First of all I had an absolute blast today. I went to a conference (more of speakers with free food but nonetheless) today about bridging the gaps between the arts, acedemics, and sports. The main speaker is a VP, baseball coach, and was a math teacher. He started off by saying teachers as a whole statistically struggle to bridge the gaps between sports, arts, and acedemics. For instance we have a hard time connecting math to painting. But they're all fundamentally connected. For instance, there's a chemical formula for the paint. There's mathematical equation that shows how much of each pigment to get this color. We make connections like rocket science, sending a rocket into space, but we come up short providing real world examples that has an effect on our students lives. For instance he was saying that baseball is an incredibly mathematical game and how it's played gives us easy to record stats. But we don't take it the extra step and show how baseball is a coordinated controlled dance from one team to the next. Or for instance marching band is an easy link to sports. But sometimes we don't explain the math behind the sets and the physics behind the sound. He went on to say that as teachers, if we can bridge that gap, the three areas become easier to teach and learn. They clump together and most students find it interesting about the stuff behind what they're learning. Real world connections that make sense to them. Overall it was really interesting.

Some of this seems like a stretch. One could do problem solving with color ratios in paint, but I’m not convinced that’s really connecting art and math...it’s contrived. And while I love a good half time show, meh the band/sports connection. Most sports fans get a beer at halftime (now there’s a connection)

I think real world connection stuff is overrated. I tell them that upper level math is like art. It's beautiful in its own right. Some of the topics have obvious applications I will mention, but if they don't, I'm not going to stretch it and give some of the contrived examples the book presents. If kids can be successful at what they are doing, they don't care so much if it has practical application.

Our state-champion marching band out-practices our football team hands down. Even 30+ years ago, I completely wore out a pair of shoes every marching season. (July to October)

Helping the kids see connections among subjects, careers, and extra curricular activities is a great way to get the kids to see why school is important. It might have to be contrived to get some on board to begin, but later it becomes more natural.

I strongly disagree with this. Students are much more likely to learn something when they see the practical, real-world application and relevance in their daily lives. When I teach, I show my students, for example, videos of how pilots use the distance formula (d=st) to determine if drivers on the ground are speeding, how their reaction times are diminished during driving simulations if they text or talk on the phone, how to use linear regression to negotiate the price of a car, how to use apps on their phones to measure the angles between two objects and the arc length formula to find the distances of nonlinear curves, how if they get lost in the woods that you should keep walking at right angles (to form right triangles) in order to move in a straight line because it is very easy to stray off your path, how geodesic lines are “straight lines” in spherical geometry and are the shortest flight paths airplanes travel due to the curvature of the Earth, (and I tie that in with the Traveling Salesman problem to show how solving that problem would be very useful to the airline industry and Air Force branch of the military), how to model flow rates in a pool linearly to see how long it would take the pool water to drain and fill, how employers use scatterplots and other types of graphical displays to measure productivity rate when considering someone for a raise, how pilots and military foot soldiers use trigonometry to launch weaponized and non-weaponized projectiles, etc. I have found that if you just teach the theory, then students are less likely to want to learn and to pay attention. After all, they will just see it as another algorithm they need to memorize to pass the test. I believe that math teachers are doing their students a tremendous disservice if they don’t show them the usefulness of math in real-world settings and in the private industry, in particular.

So does ours. I was hoping (s)he would have something logical to say but. Anyways. I'd like to see some of these people who say marching band isn't athletic march a ten minute show...

Topics like scatterplots, linear regression, and distance formula are inherently real-life. Those would be the obvious applications I am mentioning. I am talking topics like graphing rational functions or solving trig equations or finding the derivative of an inverse trig function or integrating logs or those geometry theorems about circles and segment lengths etc. Sure the book comes up with contrived word problems for each of these sections, but so much of what we do is not somethign that is frequently used in "real life", and that's okay.

Who here can name all 5 Great Lakes? Anyone can if they remember the acronym, HOMES: Huron, Ontario, Michigan, Erie, Superior Students who make connections learn and retain information better than other students. Marzano named Compare and Contrast the most effective teaching strategy. Students should always be urged to find connections between learnings and their world. If you didn't know about HOMES, for the rest of your life, you now will able to name the Great Lakes. You've gained a lifelong learning by making a connection.

I'm teaching ratios now and I know it is helpful to use contexts that the kids can connect to + understand. For example, we talk about Kool Aid for equivalent ratios. (2 spoons of Kool-Aid and 1 cup of water is equivalent to 4 spoons of Kool Aid and 2 cups of water because they taste the same.) We have also done examples with paint and this makes much more sense to the kids than something out of context. But I don't see it necessary to connect math to painting because it would take the focus away from the math.

Okay, but where do you think technology comes from? Scientists, medical researchers, and engineers use many of the things you stated daily, not to mention machinists, inventors, economists, etc. Those geometry formulas, for instance, are the reason why we have the Great Pyramids and understanding of the universe that we do. Area formulas have a plethora of application in daily life and contractors use them all the time in their line of work. Massive structures could not be built without them after all. To further demonstrate, a friend of mine who works in water resources recently asked me to check over his pool design and it involved a ton of geometry and trigonometry. It certainly is real-life to him. We live in a technological world because there is mathematics constantly going on everywhere behind the scenes. Mathematics is needed to keep society and the global economy working and running on schedule. We have the internet and modern computers and military weaponry and weather forecasting and cellphones and space travel and many, many more wonderful things because of of the work of mathematicians. Why people don’t think that’s real-life I’ll never know.

How so? Our marching band students get a 1/2 credit of PE each year, so that participating in band for 4 years meets all of their PE requirements.

I actually did. Inverse trig functions are particularly useful in the fields of circumnavigation and air travel and in many aspects of structural engineering (e.g. in computational structural mechanics to describe large shearing forces and vibrational patterns in structural joints, etc). High school mathematics doesn’t touch on many of these things I’ve mentioned and I think it is premature to say that they have no use based on the contents of a high school textbook. They have to use *some* “silly” examples because it would go right over students’ heads otherwise as mathematics has become “too difficult” these days.

Well I mean.... It was an ignorant statement. If you feel that marching band isn't athletic you're ignorant of everything that goes into it. I think the ones who have called you out on that would agree that if you did know first hand and had experienced it first hand you would think otherwise.

Okay so why are you in my thread being salty to start with then? Imma tell you just like I tell my students: this ain't the kitchen table. Keep your salt to yourself.