# What should be taught in school -- math/physics

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1. Jan 31, 2017

### Sherwood Botsford

As someone who taught math and physics for about 20 years, I've given this some thought, and I'm convinced that the whole idea of what and how we teach these in high school is upwhacked.

One of the common complaints from kids, "what is this good for". And you, know, they are right. I've had careers as a school teacher, expedition leader, photographer, house renovator, and tree farmer. I have used 2 equations, 2 unknowns twice. I've determined a few cliff heights by dropping rocks, used eyeballed centre of mass felling trees. But overall, the high school curriculum is not well used by people in their every day life.

What would I teach?

Critical thinking. This is a current buzzword, but I don't see much effort to actually teach it.
• Formal Logic

• Logical fallacies
How logic goes wrong.
• Cognitive biases
What are they, broad categories, why are they useful, recognizing when to use, and not use them.
How does advertising work? The appeal of sex, youth, vitality, being special, an insider.

.

Propaganda: Demonizing the opponent. Use of connotations in making biased sentences. Selective editing. (A video class was given 3 minutes of film of a protest march, with aobut 2 mintues of “man on the street” interviews. Each editing team was assigned a different spin. Was hard to tell that the 4 stories were of the same event.)

• Lying with graphs and statistics
How to be deceptive, and how to detect deceptive practices.

***

Math::Estimating

Approximate any series of calculations to 1 significant digit rapidly.

Fermi problems. These are problems to teach the use of common sense in estimating. You could hold your head up if you got within a factor of 10 of the right answer, and were entitled to take a bow if you could get within a factor of 3

One of the most frequently used bits of my physics education is the ability to to BOTEs quickly.

Math::Geometry
Formal Euclidian geometry -- as an adjunct to the formal logic course. Showing how long chains of logic can be put together. While I don't use theorems (other that dear Pythagorus's famous one) much, I end up 'thinking geometrically' a lot.

Math::Statistics

High school grads should understand at least average and standard deviation well.
They should also know and understand how to lie with statistics.

Physics::Vectors
This one I use a lot, from canoeing (Intuitive vector sums of of current and paddling speed) to tree felling, to whipping together a roof on a shed, to which way a knot will try to slide.

What would I take out?

Most of high school algebra. Keep it as an elective for the science majors.

2. Jan 31, 2017

### phinds

I think the thrust of what you want to do is outstanding and your chances of getting in done in the USA are zero.

3. Jan 31, 2017

### Andy Resnick

Your proposed curriculum is unobjectionable- other than the lack of K-6 topics- but the underlying drive to reform school curricula has little to do with the actual topic list (except obvious bugbears like evolution). Rather, the underlying rationale lies in the perception-right or wrong- that the 'average' US student graduates without having learned anything.

Personally, I think the perception is wrong, and I think what you laid out is nearly imperceptibly different from Common Core.

4. Jan 31, 2017

### Sherwood Botsford

No experience teaching K-6, so I don't feel qualified to comment.

As to perceptions: I am now a tree farmer, and I hire high school kids on a frequent basis. Most of them have no 'feel' for number. Doing Fermi problems gets me a blank look. Many do not know their single digit multiplication, cannot tell me that if they work for 5 hours at $12 an hour that I owe them$60. Of significance, I cannot trust them to calculate a fertilizer dose, the proper dilution for round up. Ask them what a quarter of 20 is, and they reach for their phone to for the calculator app.

Amount the kids who are serious about going to college it's not as bad, but I'm in a rural area, where a kid with a grade 10 education can make 70K a year in the oil patch, a carpenter can make \$29/hr building trusses.

I expected serious rants at me when I suggested discarding all but basic algebra.

5. Jan 31, 2017

### Sherwood Botsford

Could be done easily in private schools. Would need to be done as an enrichment stream in public schools. If you have the support of administration and parents, it could be done in addition to the standard curriculum in any school, but parents would need to understand that their kids are going to be coming home with significant homework.

6. Jan 31, 2017

### Andy Resnick

But this is my point- if they are not learning their multiplication tables now, why do you think your curriculum will translate into increased learning?

Solve the problem, not the symptoms.

7. Jan 31, 2017

### symbolipoint

What should be taught?
Every student must learn "Number Sense" and basic algebra. This means, that thing typically called "Introductory Algebra" in high school.

Sherwood Botsford, are you assuming that those things you list, fallacies, cognitive bias, progoganda, advertising..., are easier or more practical than Algebra 1?

8. Jan 31, 2017

### jack action

You could have said the same thing about reading/writing a few hundred years ago. The problem is not that kids ask the question, it's the fact that the common man doesn't use that knowledge on a daily basis.

I'm always amazed how electricians basically never use Ohm's law or how plumbers have no knowledge about fluid flow. They usually only follow known patterns.

I remember when one of my friend was renovating his house. He had plan to open up a straight stairway going to the basemen that had a door opening into a hallway. He intended to remove the door and make a simple opening in the wall between the staircase and the living room to let some natural light brighten the stairway.

I suggested to him to transform it into a winder staircase that would end up into the living room instead of the hallway. He told me: «That would be ideal, but we can't rebuild the staircase, that's too hard.» After discussing with him for a little bit, telling him I saw this as only an exercise in geometry, he asks me if I would do the plans for him; A challenge that I accepted. This stairway is probably the best part of his renovated house.

The point is that for someone like him, if asked to build a stairway, his answer is simply: «It's impossible.» He then forget about such plans and move on to the next solution that requires simpler knowledge. Then when he's asked if he uses geometry, he responds: «I never used that! I don't know why they teach that in school!»

One of the problem with the education system is that it teaches solutions to problems unknown to the students. Start by teaching problems, I mean actually doing it, not just on paper. How can we measure a tree? How can we check for square? How do you wire a three-way switch? Play with recipes in the kitchen. Comparing interest rates and terms on loans and investments; Which one is more advantageous? Let the student work on projects that will give actual results. That is when you can appreciate knowledge (or care about the lack of knowledge).

I also think we don't learn enough about math (and other stuff) in high school. Some stuff doesn't make much sense until you learn about vectors, statistics, series, calculus or system of equations. Looking back, I would have liked spending 2000 hours/year in high school, learning most of the college stuff before I turned eighteen. I would have appreciate school a whole lot more. The teen years are when we have the most energy and we work only 5 hours per day, 200 days per year? What a waste.

Last edited: Jun 30, 2017
9. Jan 31, 2017

### Stephen Tashi

Much of what you propose to teach provides useful debating and debunking tactics. For example, famous names for "logical fallacies" are useful in accusing people of using imperfect reasoning. However, if we are talking about real life, very few issues can be resolved by logic due to lack of data and the lack of agreement on what it would mean to resolve an issue. Encouraging the culture of debunking can lead to debunking everything -e.g the efficacy of vaccinations.

Teachers with great zeal for teaching debating and debunking methods are liable to illustrate these methods by attacking opinions that they disagree with. Then content of the course becomes bound up with the personal opinions of the teacher. Instruction about thinking is useful, but it should not be confined to critical thinking. Critical thinking is only one style of thinking.

I agree that estimation is a useful skill in real life. As a teenager, I resorted to algebra and trigonometry in real life since real life involved some surveying. Using a computer or a calculator is also a useful skill. It does require some skill to use a calculator - even though using a calculator is often portrayed as the easy way out - something anybody can do.

The mathematics a person uses in real life is not merely a property of mathematics - it's also depends on the inventiveness and skill of the person in finding ways to apply mathematics. If its appropriate to design the math curriculum to match the math used by a person with average skill in applying math then why not design the curricula for all other topics by the same standards? Design the History curriculum to match the history that the average person uses in everyday life, etc.

10. Feb 3, 2017

### Hlud

That's the problem i have with my old curriculum. We only focused on equation chugging. The common rebuttal to my complaints was, "Well, that's physics!" A small percent of my students would go on and actually use these equations, yet we pushed for over 75% of the school to chug them. Since moving countries, i have switched focus from equation chugging to relationships. Why does one thing affect the other?

I totally agree with you on formal logic. Teach mathematical logic and its application in all sorts of arguments. However, i think a lot of people now know these logical fallacies, but don't know why they are fallacious to begin with. Thus, i see poor logic perpetuated.

I feel like students need to be building more and more. How do things work? We throw away way too much partly because we don't know how to fix things.

I also think students need to understand the history of more than just politics. I don't know how true this is, but Adam Ruins Everything mentioned how the car industry effectively gutted public transportation. Understanding the history of stuff like that will allow us to make more informed decisions.

Something we do at my school is presentation class. I think that is important as well.

I love the endeavor; i am sort of on a crusade like that as well.

11. Jun 30, 2017

### Gayathri MK

To solve Physics problems, one need to be confident in Maths. So, The schools in India prefer Teaching Maths and Physics at top most priority comparing other Subjects. As I was good at Maths, I could able to crack Physics Problems easily.

12. Jun 30, 2017

### Merlin3189

In any specific situation, who teaches it and how, may be more important than what they teach.

Evolution rather than revolution might be a better way to improve generally. I feel the big mistake being made here in the UK is the decision that someone (the government) knows exactly what should be taught and how. So then everyone in all schools has to adopt the same content and approach. It is conceivable that they could be right, but otherwise all our eggs are in the wrong basket.
If individual teachers and individual schools are free to make their own adjustments to the curriculum, some will have good ideas and some bad ideas. Good ideas may get adopted by others and bad ideas should be abandoned. This does not always happen, since some ideas work well in the hands of one teacher, but not others. Some ideas will succeed only in niches and some good ideas will fail to take root in unhelpful environments.
Overall the curriculum will evolve and adapt in the way that most teachers and students find good. At no time is it likely to be best for everyone, but there should be diversity - the key to evolution (and to solving many other problems.) It will be able to adapt to both to local circumstances and to more long term changes in society, technology, economics, whatever.

13. Jun 30, 2017

### Stephen Tashi

The "consumers" of education plans include both the students and the various types of evaluators - evaluators of students for college admission, for jobs, etc. It's easier for teachers of advanced non-standardized courses to plan their syllabus if they know all students in a course who have taken the prerequisite courses actually studied the same material.

From the evaluators point of view, it's best if "Algebra I" is the same course for all students and that the students grade is based on standardized tests. Taking the students point of view, they want to study material that is interesting and really useful - meaning really useful to them personally. For example, some people who study physics and mathematics have the knack and inclination for applying those studies to practical situations, while others lack those tastes and skills.

The US education system could be viewed as an evolutionary process, but not one that is trying to optimize a well defined goal. It is a competition between different viewpoints. States determine their own educational curricula, but private schools in a state may be exempt from state requirements. States have limited resources to enforce the curricula that they mandate. So some teachers in public schools have freedom-via-neglect. States don't have complete freedom in establishing curricula for public schools because , over the long term, colleges and the Federal Government have various ways of influencing what is taught - e.g. by recognizing certain standardized tests as a measure of achievement in a given subject.

One (and by no means the only) interesting question about standardized education is what are consequences giving an entire nation of students the opportunity to "game the system" when they take a course ? - i.e. learn tricks to pass tests in a particular course that don't involve an understanding of the material. If you have a nation of students that can communicate over the internet, both understanding of the material and tricks will get passed around.

14. Jul 7, 2017

### cfm_phys

I think this is less of a question about WHAT is taught and more of a question about HOW it is taught.

Students are not taught algebra because they're gonna be using it a lot outside of school, but because you learn a whole set of skills through algebra. You learn to think in abstract, and to carry out operations a procedures using abstract quantities. You learn to analyze the beahivour of something based on non-numerical analysis, etc.

It is quite easy to argue that Algebra I shouldn't be a part of the curriculum, but it is much harder to argue that the skills that are developed through the learning of algebra shouldn't.

Now, on most schools, algebra is taught as a mechanical process without a real focus on the skills mentioned above. However, this is not a curriculum problem, but a teacher/school/student quatlity problem. Most curriculums in the world now focus on skills rather than contents. If this does not translate to the classroom, then it is not the curriculum that we should be changing.

15. Jul 7, 2017

### Andy Resnick

[QUOTE="cfm_phys, post: 5798785, member: 626991"<snip> However, this is not a curriculum problem, but a teacher/school/student quatlity problem. Most curriculums in the world now focus on skills rather than contents. If this does not translate to the classroom, then it is not the curriculum that we should be changing.[/QUOTE]

I generally agree with the 'snipped' part, but not with this part. It's tempting to blame teachers and students for not properly implementing a well-designed curriculum, but your underlying assumptions are that there is not only a well-designed new curriculum to implement, but also that the new curriculum was clearly communicated to the teachers and also that there is sufficient time, effort, and resources allotted for the teachers to learn how to optimally implement the new curriculum. None of these assumptions may be valid.

16. Jul 14, 2017

### cfm_phys

I generally agree with the 'snipped' part, but not with this part. It's tempting to blame teachers and students for not properly implementing a well-designed curriculum, but your underlying assumptions are that there is not only a well-designed new curriculum to implement, but also that the new curriculum was clearly communicated to the teachers and also that there is sufficient time, effort, and resources allotted for the teachers to learn how to optimally implement the new curriculum. None of these assumptions may be valid.[/QUOTE]

I agree, and maybe I should be more clear. I am a teacher myself and I'm full aware of the difficulties one may find to apply a new curriculum. I don't mean to blame the teachers, but simply state the fact that skill-based curriculum are already there, but for some reason they are not making their way into the classroom.