‘One colleague suggested turning to the calculator and using the answers as an investigation. Why does the calculator give this answer? What rules is it following? Can you write a set of rules? What would the calculator say for this sum?’by mrbartonmaths
Student misconceptions are critical to planning successful lessons! In a recent series of posts (I think he is up to 11 posts now) mrbartonmaths explains how he uses diagnostic questions to delve into the misconceptions his students have about basic arithmetic.
The quote above came from #10 in the Insight of the Week series: order of operations. As mrbartonmaths explains,
‘…the misconceptions I think students hold are different to the ones they actually make, and I want to put this to the test on a larger scale.’
While I found all of the responses interesting, I was surprised by the number of responses that indicated students were trying to place parentheses (brackets*) into the problem where none existed! These students were trying to make sense of the problem using familiar notation. The only problem I saw is that students didn’t know the ‘rules’ of brackets!
My comment to mrbartonmaths:
Teach them the rules for brackets!
To return to the thought at the beginning of this little essay, ‘have them use the calculator to evaluate the rules the calculator is using’ would require students to identify and investigate their own misconceptions- an idea I find ultimately rewarding!
For a great interactive lesson- which includes some much needed awareness of when parentheses are needed- try this Make This Number game.
As a further step in ‘teachers as lifelong learners’, I love that mrbartonmaths has embarked on something he calls Guess the Misconception, an email poll he sends out weekly to those who are signed up. What misconceptions are you holding about your student’s misconceptions!?!
I am reminded of the time I asked my Algebra I student, who was having a lot of trouble solving basic algebra problems in one variable (3x + 7 = 13 for example), why he kept wanting to start with 3x first. I had spent time working with him on the ‘unwrapping’ idea, without success. He pointed out that he was dividing by 3 because it was first. Headsmack! (Me, not him!)
Don’t assume! (You remember what that does, right? Makes an a– out of u and me!)
Thank you, mrbartonmaths, for giving us a little bit more insight (and some great ideas) into best teaching practices!