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"I have a friend who's husband is a professor in Mathmatics/Philosophy. She tried to explain it to me, but it was way over my head. LOL"
Why LOL? What annoys me are the people who are proud of being bad at math as if it's a badge of honor. BTW, it's Mathematics, not Mathmatics. LOL at the spelling mistake! Not so funny when you LOL at language error.
Math is logical and enhances critical thinking. You assess what you know and what you don't know. You have to develop a plan to determine what you want to know using what you do know. A good teacher can create wonderful games and puzzles to teach math.
I enjoyed Calculus and feel it should be taught with Story Problems as it is infinitely useful in so many real world situations. Yet it is taught as a stand alone topic devoid of links to commonly encountered problems - such as determing the heat output necessary from a heating system to raise the internal temperature of a building within a desired time span, to counteract a given rate of heat loss from a building during winter time conditions, and which has had it's internal temperature decline during unoccupied hours for energy savings.
I concur with this. I was good at math but did not do well in calculus because the teachers could never relate it to real world examples. Who cares where a point is on a curve unless you can tell me why it may be important and show a real life example of where the math comes into play. I did better at algebra and trig, the geometry (again, needed to show why and how it would be helpful).
Best way to overcome math difficulty is show it's importance in everyday life. Algebra is helpful in being a smart consumer by being able to calculate unit costs etc... even if some stores put it on tiny shelf tags. Knowing how things work is helpful in principle though I wonder if the conditioning process has ruined a lot of natural curiosity. It seems a lot of people just expect things and have no concept of how or why they are the way they are sort of like the kids who don't realize their food is from animals et al.
It doesn't mean everyone will be better at it but I believe many would apply themselves more and take time to understand principles that relate to occupations they have an interest in if they can see the practical application. As well as enhance interest by teaching it in a more investigative way to peak interest.
I don't think there is any one thing but multiple factors that combine to make math "hard." First, I very much agree with this?
My observations, from my own school years and raising my kids, is many elementary and middle school teachers dislike math themselves, even the ones teaching it. And they pass this fear on to their students. Combine that with they can't teach what they don't understand and you get kids who believe they can't do math by the time they finish elementary. It becomes a self-fulfilling prophecy.
Next, text books are mostly horrible. Everything from errors to terrible explanations to poorly written word problems. It all compounds to make even basic math hard. Some of the explanations and methods used in the textbooks seem intentionally designed to obscure even simply concept. Common core based texts for example. I was completely unable to help my youngest starting in 6th grade because the methods were unintelligible. Even my oldest, who had just been in the same class a couple years before, but with a pre common core text, couldn't decipher it.
Adding to this is the problem that our current education system in general doesn't teach abstract and logical thinking. It's all about regurgitating back the "most correct" (what the heck does "most correct" even mean?) bubble with their #2 pencil than understanding. Even English (excuse me, Language Arts) plays into it.
Higher level math requires a solid foundation AND the ability to think logically about abstract concepts. When none of those underpinnings are there, learning collapses.
Same with me. Really bad teachers in grade school. People who are good at math almost never become public school teachers. So I struggled.
Later my Mom got me a tutor, who helped a lot, as this lady actually knew math, although she was one of the rare ones who did go into public school teaching, she tutored on the side.
Got into college, majored in Physics, minored in Math, very good GPA, I learned a lot from professors WHO ACTUALLY UNDERSTOOD THE MATERIAL THEY WERE TEACHING - what a concept!
The importance of algebra and other maths is not being able to tell when the two trains will meet if they are going at different speeds. The true importance is being able to analyze the question and discern how to get to the answer. That is critical thinking in the real world.
Early in my teaching career, I was trying to interest high school sophomores in geometry. They were studying the trips of Columbus and other early navigators in their history classes. I picked up on that and asked the students about how the captains knew where they were and how did they chart their paths. We got pictures of the navigation tools and charts. I divided the classes into teams. Each team had to lay out the course the captains would have had to follow to reach their goal. Suddenly right angles and great circle routes were interesting. That is more real world thinking.
I have a friend who's husband is a professor in Mathmatics/Philosophy. She tried to explain it to me, but it was way over my head. LOL
I would appreciate knowing more about that professor, if possible. What specific courses does he teach? What was the subject of his PhD dissertation? Where does he teach? Maybe you could provide a link to his Vitae webpage, if he doesn't mind. A private message, if you prefer. I have not seen many (or any) occurrences of Math/Phil professors in the U.S. Here is a program at the Univ of Arkansas: https://fulbright.uark.edu/departmen...athematics.php
Basically what happens is that kids in the US get a very weak mathematics foundation in elementary and junior high school. Some teachers are also pretty weak. On top of this there is this weird idea that kids should not spend much time on mathematics at home..
Basically what happens is that kids in the US get a very weak mathematics foundation in elementary and junior high school. Some teachers are also pretty weak. On top of this there is this weird idea that kids should not spend much time on mathematics at home..
The San Diego Unified School District just eliminated homework as required for a class grade.
I enjoyed Calculus and feel it should be taught with Story Problems as it is infinitely useful in so many real world situations. Yet it is taught as a stand alone topic devoid of links to commonly encountered problems - such as determing the heat output necessary from a heating system to raise the internal temperature of a building within a desired time span, to counteract a given rate of heat loss from a building during winter time conditions, and which has had it's internal temperature decline during unoccupied hours for energy savings.
My 11th grade calculus teacher said that farmers need to know calculus in order to calculate the maximum sized area pen they can create with a minimum amount of fence. Somehow, I don't think they use calculus. lol. That same day, I asked her, what do you call somebody who does calculus problems for a living. Her answer was "A farmer". lol.
We teach math horribly, and it starts from the very beginning. If we taught literature the way we teach math - this is how it would be:
Once you learn to read, you are given ONE piece of literature to analyze. Shakespeare's Hamlet. First you read the kid's version. Then you work your way up to the adult verson. Eventually you memorize it so well that you can act out several of the characters parts by heart, explain their motivations, the subtext, etc.. That is how to learn and practice your literature from grades 1 though 6, from elementary school until middle school. Progressively more rigrous readings and performances of Hamlet.
Then around the time you are 13-14, suddenly the math teacher requires you have to interpret and analyze Dostoevsky's Crime and Punishment, in the original Russian. Except you have never been taught to analyze novels, only plays. More accurately, only ONE play, in English, from the 16th century. Much less Russian literature from the 19th century. There are some naturally gifted students who are able to make this transition pretty easily, around 10-12% of them. The other 85-90% are extremely frustrated. They memorized Hamlet backwards and forwards for 7 years and are now thrown into analysis of Russian literature in which they understand none of the language, nor the cultural or temporal contexts. But they are expected to answer interpretive questions.
Then we are supposed to move on to analyzing French, Iranian, and then Chinese literature within the next 3 years (Algebra-->Geometry-->Calculus, etc..).
That is essentially how we tach math. From grades 1 through about 7 we are taught arithmetic and how to solve increasingly difficult arithmetic problems. Then all of a sudden we are thrown head-first into Algebra, requiring a whole different language of signs and symbols, and told we are stupid and will work at McDonald's our whole lives if we don't make that transition seamlessly and quickly. That is literally what I was told by my 10th grade Algebra II teacher.
In elementary school, the textbooks that we used always had 13 chapters. The first 10 chapters always reviewed the same garbage that we learned in previous years. Only the last 3 chapters introduced new material. Every year, we'd spend almost the entire year on the first 10 chapters, reviewing the same garbage that I had known for years. By the time we got near the end of Chapter 10, our teacher would realize that we were running out of time and were behind schedule. So, we would then start covering Chapters 11 and 13 at the same time, skipping Chapter 12 completely. As soon as we finally got to new material, the teacher would double up on it, and there'd be one chapter each year we'd completely miss. I never had a problem with it, but I could understand somebody who has a problem with math struggling.
This continued until 6th grade. Then, starting in 7th grade, honors classes began, and I was in honors math in 7th grade. That was a huge leap, where, we learned new material on the first day of school. It was amazing to see how much there was to math, beyond what we learned in the previous years! I had no problem with it, nor did most of the students in the class since it was an honors class.
My 11th grade calculus teacher said that farmers need to know calculus in order to calculate the maximum sized area pen they can create with a minimum amount of fence. Somehow, I don't think they use calculus. lol. That same day, I asked her, what do you call somebody who does calculus problems for a living. Her answer was "A farmer". lol.
The university I attended has a large agricultural department. One day an ag professor came over to the physics department to ask for help on how to pack the maximum number of chickens onto a truck.
So the physic professors spent some months on this and finally went back to the ag department with his presentation. He was so excited that he'd found the best possible solution. He put up his first slide and excitedly started "Assume a spherical chicken in a vacuum ..."
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