Research Proposal On Education

Most excitingly, both seemed to support better problem representation.

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The substantial difference here is the geometric element in the second path.

But this element could be worked into the first instructional path, perhaps later on. Or at the end, as a way to push students’ thinking, after they have mastered the algebra?

The standard algorithm for multiplication is bound up in notions of place value, and the taking of partial products, which are then totalled.

There is no reason that teaching this procedure can’t be an iterative process-concept and skill tied into what we call “learning the algorithm.”Future studies of this kind could seek to further explore how this iteration happens.

As the authors note, domain knowledge contains both skills and concepts.

The study points to the idea that representation is complex.

One the one hand, we have a real or perceived loss of “basic skills”, usually signified in the debate through times instant recall, and on the other hand, we have the idea that our students are not good enough at problem-solving for the “modern world”, or for “the future”.

It is very worth noting that this debate is several generations old.

You can decide for yourself where the following prompt belongs in the instructional path. Our research question could be: will these two groups of students both understand the Pythagorean relationship in the same way and to the same depth?

If we can draw a firm conclusion from our research study, then we might come down on the procedural or conceptual side, and if not, then we might conclude that the endpoint of both groups is roughly equal.


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