I am waiting for my library to consider purchasing “Math Therapy , by Vanessa V. ”.

If anyone has read it please tell us about it?

I think I get what Russell was saying.

I think it would take a lot to reach many grade schoolers on that level, but I also think it’s a good idea to try things in that direction and see what can be done.

Certainly in practically any subject, the teacher and their approach make can an enormous difference, and be largely responsible not only for what students do or don’t get out of a class, but how those students relate to the subject in future.

I did not understand just how powerful it was in solving problems until college. A profound failure of our public school system.

I love what Bertrand Russell had to say about math but I just like it because it’s one of the few things in life that you’re either right or wrong on. There is no gray area. 2 + 4 = 6 and there’s no arguing that. And let’s not go into computer programming where it doesn’t give you a totally accurate number of two or four or whatever.

I taught math for a while and I certainly would have been interested in learning more about what you’re talking about at the time but I’ve now moved on because I got tired of teaching 10% of the time and behavior managing 90% of the time. But I always tried to come up with creative ways to teach math to kids because if you can link it to one of their interests than you often get a lot better results.

And yes, @Blackwater_Park and not just using mathematics directly to solve problems, but just using the critical thinking skills that you learn by doing math. So much of that is lost in how they teach math nowadays and that’s why people can’t seem to even do simple problem solving for the most part.

I have always loved math. I think it’s because the numerals have great personalities and they always do exactly what they are supposed to do, with no surprises, when placed in their proper order.

When we learn math, we have to learn the mechanics of it. We have to learn the systems of it. And it isn’t always easy for people to learn. But it seems that for those that persevere they will hit a point where it suddenly opens up into something that is more than just drudgery, more than pushing numbers around a page. It suddenly starts making sense as seeing applications opens a whole new world.

I’m not sure you can teach that. It is an understanding that comes with time and usage.

Mathematics only seems perfect and complete, like sculpture. In fact, it is endless and contains within it not just one infinity but an infinite number of infinities. What is also very strange is the fact that there are some mathematical statements that are true but which can never be proven to be true.

You wouldn’t think something as simple and apparently well behaved as arithmetic could hold within it such troubling facts.

I hit that once. In college I studied so hard and diligently that I suddenly realized that everything I was seeing was broken down into math. A tree, a bird, water, everything.
I felt like my face was pressed against a clear rubber ball and I was looking into the universe and it was all math.
It was magic.
I disagree that it was a failure of the school system @Blackwater_Park. Some kids get it, some don’t. Same with reading and writing and all other subjects. Just because you can’t teach 100% of the kids 100% of every subject doesn’t mean it’s a failure. Home life and culture affect students much more profoundly than the school system does in regards to their willingness and eagerness to learn.

@Dutchess_III We can agree to disagree. Math is not taught in an applied manner. If it was, it would not be such a mystery to many.

How do you know it’s taught @Blackwater_Park?

Also specify applied manner please.

@Dutchess_III I can answer that. When I was in school and going through geometry and algebra and trigonometry, I was memorizing formulae and learning when to use them on homework and tests. When I got into Nuclear Power School, I was learning how those formulae were used, what they were actually doing, how they fit into the real world, etc. I saw how math applied to heat transfer and fluid flow, pump theory and operation, fission processes, and many more. I started seeing math almost as a language rather than a drudgery.

How long ago was that @seawulf?

40+ years. But the math hasn’t changed all that much since then. Nor have the applications. When you start applying the math, that is when you start to fully understand it.

It way it’s taught has_ changed @seawulf. How do you know it hasn’t?
Also grades k-12 we teach the basics. After that, when the student goes to college or gets a job, then they figure our how it’ll applies to them personally.
Same with every other subject.
My husband was in HVAC for years and some of it requires special math formulas. Should the primary schools teach ALL the kids formulas for HVAC systems?
What about medical calculations they may or may not use?

@Dutchess_III IMHO Schools need to teach more applied mathematics, not just the framework and mechanics of mathematics. People retain information and finally grasp things by doing them. That’s 95% of us. Perhaps 5% or less can gain that kind of insight from just reading about it. I did not fully grasp geometry until I took drafting. That’s really getting it, not just regurgitating and working with formulas. I really “got” applied math when taking Chemistry my senior year and was able to play hands-on with the ideal gas law. That should have happened a lot earlier. It’s not that people are not getting it, they’re just not being exposed to it early enough in a way that makes them really understand it. Most technical people will repeat this ad nauseam.

Which applied mathematics would you suggest the schools teach K through 9 @Blackwater_Park? Chemistry? Astronomy?
And you just proved my point. The lower classes gives the students the basics to solve upper level problems.l

@Dutchess_III I helped my kids through school as well as friend’s kids. Many of them struggled with math and the reason seemed to be that they were taught exactly how I was taught. Expanding their thinking to what I later learned helped them all understand things much better.

But you make my point. What we are teaching our kids is nothing but the mechanics of math, not how it applies. You don’t need to teach each and every formula out there to make it clear to them.

My niece was a grade A student. When she was a senior in HS, she hit Pre-Calculus. And she was struggling. Her grade point was in danger. Her parents never reached that level of education and were lost on it so they asked if I would help her. She had 30 homework problems that had to be done and she was completely clueless on how to do them. I asked her why she didn’t understand the problems. She was always taught the formulae. You are given a bunch of variables and the variable and you punched them into the formula and you ran them through the calculator and you got your answer. These were all story problems, tying the formulas to real life. She had no idea how to figure out what they were asking for, which variables she was given, etc. Once I did one for her and then we did the next together, she understood and went on to finish the homework and get her grade point average back on track.

It isn’t learning each and every formula. It is understanding what you are trying to do and how to fit math into it. THAT is what is missing and what comes out later when you have that flash of understanding.

Well? Did you teach her?

Umm….yes. That’s what I said.

Good. There are 30 more kids in her class. Go sub for a day and teach them too. Piece of cake.

@Dutchess_III My point, is you cannot teach math effectively without teaching how to apply it at the same time. It falls on deaf ears if you don’t directly see how it is applied. All the sciences, particularly physical sciences should teach math concurrently.

As seawulf said he learned how to apply it when his niece was a senior

Please give an example of applying math for a 3rd grade lesson.

@Dutchess_III The point you are desperately trying to avoid is that the way we are teaching can be tweaked to include application. And it should be application that applies to the student…something that they can understand and that has meaning for them. Even 3rd graders are learning things that are building blocks on other parts of mathematics. But everything thing they are learning has real life applications. I’d even suggest that if we took the time to teach them to think about math this way when the students were young, the later math would make much more sense and wouldn’t lose so many students.

You guys….I’m on your side. If you can apply what you teach to real world situations it is a very good thing.
There is this thing called “cross teaching” where you find a way to apply something you taught in, say, history to a lesson in science. We do that.
But I have yet to hear your ideas on applying 3rd grade math to real world situations, other than word problems.
Use your imaginations!

I guess it would depend on what you consider 3rd grade math. I know when I was a child we did some application of things, but it was very basic at that age. Life was a bit simpler then. I’m guessing that 3rd grade would be multiplication and division, starting fractions, some basic area calculations and maybe some intro to graphs (pie, bar).

So I would start with what kids like to do at that age. If it is sports, you could tie it to sports. If it is cooking, or video games, or just about any other hobby you could tie it to that. Examples might be: You and your 3 friends are playing a video game and your team just won a prize of 1000 coins. How would you split it evenly between the team members?

Another thing that you can start to do is to have them start to figure out what information they need. For instance, you are making something in the kitchen and the recipe calls for ½ cup of one ingredient, a quarter cup of another, 2 tablespoons of a third and 3 tsps of the last. All you have is a teaspoon. What information do you need to ensure you get the right amount of each ingredient? An exercise like this would have them have to think about what they are given and what they need as an end result and what information they don’t have. This is a skill that goes on to be used in other applications as they get older.

The USA just needs to do it the way the rest of the world does.
https://www.usatoday.com/story/news/education/2020/02/28/math-scores-high-school-lessons-freakonomics-pisa-algebra-geometry/4835742002/
https://www.bbc.com/news/magazine-38568538

You can find more articles but the gist is that they teach integrative math with other subjects and they don’t beat kids over the head with it too early. Slower introduction mixed with real applications yields better mastery of the subject. We get this so wrong here in the states. As far as the third grade is concerned, it’s a little early to be teaching much math beyond basic arithmetic.

We do too. It’s called cross teaching.

@seawulf575…not all kids of a certain age like the same things.
Go teach for a day in your niece’s Sr. class.

@Dutchess_III No group of any aged people all like the same things. But just like it is now, you can teach to all the kids with a variety of examples. The key is that there are ways to teach to kids that don’t make it drudge and that can get kids engaged and understanding there are reasons for what they are learning.

On a slightly tangential view, you can also change the format of the class. When my kids were in school, I was a very involved parent. When my daughter was in 5th grade she had a history teacher that was absolutely killing the kids. They were having to write a report every night with a big report assigned on Monday that was due on Friday. That was a whole lot of homework in history on top of all the other classes. I finally went in and talked to the teacher. She was an older teacher that had been teaching for many years. I asked her why she was assigning all the reports as homework. She said it was history and that is boring for many kids. She didn’t know of any other way to get the kids to learn the material. I asked her if it was helping. She said it wasn’t. I told her of a French class I had in 8th grade where the teacher set up her class as a game room. Desks were arranged in an arc pattern. One desk was seat 1, the next 2 and so on. During the class she would ask the first seat a question. If the student answered correctly the next question went to seat 2. If the question was not answered correctly the same question went on down the line, seat by seat, until it was answered correctly. The child that answered correctly would then move to the seat that started the question and everyone else that answered incorrectly would move down one seat.

As I was explaining this, I could see the teacher getting very interested and excited. She said she thought she could do something like that. The massive report homework stopped. I checked back in with the teacher a week or two later and asked her how it was going. She was all smiles. She told me that even kids that were failing her class were telling her they were going to study so they could “win” the class. Test scores went up and interest in the subject went up.

There are many ways to change how we typically teach to get better results.

As for teaching to my niece’s class, that is moot at this point. She’s mid-30’s…no class to teach. However when I was working at the nuclear power plant, one of my friends was the AP chemistry teacher at the high school. I was a supervisor in the chemistry/environmental section at the plant. He asked me to come in and spend a day talking to his classes. The kids were very interested and I challenged them on their thinking. I even brought in some real life chemistry issues we had seen, giving them the initial indications we had and asked them to think about what could have caused them. This turned into a yearly thing towards the end of the school year.

There was also a news story I saw once that talked about a guy who had formed up a company in western Pennsylvania. He saw the need for more interest in the sciences in the schools so he got a lot of high tech chemistry and physics type equipment. He then coordinated/contracted with several school districts. For a given fee he would take a piece of equipment to the school, set it up and show the teacher how to operate it. He would do the same with a different piece of equipment at the next school, a third to the next school, etc. After a week or two he would then go and swap out the equipment for something new, usually rotating from one school to the next. So the kids got to see the equipment they might not get to see until they got to college normally. They were excited and very interested. They noted that within just one year the grades were going up and the number of students going on to study in a scientific field in college went way up. Since so many school districts were involved, the cost of the program was split up to the point where none of them were struggling with the cost and they guy that founded the company was making good money. A win-win-win.

I know how to teach @seawulf575. I know the methods of teaching too.

@Dutchess_III I’m not trying to tell you how to teach, I’m pointing out that many times our schools are caught in old habits that aren’t resulting in the best teaching that can be done. And there are other things that can be done to show real-world usage of the stuff students in our schools are learning.

Give me some specifics @seawulf575. Work up a math lesson plan for, say 3rd grade, and demonstrate how you would incorporate real world into it. Word problems don’t count.