“All students benefit when they are freed from the burden of retrieving unfamiliar facts. We should never stop building fluency through multiple means.” – Marilyn Zecher M.A., CALT
As a teacher, nationally Certified Academic Language Therapist (CALT), renowned instructor, and workshop presenter, Marilyn Zecher offers an abundance of experience and qualification, and specializes in the application of Orton-Gillingham Multisensory Strategies for teaching math. She holds a BA in education and an MA in English, an advanced professional teaching certificate, and is a presenter at the International Dyslexia Association (IDA), Learning Disabilities Association (LDA), and the National Council of Teachers of Mathematics (NCTM) conferences. She has spent the last twenty years developing multisensory strategies for teaching math based on a traditional Orton-Gillingham approach, as well as the neuroscience on how the brain processes mathematics. Below, Ms. Zecher was kind enough to embark on a Q&A with us to discuss multisensory math and other academic topics in detail.
Q: How would you explain Multisensory Math? How is it different from typical instruction?
A: Multisensory means as many sensory areas involved in the learning as possible, preferably at the same time. Students use manipulative objects to construct a meaning of broad concepts, such as numeracy or place value using simple objects. This might mean using crafts, sticks and ponytail holders for modeling place value concepts, or pipe cleaners and beads to create models of linear functions for algebra. The key is that in the constructing and the associated language—through self-talk or rationalization—the student is building a visual-tactile-kinesthetic model, which supports long term memory. Multiple pathways create multiple memory sources in the brain, which support retrieval. If there is confusion, the student can always return to that concrete or tactile memory.
The second component is the ability to transfer that understanding to a pictorial representation. This could be a drawing, a number line, or a graph. This links the mental imagery to the initial experience.
Finally, the student must use this new concept or information in an application at its abstract level of meaning, using only numbers and operations. This is equivalent to “comprehension” in reading. It involves seeing the utility of what has been learned.
Typical math instruction may include some of these features but omit the Concrete-Representational-Abstract instructional sequence or the lengths to which we go to cement meaning. Traditional Instruction may give students temporary proficiency with a formula or algorithm but they may perform it with little understanding. This is why so many students fail to retain math skills. They need this understanding that links math conceptually through a hierarchy of concepts, connecting one operation and one concept to another.
Another difference in my particular approach, is that I often begin with an inverted instructional sequence. I begin with real life and the application and lead students to see the usefulness of a particular concept as they are learning it.
In multisensory math we endeavor to meet the needs of all students through differentiation. We use evidence based strategies, a restricted set of number facts for new introductions, the Concrete-Representational-Abstract instructional sequence, and—in my courses—a lesson plan based on an Orton-Gillingham model. It includes many strands of math, which all lead to the lesson’s new introduction. Students are given multiple opportunities to interact with the number facts, which they will need for problem solving before they have to use them. We also rely on many different graphic organizers to help students summarize and codify what they have learned. In almost every conceptual level, we build, describe, and name. We build visual-tactile-kinesthetic memory, transfer that to imagery which is portable memory, build supports for an internal monologue, and give adequate practice to memory.
I reference the NCTM position paper on interventions when I say we focus on the big ideas of math. I have grouped these around four “Super Powers” that carry a student to middle school math and algebra. Without these super powers, students will continuously struggle.
So our goal in multisensory math is helping students truly understand the concepts articulated in the grade band goals of the Achieve the Core: Math Focus by Grade References as we help them catch up to keep up. We continue to build fluency even as we attack learning higher-level concepts. Even students with emerging fluency can be taught fraction concepts and linear algebra. One just has to know how to embed those concepts in accessible facts.
Q: You have an extensive background as a Certified Academic Language Therapist. Is there overlap between language difficulties and student performance in math?
A: I find that there is a profound link between the instructional language and student math comprehension. Excessive instruction can get in the way of students processing the language they need to support their own internal monologue for calculations. This is especially true as the math gets more complex.
For students with language-based learning deficits, such as dyslexia, simple, repeatable, and retrievable phrases serve to link concepts and meaning. For example we might say, “It is one of two equal parts. Its name is one half. It is two of three equal parts, its name is two thirds.” Nationally we begin to see test scores decline after the introduction of fractions and decimals especially in special needs populations.
Morphology can also help students to link math and non-math vocabulary which supports meaning for both. For example: circum- means around. This adds to comprehension for circumference, circular, circumstantial evidence, circumferential, circle, and circuitous.
Language comprehension is a huge problem for many students. This is especially true with word/story problems. I have examined the latest research from the What Works Clearinghouse Practice Guide (2018) and combined it with Eileen Marzola’s work on reading comprehension to produce some interesting parallels.
Finally, my training as a language therapist has guided me immensely in how I teach. I use a multitude of multisensory structured literacy strategies in my math instruction: coding, simultaneous processing, gross motor activities among others. As a language therapist I have been trained to break things down to fine levels, and teach smaller increments using a VAKt approach. I apply these strategies even at the level of algebra.
Q: Just as phonological awareness is a key foundational skill for reading success, what component of math instruction is key to math success?
A: From a neuroscience perspective, I believe there is a consensus now around numeracy or number sense as the most important foundation for math. It begins before a child can speak and continues on to form the foundation of number patterns for composition and decomposition of quantities. It is not just recognizing, as Marie Sander put it years ago, the “threeness of three,” but capturing the essence of what it means to be three. That has to be ingrained before a child can understand that the quantity three can also be applied to making three groups or cutting three parts.
I think one of the most important articles in recent years is the Douglas Clements’ article on Subitizing, where he distinguishes between perceptual and conceptual subitizing. Perceptual subitizing is the automatic recognition—we do a pretty good job with that in today’s classroom. The more difficult one is the conceptual subitizing with which I think we are having less success. Conceptual subitizing is more sophisticated. It involves knowing that, for example, eight can be made in different ways: 5+3, 4+4, 6+2, 7+1. It includes knowing that this set of decomposition patterns can help us reason mathematically at higher levels across place value and in operations.
When teachers work with young learners and place a heavy emphasis on counting as a strategy for getting an answer, especially to add on or to count back to subtract, they do students a disservice. It is not that counting is unimportant—it is important. It is just that strategy instruction should not replace teaching the underlying skill of subitizing. Counting is inefficient. The child who must continually count to reach sums could have been taught much more efficient methods.
I think the thing that is most evident to me is how this impacts older learners. I see middle and high school students counting on their fingers, counting dots on numbers, and so on, to collect like terms in algebra or work with integers. The student who does not know 5+3=8, will struggle with 3-8=-5, with 3x +5x=8x and more. Additionally, they will not see the implications for these patterns at higher magnitudes of numbers.
Q: How would you like to see pre-service teacher training change to better prepare them to meet the needs of the students they’ll be teaching?
A: Firstly, I would like them to have a course in foundational math itself, from the impact of subitizing and how to teach it, to how it impacts mathematics learning through the hierarchy of concepts vertically to higher math.
I also want them to know that not all manipulatives are equal for all things, and that manipulative use does not end in 3rd grade. I like my graduate students to push themselves and attempt to teach something more complex using manipulatives. I like them to pay close attention to their instructional language.
I want every secondary math educator to take a course in teaching foundational math K-5 so they can spot the instructional casualties they will find among their students. Also, I believe every elementary teacher should be exposed to teaching some pre-algebra and algebra concepts, at least up through linear functions, so that they see those connections vertically through the hierarchy of math concepts.
Finally, I want every pre-service math teacher to have a course in the ways that disabilities impact math and the ways they can modify instruction and instructional materials to meet the needs of all students in an inclusion setting.
Q: There is professional talk right now about productive struggle in math. What do you teach others about productive struggle?
A: Productive struggle is part of the problem solving process. I believe we have been so focused on getting an answer to a problem that we lose the joy of discovery, the feeling of pride in a job well done. We have over accommodated many of our students into ineptitude and then rewarded them for pushing buttons rather than understanding. This is why I encourage that reversed instructional sequence. Begin with the problem solving which includes productive struggle. I like a model in which students prove a solution “by construction.” They build, describe, draw or link to the steps in an algorithm and then must justify their thinking.
As a testament to the efficacy of this approach, I often have students who say they are happy to get up in the summer and come to algebra camp for three weeks. I also get comments from my distance courses in which adults, math teachers, special educators, and elementary educators say, “Gee, I wish I had learned math this way.”
Q: What do you think are some of the greatest challenges for students with learning differences when it comes to mathematics specifically?
A: I believe a new significant finding is that when the brain processes quantities, makes estimates, and visualizes numbers it occurs primarily in the non-language hemisphere of the brain.
However, when the student begins learning facts for which there is no visual representation, such as multiplication and division, the activity switches to using more of the language hemisphere. This is a profound insight for students with language-based learning deficits or dyslexia. We know that many students with dyslexia struggle with learning multiplication facts. Now we have a clue as to why: word retrieval. Once you know a possible “why” you can come up with possible solutions. I like to say teach “fewer facts at a time to develop fluency over time.” I include multiple strategies for teaching multiplication and division facts in my courses. And, I advocate teaching inverse operations at the same time. Learning the multiplication tables once is difficult enough for many students.
Other than that, I believe most of the challenges for students are instructionally based. When procedure is the primary goal, it is language-based and many students will struggle. If the instruction is conceptually based and grounded in real life with meaningful application, they struggle less.
Finally the greatest challenge I see for many of my students is the over dependence on calculators. We would never say a 3rd grader who is failing to learn to read should simply give up and exclusively use talking books, which is exactly what we do in math. We just give out a calculator so that the student can get an answer for the test. The first thing I do is take all calculators away for general class instruction. I teach the facts we will use and we use them repeatedly. We use “friendly” numbers for general instruction and accommodations for tests, quizzes, and independent work. All students benefit when they are freed from the burden of retrieving unfamiliar facts. We should never stop building fluency through multiple means.
I do understand a parent’s desire for accommodations and to see their student struggle less and succeed more. I understand the student’s desire to keep up with the class. There are, however, ways to accommodate learning differences and increase skills at the same time. It is a central focus of my courses: helping students catch up to keep up. We can do better than sending our students to algebra unprepared and underserved. Nationally, only 8% of our special needs students are proficient in math in 8th grade when they begin formal algebra training. We must do better.
How Hill Learning Center Can Help
We can make a difference. Hill Learning Center is committed to transforming students with learning challenges into confident, independent learners. Contact us if you’re interested in taking the next step.