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
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 does! For 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 mathematics. Here is a mathematizing choice board that you can share with parents and encourages students to mathematize their own worlds.
Mathematizing Choice Board for Families
|Budgeting Screen Time
How do you spend the two hours before you go to bed? Keep a chart for two days. Use that information to decided how you can change how you spend your time to do something else you want to do.
Pay attention to how food is served at dinner. Estimate what fraction each person served themselves and how much is left over.
Pay close attention to how you earn the most points on your favorite video game. What is the best move to get the most points? How many times do you have to do that in order to level up?
If you want to safely play with your friend across the yard or fence, where could each person stand and still always be safe 10 feet apart?
|Calories, Carbs, and Protein
Sometimes athletes keep track of how they fuel their bodies. Look at the label on the foods you eat and pick something that you can keep track of for a few days. Some ideas are Sugars, Protein, Carbohydrates, Fats, Sodium, etc.
Set a goal to read a certain number of pages each day. OR, set a goal to read for a certain amount of time each day. Do that a few times and figure out how many pages (or books for younger students) you can read in an hour.
Ask mom or dad if you can download and use a free decibel meter on their smart phone. Decibels measure how loud sound is. Find a place outside where you can make a really loud sound and see how many decibels the sound was. See how softly you can speak and have the meter still measure a change.
What other sounds can you measure?
Many of the sports-focused channels are putting older professional sports games on TV.
When you watch a game, think about how the rules have changed to modern games. How does that affect the final score?
Write some jokes that a circle might tell a square.
On the internet look up how to cut out perfect squares of paper. Use thee squares to create some origami shapes. As you make the folds, describe the shapes you are making and how your folds are changing the shape.
|Break a calculator
Use any numbers and any operators (+ – x and ÷ are all operators) to make the highest value number you can. What does your calculator do when you go too high? What operators do the best? (Older student can include exponents).
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.
A 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!