As a math specialist at the Institutes for Learning and Development, I am often confronted with a dilemma: How can I better help my students develop conceptual, rather than procedural, knowledge? It’s good to have a list of “steps,” but it’s the conceptual knowledge that matters.
Take the topic of integers — those pesky positive and negative numbers that are just alike but oh so different. What works for one student clearly doesn’t work for another. By answering some essential questions, we can differentiate math instruction to align with an individual student’s learning style.
At the regional National Council of Teachers of Mathematics conference, I was happy to have the opportunity to attend a workshop conducted by Ellen Boiselle and Mindy Eichorn, who are members of the Boston Children’s Hospital Learning Disabilities Program assessment team. They introduced their assessment protocol, which includes the Mathematics Learning Profile (MLP), created by Maria Marolda and Ellen Boiselle.
The MLP delineates different kinds of math learners depending on the student’s responses during the entire day-long neuropsychological and learning assessment. While standardized tests look at the product (is the answer correct?), they do not provide information about how to go about making sense of the concept for a given student.
Since success for students with learning differences is all about the “goodness of fit” of the curriculum, knowing what materials to use with a given student is helpful. As educators, we need to be able to answer some essential questions in order to differentiate math instruction successfully.
Essential Questions of Differentiation
- Consider how the student processes information best
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- Linear, step by step?
- Visual-spatial learner?
- Do concrete materials help?
- Do “real-life” contexts help?
- Consider the student’s “executive function processes”
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- Can the student organize the work on paper?
- Does the student have difficulty with working memory?
- Would the student benefit from memory strategies?
- Can the student integrate parts and wholes?
- Consider output and automaticity
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- Is the student fluent with facts?
- Does the student work slowly?
- Consider self-efficacy and anxiety
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- Does math increase the student’s anxiety?
The answers to these questions will help a math educator select strategies aligned with the way an individual student learns best.
Differentiated Strategies for Adding Integers
The Addition of Integers is a good topic to choose for differentiation because there are so many approaches that work for different learners. Listed below are strategies with websites for more information.
- Kinesthetic Learners
- Visual Learners
- Linear, Step-by-Step and Verbal Learners
Integer Rules Song (to the tune of “Row, Row your boat”)
Integer “Scoreboard” or “T-Chart”
For many math topics, different approaches will appeal to different students, depending on their math learning profiles. As a teacher (or tutor or parent), our job is to introduce students to a variety of strategies and then help students select the strategies that not only lead to the right answer but also help them to successfully conceptualize the topic and implement the procedures accurately and successfully.
- Joan Steinberg, M.Ed., Director of Educational Services, Institutes for Learning and Development