Students who can’t understand instructions for math problems face unnecessary barriers to … [+]
Students who don’t read well or lack crucial vocabulary often face unnecessary obstacles—not just in reading but also in math.
Years ago, when I served on the board of a charter elementary school, teachers told me about an odd phenomenon they’d noticed. Sometimes when children couldn’t do math problems on their own, teachers would try reading the problems aloud—and suddenly the kids could solve them. Apparently, those students could do the math. They just couldn’t read the words.
Later, when I was researching a book on literacy, I visited a first-grade classroom to observe reading instruction, but it turned out the time was being used for math instead. I decided to observe anyway, and I discovered how difficulties with oral language comprehension—not just reading—could interfere with students’ ability to do math.
While the teacher met with one small group, the other children were working independently using digital devices and wearing headphones that enabled them to hear instructions for the problems read aloud. So despite the fact that their reading skills were quite limited, the teacher must have assumed they would be able to understand what they were supposed to do.
But as I discovered when I wandered around the room, that wasn’t always the case. One boy heard the instruction “Combine 8 and 3,” but he didn’t know what combine meant until I told him it meant “add.” Another was looking at a number line extending from 80 to 90 and listening to the question, “What number comes before 84?” After watching him click on 85, 86, and then 87, I found out that he didn’t understand the word before. Once I explained it, he immediately clicked on the right answer.
I saw other first-graders working on problems that said things like “Round 119 to the nearest ten,” and “Find the area of the following triangle in square units.” Did they know the meanings of words like round, area, and square units, I wondered?
The elementary curriculum rests on the idea, reinforced by standardized tests, that all important learning falls under the headings of “reading” or “math.” One problem with that conceptualization, which I’ve written about before, is that it takes too narrow a view of what reading entails. In order for students to understand what they read, they need to acquire the kind of vocabulary they can get only through immersion in topics in social studies, science, and the arts—subjects that have been marginalized or even eliminated to allow more time for reading and math.
But another issue is that reading isn’t entirely separate from math. If you can’t read a math problem, you can’t solve it. And even if you can read it—or listen to someone else read it—if you don’t have the vocabulary you need to understand it, you’re also out of luck.
At least a couple of other observers have noticed this problem. Writing in The74, Lynne Munson—who led the creation of a curriculum called Eureka Math and has a dyslexic child—recently explained how dyslexia can interfere with math performance. After receiving a letter from a dyslexic sixth-grader pointing out that the language used in Eureka Math was hard for her to read and understand, Munson and her colleagues revised the curriculum to use simpler words and shorter sentences, and to generally contain less verbiage.
To make math accessible to all learners, Munson argues, schools should use curricula that take into account whether students have the skills to read the problems they’re expected to solve. She advises teachers who create math lessons to bear in mind a few principles—for example, using a lot of white space in workbooks and quizzes, along with easy-to-read fonts, and explicitly teaching “words that may be difficult but that students need to learn to build their math vocabulary.” That might include words like combine, sum, and total—and, for some students, even before.
A recent study involving students who are still learning English sheds light on another aspect of the problem—and what can be done about it. English-language learners are the fastest-growing segment of the K-12 student population, numbering almost five million. As a group, they score substantially lower than native English speakers on standardized math tests.
The researchers worked with a teacher of third-grade English-language learners who had also been diagnosed with math learning disabilities. The focus was on word problems, an area where the students struggled because of unfamiliar vocabulary. The teacher was coached not only to model math concepts, but also to define vocabulary and provide context for it, have students discuss the problem, and rewrite it on the board as a sentence beginning, “The question is …”
Researchers classified word problems at four levels of difficulty based on both the concepts and the math terminology used. All students started at level one, but after about twelve 20-minute sessions of instruction, all had progressed to level three or four. Follow-up testing showed they retained those gains.
True, the study was small, involving only one teacher and nine students, divided into groups of three. But we shouldn’t need a large-scale study to convince us it’s important to make sure students can read and understand the math problems we expect them to solve.
The study highlighted one potentially helpful approach: having students write about the math content they’re learning. The researchers noted that students made comments such as, “I like how the teacher taught us in steps with writing, and we got to talk about math with writing.” The teacher also appreciated the “basic writing steps to solving word problems.”
Generally, studies have shown that having students write about math content—as well as social studies and science content—boosts learning. That doesn’t mean, however, that any writing involving math will be beneficial. For example, asking students to keep “math journals,” in which they record their thoughts about and experiences with math, may not work for students who find writing to be an overwhelmingly difficult task.
An effective approach for many students is to use explicit writing instruction that is embedded in whatever math content they’re learning, beginning at the sentence level to modulate the heavy cognitive burden writing imposes. For example, if the topic is the relationship between fractions and decimals, students could be given the phrase Fractions are like decimals and asked to turn it into sentences using three different contractions: because, but, and so.
Students might create sentences like these:
· Fractions are like decimals because they are all parts of wholes.
· Fractions are like decimals, but they are written differently.
· Fractions are like decimals, so they can be used interchangeably.
Activities like this, when carefully crafted, reinforce crucial vocabulary and math concepts while simultaneously familiarizing students with complex syntax that rarely appears in conversation. For example, once students are familiar with using but, they can try using the more sophisticated although, as in: Although fractions are like decimals … (These examples are drawn from a book I co-authored called The Writing Revolution: Advancing Thinking Through Writing in All Subjects and Grades. I have no financial interest in the book or The Writing Revolution organization.)
As the anecdotes at the top of this post indicate, it’s not just students who have dyslexia or are still learning English who could benefit from clarifying the language used in math. With only 34% of eighth-graders performing at the proficient level or above on national tests—and only 15% of those whose parents had no education after high school—it’s clear we need to remove whatever barriers to learning that we can. And ensuring that kids can read and understand their math problems shouldn’t be all that difficult.