Theoretical Portraits of mathematical understanding (1)

Posted: November 28, 2013 in The root of the matter


In this chapter, Jennifer provides different theories of mathematical understanding. I will focus on mathematical understandings from a Constructivist perspective:

We have two levels of understanding:

Conceptual-knowing what

Procedural-knowing why

Relational understanding relates the procedural and conceptual; and focuses on knowing why they go together. As educators, we want our students to develop relational understanding. How do we do this? The objective of relational knowledge is to combine conceptual and procedural understanding in order to make sense of, and solve a problem. I feel that the use of alternative algorithms can help students make sense of mathematical concepts such as subtraction.

Subtraction can be imagined in two ways: by taking away, and by comparison, or difference.

We can use different algorithms dependent on how we wish to view subtraction:

62-38 = 62-(40-2)
…….. = 62-40+2
…….. = 22+2
…….. = 24



In class, we played the race to 100 game, and it was really fun and challenging at the same time. I have included two templates that use different strategies but still focus on making math meaningful.



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