Why the Procedural vs Conceptual
(Maths Teaching) Debate is Flawed
The Procedural vs Conceptual debate has been a long-running affair concerning the teaching of mathematics. It begs the question: should mathematics continue to be taught procedurally – an approach that has traditionally been used – or should we adopt a more conceptual approach?
This debate has divided mathematics educators into two opposing camps: the proceduralists and the conceptualists. The arguments from each camp have tended to be mutually exclusive.
This debate has divided mathematics educators into two opposing camps: the proceduralists and the conceptualists. The arguments from each camp have tended to be mutually exclusive.
This article aims to explain why the mutually exclusive ‘Procedural vs Conceptual’ debate is flawed. I’ll argue that both approaches contain necessary prerequisites for students to be successful with high school mathematics and that a hybrid approach combining techniques from both camps is a superior teaching approach.
Conceptual vs Procedural – What’s the Difference?
The procedural approach is a highly teacher-centred approach, i.e. driven by the teacher. The primary aim of a teacher using this approach is to explain the procedures involved in the activity, making the approach highly structured. Historically, this has been the most popular approach and is one that most of us will be familiar with from our own experience of learning maths at school.
On the contrary, the conceptual approach to teaching mathematics is contingent on conceptual understanding. The primary aim of a teacher using a conceptual approach is to have students genuinely understand what it is they are doing within an activity. It also helps that the conceptual approach is student-centred so that student responsibility for learning is maximised.
Note that contrary to a popular misconception, a student-centred, conceptual approach can also be highly structured in a way that affords the teacher a great deal of direction over the learning.
On the contrary, the conceptual approach to teaching mathematics is contingent on conceptual understanding. The primary aim of a teacher using a conceptual approach is to have students genuinely understand what it is they are doing within an activity. It also helps that the conceptual approach is student-centred so that student responsibility for learning is maximised.
Note that contrary to a popular misconception, a student-centred, conceptual approach can also be highly structured in a way that affords the teacher a great deal of direction over the learning.
Why can’t we use an approach that is both procedural and conceptual?
When we consider the advantages of each approach it is easy to see that both the conceptual and procedural approaches offer essential prerequisites for students to be successful with high school mathematics. When students do not properly understand concepts, the task of learning and correctly applying procedures becomes much more difficult.
Conversely, students who are competent with procedures are much better equipped to solve mathematical problems.
The Procedural vs Conceptual debate is flawed simply because it shouldn’t be a debate at all; both approaches need to be combined to best improve the way we teach maths today.
Conversely, students who are competent with procedures are much better equipped to solve mathematical problems.
The Procedural vs Conceptual debate is flawed simply because it shouldn’t be a debate at all; both approaches need to be combined to best improve the way we teach maths today.
Call to Action
The Hybrid Conceptual Approach is an approach which integrates the best of the conceptual and procedural approaches. For a more detailed exploration of the hybrid approach check out this article.
Anyone interested in a comprehensive online course which guides teachers as they explore and implement this hybrid approach might want to check out these reviews first.
Anyone interested in a comprehensive online course which guides teachers as they explore and implement this hybrid approach might want to check out these reviews first.
Your comment
Where do you sit within the procedural vs conceptual debate? What points in the article do you resonate with (or disagree with)? We’d love you to hear from you.
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