Studying What Is the Best Path to Learn Math?

[John_Williams]

Hi,

I was hoping I could get a good idea on the best "path" or "progression" to learn math starting from around a 4th grade level. My son has become very interested in math and wants me to get him some books and teach and help him when he gets stuck. That has inspired me to learn more maths as well. I was wondering what would be a good book for him to start. Pre-Algebra maybe? I don't really know what is before that so any tips on what a 4th grader would be able to do and maybe a book that would pique his interest. For me, I plan on getting a Calculus book (suggestions welcome on the best one to get) to refresh my calculus knowledge but then I am unsure what I should take on next. Thanks in advance for helping out some Maths enthusiasts!

 

[fresh_42]

Open Stax has a variety of freely available books:
https://openstax.org/subjects

I think they are meant to close the gap between all the different high schools and what is expected to know at colleges. But they are rather elementary, and I assume suited.

Just two things that should be considered:
If kids learn stuff ahead of what is taught in schools anyway, they might get bored at school and this could lead to the opposite effect.
Mathematics is rather different from what is taught at school. I like to say "school math is calculation, not math."

A possible first step that avoids those conflicts would be geometry: compass, ruler, and logic.

 

[berkeman]

My son has become very interested in math and wants me to get him some books and teach and help him when he gets stuck.

Welcome to PF. That is great that your child is already interested in Math and STEM.

Mathematics is rather different from what is taught at school. I like to say "school math is calculation, not math."

I think it's a bit worse than that, at least for basic math as taught to 6-16 year old students in the US. I believe that math is now taught to young people in schools with tricks and techniques different from the math techniques that we learned. And trying to teach a young student our old way of doing things can just confuse them when they try to do it the "school" way. I experienced that a little back 15 years ago when my kids were young, but apparently now it is much worse.

I'm not sure of the best way to handle this, but it may involve trying to get hold of some of the learning/teaching materials that will be used in your area schools when your child is in school. Do you have any contacts at your area schools?

https://www.understood.org/articles/en/9-new-math-problems-and-methods

https://www.parents.com/kids/educat...math-method-explained-for-millennial-parents/

https://en.wikipedia.org/wiki/New_Math

 

[symbolipoint]

Pre-Algebra maybe? I don't really know what is before that so any tips on what a 4th grader would be able to do and maybe a b

"Pre-Algebra" can often be a weaker form of "Algebra 1". It is not a bad choice to give a bridge between General Mathematics and Algebra 1, but it is unnecessary for some students. Likely unnecessary for most students.

Books for before Pre-Algebra could be basic Arithmetic and topics instructing on whole numbers, fractions, signed numbers, decimals, percents, the very many numerous applied General and Consumer Mathematics including pictorial ways to represent numerical information. Look for some treatment of prime and composite numbers within books you try to evaluate. Also, books which instruct on common Geometry can be useful. The G.E.D. Mathematics books will typically these topics of instruction. Otherwise, I have no specific books names to recommend.

I prefer to suggest skipping Pre-Algebra. Once a student has understood and spent enough effort on Arithmetic and General Mathematics, even if he has not mastered it, he can go directly to Basic Beginning Algebra. You can find good old, USED books at library book sales for very low prices. Since you studied through Calculus in your college days, you will know what to look for when you examine these. A few useful authors of these books to help identify them are: Write & New, Larson; Larson & Hostetler, Aufman; Aufman & Barker. I cannot remember some others.

 

[symbolipoint]

Open Stax has a variety of freely available books:
https://openstax.org/subjects

I think they are meant to close the gap between all the different high schools and what is expected to know at colleges. But they are rather elementary, and I assume suited.

Just two things that should be considered:
If kids learn stuff ahead of what is taught in schools anyway, they might get bored at school and this could lead to the opposite effect.
Mathematics is rather different from what is taught at school. I like to say "school math is calculation, not math."

A possible first step that avoids those conflicts would be geometry: compass, ruler, and logic.

I do not completely agree with all of that but I like the posting anyway. Readers, use the passage for your own thinking the best ways you can. Additionally, "Geometry", the course, is one if not the only one which has a laboratory component to it (for Mathematics courses grades 1 through 12 in K-12 systems).

 

[symbolipoint]

berkeman in post #3,

I had seen some strange and confusing instructional parts of some books in certain schools directly, several years ago. Only thing I can say is some crazy exercises shown without any meaningful motivation or identification of concept or skill to be learned.