Where is the Math?

In a recent article entitled “The Missed Opportunity in STEM Education,” Dr. Sten Odenwald (an astronomer with National Institute of Aerospace and NASA) argues that math is mainly missing from STEM activities in high school. He states:

“…The problem is that adults, including some educators, still haven’t figured out how to make peace with the ‘mathematics’ in STEM. Everyone applauds classes in high-tech robotics as the sine qua non of a good STEM program, but ask them to explain how they integrate any mathematics content into the robotic curriculum and you may be surprised that most of these programs do not even work with mathematics teachers to legitimize themselves.”

You can access the entire article here:

I have been around VEX Robotics for three years but have seen very little evidence that teams utilize math (beyond elementary stuff) in the design or control of their robots. Perhaps we (as a community) should do a better job of encouraging, guiding and supporting teams to better showcase the use of math in their work.

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Honestly, I’ve never seen any use for it. The level of math/physics I know and can effectively use only applies in a perfect world that’s in a vacuum. The problem as I see it is that math is either so simple that it can’t actually apply in the real world or so complicated you need a degree in order to understand it. And, honestly, that second kind of math is overkill in VEX. The most complicated math I’ve ever needed was trying to figure out the friction between antislip and the foam tile for proof of concept for a braking mechanism, and all that comes to is Friction = Mass * Gravity * Coeffecient of Friction, which isn’t exactly high level math.

I agree. This year I plan on doing things the right way.

What kinds of formulas and equations are generally used in vex?

the most we do is add the weight of the pieces we are putting on our bot

If you take a look at our 2013-2014 engineering notebook, you will find us using tons of math. The math levels include algebra, pre-calc, trig, geometry and lots of basic math. We also use tons of physics when designing our robot. Math and Physics is a HUGE part of the 323Z design process.

It is very easy to use trigonometry and geometry when designing your robot, and although most may not pay attention, you are constantly using it when designing with a program such as SolidWorks or Inventor.

Additionally programmers use a good amount of math, specifically if they get intricate with their programs such as PID loops, etc.

At the end of the day though, while you may not use a lot of math in this competition, the majority of the students that participate in VEX or FIRST or whatever end up going on to college to major in some STEM related field where they will end up taking mathematics. For example, I was originally going to major in Architecture before I started doing FRC, and am now a Mechanical Engineering major who will have to take math up through Differential Equations, as well as the many ME specific classes that will use math.

While these competitions can help teach different parts of STEM, it’s biggest benefit is the increase in people majoring and pursuing STEM careers because they participated in it.

All of that being said, if you feel your team isn’t using enough mathematics during your season, there are plenty of ways to include more, and it may help your team perform better.


So while in college I’m a mathematics major and computer science major, I tend to use a lot of mathematics.

Trig is used heavily in a lot of our work, as is basic arguments from geometry.

More advanced programming and incorporation of certain sensors and the theory behind them involve more math as well.

Of course there’s more like properly figuring out the velocity of a rotating body with variable acceleration, knowing that Diff Eqs could be used for finding the Radial and Tangential acceleration.

A lot of physics can used Calculus arguments as well.

The amount of linear algebra that can be included in robotics is also big. I think all engineering notebooks to be competitive should include relevant formulas and analysis of subsystems of their robot.

But including math just to include it is not ok. It’s just fluff.

But a large part of it breaks down to how Math education is in schools. I’ve had issues with it for a while, and part of the work I plan to do is to change how we change math education.

We are currently working on solving for the logarithmic curve generated by motor input value and motor speed, and trying to reverse that and achieve joystick control linearization.
We are also working on adjusting angles of our holonomic drive to achieve the best speed-torque combination.
We are using remainder function for gyroscopes and IMEs to convert a raw input to a state function.
We are also currently working on testing out the function between robot speed and battery voltage under a constant motor input condition, so that no IMEs will be used to program the base to finish a precise task under whatever battery conditions.

I can go on and on to explain how we use math to aid our robot program. But the thing is, neither robotics nor stem is a math course. Therefore, it does a good job encouraging us to use math, but teaching students math is not stem program’s duty.

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I encourage you to write a short article explaining and illustrating how your team has used math concepts and techniques to address design problems; it would be a great contribution to the community. You could publish it on your website, and other relevant sites. Depending on how you approach the project, you may even be able to distribute it via Amazon. For example, see “A Tooth for a Tooth: A VexIQ Gear Handbook,” written by the members of a VexIQ team. Here is the Amazon link for it:

By the way, the handbook presents an interesting use of permutations and combinations for gear design!

In part, this is what the author of the article argues about…that there is little evidence that math is being used for designing better robots. Nick, as a college student, perhaps you are in a better position to demonstrate how math can be used to produce a better (or even an optimum) robot design.

It is not sufficient to just say “Yes, math can be used, or is being used.” We need to demonstrate that our teams have the ability to effectively use it, here in robotics.

This is great! Let’s bring all of this work out into the open. Share it, publish it! Let students see potential uses of math in robotics.

Sivand Lak~
Educator, Coach/Mentor, Parent

Just a very quick example off the top of my head is using trigonometry and geometry while designing an arm/bar linkage/whatever to figure out how to best optimize your reach while fitting into a certain starting size.

Also, I am sure there are a lot of teams out there who don’t pay much attention towards looking into figuring out how to best optimize say their drive trains given the constants (i.e. how many motors, how much stall torque, friction, weight, wheel size, etc.). I guarantee there are teams who are out there who could have been running their drives faster last year if they looked into this and I’m sure there are also teams who could have avoided browning out their motors constantly from trying to run too fast.

There is detail with that kind of analysis that even I haven’t touched such as your current draw, battery level (really a lot of the electrical components) that would effect how a drive performs.

A great example is how last weekend so many people were amazed at how fast OYES was running on the college field and they were tested for motor mods so many times. If people just sat down and looked at things, you could tell that the 3:1 ratio they were running was feasible, it’s all just a matter of how heavy the robot is, how much the robot weighs, etc. I guessed a few days ago based off some constants that there robot couldn’t have weighed much more then 15lbs and was told that it indeed weighed just about 15lbs. Their drive would still brown out sometimes when they changed direction suddenly at full speed. This is the kind of example that even I haven’t gotten into much yet as that involves more of the electrical side, but you could predict and figure out that performance as well.

Of course I wouldn’t expect high school students to be able to figure most of this out, and honestly I didn’t figure all of this out on my own, I’ve done it over seasons of work and with mentor help. That’s the key. Ask your mentors about how to look into more of the mathematics and formulas and what have you to do some of this.

Keep in mind that all of that work is theoretical and isn’t always accurate in reality. VEX does a wonderful job of teaching that lesson to students. However, you would be surprised how accurate some things can be.

The thing is, you don’t really use math unless you’re optimizing stuff. The space shuttle needs to be designed *exactly * it’s needed, as an extra kilogram costs thousands of dollars if it didn’t need to go to space. However, here you see non-critical components, with large margins for error and large tolerances. Robots rely on being able to intake/drive robustly under any conditions, not do something really precisely. So you can’t just ride a 20% safety factor because some external factor is going to push you over and break something. Robots need whole inches of clearance, 50-100%+ extra lifting force, and so on. This means that if you’re somewhere between 60-100% extra on something, that’s good enough. Hence, you don’t bother with proper analysis.

Now, in some places where you do use math, it’s almost always going to be a really rough calculation. You need to know concepts like exponential curves, integrals/derivatives, but only at a basic level. Order of magnitude calculations tell you it’s within the realm of feasibility. Linear/inverse/logarithmic relationships are good to know. But you will never try to actually calculate them because unless you have a crazily detailed model of the actual world, all your theoretical calculations will be off by at least 20%, or just completely wrong. I don’t need to pull out a graphing calculator to start guessing what the answer is going to be in an equation; just knowing what the equation is and what regular values are is good enough.

If that counts as math, then hooray but remember, this is Engineering, not just science. You can do whatever calculations/experiments you want, but at the end of the day if it works, it works.

Don’t think people use math in robotics.

Check out this thread:


Enjoy! :slight_smile:

Aura uses math too:


Enjoy this too! :slight_smile:

The funny part was that I wrote my Math IA (IB Stuff) on why the NZ design was so popular in Gateway. I got one of the highest predicted scores in my class.

Since then, my younger members have been following in my footsteps, using calculations to the best of their ability.

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Ah we have another IBer? Awesome. I wasn’t allowed to select what I wanted to do my math IA on. I should’ve done by EE on something different than Chemistry.

I remember one of my judges for our notebook in the college division this year ask many physics and numerically intensive questions on stress analysis and structural integrity and forces regarding our subsystems that weren’t the robot-base. We didn’t do that, but for this season, we might.

If you wanted to get really in-depth into it, you could do some Finite Element Analysis and test models of everything, using physics equations.

I have a goal this season for whichever college team I’m on to include a more rigorous treatment of mathematics.

Want some math?

Read Chris Seigert’s blog.


At its core, engineering is applied science. Here, building by trail and error is not engineering. Yes, you may be able to build a winning robot by trail and error, but that is not engineering. Engineers, at least the traditional ones, must be able to apply science/physics to determine the behavior of designed systems.

If we insist that this activity promotes, and benefits from, STEM disciplines, then we need to be prepared to engage students in STEM learning while they build, compete, and develop their communication, leadership and interpersonal skills.

Yes, Chris clearly has demonstrated various applications of math and physics for high school robotics. The challenge seems to be to get students to work towards understanding such concepts and then to apply them in their projects.


Building robots isn’t really trial and error, but it’s not math/physics either. Engineering relies heavily on experience over teachable topics, because while it’s fine to know about surface finishes, friction, materials and how those principles interact, that doesn’t tell you that a 1 thou (.001") clearance on a moving part isn’t enough (it’s a press fit). Real engineering books are full of tables, rules of thumb and charts.

So in the same way, both real engineering and Vex engineering do rely on design, but not on rigorous simulation and calculation (unless it’s important). You have to think about it ahead of time and understand what’s going to happen, but the numbers don’t really matter. You’re probably going to need to shoehorn in any math if you want to use it for education.

Mind you, I do think all the STE(A?)M things are important, but it’s not really coming forward in Vex. You can do Science! in a classroom with Vex as a platform, but it’s not a competition thing.

People who design applications, like simulators and CAD programs make heavy use of math. The hands-on aspects of robotics (and Vex in particular) make it appealing for students, but moving from users of applications to designers of them requires “leveling up.” Unfortunately, not many students have the patience to stay with it to the upper levels.

Over 20 years ago, I worked on an early version of cochlear implant at U. of Michigan. While animal studies were used, we tried to minimize animal use by creating mathematical models of the transducer properties of parts of the ear. Your ear converts mechanical motion (ear drum vibration) to electrical signals (nerve impulses), which your brain then converts to a perception of hearing of certain sounds. Modeling this process required the use of Fourier transforms and Wigner distributions, advanced math concepts beyond calculus.

In the reverse direction, we collected large amounts of data (with sample rates of up to 100Khz), requiring signal processing (more Fourier transforms) and statistical analysis. Doing the “right” analysis yields patterns which can represent the information in meaningful ways, while the “wrong” analysis makes it look like gibberish. Voice recognition and face recognition depend on filtering/recognizing the “right” patterns. I imagine the folks at Facebook who design the applications to tag photos are using algorithms that depend on some fairly sophisticated math.

You can always create simple models using “easy math”, but sometimes these simple models are crude approximations which need refining, comparable to a stick figure vs. a photograph as a representation of a real person. For example, a car’s value can be approximated with the linear model

v(t) = 20000 – 3000t, with original value at $20K, losing $3K/year

This crude model is a poor representation beyond ~ 4 years. A 7-year-old car doesn’t generally have a value of negative $1K, as calculated using this model.

A better model is an exponential model:

v(t) = 20000*e^(-0.15t), with 15% depreciation annually.

Using this model to calculate value, a 10-year-old car has a value of $4463, closer to real life. The constant (15%) can be tweaked accordingly – a Honda Civic depreciates more slowly than a Dodge Caravan.

But even the exponential model breaks down under certain conditions. For example, iPod sales may show exponential growth in the early years, but will level off as the number sold approaches the total world population. In this case, a more sophisticated model like the logistical model might be appropriate:

v(t) = c/(1 + a*e^(-bt)), where c is the “level off” value

And so it goes. Life is complicated, so the formulas that represent it have to be, too. The upside is that once a good representation is made, math can manipulate the data in a way of your own choosing without the physical limitations of real life.

A simple example of this using only Algebra II is the transformation of parabolas, as used in the movie Avatar. The movements of the Blue people were created by modeling the movement of cats. Rather than tossing cats from a 100-ft cliff, they were dropped from more reasonable heights (like 10 ft), and their motion was recorded, modeled, then stretched and shifted accordingly. There are lots of computer calculations in CGI, which require math as the foundation.

Finally, some students encounter difficult formulas and think that complicated means obscure, as in, “It’s so complicated that I’ll never use it.” One example is the two-sample z statistic, an rather nasty-looking formula:

z = (x1 – x2) – (m1 – m2)]/sqrt(s1^2/n1) + s2^2/n2)], where many of those variables are not a just single value, but means or sum of squares means calculated from hundreds or thousands of data points.

It computes the difference of difference of means of 2 populations, a concept I encountered in Time magazine (a relatively non-mathy publication) in an article about a cholesterol medication which appears to be more effective for men than women. Two populations: men and women. Difference of means: average cholesterol level before and after medication (aka, improvement). Difference of difference of means: men’s improvement is greater than women’s improvement. I took a look at the original data to decide whether this medicine was worthwhile for me (it wasn’t, as I’m a woman).

There are many connections between math and the scientific/technical world, but it takes some knowledge and awareness to find them.

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