A blog about teaching and learning in a maths classroom.

Wednesday, 16 September 2009 | 5 Comments

Year 8 were recently assessed on *solving equations* and I was a little perplexed by the results.

For one-step equations like,

or

54% of students in one of my classes got both questions right. But even many of those showed a solution like this:

rather than something a little more formal like:

I can understand, these are simple questions with obvious solutions.

Question 2 were two step equations like these:

or

This is where I noticed things going wrong. These questions are a little beyond intuition – 27% of the students got both correct. The wrong answers tended to show an intuitive approach or a guess and check approach using a calculator.

My conclusion from looking at this task – when it comes to assessment, many of these students reverted to prior knowledge gained in primary school rather than a more formal process they’ve seen this year.

This can be clearly seen when only 4% of students correctly solved:

I teach equations by jumping into the formal solution in the first lesson. Having said that, I “jump in” pretty gently with a fairly simple idea… keeping a seesaw balanced:

Solving Equations from Simon Job on Vimeo.

From here, I’ll start with one-step equations, and over subsequent lessons build up the complexity of the equations we’re solving.

I have looked at some of the explanatory methods like “backtracking”, but found that my students struggled with those even more. (For further discussion of three methods: 1. Guess, Check and Improve, 2. Backtracking and 3. Balancing, have a look at this PowerPoint file titled Reviewing the Models for Solving Equations found on the MANSW site.)

Dan Greene at *The Exponential Curve* is also discussing this issue in his post: Algebra 1: Solving Equations.

What’s my solution? I don’t really have one at the moment… have you seen the same issue of students reverting to prior knowledge, even though it’s no longer adequate? What am I doing wrong here?

Posted in • Lesson Idea • Algebra • Equations • Media • Video • Reflection | Short URL: http://mths.co/1629

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**Simon Job** — eleventh year of teaching maths in a public high school in Western Sydney, Australia.

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