I am a Marilyn Burns super fan! Since I started my career 17 years ago, I have been using her publications and resources for teachers to support instruction in mathematics. One resource that has been invaluable in rebuilding foundational skills for students is Do The Math, an intervention program for students in grades 1-5. In reading about Marilyn's approach to vocabulary instruction as part of the program, I had to grapple with what I thought I knew about supporting language in mathematics.
Here's the phrase that caught me off guard: "It’s important that developing understanding
of mathematical concepts always precedes teaching vocabulary, so that new terminology
has an anchor in understanding."
As a student, math class often consisted of sitting down, taking out a notebook, and recording vocabulary and notes for what we were learning for the day. When I began my career as a teacher, I emulated that. I believed that if students were going to learn new content, I had to give them the words first so they would know what I was talking about. So what would it look like in the classroom if students were to experience the math first and then get explicit vocabulary instruction? Surly students would struggle to understand the concepts.
In all her wisdom, Marilyn Burns also says, "sometimes we need to unlearn to relearn." I thought about how my own children learned words and made meaning from them. If I told my 2 year-old years ago, having no experience with bouncy balls, to go grab a ball so we could play, she would have stared back at me confused. Context and experience matter. Instead, my daughter and I would pass the ball and I used language to give her exposure. I held the ball and said, 'ball' while we were passing. Later, when I told her to go get a ball so we could play, she had a frame of reference. The word meant something to her.
What does this look like in the math classroom? I think it's highlighted best in a classic experience students have in Do The Math. In the first lesson of one of the multiplication modules, students start with an introduction to the game Circles and Stars. Students first roll a dice to determine the number of circles to draw. Then, they roll again and use the new number to tell them how many stars to draw in each of the circles. Consider a turn where a 4 was rolled followed by a 3.
Students are then asked to think about how they could tell the total number of stars. When working with students, some of the most common responses are; "I counted them all and got 12." "I counted by threes." "I added 3 plus 3 plus 3 plus 3." "I know that two groups are 6 and another two groups are 6 and added that to get 12."
For the remainder of the first lesson, students explore different numbers by rolling their dice to tell them the number of circles to draw followed by the number of stars to draw in each circle. It's on lesson two where the teacher now connects the learning experiences to mathematical language. Students return to their circles and stars and think about how to record their work in different ways and how to talk about the math using mathematical language. Notice the board below.
As you can see in this example, we started by thinking about what we knew about multiplication. Students had some math terms and knowledge from their prior experiences. Then we went back to the image of 4 circles with 3 stars in each. Students shared the different ways that they knew there were 12 total stars. We could now specifically name each of the parts and record them on a vocabulary chart that students could use when talking about their thinking. Pointing to the student generated equation 3 + 3 + 3 + 3 = 12, I could say, "We call this an addition equation. What's the word? It shows all the addends represented in our picture. Each of the 3's is repeated four times." Then, I could add, "Notice that you also said this picture shows 3, four times. We can record that as a multiplication equation of 4 times 3, or 4 groups of 3. This shows 3, four times." By the repeated language and connection to the representation, students can access the language meaningfully. I ask that students repeat the word and watch as I add it to the vocabulary chart with an example.
When I think about how our brain learns, I know that it's essential to connect new learning to what students know. By having the experience first, students can access those ideas and give them a name. The word has meaning as it is anchored in an experience.
It was through my experiences with Do The Math that allowed me to shift my practice in teaching mathematics vocabulary. I could see how reversing the order in which students were given explicit language instruction would only help students to retain and use mathematical language. When I plan lessons, I often think about what mathematical vocabulary students will need to know to successfully communicate. Then, I start lessons with an experience to elicit familiar words they are using and know. If I expect concepts to be new to a majority of the students, I structure the lesson for students to explore the math concepts first and provide explicit vocabulary instruction later. This may happen in the same day or in subsequent days. Then, it's key that I use those words as often as possible while also asking students to try out the words when they are explaining their thinking and reasoning.
Try it out and let me know how it goes! Also, see my 'meeting my hero' moment below.
Take care,
Holly
Burns, Marilyn. Do The Math: Professional Learning Guide created by Heinemann. Portsmouth, NH. 2021.
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