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Instructors may model how they accomplish these activities as an expert. In order to do so, instructors may perform the (mental) steps in front of your students using a subject-specific example. explicitly highlight critical operations. use metaphors or analogies for the (mental) steps. Question 4 - How can I give my students practice and feedback?
The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills. [2] [3] [4] The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.
For example, Math Circles are after-school enrichment programs where students engage with mathematics through lectures and activities; there are also some teachers who encourage student engagement by teaching mathematics in kinesthetic learning. In a general Math Circle lesson, students use pattern finding, observation, and exploration to make ...
It is critical that students learn math concepts using a variety of tools. For example, as students learn to make patterns, they should be able to create patterns using all three of these tools. Seeing the same concept represented in multiple ways as well as using a variety of concrete models will expand students’ understandings.
Analogy is a comparison or correspondence between two things (or two groups of things) because of a third element that they are considered to share. [1]In logic, it is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction.
Expanding on the last two examples, there is an analogy between knots and prime numbers in which one considers "links" between primes. The triple of primes (13, 61, 937) are "linked" modulo 2 (the Rédei symbol is −1) but are "pairwise unlinked" modulo 2 (the Legendre symbols are all 1).