NOT REALLY CHEATING...

Sometimes I find myself looking for some sort of a “cheat sheet" (for lack of a better term because it is not being used for cheating) that will sum up all I need to know in one place. This holds true when trying to organizing my brain around what I should be thinking about when I teach math, especially from the angle of teaching it effectively and making it relevant to my students.  I believe I may have found a good summary, thanks to Jennifer Suh, assistant professor of mathematics at George Mason University in Fairfax, Virginia and her article “Tying it all Together: Classroom Practices that Promote Mathematical Proficiency for all Students”.  

Here is a link to the article.

http://mason.gmu.edu/~jsuh4/Tying_It_All_Together.pdf

I find this article very resourceful for thinking about teaching mathematics because it outlines the National Research Council’s “Five Strands of Mathematical Proficiency” and goes on to discuss what the author coins “Modeling Math Meaningfully”.  This modeling is illustrated with a great graphic known as “Lesh’s Translation Model”.  When I look at these three things, I feel like I have gathered a "cheat sheet" for my future teaching.  This article sums up so much of what I have been learning about how to teach math in a way that is meaningful and purposeful. 

  

Of course, "cheat sheets" are not meant to take the place of a real understanding of the content, which I feel I do have.  The Five Strands of Mathematical Proficiency include conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.  Basically, if you read the article, you will notice how these strands involve the learning of mathematical ideas, the skills in carrying out math procedures, the ability to apply those skills to solving math problems, the ability to make sense of what is learned via reflection/explanation/justification, and the attitude that math is personally useful/valuable/learnable.  I can see the value of setting up my classroom and designing my instruction in such a way that each of these strands are hit upon.  

Also of value to my future teaching is Suh’s “Modeling Math Meaningfully” activity.  This is an activity where students model their math understanding in each of five modes.  You will see these modes illustrated in the article via Lesh’s Translation Model.  They include (not in any set order, for their uses can be intertwined) using real life situations, pictures, verbal symbols, written symbols, and manipulatives.   In order to demonstrate understanding students explain their math through writing numbers, verbal explanations, drawing pictures, using manipulatives, and writing real-life stories or situations where the problem can be applied.

The article also has an example of a very useful rubric and graphic organizer.

Out of curiosity, and as a side note (because I always like to add side notes), I decided to Google “math cheat sheets for students".  Of course I would never let students rely on these without understanding the deeper concepts behind the math, but perhaps they could be useful at the right time (maybe in developing fluency) in their learning.  Here are some links.

Scroll down to “Math” in this link:

http://www.teachingdegree.org/2009/07/01/100-terrific-cheat-sheets-for-k-12-teachers/

Click on “Basic Math and Pre-Algebra” categories in this link:

http://www.cliffsnotes.com/Section/Basic-Math-Pre-Algebra-Cheat-Sheet.id-305499,articleId-29841.html

Check out the "Pre-algebra" section in this link:

http://www.sparknotes.com/math/

P.S.  If any bloggers out there can come up with a better term than "cheat sheet" (because it is not really cheating) I am open to suggestions.  Resource Sheet?  Summary Sheet?  Any creative ideas out there?