I once had a college student who made it his mission to prove to me that he could go an entire day without using math. This was not a just out of high school kid sitting in my math class. This was what the higher education world calls an “adult” learner or a “returning” learner; someone who already had some life experience under his belt.
He wasn’t super confident in his math ability, and I don’t think he saw himself as a math person…yet…but he was willing to put in the effort, ask the questions, and challenge the ideas presented. This, along with our lively class discussions, led to his assertion that he could go an entire day without using math.
Can you relate to this at all?
Each day, he would eagerly come into class and tell me the things he did the previous day, and each time I would respond with the underlying math ideas involved. This was well before I had developed the language I use now about interacting with mathematical ideas and what it takes to be a math person.
I guess in some ways, this student set me on the path to where I am today in my belief and in my message to you in each of these posts and podcast episodes.
At the time, I knew there was math hidden in everything, even if the awareness of it isn’t at the forefront of your mind. Like the math involved in building your home, or in the inner workings of your computer or cell phone, or even in the trajectory of a baseball as it comes off the bat.
Does noticing the right angles of your doors and windows as you enter your home or unconsciously choosing to wash the silverware first and save the greasy pan for last make you a math person? I’m sure there are people out there who disagree, but I say yes.
Because those thoughts have roots in mathematical ideas.
Because all it takes to be a math person is to be a person and interact with math.
Because something like mentally comparing and sorting the dishes is so automatic for you that you do it without thinking has to mean you are a math person.
I hope you sit with that for a minute or two.
We’ve now come to a point in our mathabet journey where ideas get a little thin. There just aren’t a lot of distinct math terms beginning with J that everyone has heard of or that you regularly encounter. So today’s ideas that begin with the letter J might seem like a stretch, but if you stick with me, I think you’ll recognize when and where you use them and see the connection.
Jump
The first idea is pretty straightforward, although you might know it by a different term. The word jump might bring to mind a basketball player or what your child does on the furniture, but in math it has a few different applications. The one you are most familiar with is jump counting, which you may know as skip counting. When you count by twos or fives or tens, you are jump counting, meaning you are “jumping” numbers on the number line when you count. If you’ve ever counted a pile of objects by twos, or a stack of five, ten or twenty dollar bills to see how much money you have, you have jump counted.
Similarly, jump is a strategy you might use when you add numbers in your head. As an example, if you are adding 12 and 45, you might recognize 12 is 10 + 2 and say in your head,”45, 55, 56, 57” to arrive at the sum. You jumped from 45 to 55 before counting on to get the total.
There are many scenarios where you might encounter jump, or skip, counting or where you might use this strategy to help you solve a problem. If you use jump counting or the jump strategy, you are a math person.
Justification
Justification is another word beginning with J that has a connection to mathematical thinking. In math class, you might be asked to justify your thinking. This means for each step in your thought process as you solve a problem, you provide some mathematical reason for why you did it. You probably aren’t often asked to justify your mathematical thinking in real life, but you do use justification in other areas.
- You justify why you need to spend money on something that is outside your regular budget.
- You justify your decision to not let your child participate in some activity.
- You justify why it’s okay for you to skip doing laundry today.
Justification has its roots in logical thinking. And logic and math are closely related. So, if you are using logical thinking to justify your actions or decisions…and I don’t know anyone who does not do this…you must be a math person.
Joint Variation
I almost didn’t include joint variation on this list. In fact, it was a last minute addition to this discussion. My problem is that I just don’t know how many people interact with this idea on a regular basis, so I wasn’t sure it was worthy of a mention. Ultimately, here it is because there are a couple of real life scenarios that I think most people can relate to.
Joint variation means that something is the product of two or more variables. Product meaning multiplication and variables meaning values that aren’t fixed. If you have a job and get paid by the hour, for example, your paycheck varies jointly with the number of hours you work and the hourly pay rate. So, anytime you are playing with the numbers, so to speak, to see which job scenario gets you the bigger paycheck or how taking a day off will affect your pay, you are interacting with the idea of joint variation.
Similarly, distance varies jointly with rate and time. You might even remember the formula d = rt from math class. If you are headed on a road trip, you can figure out about how long it will take you to get there if you know how far you are traveling and can estimate your average speed. These days, I guess most people just use the map app on their phone for that.
But, maybe you are a runner and you are training for a race. The same idea applies. If you know your typical speed and how far today’s training run is, you can estimate how much time you’ll need to complete it.
Joint variation probably isn’t a term that’s on your radar, but when you are thinking about hourly rates or distance and speed in any kind of scenario, you just might be interacting with this idea. And that makes you a math person.
It’s been a joy to host this discussion today! I’m on a mission to change the way the world sees math, and that starts with you. If you found value in this post, if something you heard made you pause, or if you suddenly realized the hidden math in something you do every day, now is the time to join the movement!
When you comment here and share this site, or when you subscribe to, rate, and share the I See Math People podcast, the algorithms will show it to more people and the more people who get the message, the more mindsets can begin to shift.
That, my friend, is how movements gain momentum.
I appreciate you joining this discussion of a few of the mathematical concepts beginning with the letter J. I truly hope you heard something about jump counting, justification, and joint variation you are able to relate to and that it makes you stop and think about where math shows up for you on a daily basis. Noticing where you interact with math is the first step to shifting your mindset and seeing yourself as the math person you really are.
I’m Jennifer Mason Hardin and everywhere I look I see math people just like you.
