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10 votes
Accepted

Scientific results on the usefulness of physical units in secondary education?

This is not exactly what you seek, but at least you can find educational research articles under the key phrase dimensional analysis. Below [1] says it's useful, [2] questions that usefulness. [1] ...
Joseph O'Rourke's user avatar
9 votes
Accepted

Problem "seeing" the perimeter of a figure

This is pure speculation — I don't have enough information to know what the student was thinking — but they may have only known how to compute the perimeter in one way: taking the lengths of each edge ...
Daniel Hast's user avatar
  • 4,893
7 votes

Mathematical difficulty

difficulty in understanding the interrelation of mathematical constructs. or difficulty of fitting a mathematical problem on just one line or difficulty in compressing the problem to a ...
James S. Cook's user avatar
5 votes

Problem "seeing" the perimeter of a figure

Perhaps a targeted illustration, a "proof without words," might suffice to break the grip of algebra and computations, which might be confusing her...?          
Joseph O'Rourke's user avatar
5 votes

Problem "seeing" the perimeter of a figure

Give her a collection of 5 such shapes on graph paper, all of which have the same perimeter, and have her compute. Then see if you can talk about why these shapes all have the same perimeter. See if ...
Steven Gubkin's user avatar
4 votes

Is metacognition ever bad?

First, metacognition may sometimes actively interfere with task performance. Second, the costs of engaging in metacognitive strategies may under certain circumstances outweigh its benefits. Third, ...
binish shahzadi's user avatar
3 votes

Problem "seeing" the perimeter of a figure

Your approach sounds a bit stiff to me. Put a picture inside the shape. "Adding up the lengths of the edges" might be "How far is it round the edge?" for a start. It doesn't take long before the ...
John Orford's user avatar
3 votes

Problem "seeing" the perimeter of a figure

"Adding up the lengths of the edges" really is an adequate definition for the perimeter of a figure. The concept she might be missing is that it doesn't matter how long the individual edges are, the ...
user7868's user avatar
  • 131
3 votes
Accepted

Need scientific source to prove the difference between arithmetics/calculus and real mathematical skills

I think the OP asks a difficult question that will not have a succinct answer. Permit me to point to one publication, Schoenfeld, Alan H., ed. Assessing Mathematical Proficiency. Mathematical ...
Joseph O'Rourke's user avatar
2 votes

Problem "seeing" the perimeter of a figure

I often see a "shift" among my fourth graders when we move into geometry units. The students who have been quite successful with computation and even algebra concepts begin to struggle to "see" ...
Patti J Dieck's user avatar
2 votes

Problem "seeing" the perimeter of a figure

Is it just a simple matter of pointing out two pairs of congruent segments? It is evident that the perimeter of the rectangle is 4x7=28.
user52817's user avatar
  • 11k
2 votes

Mathematical difficulty

Difficulty to keep the thinking abstract e.g. using symbols instead of "real" world objects
Thinkeye's user avatar
  • 741
2 votes

Mathematical difficulty

Gaps in basic knowledge which make progressing difficult
Amy B's user avatar
  • 8,017

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