There are many common misconceptions that my pupils have. Many of them relate to simplifying algebraic expressions.

This week there have been two particular misconceptions gathering momentum around my Higher maths class. We have been completing work on stationary points and optimization – which relies on being able to solve quadratic equations.

The first is when taking the square root to solve a quadratic equation in order to find stationary points, such as x² = 16, many of my pupils only write x = 4. Why do they forget about the other solution? I think part of the problem is that when the pupils are younger, we teach them only about the positive square root in order to solve problems using the Theorem of Pythagoras. There is no need for the negative solution since x is representing a length. It is not until senior school that we, as teachers, use both positive and negative solutions for square roots. I don’t want to penalise my pupils for inconsistent teaching so I have made this poster to display in order to reinforce the concept.

The second misconception occurs when pupils have factorised a quadratic equation and try to solve it. The pupils have no issues solving expressions such as x² – 5x – 24 = 0

but often forget a solution when solving x² + 2x = 0. Here’s what I see often:

Why is it that pupils forget that x = 0 is a valid solution?

Here is a poster I am going to display to try and help my pupils.

Hopefully these two posters will have the desired impact. Here are the links to the two posters:

Square Roots

Zero Product Property

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I think the trouble with factoring is rooted in a student ability to abstract what exactly a “term” is in algebra. 4 is sometimes a term, but we also call it a constant. X can be a term, and so is 4x. But 4 is not a term, it’s a coefficient of the term 4x. 2(x+3) can have many terms and coefficients. Depending on what you want to focus on.

Why should I distribute 2(4+3x) and not 5(5-10+6). Wait what do you mean it’s not 5(-11) I subtracted. As always student reach each a new unit or year with an incomplete picture of what came before. It affects just about everything. To compensate students and teachers settle for half truths and partial understandings. It’s the economic decision all parties make when forced to cover content.

Not trying to be a downer, just don’t beat yourself up if the poster doesn’t just fix everything. It is sufficiently colorful and eye catching.

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Very true. I think misconceptions also arise because pupils have many different maths teachers and there is not always consistency of approaches.

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Thanks for this post!!

Students often don’t remember to use GCF when factoring x^2 + 2x

Perhaps a graphical representation?

https://www.desmos.com/calculator/b35otgqlyb

As far as x^2 = 49, I have taken to calling the -7 the lost dog and tell students don’t lose your dog!! LOL

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