# Where is the Math?

I have struggled with how much math to throw at the kids. Most of the middle schoolers don’t have the math yet to really explain the concepts properly. But I throw it in anyway and that is starting to show some benefits as they get ahead of the curve when it hits them in class…

Without some of the math, the concepts are just that, concepts. Throwing in math and engineering helps reveal what’s behind the curtain. They may not get all of it but it lets them know there’s more to learn. Some kids think once they program and build the robot they have nothing more to learn. Oh contrere!

I don’t attribute all of it to pure math. How much force before your axle twists is not math, that is engineering where the math is applied. We talked about the new shafts the other night and how the extra 1/8 inch was cubed in its effect on the twist angle.

Trigonometry and the sin/cos/tan concepts are all over the place when dealing with force vectors. Vectors are one of the biggest set of building blocks for the students as it leads to more of the more static force analysis and kinematics.

In our line follower class, I threw at them how to figure out how much of an angle you would have for the outside line follower based upon how far in front of the center of rotation. Then we talked about instantaneous center of rotation in wheels not spinning at the same speed as well as using your gyros to know when to give up looking for the line (if they were in stock that is).

Position - Velocity - acceleration - jerk flow is really teaching them derivatives. Going the other way is integration. Granted they are not learning the formulas and various tricks of integral calculus but it is a darn good practical start that colleges tend to teach in the opposite direction of learn the math and then I will teach you all the cool engineering stuff.

I can go on and on but yes, I would like to see more math to prove they are learning too. But there’s a wide age range in Vex where they need to catch up to the math from the concepts they are learning.

Vex opens the door for interest and when they want to get better, the math follows along with the engineering. Showing the math is good for some areas but lets get the kids interested enough to want to need the math.

I make it a point of inserting math and science concepts into the Vex process whenever I can. When my middle school team had to write their autonomous program using encoders, they were forced to incorporate the concepts of circumference and degrees into a real world application. These were new concepts to them at the time. It made what they were learning in the classroom relevant to the real world, something their textbooks can not do no matter how hard the textbook writers try.

I also opened their eyes to torque vs. speed curves, and suddenly those graphs they were being introduced to in school were shown to be relevant, too.

I know this is very basic stuff. It’s middle school stuff. But working with machines teaches them that math is directly relevant to solving problems in the real world. I half laugh, half cringe when the school textbooks try to provide examples using football or some other sport - the Concussion Club is no place to inspire math and science… unless, maybe, you are calculating g-force loads on brain tissue when skulls clonk together. :eek:

Of course, Europe’s cathedrals were built with very little mathematical understanding, but today we see only the ones still standing. You can chose to use Vex to enhance your understanding/teaching of math and science, but you’re missing half the fun if you do not take advantage of this wonderful opportunity which building robots offers.

I always hated those sports “examples” in math textbooks growing up. They offered nothing for me.

Please don’t degrade the beautiful game of football by confusing it with the ridiculous spectacle of handegg.

Rather ironic to see such a closed world view and elitism in a post about exposing kids to different maths and real world applications, but I guess I shouldn’t have expected any better.

OT: TGN hit the nail on the head with his post. No amount of torque calculations and friction constant testing is useful without empirical evidence backing it up.

This should not be an either-or proposition. Hands-on experience, judgment, creativity, and experimental validations are certainly important, so is the ability to use math/science to better understand system behavior. You would be hard-pressed to find any engineering curriculum (in college) that does not rest on a solid set of engineering science courses.

I agree whole heartedly that the knowledge and the concept is important and can’t be ignored, but I don’t think that necessarily makes for that much better robots.

To me, the understanding is demonstrated through the application. Every use of math I have had in robotics has been for purpose and to complete a specific task, which deviates I suppose from the original topic and questioning.

It is a chicken and egg scenario, where you can create tasks that need math, but it doesn’t seem relevant to the student and vice versa.

In my opinion, the role of mentor and teacher should be to provide the math when it is needed, and not to worry so much about shoehorning it in, within reason.

I couldn’t agree more.
NASA uses math because they don’t have a choice, they can’t just send a bunch of shuttles into space until they get it right, they don’t use math jus for the sake of using math.
Likewise, teams should only use math when necesary, not just try and use math when it would be faster to just test it and see if it works.
There’s no point forcing yourself to do unnecessary math just because someone said Vex Robotics was STEM

I guess I was wrong when I thought the whole point to mentoring Vex teams was to teach them something about robotics so they might have the intellectual ability to someday handle things beyond high school.

I agree with Botfather and Yoder. In VEX, it’s usually easier to just build the thing rather than do mathematical analysis beforehand. We usually have the freedom because of the relatively low cost of parts. I always do basic math before I build (simple trig stuff for dimension), but I’m planning on doing more of the in-depth engineering maths as post-analysis. I’ll still be learning the math, but just because I’m not doing it beforehand doesn’t mean I won’t be learning the math.

Of course, in real life we use math/science/… when it is relevant, when it actually helps solve problems. In education areana, however, the goal is not to solve real-life problems, rather it is to prepare students, to help them understand basic tools and techniques and have them practice so that they would develop the knowledge and ability to use math/science later on in their professions. Robotics is a fertile ground for that kind of learning. If we continue to insist that the goal in VEX Robotics is to just build the best robot, and to compete and win, then we have taken a great (STEM) learning opportunity away from the kids. I suspect that is the central concern of the author of the article I quoted at the top of this thread.

when I use math in robotics it is usually because I learned it and **wanted **to apply it as apposed to it being easier, expect for certain parts of geometry which I find very useful in vex. (I also use a lot of math in my code)

You don’t need math to win but using math pays off when everybody but you in your math class is groaning because they have memorize common triangles. (3,4,5 30,60,90 etc.)

I think this is the crux of the issue. The robots of today are the Gateway (2011) to broader knowledge that can be used in many arenas. I liken education to the acquiring of a tool kit – you often buy a full set of drill bits, even though you only need a 3/8 bit now, because somewhere along the line you might need the others. Some people think, “I’ll go back and get each drill bit as I need it,” but sometimes this isn’t practical. You may not be near a hardware store (or it may not be open) at the time you most need that drill bit.

Similarly, certain types of learning are much easier when you have parents to pay the rent (freeing up your time) and before you have children (diverting much your time elsewhere). Also, learning is enhanced when you are geographically located near people/institutions that can inspire and help you (although online learning has lessened the second constraint). At the time you most need it, you might not be near a college or have enough money (or non-sleep-deprived brain cells) to acquire the math you need for a certain job.

Although much learning occurs on the job, it is more efficient if you had previously learned something similar – migrating from C++ to C# is easier than starting from scratch. Also, if your boss says, “This will require matrix calculations”, and the person next to you says, “I can do matrices”, they’ll be considered more valuable than someone who says, “I know I can learn matrices if you just give me some time to figure it out.” BTW, as a teacher, I use matrices frequently in grade calculations for deciding how much to curve an exam and how to curve it. Using a sophisticated tool, I can assign grades with “surgical precision”, compensating just enough in the right places if I’ve given a difficult exam.

Many people find “workarounds” to get by without doing much math, just as many people get a job done without the proper tools (you can shorten C-channel with a file, but a dremel cutter works so much more nicely). But there comes a point when the work-around is more trouble than using the right tool. I once helped a friend complete a job by performing a 3-minute mathematical calculation – had he done the job the way suggested, it would have taken 2 workers 2 hours each, with overtime pay, as well as driving/lugging equipment to a site 10 miles away.

1 Like

I liken learning to putting new things in your toy box. With more toys in your toy box, you can be more creative. You can solve engineering or scientific problems in the shower - experience unexpected aha! moments while you were washing your hair and thinking about what to do about your girlfriend’s cat peeing on your shoes.

Without a well-filled toy box, you end up taking showers and washing your hair and thinking about what to do about your girlfriend’s cat peeing on your shoes -and that’s all.

If you’re mentoring a Vex team then fine, tell them they can use math here and they’ll be happy, they’ll have used their knowledge from school to build the robot and that is a great thing.

My team (5 HS students) doesn’t have any mentors, we just do everything on my own and trust me, it’s much more useful to just build a robot and have to figure it out on your own when you need to use math because then you go “Ah ! That’s what it’s for !” rather than “Oh yeah I do STEM programs we use robotics as a pretext to do math but I don’t actually why we use it”

I know this sounds exaggerated, and it is, but it’s jus to say that they’ll learn much more by using math where necesary and figure that on their own rather than just applying math where told to - not that that’s bad, it’s also a good thing.

So I guess it’s not so much about learning the math in Vex, but rather just having all the tools/knowledge from classes and whatnot, and having them on hand for when you need them.

I’d have to disagree slightly about the “knowing vs. knowing how to learn” point. You simply can’t know everything you might need before starting a job, especially in something unfamiliar, but you can always use the ability to learn the stuff you don’t know yet. I’d recommend just being moderately aware of the various tools and maths you haven’t learned, and if you see a situation where it can help, just look up how to do it.

The success of most college-level engineering programs in the U.S. is measured, in part, by the outcome of the educational experience (curricula) they offer. More specifically, the following student outcomes need to be demonstrated by students and documented by the program, if it is going to maintain its viability/accreditation.

Should educational programs such as VEX Robotics play a role in achieving such outcomes? even as early as in high school? Why not? Could/should this be documented (primarily at high school and college levels)? Yes! Is it being documented? some items are some are not, hence, “show me the Math…show me the Science…show me the Engineering… Okay, you don’t need to show me the Technology, I see it on display.”

Student outcomes are outcomes (a) through (k) plus any additional outcomes that may be articulated by the program.

(a) an ability to apply knowledge of mathematics, science, and engineering

(b) an ability to design and conduct experiments, as well as to analyze and interpret data

© an ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability

(d) an ability to function on multidisciplinary teams

(e) an ability to identify, formulate, and solve engineering problems

(f) an understanding of professional and ethical responsibility

(g) an ability to communicate effectively

(h) the broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context

(i) a recognition of the need for, and an ability to engage in life-long learning

(j) a knowledge of contemporary issues

(k) an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.

I think that VEX is an experience with much more to learn than just STEM, and that we should’t force anybody to learn math in Vex. If students are really interested they’ll start figuring out when they need to use math and when they don’t and THAT’s when they’ll learn. The effort has to come from the student, we’re not here to force feed anybody plus they’ll learn much more on if they discover it by themselves

I agree. Students cannot be forced to learn math or any other subject for that matter; they must want to learn. All we can do is to provide learning opportunities for them.

I agree with both these statements to a point. However, I come from an Asian family where math was forced at certain junctures, with a generally good result.

I’ve mostly liked math, but in middle school, the jump to algebra did not come easily – at one point, I was earning a “D.” My father sat me down for 2 hours every night for 2 weeks doing routine “drill and kill” exercises with me, which I hated! Suddenly, something went “click” – parroting formulas by rote memory started to flow into understanding. Math became fun after I understood it – it did not start with fun that led me to understanding. Once I was taught to “drill and kill”, I used this technique on myself without my father’s help whenever I ran into a difficult concept in math. I’m not sure at what point “knowing” stopped and “knowing how to learn” began, but those 2 weeks of algebra practice were about much more than the algebra concepts I was struggling with at that time.

While the philosophy of, “You don’t have to like it; you just have to do it,” has positive aspects, it can be taken too far, leading to disastrous results – there’s a reason why Asians have higher suicide rates than some other populations. With my own kids (and team students), I take a limited liability approach. Test the waters for a few sessions, then make a decision – are you in or out? If you’re in, you’re in for the whole season/year, but you can opt out for the next year if you like. While my son followed robotics all the way through his middle/HS career, he signed on for 2 years of piano and opted out in year 3. Once in college, he commented, “I wish you had made me stay with piano – at age 12, I didn’t fully understand what I would miss by dropping out.”

The best part of mastering the math is I now teach it, so I get to bestow/inflict all this fun/misery on others!

1 Like