you access to the percentages and student explanations here.

Next week we have Fractions (uh oh!), and I will be back with some more insights based on students’ responses.

Take care of yourselves, thanks for reading and stay safe
Craig and the Eedi Team

Written by
Craig Barton