Mathematical Understanding and Multiple Representations


What convinces (or doesn't convince) you in the authors' argument?
-       “The development of students’ thinking is directly connected to their ability to operate with mental images. The use of representations to develop students’ understanding is related to their ability to operate with the representations.”
-       I, myself, use lots of visualizations or mental images as much as possible when trying to learn and absorb new mathematical materials. I cannot imagine how I would understand or solve advanced math questions without mental representation.

What kinds of mathematical representations are included and excluded in this article?
-       Graphs, pictorial representations, enactive representations (geoboard as manipulative aid), modeling, drawing, imagining, mapping, numerals, algebraic equations, tables, diagrams, and charts.

Can you think of an example of a mathematical representation of a particular math concept (from secondary or elementary school curricula) that is not included, but that might be helpful for students in developing understanding? Describe briefly how you might teach using this representation.
-       Using playdough, students make various 3-D figures and study cross sections – parallel, perpendicular, and diagonal – in order to identify the shape that results. Also, students can be asked if the cross section is similar or congruent to the base or face.

Comments

  1. Susan GerofskySeptember 15, 2019 at 10:36 PM

    Very nice, David! You've written concisely and interestingly on this topic. I like the idea of using playdough or modelling clay to create and understand 3D geometric images!

    ReplyDelete

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