Teaching calculation skills better and more creatively

In GCSE Science students often struggle to remember how to do calculations properly (when to convert units, rearrange equations, use principles such as conservation of momentum, etc).  When I have given students several calculations to do (after going through a worked example) I often work harder than the students do as I have had to go around helping a lot of them, while others are waiting for help.  And this is with a culture of students trying all the questions before asking for help and asking the other students on their table for help first. This has made me reflect on how I can make sure students get the feedback and guidance they need, just at the time they need it, and doesn’t require me to personally deliver it. Below are two strategies I’ve used to try to do this.

My first strategy was to give the students the answers to the questions, but in the wrong order. This allowed students to check their answers and get immediate feedback as to whether they were right or not. However if students went wrong, although they now knew they were wrong they didn’t know why. To help students try to identify their own mistakes I next got them to check their work against these common mistakes:

  • Did you copy down the equation or any of the numbers wrong?
  • Did you write down the rearranged equation? Write it out and then underneath replace each symbol with the number it represents.
  • Did you rearrange the equation properly? Check with your table partner.
  • Have you converted units? E.g. km to m, kJ to J, g to kg
  • Did you make a mistake when pressing the buttons on the calculator? Try it again. [I call this ‘fat finger syndrome’!]

This helped and cut the number of questions from students by more than half.

Now this is fine for fairly simple calculations (such as using a formula such as speed=distance/time), but not for multi-step calculations, e.g. conservation of momentum style questions.  For these types of questions students need to have a ‘strategy’ and know where they’re headed. In my experience this is difficult for students, even when they are fine with all the individual steps – it’s knowing how to put them together that they often struggle with.

At the time I was thinking about this, I discovered this video by Dan Meyers about making maths lessons more engaging. In the video Dan quoted Daniel Willingham: “Sometimes I think that we, as teachers, are so eager to get to the answers that we do not devote sufficient time to developing the question”. He goes on to discuss video games and argues that they are engaging because they allow choice in how tasks and puzzles are completed and solved and there is a low cost of failure and error (you can re-try something so you don’t have to start the level over again, etc) [he discusses other reasons as well, which are out of the scope of this post]. Also worth watching is this earlier Dan Meyers video where he discusses some of these ideas to create three act maths problems.

I applied these ideas when I next taught conservation of momentum (strategy #2). Instead of opening with a video (as Dan Meyer does) I used a Newton’s cradle and discussed with the class what was happening and drew out that momentum was conserved. I then asked the class what information would we need to find the velocity of the last ball after the first one has hit, allowing students to discuss this in their groups first. After this I gave them the information they had suggested (such as the masses of the balls and the initial velocity) and also gave them the final answer that they were aiming for but rounded to the nearest whole number, asking them to work with their partner to try to work out the velocity to two decimal places. The students responded well to this, they instantly could tell if their answers were right or wrong and felt that if they got a wrong answer they could simply try again and adjust their method, allowing me to circulate and listen to their conversation.

Through this process most students were able to calculate the correct velocity. After getting a couple of students to demonstrate their solutions, I then got each student to write a method as a set of steps for how to do the calculation. A lot of the students simply stated the numbers in their methods, so after they had written it I got them to replace the numbers with what they represented (e.g. momentum before collision, velocity after the collision, etc).

The students then applied their method to a simplified problem involving cars, before moving onto a past paper question. This worked well and at the end of the (double) lesson the students had applied their methods to answering the past paper question correctly.

Both of these strategies were successful in that they met my objective of reducing the amount of reacting I was doing in lesson and so freeing me up to circulate and assess how the students were getting on. For the second strategy the students seemed to enjoy producing their own method and they definitely did more thinking, and so should remember more.

Update: Since doing this I came across this excellent idea of having all the calculations projected on the board and if someone is stuck on a problem then they write their name on a post-it and stick in on the question on the board, allowing you to see who’s stuck on what and if you need to go over something with an individual, group or the whole class. I’ll definitely be trying it out!


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