Question 5
In a math class activity, students are trying to invent the formula to calculate the area of a square while also contrasting it with calculating the area of a rectangle and triangle. Students are given the right answer after the invent and contrast activity. What are the likely benefits student would get out of this activity of inventing and contrasting cases?
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Students will remember these formulae for a long period of time as compared to the just listening to lectures. They will be able to transfer this learning to their final exams as well and not only tests taken after the lesson. Students will also better select right formula for the problem as they know which formula applies for which shape.
Contrasting cases are helpful for convergent thinking, which leads to come to one correct answer. Invent-with-contrasting-cases (ICC) helps with delayed recall and also helps with contextualize, which can make learners pay more attention to those deeper structures of the problem and is also beneficial to transfer learning.
This is an ICC/invent-then-tell instruction. The benefits of doing so always result in better far-transfer and deep understanding and a longer time of recall. Among the options, 'students will perceive better learning of the surface area concept' is correct since it means a deeper understanding of conceptual knowledge.
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Contrasting cases can facilitate sense making by indicating key features of the domain\'s deep structure by highlighting key similarities and differences. This means students are more likely to understand how the formulas relate to the answers they produce, and thereby students may be more deft in their applications, and better able to recall the formulas in the future. I am unsure what "perceive a better learning" means. Is this about their metacognitive awareness/perception of their own learning? I.E. they will \'feel\' that they learned more?