The Institute of Educational Science (IES) has a number of recommendations or educators when providing mathematics support to struggling students. Their primary recommendation is to use a systematic approach to instruction and intervention. This means from the start of the school year, educational tools and resources used to teach math should incrementally build knowledge and provide adequate support for students to learn and understand new concepts and procedures (IES, 2022, p.5). Moreover, as content is being taught incrementally and explicitly, teachers must also regularly review and integrate previously and newly learned content to build students’ foundational knowledge. I feel this systematic approach is valid for teaching any subject. Teachers often use it in literacy instruction when teaching phonics, spelling and phoneme awareness. Yet, I believe it is especially well suited for teaching math.
Math concepts naturally build on each other to solve larger problems. We cannot solve advanced math problems without having prior foundational skills and knowledge. Language has many shades of meaning, but when solving a math problem, the result is typically binary — the answer is either correct or it is not. However, how we get to the answer can have many paths, and the ways in which students learn effectively can likewise vary. The ambiguity of language can be confusing when teaching math or when students struggle to understand what a math word problem is asking. Should we say, “minus, subtracted by, or take away” when teaching subtraction? We want to be consistent and use simple language for our primary grades but what happens when our students start taking standardized tests and the language they use is different? What if the next grade teacher uses different language to describe the same mathematical concepts? To solve this, I think we will need to explicitly teach different variations of phrases and words which essentially communicate the same thing.
Students will certainly need to understand mathematical language to progress further in their math studies beyond the elementary school level. As they gain more a sophisticated understanding of math, students will be expected to solve more complex problems. The IES suggests that educators primarily use academic mathematical terminology to maintain consistency and prevent confusion as it “conveys a more precise understanding of mathematics than the conversational or informal language” (IES, 2022, p.18) I agree that it is important to teach mathematical language; however, I also think teachers need to teach the simplified informal language. I would argue it is better to start with something easy to understand, and be consistent when using it. After mastering the concepts, we can explore alternative ways of saying the same thing and this includes the formal academic labeling language. Which is easier for a grade two student to say and understand, “the flip-flop property” or “the commutative property?” The IES suggests that such informal language “can cause serious [emphasis mine] confusion later in the students’ schooling when other teachers do not use the “flip-flop property.” I find their thinking to be hyperbole. I suggest that we teach the informal and formal at the same time. Informal speech conveys meaning that is easy to grasp and the formal language provides the academic labeling needed for advanced math. To prevent confusion, we can work together with other teachers in coming to a consensus as to what “informal” language is suitable.
Teaching literacy and numeracy usually uses explicit instruction when introducing new topics to novice students as it helps them better understand the content. I would use the same teaching methodology for learning specialized mathematical terms. It important to not only explicitly teach the language for understanding what is being asked but also the language used to explain their math solutions as well. In my formative assessment exit tickets, I prefer to use a fill-in-the-blank style for early learners to model the language structure and make it easier for my students to fill out. However, students will need to eventually write and explain their own answers independently. It is important that we do not skip over practicing this skill when trying to improve student math literacy.
To support learners with literacy issues we should find ways to use simpler words and shorter sentences, and avoid verbose language (Wexler, 2022). I feel as teachers, we must also reflect on why we use language differently. Using the phrase “take away” to mean subtracting implies that one group is losing something. However, is such phrasing useful for this word problem: “Jill has two more buckets of water than her brother Jack. Jill has 8 buckets. How many buckets does Jack have?” In this case, no child is losing anything so should we use “take away?” For this example, a number line becomes an easier way of understanding and solving the math problem as we can translate it visually. Using a number line to help novice learners understand math concepts is another recommendation by the IES (2022, p.29). I am supporter of using manipulatives and other forms of visual learning like number lines to explore different ways to solve a math problem. Visual aids and number lines help to deepen our students’ understanding of math concepts and can lead to inquiry-based learning. One caveat though, we must ensure that our students do not become dependent on manipulatives and eventually transition to using mental math for solving a problems once they understand the mathematical concepts.
References
Institute of Education Sciences (IES). (2021). Assisting students struggling with mathematics in the elementary grades. (ed.gov) pp 1–55.
Retrieved from https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/WWC2021006-Math-PG.pdf#page=12
Wexler, N (2022). When language prevents kids from succeeding at math. Substack.
Retrieved from https://nataliewexler.substack.com/p/when-language-prevents-kids-from