Tag Archives: algebraic thinking

How to grow algebra eyes and ears

Math teachers should grow algebra eyes and ears.  To have algebra eyes and ears means to be always on the lookout for opportunities for students to engage in  algebraic thinking which involves thinking in terms of generality and to reason in terms of relationships and structure, etc. In the post Teaching algebraic thinking without the x’s I described some tips on… Read More »

What is proportional reasoning? Does cross multiplication help learn it?

Proportional reasoning is a capstone of children’s elementary school arithmetic and a cornerstone of all that is to follow (Lesh & Post, 1988). But for some reason, the teaching of elementary school mathematics topics either become an end in itself or has become more a preparation for learning algebra. Proportional reasoning is not being given… Read More »

Teaching algebra – it pays to start early

I believe in early algebraization. I have posted a few articles in this blog on ways it can be taught in the early grades. Check out for example  Teaching Algebraic Thinking Without the x’s. All the lessons in fact that I post here whether it is a number or geometry or pre-algebra lesson always aim… Read More »

How to scaffold algebraic thinking in teaching integers

One way to make algebra make sense to students is to show where those mathematics objects (e.g. algebraic expressions/equations/formula) come from. It will even makes sense more to students if they themselves can generate those objects. As John Mason puts it, The mechanics of algebra (algebraic manipulation) are concerned with studying the effects of combining,… Read More »

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