What are the major misconceptions that students have when it comes to Stem and Leaf Diagrams at GCSE? Surely nothing can go wrong in this lovely topic?...
Using real life data and explanations from students all around the world from my Diagnostic Questions website, we can find out! :-)
Have a look at the question below.
What percentage of students do you think get it correct?
What is the most popular incorrect answer?
What explanations do students give for the incorrect answers?
Give the question a go yourself, and try to come up with an explanation of the correct answer that would make sense to students:
At the time of writing, this question has been answered 223 times, and has been answered correctly just 22% of the time. By far the most popular incorrect answer is D, which 53% of students go for,
To see this data, read student explanations, and filter by things such as gender and age, just visit the Data Question page.
Now, Stem and Leaf Diagrams are one of those topics that I am often tempted to brush over during GCSE Maths revision. After all, students first meet one in Year 7, and then keep meeting them every year onwards. And they never change. You always need to put the numbers in order, come up with a decent stem, ensure you don't miss any numbers out. Oh, and remember your key. Always remember your key.
And students who will look at disdain at the sight of a quadratic question or a circle theorem, will usually smile sympathetically at the sight of a stem and leaf diagram, as they can't possibly do them any harm. Can they?
Well, I got the inspiration from the question above following a review of the June 2014 GCSE Higher Paper 1 from Edexcel. We were presented with a student's answer that was similar to the one above and asked to mark it. Almost every teacher gave full marks (including me!). But there is a mistake! And apparently it was a fairly common mistake amongst actual, real life GCSE respondents. And okay, it is only going to cost the students one mark, but that one mark could be the difference between a D and a C, or an A and an A*.
So, what did the students on Diagnostic Questions make of it?
Correct Explanations for B
Some students spotted the mistake, and explained it beautifully:
The question asks for the height, and the data represents centimetres, not children as the key suggests
The question asks for the height and the key states children which the question was not asking for
because the key should say 125cm not children as its taking about height in cm
Incorrect Explanations for A
Thinking the stem should only have one number in it is a misconception I run into a few times with students each year. Here is how they explain it:
The stem should have just 1 number in it not like this one where it had two numbers in
I think this is the answer because you are only meant to put one number down the side
Because the number on the stem should only have one digit as it represents a "ten"
Incorrect Explanations for C
Here I wanted to test if students could correctly match up the numbers in the list to those in the diagram. It is interesting what they thought the problem was here:
because the number 113 is missing
There's a 100, but 100 is not plotted on the diagram
there is not another 105
These careless mistakes cost lots of marks!
Incorrect Explanations for D
By far the most popular answer, amongst teachers as well as students. And here, I suspect it is people just glancing at the key, acknowledging its presence, and then moving on. Or maybe they are going one stage further and checking the coding 12|5 does represent 125. But are they going that extra stem and looking at the actual units? I don't think they are. The students explain this very well, and it is interesting that they all make mention of the key:
Because the key is right, the diagram is right and no numbers are missing and in the stem its a 2 digit number because it's representing 3 digit numbers
There are no mistakes - it seems incorrect due to the two numbers in the stem however this is because of the fact that the number in the stem and leaf diagram is a 3 digit number
The key works to show hundreds and the stem and leaf diagram shows all the data given
So, how do we deal with all of these? I think it is the age-old advice of telling students to check over their work. And yes, before you say it, my students never listen to me when I say that either. But when they did this question as part of the GCSE Maths quiz below, it did provide a talking point that I hope will stay with them.
This question is taken from the Edexcel GCSE Higher Paper 1 quiz that can be used as preparation or a follow up to the actual paper copy. All the questions and numbers are different, but the same skills are tested. I hope you find it useful.
Below is a video showing you how to access all the pages and information discussed above: