My middle school math department is having a debate on how to teach solving equations.
I have a strong opinion on this, but am going to withhold it for the sake of an unbiased conversation. Our main differences are on whether teaching students to solve equations vertically or horizontally will lead to deeper understanding and accuracy. We’d like to teach them consistently across all 3 grade levels and are particularly interested to hear from teachers who teach algebra and higher level high school classes. Is one method more powerful for students than the other? Does having an entire math department teach one consistent method lead to more students understanding equation solving in more complex applications?
One new aspect which I plan to adopt is what a new teacher to our department taught us (I should mention that she’s new to our school, but taught 15 years in Oakland before coming to Berkeley). She uses a vertical line through all the equal signs (see below) to help students ‘see’ that equality is always maintained.
With no further adieu, I present vertical and horizontal: (and by all means, feel free to critique both notations)
And I need to make a public thank you to Donors Choose who got Chevron to give a whole lot of money to fund California teacher’s grants. I just got a $2000 tablet PC laptop and Fluid Math thanks to them.
And finally, this is no longer very timely, but 2 posts ago there was a really great conversation about how to best help students see and correct their errors.
What I tried:
- I made a spreadsheet of what % of students answered each answer choice for each question (it was an all multiple choice exam).
- I analyzed the data and chose the 6 most common errors. I used examples of students’ work and handwrote a worksheet where there were 10 problems on these 6 topics. I told students that 6 were wrong and 4 were right. I broke them up randomly into pairs and they had to analyze the student work and find and correct the 6 errors. We then discussed some of the problems whole class.
- Finally, they had 20 minutes to look at their exams and correct any mistakes they found. It was a test taking time (i.e. no talking, notes, etc). I DID NOT tell them which ones they had gotten wrong, I just wrote at the top of their exam how many problems they had wrong and how many errors they needed to correct to move 1 grade higher on the exam.