Question

High schoolers, What is something your teacher did that really engaged you when you learned about linear systems? (or what would make it more interesting?)

Answer 1

Nothing. Just nothing because my teacher does not give a freak about what we think about linear systems.

Answer 2

well, that's not a very nice approach. Sorry to hear that. As a teacher, it bothers me when students get that feeling. I'm asking, so that doesn't happen in my class. What do you think they could have done better?

Answer 3

They should probably highlight the practical applications of such an invaluable subset of math. There are too many to count really, but students don't get much insight nowadays. To them it's simply matrices, or if your students are in algebra, maybe even just systems of equations.

Answer 4

I have taught mathematics as well.
And a very common problem I encountered during my lectures and the previous knowledge the students had in terms of linear systems are:
- The interpretation of the results in a referential system.
- When the simplified raw form of a line ax+by=c is not given.

Answer 5

it is algebra(but I would like to introduce matrices anyways since they teach it, just not the notation). And maybe I'll start with some practical questions to create interest? What do you think?

Answer 6

Well personally, linear systems are the easiest. There is not much to think about except y=mx+b.

Answer 7

I am worried about previous knowledge. The school I am at has severe issues with fractions, decimals, percentages, etc. They seem to steamroll through even if the kids do not understand the material

Answer 8

I can relate to that, FC.
And I personally think it is best to present the most common situations when facing linear system, these being infinite, one or no solution.

Answer 9

Well my teacher taught us Linear systems but it was quite hard. Maybe if the teacher would be more open and show us in a more fun way then we will learn or make is a bit more interesting. Because teachers are there to teach, yes, but they are also there to make us comprehend everything like make it stick in our heads and some different kids have different necessities and opinions. So what I think will make it more interesting is make it more fun or in a way try something different, a different way of teaching it perhaps.

Answer 10

The issue is, they rely heavily on calculators. and the book they use, isn't that great. It really highlights little things and does not explain processes. I plan on doing a full 15 minutes(longest lecture I'm allowed to do without a break) with examples followed by a try it out. Then another 15 on the next method etc.

Answer 11

15 minutes without break? really?
What kind of school are you teaching in?

Answer 12

thanks jabez, I'm trying to come up with some interesting ways for just that reason :)

Answer 13

With my sentence I mean that a 15 minutes lecture is too little to cover everything in regards to the theory involving linear systems.

Answer 14

Matrices would be tough to get across to struggling students, it's still a rather abstract concept. I mean they are just boxes with numbers

Answer 15

As I called Linear Algebra, Box Math 101

Answer 16

A high school-a normal public high school. I wanted to format the class in a
homework quiz~5min
lecture~45 min
break~10 min
group activity~20 min
free time~10 min(if earned)

But, the teacher I'm working with said that wasn't doable as they only can manage 15 minutes at a time...

Answer 17

High schoolers aren't able to manage more than 15 min? You have quite the task ahead of you

Answer 18

for matrices, I take a "mathematicians are lazy" approach to teaching them. It's how I explain the evolution of math, so I'm not so worried about that

Answer 19

yea... so now I'm trying to come up with something interesting and short. It's quite a struggle.

Answer 20

Enthusiasm is key no matter what you do. Keep your demeanor silly and excited so your students are more willing to view it as more than a chore

Answer 21

I had planned on using some sort of system for basketball(they are super obsessed with it), as a "what you can do with this!" to get some interest, but to be honest, these kids already hate math. Not to mention, I'm coming in over halfway through the year

Answer 22

I am completel repellent to just writing the formula and explaining things as if they were intuitive.
Mostly I would build it from the ground up, and so prove the propositions utilized in class and future concepts.

Answer 23

they can't handle formal proofs. I'd lose them immediately. and like before, background knowledge is shaky at best

Answer 24

Well, they'd most likely fail my classes haha.

Answer 25

so I was trying to think of a gimmick to get them engaged

Answer 26

(the school is barely equipping them for community college)

Answer 27

The culture of the school is lackadaisical to say the least. There really is no homework, discipline, or will to be there. The school says that they are preparing kids for college, but really, even the AP students will have a tough time hacking it

Answer 28

I must say that here in Sweden the problem is the same to some extent.
For example, I usually use multiple literature and refuse to use the book written by pedagogs (who aren't even math teachers) since I also teach the method of researching and investigating the concepts.

Answer 29

I don't understand why math teachers(or mathematicians) are not writing books at a high school level. It could really change things, but I doubt they'd even be accepted here. The US has some odd education choices. For example, this algebra 1 class is comprised of 9th and 10th graders(anywhere from 13-17 year olds)

Answer 30

Most of the country considers calculus to be an advanced class. I just talked to a guy with a BS in math where calc 3 was a junior/senior year class.

Answer 31

We lack parental support in education, so we have to come up with ways to instill intrinsic motivation without much support from an extrinsic side.

Answer 32

That's what I'm asking myself too, mathematicians should be the ones writing the academic books for highschool and not pedagogs who are not specialized in mathematics.
To solve that I recurred to some sections of some literatures writen by mathematicians which have the formal proof of the proposition.

And yes, if you take a read on the academic book teacher used in that school I used to teach, you would instantly rip your hairs off, since they dedicated just one page of theory, and about 10 of exercises.
Now, I do think that it was written that way so that the teacher introduces the solving methods, but that is not the case, it is 10 pages of painful repetition.

Answer 33

Over here, theory is not really taught till college-if at all. I do think pedagogy needs to be given its due(ya know, can't teach calculus to a first grader due to lack of abstract thinking), but the math is just not presented logically and there is a lack of emphasis on arithmetic sans calculator in those younger grades

Answer 34

Oh, I am also repellent to using the calculator, so I used to put exercises that only involved generalized numbers.

Answer 35

That's how I feel. To me, a teacher taking the time to use convenient numbers shows that they put effort in. Not only that, but what about when they are not allowed one in college? I was not allowed a calculator for any college course of my math degree.

Answer 36

When our teacher taught this stuff he did it really well
some students were nicely listening to what he said and were asking doubt questions to grasp the topic better but some were not at all interested
i think the kids start lacking interest in math when they get confused with some topic and then if they don't get it cleared they just leave it and then all the topics which are taught next related to that topic which the kid missed are also not understood fully by the student and from here the student starts lacking interest

to make the students develop interest i think the teacher must ask the students if they have any doubt and give examples of different types of questions in class