Forgetting Previous Math Topics

Let's face it. Anyone can learn math chapter by chapter and section by section. However, how do we keep previously learned topics and ideas fresh in mind several chapters later? For example, I am currently in Chapter 2, Section 2.5 in my Calculus textbook.

What can I do to prevent forgetting Section 2.5 or 2.6 or 2.7.or 2.8, etc a few chapters later? The same thing can be said about courses. For example, students take Algebra 1 and 2 probably in freshman year high school. By the time they start their sophomore year, most of the Algebra 1 and 2 material has been forgotten.

You say?

 

math doesn't work that way
you always need keep previously learned stuff, everything is connected

 

Why do you think I like to post problems that cover previously learned topics and/or ideas? I also think that learning how to solve problems without actually learning THE WHY of what's going on is a big reason why students often forget what they have been taught.

For example, most students easily pick up the Pythagorean Theorem (a^2 + b^2 = c^2) but do they actually know what Pythagoras meant by this theorem? The answer is no. Understand the concept, the idea helps to know what is going on in the calculation itself. For example, x + 5 = 10. We know that x must be 5. Why does x = 5? Why is x not 6, 7, or 8? Most students don't know THE WHY of solving problems.

You say?

P. S. Be on the look out for some word problems throughout the week. I may also want to post some previously learned topics like trigonometric identities, geometry, area, perimeter, functions, graphing, etc. We return to Calculus on Friday, Saturday and Sunday.

 

if x + 5 = 10 and you know that x must be 5, means you know THE WHY

 

Mira,

What I meant to say is that, yes, students know THE WHY in this case. We know that x cannot be anything but 5. Students will argue and say that x = 5 because, after solving for x, I ended up with 5. They will not say that x = 5 because 5 + 5 = 10.

What about linear equations? Students know what
y = mx + b means, but don't know that this equation represents a straight line. They don't know that linear equations are FIRST DEGREE equations because the highest exponent is 1. They don't know THE WHY. They are taught to be robotic and mechanical in terms of solving math problems.

I fall in this category. I feel that I've been cheated out of a solid educational foundation, which explains my weakness in mathematics. I am a victim of the NYC public school system. A system that pressures teachers to teach the test and not teach to learn.

 

linear equations -> the probably know what linear means

when students learning some new terms, first thing what teachers do is explain what that terms mean
example:
linear equations-> explain what that mean
y = mx + b -> how is mathematically represented, what y, m, x, and b represents

ones students grasp it, they are ready for problems to solve

ones they really understand it, they are not going to forget it because they are going to use it constantly

 

I was a sub teacher for 8 years. I recall writing some fraction problems on the board for 7th and 8th graders to solve before giving the class FREE TIME.
They could not add, subtract, multiply and divide REGULAR fractions not algebraic fractions. Reason: WE HAVE NOT DONE FRACTIONS IN A LONG TIME.

 

if they could not add, subtract, multiply and divide REGULAR fractions => they never actually learned it

 

Exactly my point.