Remedial students struggle with factoring

Remedial students have seen quadratics before but, perhaps they don't elicit positive memories. The textbook (designed for people taking the course for the first time, not for remedial students) spends a long time on "multiplication of binomials" before there is any factoring. The idea (I think) is you will see the patterns such as "difference of two squares" and the "perfect square trinomial" then, when it's time to factor, you can recognise these patterns in the new context.

Many remedial students lack confidence in their abilities, when they see patterns they don't seem to trust themselves to have recognised something significant. They have no problem learning to multiply the binomials. But, this time feels wasted because when we move to do the reverse and factor I'm met with silence. In addition, multiplying binomials isn't hard, especially for students who have done it before. What's worse, I risk boring them.

When I start factoring examples, I always start trying to nurture their intuition. But I feel like it always ends up being an algorithm.

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