Editor’s note: This is an updated version of a blog post originally published on July 17th, 2017
When planning a lesson that introduces a new topic, a teacher will expect that some pupils will struggle. It’s widely agreed that struggle is a natural part of the learning process, but at some point struggle stops being helpful and is simply a waste of time. If the lesson is on multiplying fractions, for example, pupils need to know what fractions are and what multiplication is. To see if a pupil is ready, there are a few simple things the teacher can look for. For example, in the case of fractions these could include the following:
Does the struggling maths learner understand what a fraction is?
Can they explain that when you cut a whole into 3 equal-sized pieces, each of those pieces is a third?
Even if they don’t have the language to explain it, do pupils understand that the pieces can be equal even if they are not congruent? Maybe they can show the fraction using concrete materials.
Conventionally (i.e. the conventions that we use to explain and write fractions)
Do they understand the denominator tells us how many pieces the whole has been cut into?
Do they understand the numerator represents how many of those pieces we have?
A teacher might check that the pupil can apply the fraction to an everyday situation. For example, three of us shared a cake equally, how much of the cake did we each get?
Does the struggling learner understand what multiplication is?
Can they explain multiplication conceptually in a variety of scenarios? For example, 3 groups of 5 apples?
Do they know how to write a proper multiplication sentence, such as 3 × 5 = 15?
If pupils are capable of most of these things and, in particular, they understand the concepts, the teacher may take the view that they are ready for the lesson.
If they don’t understand equality or have no concept of multiplicative structures, they will be wasting their time in the lesson and the teacher must address the gaps in their knowledge before going any further.
The danger is to deny struggling learners the lesson because of superficial concerns, such as they haven’t remembered all their multiplication facts or they are still not fluent with some of the conventions. The Maths — No Problem! curriculum, can provide valuable help and guidance for teachers seeking to enable independence through struggle for all learners.