by Kate Fanelli
I write a lot here about the need to use a Concrete-Representational-Abstract approach to instruction, not just with students who struggle, but as part of a strong Tier 1 instructional program.
In the morning keynote at the 1st Annual Making Mathematics Meaningful Through Collaboration conference this week (held at Macomb Intermediate School District in Clinton Township, Mich.), Dr. Karen Karp of Johns Hopkins University talked about the importance of making connections. She showed a circle with an orange dot at its center and blue dots around it. Then she showed another circle, with another orange dot at its center, but with blue lines extending from the orange dot to other dots. Below is my version of what that looked like.
The orange dots represented new information. The blue lines represented connections to previously known information. Dr. Karp pointed out that teachers drop orange dots all the time, but we also need to draw those blue lines for students to explicitly make connections to things they already know.
Some students may be able to draw those blue lines by themselves, but for many of our students, including those with special needs, they cannot, or do not, make those connections on their own.
One tech tool that can support this type of teaching is Thinking Blocks. Like models such as tape diagrams, or those used in the Singapore Math program, Thinking Blocks uses diagram literacy to build and support student understanding of operations and equality.
Diagram literacy is the ability to “read” a diagram. Students who can create diagrams to express their thinking, and interpret diagrams to receive new information, are working at a conceptual, representational level to make connections, look for and make use of structures (Common Core Standard of Mathematical Practice #7), and model mathematically (Standard of Mathematical Practice #4).
Thinking Blocks can be used via the web or an app. They provide video tutorials and opportunities to practice using diagrams to model and solve addition, subtraction, multiplication and division word problems involving all types of numbers including whole numbers, fractions, decimals and percents.
Whatever tech tool you use, supporting student thinking and drawing those blue lines with diagram literacy, is an evidence-supported, effective, and common sense way to support mathematics teaching and learning for all students.
Kate Fanelli is the math accessibility specialist for Michigan’s
Integrated Mathematics Initiative (Mi)2, 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) or on Twitter (@MI2_Math). Contact Kate at firstname.lastname@example.org.