Why Structure is Necessary For Some

In my seemingly recent memory I was a high school student, furiously taking step-by-step notes on math rules from a chalkboard and then completing textbook work quietly in my seat (and finishing the leftovers at home). Now as a teacher of math the methods of teaching have evolved to become more student driven with an emphasis on problem solving (The Ontario

Curriculum: Mathematics Grade 9 and 10).

As I begin to plan for lessons, I’m looking for ways to make connections to my students lives in meaningful ways that will spark their curiosity about math. We take for granted that we are able to infer patterns and connections as well as be reflective, plan and self-regulate our own learning. These skills make up a person’s executive functioning skills and when a student has a learning disability that impairs their executive functioning, the modern methods of teaching Math may not be helping these students out. When executive functioning is impaired students struggle to plan, organize and self-regulate and these are arguably essential skills related to successful math completion.

How then can a teacher support students with executive functioning challenges and still create a classroom that allows for discovery? Roditi and Steinberg’s chapter “The Strategic Math Classroom” provides some sound advice. This advice is outlined below to help teachers enhance the learning for a subset of learners in four key areas:

Support Memory:

Memory strategies help enhance the automatic recall that is essential in math. Remembering the nuances and details required to solve problems can be overwhelming to young learners. Verbal strategies such as acronyms are a great way to help students remember sequences and allow students to attempt problems in a structured way. BEDMAS is one such strategy that can help with algebra. Similarly, the acronym KNOW can be used as an overall strategy (Key Words, Numbers, Operations, Work it out). Visual strategies, are another way to encode information these may include drawing cartoons or concept maps. Last but not least, hands-on strategies are a great way to consolidate information (e.g., manipulating tiles and pipe cleaners).

Organizational strategies:

Students with weak organizational strategies are easily overwhelmed and often approach problems with out a specific strategy. The students benefit from direct instructions which not only include order of operations but how to differentiate between essential and nonessential information. Having students have dedicated pages in their notebooks that outline strategy tools such as vocabulary lists, charts, tables or mnemonics are helpful and essential resources for students with executive functioning difficulty. A strategy new to me would be RAPS: reread and rephrase (promotes understanding), artistic (multiple depictions may help with problem-solving), predict (supports problem-solving) and solve (using procedural knowledge). Alternatively, students could use a Three-Column note taking technique where students use one column for each: important terms, definitions and examples. Check out page 247 in Roditi and Steinberg article for pictorial representation.

Shifting representations and formats:

As teachers we likely do this already but it’s important to note that some students need to different representations that link two concepts they already understand in order to bypass difficulties. It’s just about shifting perspectives, but not expecting students to make the leap on their own. One should be aware that subtle changes in language or format can be very challenging for students with executive function problems. This is where study guides help students practice their test taking abilities.

There are also times that students struggle to select the appropriate strategy to solve a problem. If disorganization reigns as a part of executive function problems it’s easy to see why students would have difficulty solving problems with multiple steps. Teachers can use templates with sequential steps that will help students discern between important information. An example of this is teaching linear equations. Once they’re anchored with their template students can use this to move on to more complex reasoning.

Checking strategies:

Making efficient use of time during tests and the ability to self-monitor and check work can make a huge difference in achievement. How can teachers help support those who do not have the strategies which seem innate to others? Error analysis in which the teacher works with the student to identify individualized common mistakes. They can then come up with “strategy tips” that a student can write at the beginning of the test as a means of reference for checking.

Remember that learning by solving problems without rules, routines or repetition can cause some students to feel lost in the nebulous that is learning. With just a few quick strategies implemented into teaching lessons and paradigms students with executive functioning difficulties can benefit from some of the old styles that many of us grew up with. It is not about making major changes but rather about embracing the past and mixing it with the future.

For more examples consult:

Roditi B. N. & Steinberg, J (2011). The Strategic Math Classroom. In L. Meltzer (Ed.). (2011). Executive function in education: From theory to practice (p 237-257). Guilford Press.