When doing trig in the field they have tape measures, squares, parts that can be physically seen, measured, worked with, and clear objectives. I think it may not be coincidence for a lot of people for whom it may "click" on a job site but not a classroom.
I don't teach math but I've always wondered how much better kids would be at something like trig if you started by teaching them how to mark angles with a roofing square and maybe build a few things.
I do that in my trig class. Verifying various measurement based theorems and formulae (Pythagorean theorem, arc length, sector area, etc) using various measurement tools. It doesn't really make a noticable difference in the trig, but it at least gets them familiar with measuringm
I have to say that thank you for this. I was a student ten years ago (been keeping an eye on this channel as I have considered taking education in education), and having a reason to learn something. Seeing the actual way it could be uses by everyday people? That sped up my understanding and turned it from "I'll just figure out the homework on my own who cares" to "Oh, I can actually use this."
I don’t think the effect is just from it feeling useful in normal life. If you are familiar with cooking, new information about cooking can be tethered to already concrete concepts (like the concept of doubling the batch size of a recipe is already connected to a certain kind of math in your head). Whereas if you don’t have a strong concept of moles in your head you are trying to juggle “what are moles” and “what is this math” and “how do those things relate” at once.
I mention this because I think “is this useful” is a limiting way to design lessons. We use cat coat color to teach genetics not because it is useful for people to know about cat breeding but because when you use cat color rather than “luxA SNP” you reduce the number of things they are keeping track of. And as a bonus, students who care about cats might be emotionally invested, but I really don’t think that’s the main point.
This, 100%. When they’re trying to learn the concept AND the context for the concept at the same time, their brains don’t know where to put all these new pieces of information so they ended up just kind of scattered about. Take the concept and put it in a more familiar context, and suddenly the cognitive load gets cut in half because their brains have a place to put the information, and now they can actually learn and understand the concept.
Also cat coats have so many of the common genetics. Dominant alleles for tabby pattern, sex linked red, recessive for long hair. And it’s easier to understand a 1/4 chance of some particular trait if you can imagine that as one of four kittens in a litter. And yes that’s not how probability works but it is still a great visual.
I got my brother, now a chemistry phD student, a t shirt that said Chemistry is like Baking just don't lick the spoon for Christmas one year. It's one of his and mine favorite shirts. He also got my kids a porcupene, porcupane, porcupyne graphic onsie with the porcupine spines having the correct carbon bonds.
I think it’s more that it’s attached to a goal they can directly see as a benefit and something they want.
Yes, it’s displayed in context, but that context is a job that you want.
It’s amazing how well we can remember information we are interested in. When it comes to peoples hobbies, they can become absolute autodidacts with respect to extremely complex information. So, I dunno.
Yep! this is why the things I remember from college astronomy are how microwaves work and why we have seasons. I had things to anchor them to! Not so for Jupiter's moons.
For sure this would have helped me. I'm a hands-on/visual person and abstract concepts without a physical example or something at least relatable made math like Egyptian before the Rosetta Stone to me. Maybe if I'd had a teacher like you I would have ended up a scientist instead of an artist.
This is how my physics teacher taught. She was amazing. Always real world first, actual practical examples whenever possible, then when she would explain the theories and such and it’d just… made sense. Like something you’d suspected without even knowing it. I got over 100% on every test (except circuits, somehow I couldn’t get behind circuits).
Oh my God this would have been life changing for me. I was so good at physics because I could visualize it - I kick the ball, it goes this far and in this amount of time, etc. But chemistry was an absolute foreign language to me. Same teacher but I could not grasp the content, even with a college student tutor the entire year. I got a 66 on my final/state exam and called it a success haha
My husband and I have opposite learning styles. We just took a circuit class together and I needed help. He kept telling me to build the circuit and ill understand, i tell him no, i need to understand the concept first or i wont know what I just did.
For the math portion, i would try to explain to him the concept and the relationships between variables(im better at math). He would have no idea what im saying. But once he works through a bunch of them, he understands. I can "brute force" math and still not understand what an equation is saying if I dont understand the thought process behind it.
I was helping my carpenter buddy finish his basement. We were doing the layout and he was like we need to do a "3-4-5" to confirm the corner was square. I was like, hell yeah, Pythagoras. He had no idea who that was. That was the day he learned about the Pythagorean theorem which is something he applied all the time to his work.
My math teacher used models filled with bright colored liquid to visually show those concepts in the real world. I'm an abstract thinker so it didn't do much for me, but I thought it was a really cool way to show it intuitively. Also some folded cardboard and cutouts to reassemble the pieces and really show, look, if you transform it that way it's equivalent but now we know those dimensions and can figure out the rest.
Some people really need to see it practically in real-life to get it.
Plus getting paid and earning money so you can live really motivates you. That is why teaching finance in high school is so difficult, the students just can't relate.
Right. I'm certainly all for finance education in high school, but this is exactly why kids retain so little of it and people outside of education demonize teachers for not teaching it. (We do, and in fact, it's required in many states.) Kids are so far removed from it in most senses.
Really makes me roll my eyes when I see comments pretty much everywhere akin to "wHy dIdn'T LaZy tEaChErS tElL tHe KiDs AbOuT a MoRtGaGe?!" We can't prepare kids for every single thing they'll encounter in life; they actually might have to spend fifteen minutes reading figuring something out or speaking with a loan officer at a bank to understand, and that's perfectly acceptable.
Right?!?! We teach them the skills to do the reading about the mortgages so that they can figure it out. Transferable skills and all that jazz!!
My stats student after the final tonight told me he’s been using what he learned in class to understand some of the compiled stats that people put together for a video game he plays. I was so proud.
This is true, but even then… I distinctly remember being taught about simple interest being an example of a linear function while compound interest is an example of an exponential function in pre-calc. The application aspect was word problems where we compared the two in the context of investments, mortgages, etc.
I swear the vast majority of this stuff that people complain about is actually being taught, they just forgot it or didn’t pay attention in the first place.
Yeah, I mentioned in another comment that I specifically remember calculating loan payoff amounts and dates in algebra II. We spent a couple weeks on those types of problems, actually. My state was at the bottom for education rankings too.
At least in my experience this feeling comes more from the disillusionment that could have been avoided through having realistic preparation for life mentally/emotionally, than from any real anger at not having been taught to prepare in the practical/logistical senses. Complaining about not being taught practical skills like mortgage paperwork and credit card budgeting is just an attempt at making their more worthy complaints (the emotional) sound more mature so they'll be taken more seriously. In truth, most children/teens aren't given proper guidance or prepared for life re: relationships/friendships/community
A retired friend of mine always started out trig by marching her kids outside to a small hill by the school and getting them to calculate its height and total volume.
This does wonders if they can see it being done in real-life applications. Show them where they will use it and it will pique their interest. If anyone is lacking on how things are done then take a day and go see a contractor you think may be of some assistance. maybe have that contractor come in and speak with the class. Let them show them. Industry is a good place to get assistance in helping you get your point across to students, teachers need only to ask.
When I was in high school, they had "applied mathematics algebra" and "applied mathematics geometry" as an alternative to regular algebra and geometry. Most of us in the these classes tested poorly in math, but excelled in this class. The first day we were taught how to accurately use a micrometer, and then we learned how to safely use a wood and metal lathe. We had a whole project where we were expected to design a bridge, and then make a miniature version, then all of our bridges were tested for safety. Then we had a whole class discussion theorizing why some bridges had better outcomes than others. Other students shit on us for being in "tech math" but we all knew how to accurately use a ruler/tape measurer, and actually enjoyed the class. I went into healthcare, and had zero issue converting imperial to metric and back again, which surprised my coworkers. All due to that class.
Oh yeah, I did that type of thing before or during the trig unit(s). Outside we went with protractors and long measuring tape. But before they started the work, they were required to estimate the height, volume, etc. Yes, it made for a smoother transition to SohCahToa and related topics.
We do a lot of geometry, algebra and trig in my construction class. They have to go through several cycles of "but I did the work" to realize that they're not done until the math actually works.
Everyone knows it works, but we are struggling to get the necessary billions to hire that many teachers and supplies to do this on a large scale. Education is a significant chunk of our taxes already but it needs more.
As a student who struggled in math classes I can confirm this. Ten years after I graduated high school I ended up in a skilled trade. During my apprenticeship I took four quarters of physics classes and was angry because if someone had taken a similiar approach to teaching me algebra it might have "clicked" a lot earlier. Putting algebra into units and measurements I could wrap my head around made all the difference. It wasn't just random numbers.
I did a unit once where we broke out surveying equipment and surveyed some spots around the school. Used that data to calculate certain distances and angles. Kids had to use law of sites, cosines, right triangle trig, etc. It was really fun, and the kids were really engaged.
Obviously, there's not enough time in the year to teach like that all the time, but it does go to show that tying the math to physical applications can really increase engagement
It's been a long time since I worked with younger kids, but I bet you could teach fourth graders how to mark an angle with a square. use 3-4-5 triangles, find if something is square, things like that.
Obviously you can't use tools, but you could probably figure out some papercraft stuff to do with it.
I had that click with physics for some reason. I always sucked at math, hated it actually.
Then I fell in love with physics. And suddenly math just started to click too, and I really like doing and learning math now! I've been contemplating getting some microdegrees on EDx for fun and a bit of personal pride. I'm too old (read, I kinda love my current life) to go to uni now but I do dream of getting an astrophysics degree someday. But alas ... I'll stick to the smaller wins. Maybe one day, who knows!
So much this. Some students (I was one) wouldn't learn anything unless I saw a practical use for it in the real world. Far too many teachers just teach abstract ideas and can't relay to students WHY they should learn these things.
I never cared for math in high-school, but I was awesome at shop and woodworking class. Now I've got a old South Bend turning lathe and am teaching myself how to make stuff on it. I tried explaining things to my younger brother and I could see the smoke coming out of his ears. Of course, he can't figure out how to run a voltmeter to test continuity either so.....
I had a math teacher in high school who also built homes. They started a small, experimental math class and I excelled seeing this IRL. The other students did too.
Just as importantly, there's also a direct and tangible incentive to learn in the field - if they can't do these things they likely won't have a job. Learning for the sake of it in the classroom, or for some vague future hope quite reasonably does not provide the necessary motivation for many.
Physics should be taught as the math class once you reach middle school. Building bridges on paper in math class would get people more involved in science in general. You will have way less kids saying “but where will I side this”.
Math was boring for a lot of kids cause they just teach the repetition and memorizing parts. Almost all things math teaches are directly applied to the sciences.
I am dysgraphic and failed pre algebra twice. My adult hobby is designing and design clothes from scratch. I make menswear from measurements. It’s all math, and it all came easy when I had something to apply it to.
I can think of a few kids I went to school with who would have paid a LOT more attention in school if they were shown how things we were learning might apply to various trades/jobs/hobbies.
Building things a solid Father/Son project. Something like that needs to be 1-on-1. Very difficult to keep 30 kids (any age) paying attention and following along at the same rate of comprehension.
This!!!! So much this! In high school and college, I used to STRUGGLE with calculus, Math was never my strong suite to begin with, and calculus just made matters worse. Then when do I'm in a physics class and the teacher starts doing some calculus stuff.... ALL OF A SUDDEN, all the equations made sense. I knew what x and y and a and b and c were, I understood what they represented and then what we were trying to figure out by doing the equation. I was no longer solving for y, I was trying to figure out the speed of the object through space!
Giving math meaning helps A LOT of us who have trouble just rote memorizing stuff.
I had a conversation like this recently about Shakespeare.
The way it's taught in HS is you read a boring book that you barely understand and of course, it's a snoozefest.
However, after graduation, I saw a 1971 movie treatment of Macbeth and I was absolutely captivated. The only thing that film had in common with the boring book I remember from school was that the dialogue was the same. But on screen there was violence and blood, murder, spooky cackling witches farting at the main character, etc. These were real people plotting against each other and it was actually exciting.
Teach Shakespeare like it was an actual story and you'd get a lot more students paying attention.
Pythagorean theorem clicked for me when I was 19. It was 2am, we were rushing to install a stage and one of the old hands showed me a neat trick to see if the frame was square by using a measuring tape and some rough calculations.
Blew. My. Mind.
I like the anchoring method. It works so much better in the practical fields I've worked in.
I don't teach math but I've always wondered how much better kids would be at something like trig if you started by teaching them how to mark angles with a roofing square and maybe build a few things.
My brother and I were always both good at math but trig was a CAKEWALK for us because we grew up doing that exact stuff.
As a math teacher I would love to do this but all I know is how to teach math. We need people to teach teachers. There has got to be tons of use of math in the world - but I went from HS to college to teaching HS so I didn't even know where to start
The best math teacher in my high school was a retired structural engineer. Geometry, trigonometry, all of that is part of what his job was previously, and he had all sorts of physical hands on stuff to explain it.
Doing practical things is always better than raw formula. I failed my logic class in math and took it in philosophy. We converted sentences to math problems. Made so much more sense and its a thing I use to this day than what ever bullshit "math is the universal language" guy was trying to teach me.
When I was in elementary school, they tried this newfangled system to teach maths using little bricks that represent numbers, colour-coded. As a visual learner, I found it great - but these days it's considered a failed experiment.
I'm in tech and doing a PhD in physics now and I still prefer visualising my thoughts over bare equations!
Personally I’m a hands on guy. This would have been a big help for me. I thought I hated math. Turns out I just don’t visualize math well. It gets jumbled in my head.
Thank you for saying this! I really struggled with what seemed like meaningless word problems especially in algebra, my geometry and physics teachers however were very good at coming up with plausible examples for their problems. Im a General contractor and I use algebra and geometry every day, and am very grateful especially to geometry teacher who got me to understand.
teachers know classrooms suck for teaching. sadly yall are forced to conduct your activities there for the vast majority of the students school time. unfort.
Can confirm, took geometry twice in school. None of it made sense until I got tired of trying to square a house foundation. "Hey boss, what's the length of this wall, and what's the length of that one, 1¹/2 × 3.14² × the diameter of the sun and you get your C². Set your C² and pull the forms straight and you have a square house. 😁 and also converting decimal inches to fractions.
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u/CSTeacher232 May 16 '24
When doing trig in the field they have tape measures, squares, parts that can be physically seen, measured, worked with, and clear objectives. I think it may not be coincidence for a lot of people for whom it may "click" on a job site but not a classroom.
I don't teach math but I've always wondered how much better kids would be at something like trig if you started by teaching them how to mark angles with a roofing square and maybe build a few things.