Coaching Case Studies #3
Misconceptions and going through tests
I hope you are all well.
Time for another round of coaching case studies where I reflect on some of the things I have learned from working with fantastic teachers around the country. You can read the previous coaching case studies here and here)
Case Study #1
Early on in a lesson about choosing the most appropriate average, students were challenged to calculate the mean of the following set of numbers using their calculators:
63, 86, 64, 67, 71, 42, 79, 64, 80, 64
Students wrote their answers on their mini-whiteboards, and the teacher circulated the room offering feedback and support where needed. Most students got the correct answer of 68. But during circulation the teacher discovered that two students had an answer of 622.4.
Can you see where that answer came from? I couldn’t!
Fortunately, the teacher was able to diagnose the issue on the spot: students had added the 10 numbers on their calculators, but not pressed equals before dividing by 10. Hence, as they follow the strict order of operations, their calculators had only divided the final number by 10 and then added that result onto the sum of the previous 9. As I say, the teacher spotted this and was able to support those two students in getting the correct answer.
During the coaching session that followed, we discussed how mini-whiteboards had made both the circulation easier and the subsequent check of whole class understanding when all students held up their boards. But we also talked about how more could have been made out of the answer of 622.4.
Following the whole class check of understanding, the teacher could have borrowed one of those boards - or anonymised the answer by writing it herself - and said to the class:
Imagine someone wrote an answer of 622.4. First, how do we know straight away that it cannot be correct? And second, can you figure out how someone might have got the answer?
Students could be challenged to think about this themselves and then discuss with their partner, before the teacher chose some pairs to share their thoughts.
The feasibility of answers and correct use of a calculator are both big issues in maths and worthy of such consideration. Students who might make similar mistakes will certainly benefit from thinking about this explicitly, but even students who are secure with these ideas will benefit from trying to diagnose issues and then offer explanations.
The teacher vowed to make more of these opportunities that her excellent practice had generated in the future!
Case study #2
Something a bit different here. In all my coaching sessions we work together to plan an upcoming lesson where the coach can put the ideas we discuss in the coaching session into action. With one colleague we had planned the start of the lesson based on my feedback, but we had about 15 minutes left, so decided to look where the lesson was going next.
It was a revision lesson for Year 11s. Students had just done a past paper which the teacher had marked. Her plan was to give the assessments back to the students, put the three worst answered questions on the board for students to have a go at, then go through them herself so the students could make corrections accordingly.
This pretty much mirrors exactly how I went through exam papers, assessments and homeworks for the first 12 years of my career.
But there are a few problems:
As soon as you give the papers back to students, you have lost them for 10 minutes whilst they focus exclusively on their scores and the scores of their mates
When you finally get their attention back and ask them to have a go at a troublesome question, the students who have got it right on their test have nothing to do, and the students who got it wrong probably can’t figure out why (or they would have done so the first time around!)
When the teacher models the correct solution, how does she know that the kids understand? Copying down does not equal learning.
Instead, we planned a new approach:
The teacher would not give the papers back at the start of the lesson
She would put the first troublesome question on the board
She would announce that she is going to go through how to do it nice and slowly, and then give students an opportunity to ask any questions
She would also announce that after she has done this, students will be given a similar question (taken from the shadow paper) to try on their own, and if they cannot do that the only possible reason is that they have not been listening
She would check students’ effort and understanding by asking them to write their final answer to this follow-up question on their mini-whiteboards
Having done this for each troublesome question, the teacher would then give the students their papers back
So, what happened?
Well, it went really well. The realisation that they were all going to be given a follow-up question meant that the students were all engaged in the explanation, and everyone then had a really good go at the follow-up questions.
But there was a twist!
Here is Question 1 from the assessment, and the follow-up question from the shadow paper that was used to check students’ understanding after the explanation:
Every single child got the follow-up question correct.
Now here is Question 2 and the follow-up:
Can you guess what happened?
Most students got this wrong! Why? Because they divided the bottom right angle by 3 (as the teacher had done for the original question) instead of by 4 as was required.
In our subsequent coaching session we focussed on all the positives of the new way of going through tricky questions, but also spoke of the need to strike a delicate balance with the follow-up questions. It needs to be similar enough to the original question so it is testing the same skill, but different enough so students have to do some thinking and not merely swap a few numbers around. Had the follow-up question for Question 1 been more varied, I suspect students would have been more vigilant when taking on the follow-up to Question 2.
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Thanks so much for taking the time to read this