As a math teacher for over 20 years, I’ve worked with so many unique students. I’m sorry to say I haven’t found any general rule that makes math more or less understandable. Still, it is rare for me to have a student that doesn’t find some level of success in my classes. Knowing there’s no magic potion, I’d like to share some of the strategies I’ve used with my students to improve their math learning. If you follow at least some of my advice, I truly believe math will become more understandable, more interesting, and, dare I say, more fun!
Beyond The Classroom
To begin with, when you hear “math” do you think of a subject in school or something else? If math for you is a subject in school, learned at a certain time each day, with a specific teacher, specific agenda, and a specific measure of success, then you’re missing out! On what, you ask? Consider an analogy.
My friend Brendan loved basketball. He would watch basketball on TV. Collect basketball cards. Go to the park to shoot baskets by himself. Play pickup games at the playground. And, yes, play on a team. True story! Think: What if Brendan only played basketball at basketball practice?
To make math more understandable, you need to engage in math beyond the classroom. Here’s a list of ten ways to get started:
- Play board games like chess, go, or othello
- Play card games like gin, rummikub, or cribbage
- Do sudoku or logic puzzles (try brainzilla.com)
- Make origami models
- Read books with mathy ideas (try “The Phantom Tollbooth”)
- Build with legos, magnatiles, and blocks
- Tinker with robotics, programming, and circuitry
- Build scale model airplanes and rockets
- Assist in shopping, cooking, and gardening
- Join math club or enter competitions
Bottom line: Get busy doing mathematical things in your everyday life! It doesn’t need to literally be every day; you don’t have to do them all. But, gosh, do you really want to only do math in math class? Or only play basketball at basketball practice?
Behaviors of Success
Besides learning math outside of class, there are things you can do in class to make it more understandable. If you read my blog about the 3 Rs reimagined, I discuss using reflection, revision, and resourcefulness to improve learning. Let’s apply them to learning math.
For reflection, I give my students the checklist below. I ask them to check off any boxes that describe their efforts in math class under the headings of patience, practice, and persistence. Go ahead, try it for yourself!
Patience
◻ I accept that I often won’t “get it” the moment “it” is presented
◻ I take time to study each example presented by my teacher
◻ I am willing to use class time to help classmates
◻ I accept that lots of practice is necessary for mastery
◻ I believe I am capable of learning hard things
◻ I give an honest effort to master the material
Practice
◻ I take good notes
◻ I complete all assignments on time
◻ I participate in class activities for the sake of learning
◻ I review notes, classwork, homework, and other materials
Persistence
◻ I meet with the teacher and/or another student to study
◻ I discuss and fix mistakes
◻ I ask questions to begin, clarify, or extend my learning
◻ I give and get help
◻ I use online and/or supplemental resources
Patience is accepting the time and effort necessary to learn hard things. Practice is those everyday behaviors that allow you to fully engage with the material. Persistence is follow-through. It’s getting over hurdles and not giving up.
Next, I ask my students to look at the boxes that are not checked. This is a recipe for action. Any unchecked box is an opportunity to change a behavior. For example, If you didn’t check “I give an honest effort to master the material,” what might that look like? Maybe you rush through assignments. Maybe you leave the harder problems undone. Maybe you copy answers from a friend. All of these little things add up. They destroy your patience. They destroy your persistence. They make math class more about getting stuff done than actually learning anything. How sad!
Lastly, I have my students set a goal. Which unchecked box (or boxes) will you focus on for the next unit? What specifically will you do differently? Notice, reflection has turned into revision. You are revising your behaviors to target areas in need of change. Using the same unchecked box “I give an honest effort to master the material,” maybe your goal is to try every problem before asking for help. Maybe it's doing an assignment in two phases.
Phase one: Do the ones you can
Phase two: Take 15 more minutes to try the ones you left blank
Whatever your goal, it should target an unchecked box and name specific things you will do differently.
Holding Yourself Accountable
You’ve got to stick with the plan! That is, hold yourself accountable. Accountability relies on resourcefulness. Share your goal with your teacher, friends, and parents. Display your goal somewhere that you will see it–maybe on the cover of your math notebook! And monitor your progress. It could be as simple as each day keeping a tally of whether you did or did not change. Or you could ask a friend, teacher, or parent to check in with you regularly. Even better, reward yourself with something you like for each day of success! Just find a way to keep yourself focused on the daily struggle of changing a not-so-great behavior into a better one.
Exploring Options
You've now learned how to use the 3 Rs along with the 3 Ps checklist (i.e. patience, practice, and persistence) to set goals and monitor your progress. That is almost enough to improve math understanding. But there’s actually one more thing. It relates back to the question of whether math is a subject in school or something else? You now know that math can be experienced in many different ways. You can choose activities that allow you to think mathematically. But even when you are in math class, with the specific agendas and specific measures of success, there’s more than meets the eye! Frankly, math isn’t just following procedures to get the correct answer. Math is actually playful, creative, and artistic. In a nutshell, math is problem solving.
Good problem-solvers are good decision-makers. And to make good decisions, you need to have options. Suppose you have 6 packs of soda and each holds 12 cans. How do you find the total number of cans? Of course, you can use the standard algorithm (strategy 1). But, you can also decompose 12 into (10+2). Now, 6x10 is 60 and 6x2 is 12. So, 72 is the total–no regrouping needed (strategy 2). Or you could line up the cans and count them one by one. Maybe that’s impractical but it would work. As a compromise, try using a model (strategy 3). Or you might calculate 2 packs is 24, so 4 packs is 48, and another 12 makes 60, so 72 is the total (strategy 4).
Strategy 1
Strategy 2
Strategy 3
Strategy 4
I’ve just described 4 distinct ways of solving (see table). We now have options! Which is most efficient? Which is most creative? Which makes the most sense? When you ask and answer these sorts of questions, you develop a deeper understanding of math. Because you become a good problem-solver! Don’t do one strategy just because “that’s what you were taught.” That is quite possibly the worst version of math. Not much thinking. Not much creativity. Not much understanding.
Real mathematicians are artists. They use symbols, patterns, and relationships as their paint brush. They see the whole universe as inspiration. They approach their work with a playful intensity that allows for familiar paths to be questioned and new paths to be explored. Real mathematicians do not do problem sets with answer keys. They ask questions that have not been asked and answer questions that have not been answered.
Go Wild!
As a mathematician-in-training, there’s definitely value in learning tried-and-true math concepts and skills. There’s definitely value in doing problem sets with answer keys. That’s similar to practicing layups and free throws at basketball practice. Or learning a new play to try with your team. These things matter. They help you improve. But, if you’ve ever played in a real basketball game, you know best laid plans don’t always work out. Real game play is very different from practice. Real game play requires quick thinking, fast reactions, and creative ideas.
Similarly, real math is quite different from school math. It, too, requires creative thinking expressed through problem solving. It also requires questions that extend your learning. Think back to the 6 packs of soda example. Here’s some questions a mathematician might ask:
- Why do packs hold 12 cans? I’ve seen 8-packs. What is the best number?
- What influences the shape of the box? Is it refrigerator shelving? Store shelving? Size of shopping cart? Consumer preference? Packaging limitations?
- What is the most environmentally friendly packaging? What uses the least amount of material? What material would be most sustainable?
- Why are cans shaped as they are? Are there other designs that would work better? How would that influence the number in a pack?
I could go on and on! Each question leads to another. Each requires research along with charts, diagrams, graphs, models, calculations, measurements, and scratchwork. There might be one best answer or multiple answers that compete with one another (e.g. consumer preference vs. environmental friendliness). Math is wild, unkempt, ever changing, and ever growing. We need you to help us ask questions that haven’t been asked and answer questions that haven’t been answered.
Answer The Call
My advice must end, but your journey has just begun. You now have some really great ways to make math more understandable! It may not happen overnight. Often the things in life worth pursuing require lots of time and effort. Give yourself some grace. Then start making some small changes that will lead to big results! Start doing some mathy things in your freetime. Change some not-so-great classroom behaviors into better ones. Try to have a playful intensity when solving math problems–find more than one way! Lean on your teacher and classmates for support. And start asking questions, not just when you need help, but also when you’re curious! All of these things add up. They make math more understandable, more interesting, and, dare I say, more fun!
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