Wednesday / July 24

# Mathematizing for Families!

Math practice doesn’t have to be all exercises and worksheets. You know that, but do your students’ parents know that?

Families probably know far more about teaching now after supervising hours of Zoom lessons during the various degrees of sheltering in place that families have experienced since the coronavirus pandemic began in early 2020. But memes keep popping up on social media about “the new teacher” (parent) teaching addition “the old way.” Fortunately some of the memes show a positive direction, with students protesting that their teacher does it the easier way, while the parent insists on “carrying the one!”

All fun aside, this has been a trying, and for some, traumatic time. The emergence of choice boards, a collection of worthwhile activities from which students might choose a learning task, have introduced us to a new range of pedagogical practices that just might work in classrooms as well. They may also continue to work for families as we move into the summer break.

Mathematizing is a human activity. A calculator can’t do it. Nor can a computer. A mathematizing human examines a situation and decides how to translate what they see in a useful mathematical way. Popular culture might suggest that people don’t often use mathematics in real life, but it’s more likely that we simply don’t talk about it. One way you might unknowingly mathematize is when you are simply watching a video streaming service over a long stretch of time.

“Bingeing” a television series is something you may have done this spring. But with work and family responsibilities, you still want to set a bedtime that will help you function the next day. If an episode of your series is 42 minutes long, how many can you watch and still go to bed around 1 am? It has to be at least four episodes because the episodes are less than an hour long and there are four hours between 9:00 pm and 1:00 am. Then you might round this to ¾ of an hour, starting at 9:00.

9:00 – 9:45

9:45 – 10:30

10:30 – 11:15

11:15 – 12:00

12:00 –12:45.

5 episodes!

If we wrote this mathematics into a word problem, it would seem strange and even tricky because you might have used a different strategy for calculating the television watching than the book doesFor most word problems students do, the mathematics they are currently working on drives the choice of strategy. When we mathematize our world, there are no such constraints because we make sense of and solve a problem in the way it makes sense to us. Here are some equations that represent the mathematics we used to mathematize the television binge-watching situation.

4 hours ÷ ¾ hour per episode x episodes x = 5 1/3 episodes  (or just 5)

9:00 to 12:45 is 4 hours – 15 minutes3:45 (three hours forty-five minutes)

Estimate 42 minutes per episode x 4 episodesx = 40 x 4 = 160 minutes

Estimate 42 minutes per episode x 5 episodesx = 40 x 5 = 200 minutes

Each of the interpretations we did of our TV watching time is an example of mathematizing the situation. The calculation that follows includes mathematics from many different units: fraction division, elapsed time, estimation, Equal Groups multiplication or even a proportional problem. You could sit down at 9:00 to watch TV and do none of these calculations, but making decisions, budgeting our time and money, and making choices that benefit us can be evaluated with mathematics. How do you mathematize your world?

As teachers across the country worked to make sense of online teaching, or as some call it “Emergency Learning,” creative new ideas arose to accommodate students whose lives had also dramatically changed. One strategy was the choice board, one that offered students freedom to choose an activity, but also kept them thinking about mathematicsHere is a mathematizing choice board that you can share with parents and encourages students to mathematize their own worlds.

### Mathematizing Choice Board for Families

Encourage families to allow students of different ages to mathematize the situations differently, and then help children translate their thinking into an equation or number sentence as we saw in the television-watching situation.

choice board is flexible enough to use now if you are still teaching online, but it can also be an alternative to traditional homework, or a summer learning idea.

When should we buy more rice? (Show a partially filled container. Estimate one meal. Figure out how many meals are left in the container.)

As you engage students in mathematizing thinking, always ask how they are thinking about the situation. What is your reasoning about what math to do? Why are you doing it that way? Tell me some numbers to help me make sense of your reasons. By bringing numbers, shapes, data, and measurements to the front of students’ everyday activities, they learn to mathematize  similar situations and word problems won’t seem as scary.

Be well and mathematize!

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Kimberly Morrow-Leong is an adjunct instructor at George Mason University in Fairfax, Virginia, a part-time researcher at American Institutes for Research, and a consultant for Math Solutions. She is a former grade 5–9 classroom teacher, K–8 mathematics coach, and coordinator of elementary professional development for the National Council of Teachers of Mathematics (NCTM). She recently completed an elected term as vice president and 2018 program chair for NCSM, Leadership in Mathematics Education. She holds a BA in French language and a masters in linguistics (TESOL). She also holds an MEd and PhD in mathematics education leadership from George Mason University. Kim is the 2009 recipient of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST) from Virginia. She is happiest when working with teachers and students, putting pencils down and getting messy with manipulatives!