3.5. Teaching lower achieving students
What I used to think
In the two secondary schools where I have spent the majority of my career, students in maths were placed into sets by some measure of achievement (usually a combination of Key Stage 2 SATs score, GCSE target, and internal assessments throughout the year). Both of my heads of department were very keen to share classes evenly and fairly across staff, and so most years I would be given either a bottom-set or a next-to-bottom-set class in Key Stage 3.
I’ll be the first to admit that I do not consider myself particularly effective at teaching lower-achieving students (for want of a better phrase, although all options seem either patronising or limiting). Perhaps it was because I felt I could relate more to the high-flyers, or maybe because I enjoyed the more complex areas of mathematics. Either way, I found it difficult. The main issue was that my instincts told me that I needed to teach these students differently to how I would teach a top set. The idea of explaining a concept, modelling a worked example, and then getting students to complete a series of related questions seemed, well, too formal somehow. Surely such an approach would be daunting and off-putting for the students, many of whom had endured a negative relationship with mathematics for many years? Surely it was better to adopt a more informal approach? Let them play with numbers, let them experiment, let them discover.
The problem was, they never really seemed to learn much this way.
Sources of inspiration
My takeaway
We have seen in the previous sections that less guidance during instruction is simply not suitable for novice learners. More often than not, novices’ lack of domain-specific knowledge leads to a frustrating, demotivating experience. Given that the students in the bottom sets are novices in many areas of mathematics, it follows that a more teacher-led, explicit form of instruction would be more effective.
Indeed, in a review of relevant studies into students who struggle with mathematics, Gersten et al (2009) provide eight recommendations, some of which are aimed more at a senior leadership or governmental level. However, one recommendation is directly relevant to our discussion in this section:
Recommendation 3: Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.
The authors conclude that the evidence supporting this recommendation is ‘strong’, and in the subsequent discussion they state:
Explicit instruction typically begins with a clear unambiguous exposition of concepts and step-by-step models of how to perform operations and reasons for the procedures. Interventionists should think aloud (make their thinking processes public) as they model each step of the process. They should not only tell students about the steps and procedures they are performing, but also allude to the reasoning behind them (link to the underlying mathematics).
There is no reason why the model of teaching suggested by this recommendation – and which is developed and expanded upon throughout this book, complete with carefully planned explanations, example-problem pairs, Intelligent Practice, tests of retention, formative assessment, and carefully structured desirable difficulties – cannot be used with students who struggle mathematically. Indeed, you could very well make the argument that these are the first group of students such an approach should be used with as they are the ones who would benefit from it the most.
In a chapter in Standards of Education summarising research into teacher effectiveness, Rowe (2007) argues:
The problem arises when student-centered constructivist learning activities precede explicit teaching, or replaces it, with the assumption that students have adequate knowledge and skills to effectively engage with constructivist learning activities designed to generate new learning. In many instances, this assumption is not tenable, particularly for those students experiencing learning difficulties, resulting in low self-esteem, dysfunctional attitudes and motivations, disengagement, and externalizing behavior problems at school and at home.
It may feel unfair to teach students in this way – but I would argue that it is unfair not to.
What I do now
I consider myself pretty poor at teaching students who struggle mathematically, and I have no large sample of reliable data to suggest that recent changes I have made have been effective. All I can offer is the subjective observation that my students seem happier and are retaining more now that I am following the principles of teacher-led explicit instruction.