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Summer School Insights: Week 5 Fractions

Craig Barton

Hello everyone,

This is the fifth 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 5’s quiz is Fractions

Our group of 10 and 11 year olds did well at this quiz, scoring an average of 70%. But it is worth noting that this is the lowest average score seen across any of the quizzes so far.

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 10 is the one that caused our group the most problems. What is Question 10, 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:

Why did approximately 2 in 3 students get this question wrong? More specifically, why do more students believe the correct answer is 1/4 than the actual answer of 10/15?

Let’s have a look at some examples of student explanations to see if we can get to the bottom of it:

All the common denominators can be divided by five but the one over four fraction can’t be divided by five

it's the only fraction that isn't in the 5 times tables

C is right because the 4 should be a 5 so it can go on the number line but it can't because it is a 4

This selection of three explanations represents the most common reason students opted for answer C. It is almost like they are answering an “odd one out” style question, where they have identified C as the culprit because the denominator is not a multiple of 5.

There were some attempts to make the fractions equivalent that went wrong and led to answer C, such as this:

Because 2 fifths will go nicely in the middle and 75 over 150 and 10 over 15 are equivalent to 2 fifths

But those were few and far between.

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?

Fractions have the potential to be a minefield of misconceptions, so it is perhaps no surprise that this week’s scores are lower. Below we will see examples of other questions in this quiz that caused our students problems, but for now let us focus on this one. Why did it prove so difficult for our students?

Well, let’s consider what is involved in order to get the correct answer. Students must:

  • Realise that this question requires the comparison and ordering of fractions
  • Find suitable common denominators for each comparison
  • Correctly adjust the numerators to find equivalent fractions
  • Realise that the question wants a fraction that does not fit between the two fractions, as opposed to one that does

That is a lot to ask. In the language of John Sweller, students may be in danger of reaching a state of cognitive overload whilst considering all this. And in their confusion, they simply opt for the answer that looks least like all the rest and go for answer C.

I have written a lot about cognitive overload in my two books and I cover it in even more detail in my Focusing Thinking course. One of the most significant changes to my own practice since reading the related literature has been to be more selective about when I present my students with problems like this. When students approach this question I want their thoughts to be focussed on strategy - in other words, how knowledge that they are familiar with should be combined to solve this problem. If students are not familiar and comfortable with each of the substeps (choosing appropriate common denominators, finding equivalent fractions, ordering fractions, and so on), then attempting to apply these substeps, whilst simultaneously trying to process exactly what this question is asking them to do, is likely to be too much, leading to frustration, guesswork and little learning.

Whether we label the process of dealing with these substeps as Atomisation or simply assessing prerequisite knowledge, for me it is an essential process to help equip our students with the knowledge and confidence to not only succeed at questions like this, but also to learn from the process.

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 Fraction, Decimal and Percentage equivalence, 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
Head of Education

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