*by Kate Fanelli*

*@AltShiftEd*

This month I’m going to introduce two low-cost, low-tech, high-yield tools. I’ve found that they help struggling students make their math work more accurate, and make connections between math concepts more secure.

## Graph paper

Graph paper can be purchased by the ream, be created and printed out via word processing software, or be customized and downloaded from a number of websites. One great source for customizable graph paper of all kinds is Dynamic Paper from the National Council of Teachers of Mathematics.

For students with fine motor difficulties, the use of graph paper can help them keep lines straight, making for more accurate work with shapes, tables, and graphs. Not only will these mathematical figures be drawn more accurately, but graph paper may help students visualize concepts such as perimeter and area of shapes, the area model of multiplication, slope of a line, univariate data (for example, when making line plots or bar graphs), bivariate data (for example, when making line graphs or scatterplots), and quantity in general.

I kept graph paper available next to plain white paper and lined paper so that students could use whichever paper suited their needs and the math task best. Many students opted for graph paper regardless of the math topic because it helped keep their notes organized. Simply making graph paper available increased productivity and accuracy in my classroom.

## Foldable notes

I first learned about foldable notes through Dinah Zike’s Teaching Mathematics with Foldables, which is specifically written for math teachers, although she has an extensive product line that covers a variety of content and topic areas. Foldable note formats can be used for a variety of purposes. Foldable notes are made by folding and cutting paper in specific ways to create tangible graphic organizers that students fill in and use to see connections and recall information.

One example is to take a piece of 8 ½ x 11 inch paper and fold it “the long way.” Place it horizontally in front of you and, using just the top flap, make two vertical cuts to the fold, creating three flaps. On each of those flaps, students may write, for example, “table,” “graph,” and “function” and then under each flap provide an example. Or maybe write “mean,” “median,” and “mode” with examples under each. The “Systems of Equations” graphic in this article was based on a quick Internet search of foldable notes that follows this model and is about systems of equations.

The graphic organizer helps students see relationships and differences between the terms. I had my students make each foldable note in the same color. For example, everyone’s basic geometry terms foldable was yellow. Having everyone’s yellow made it easy to locate in their folders, and for me to refer to (“Did you check your yellow vocabulary foldable?”).

Resource books, such as the ones by Dinah Zike, and Internet searches on “foldable notes for math” are a good place to get started using this tool with your students.

Keep in mind that any tool you use with students should align to the math you are teaching, to the needs of your particular student or students, and should support meaningful learning of mathematics procedures and concepts, and not simply serve as a way to help students memorize procedures or vocabulary as facts and definitions. When tools are selected and used thoughtfully they can be effective supports for learning.

*Kate Fanelli is the math accessibility specialist for Alt+Shift (formerly Michigan’s Integrated Mathematics Initiative), a state of Michigan initiative that promotes and supports high quality mathematics education for ALL students. Follow (Mi)2 on Facebook (www.facebook.com/mi2.page) and/or Alt+Shift on Twitter (@AltShiftEd). Contact Kate at kate.fanelli@AltShift.educatio*n.

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