More Accessible Mathematics

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huntRoseMary Hunt

Math Teacher, Turtle Lake Elementary, Shoreview

Math Instructional Coach, Mounds View Schools

MCTM Region 4 Director

For my article in September, I used the book: Accessible Mathematics: 10 Instructional Shifts that Raise Student Achievement by Steven Leinwand as a springboard for some ideas to reflect upon as the new school year was underway.   As a reminder, the lens is pointed to “engage, and focus on understanding and application.” (p.2)  The 10 intentional shifts Leinwand addresses in detail are (p. 4-5):

1) Incorporate ongoing cumulative review daily.

2) Apply what works in our literacy program to our mathematics classroom.

3) Use multiple mathematical representations.

4) Create a language-rich classroom.

5) Develop number sense everywhere possible in the daily work.

6) Use data, graphs, tables etc to build lessons in problem solving and computation.

7) Increase the use of measurement and phrases such as “How big?” “How much?” “How far?” to naturally practice estimation.

8) Minimize what is not “important” and focus on what IS “important.”

9) Use real-world situations to get at the mathematics.

10) Require explanations of strategies to solutions for problem solving. “How do you know?” “Can you explain/justify your thinking?”

In September I focused on #2, 4 and 10.  At this time I will focus on #1, 3 and 9.

Incorporating cumulative review each day (#1) is part of the package of routines set up in the math classroom. In my visits to math classrooms, I see these reviews in many forms: four boxes with a sampling of problems that students complete before the lesson of the day; a few questions that review a skill needed to move forward with another; showing the number of the day in many forms and contexts, a brief number talk.  The benefits: the cumulative review keeps skills sharp; provides students more opportunities to see and practice the skill which leads better understanding; no wasted time in the classroom–math begins immediately; a re-teach opportunity if needed (p. 14).  

Use multiple representations of mathematical entities (#3).  This could be part of a warm-up. Given a number, how many ways can it be depicted? Where is it on a number line; can it be decomposed; can it be written as a decimal number; a fraction; represent it using base 10 blocks; can you write it in base 5; how many tallies is that? By using multiple representations, we help deepen the conceptual understanding of number, operation, properties.  This encourages a departure from a dependency on rote, procedure, memorized steps. There needs to be a connection between concept and algorithm. Too often, the algorithm is mastered with no conceptual understanding. When this occurs it is more difficult to go back to the conceptual.  A variety of representations also provides multiple opportunities for understanding. One representation may not help a student, yet another is what turns the light on.

Finally, #9, using real-world situations to get at the mathematics.  This is a “two for one” opportunity.  It partners well with #3 — use a variety of representations. The real-world problems offer opportunity for a variety of representations, contexts,  and relevance of the math.  If we want students to appreciate the relevance of the math and to be successful it is imperative to choose problems that they can relate to.  Use student names in the problems you choose or create; create problems that have a connection to what is going on in your school. Is there a food drive happening (pounds of food collected, food per homeroom collected); fun run (laps run, students participating, money raised); math books ordered (books per box, price per book); follow a sports team through the season of the sport (total goals scored, total penalty minutes, hitting average, slugging percentage, ERA, total yards gained, attendance trends for the season or part of the season).

These are simple, yet very powerful steps we can take to make math more relevant and engaging for students. These uphold NCTM’s “Eight Mathematics Teaching Practices” (Principles to Action, Executive Summary p. 3).