Teaching Mathematics Using An Approach That Is Both Conceptual And Procedural -
Nine Keys To The Hybrid Conceptual-Procedural Approach
Key #4 argues in favour of a hybrid procedural-conceptual approach
The procedural vs conceptual debate is flawed because the common belief (that the two approaches are mutually exclusive) is a misconception. A hybrid approach is possible which includes the essential prerequisites from both approaches - the explicit teaching of procedures AND the ‘enabling of students to understand what it is they are working on', ideally from the time they commence working on it.
Key #4 unpacked
As we have already noted:
However, the (hybrid) conceptual approach includes the explicit teaching of procedures as a natural, organic part of the approach. Therefore this hybrid conceptual approach can be equally effective in teaching students procedures and, as we have already noted, is more effective at enabling students to understand what it is they are doing.
Note: For the remainder of the article we shall refer to the hybrid approach as the hybrid conceptual approach (rather than the hybrid conceptual-procedural approach) because the approach is essentially conceptual - everything about it is premised on the need to have students understand what they are working on - but it also includes the teaching of procedures.
- proceduralists believe that teaching procedures is the most important aim when teaching mathematics and that a procedural approach is by far the best way to achieve this.
- conceptualists believe that having students understand concepts is the most important aim when teaching mathematics and that a conceptual approach is by far the best way to achieve this.
However, the (hybrid) conceptual approach includes the explicit teaching of procedures as a natural, organic part of the approach. Therefore this hybrid conceptual approach can be equally effective in teaching students procedures and, as we have already noted, is more effective at enabling students to understand what it is they are doing.
Note: For the remainder of the article we shall refer to the hybrid approach as the hybrid conceptual approach (rather than the hybrid conceptual-procedural approach) because the approach is essentially conceptual - everything about it is premised on the need to have students understand what they are working on - but it also includes the teaching of procedures.
Hats off to quality procedural teachers
At this point, it is only fitting to give a shout out to the proceduralists! I realise that reading a pro-conceptual article can be confronting for procedural teachers because it can appear that their expertise is being criticised.
I have witnessed phenomenal practitioners who are traditional, procedurally-based teachers. Hat’s off to you all because you possess a great deal of skill and do what you do very, very well. However, I’d love you to be open to discovering the ‘hybrid conceptual approach’. Why? I honestly believe you will see an enhancement of your explicit procedural style once you add a conceptual focus to it.
I have witnessed phenomenal practitioners who are traditional, procedurally-based teachers. Hat’s off to you all because you possess a great deal of skill and do what you do very, very well. However, I’d love you to be open to discovering the ‘hybrid conceptual approach’. Why? I honestly believe you will see an enhancement of your explicit procedural style once you add a conceptual focus to it.
A quality procedural approach is more than just the teaching of procedures
Throughout this article, I reference that procedural teaching is ‘the explicit teaching of procedures’. We all know that the procedural teacher delivers more than just procedures - e.g. mathematical backstories, maths history, real-world examples, rapport-building jokes etc. However, for the purpose of this article, ‘I’m keeping it simple’ and focusing on procedural teaching as ‘the teaching of procedures’.
Return to the parent article
|
Contact
|
Customer Service
|
PD & Courses
Understanding & Agency in Mathematics
|