What's up with students' memories?

[Starman71]

Originally Posted by Retroit

I think this may be the problem. What's more important: knowing how to use a formula or knowing what a formula means? A formula is not just something we mere mortals were given from on high to mindlessly plug numbers into. A formula reveals a truth about how the real life components of a formula interact with one another to produce a desired outcome. To understand the formula by memory is to understand the whole concept of what truth the formula expresses. Plugging in the numbers will come easy only if they understand the formula enough to have it memorized.

Understood, but must respectfully disagree - to a point.

In the Calculus-based AP Physics, much time is given over to the derivations of the formulas. That is fine for what the class is ultimately trying to teach these future engineers/physicists. etc. This class also doesn't cover as much material, which allows the time for this. For Algebra-based physics or general HS physics, because of state/college board standards, there is very little time to show how each of the multitude of equations were derived. Too much material must be covered. The same goes with many of the equations in general or AP Chemistry.

Now we could allow the Physical Science teacher to do some of this for us, at least on a small scale to show them how it's done for a few of the basic equations, but they also have their own end-of-course exams to worry about, along with all of the specified material they must cover.

In an ideal world, teaching how these formulas came to be would be excellent. In that, you are correct. If there were fewer standards on which to cover, we might have the time for this. But having taught for almost 2 decades, I can state that most students learn the relationships between formulas and equation by putting them into practice - and practice, and practice - showing the different ways they can be applied. Some may never learn the relationships/derivations, because as another poster stated, there are 2 types of math students.

Then, if we consider the general student - not the AP student - most will never care enough to learn what the formula means. If we as teachers can't even get them to be able to simply re-arrange the d=m/V equation to solve for V, then the 'meaning' of the equation is less than useless. We can show them the relationships between the 3 variables, but they still have to be motivated enough to listen.

[villageidiot1]

Originally Posted by nana053

I disagree with this. It is true that you must have a foundation of knowledge on which to build critical thinking, but that does not mean you should neglect critical thinking even in the earliest grades.

A Tale of Two Schools Thinking Deeper - Voice of San Diego: Education

How to Encourage Critical Thinking in Science and Math | Teaching Science and Math

New practices have more to do with what teachers don't do, than what they do. For example, when pupils struggle with problems, it is important to step aside to let them work out solutions with their classmates rather giving them quick answers.

To really teach critical thinking, you have to:
Ask open-ended questions.
Categorize and classify.
Make decisions.
Find patterns. (This one is particularly appropriate for math).

It's still important for your child to know his multiplication tables, but it's just as vital for him to know how and when to use them.

After seeing first hand what is occurring in education today, I think it would be a huge improvement if 99% of students graduated with proficiency in basic arithmetic including multiplication and division, and fractions and decimals.

Before we can address critical thinking, we need to teach students how to be able to read, understand and follow simple directions. We have many students capable of moving on to critical thinking in elementary school and middle school, but many are not capable of critical thinking in high school. This is why we need to go back to some form of tracking where students who are capable of critical thinking are placed in the same classes, while students who need more individual support and repetition are placed in classes with similar students.