Maths Problems

[Aspergers_Aspie]

When I was at school, you would get marks for 'showing your working'. Even if you gave the right answer without doing this. But on an episode of Countdown, both contestants solved the maths puzzle, but one used all the numbers and people in the show noted this. But if using all numbers isn't required I don't see what the bug deal is

 

[Neonatal RRT]

As an educator,...and as a former student,...it is important to show your work, as it is (1) a way to demonstrate your understanding, (2) your technique, and (3) that you didn't guess or cheat. We have to think of situational context in these cases. In the working world,...i.e. an engineer sitting in some corporate cubicle, with a computer that does all your calculations for you, and time is of the essence,...you generally don't have to show your work, per se. Just get to the answer and move on.

 

[Aspergers_Aspie]

I wasn't trying to cheat. I couldn't care that so much emphasis is on working anyway, I knew getting the answer I was smart

 

[Neonatal RRT]

I wasn't trying to cheat. I couldn't care that so much emphasis is on working anyway, I knew getting the answer I was smart

As I suggested,...situational context. Within the context of an educational environment,...it is important to understand and demonstrate your method,...and achieve the correct answer. Achieving the correct answer is not the only metric of success in terms of learning. In the situation where you achieve an incorrect answer,...from an instructor's perspective, it is critically important to understand whether the student did not understand the method,...OR was the method correct and the student simply made a "simple, stupid, mistake" (a + instead of an -) for example. It is this discrepancy that allows the instructor to help the student understand, learn, and not make those mistakes in the future.

What student's don't often appreciate is the instructor's perspective and goal in their teaching of their students. For example, in physics,...is the student simply plugging in values into a memorized or given formula,...OR does the student understand how to derive the formula and come up with the correct answer. These are two different levels of understanding.

 

[Raggamuffin]

Maths problems used to feel like something was tightening in my head. The longer I spent trying to work out the answer, the more the screw kept tightening.

I think video games and pay days are the only times when numbers interest me these days.

Ed

 

[Nervous Rex]

There are two approaches to math:

1) Using math to solve things: This is the use that most everyone thinks of when they think of math. You learn a formula or a technique, and then use it to solve problems. It's like a fry cook following a recipe - they know the recipe works and they just want to follow the recipe to get food on the table. With this approach to math, it's easy to say, "I got the right result. Why do I have to show my work?"

2) Proving that math is correct: This is the approach that mathematicians take. When you create a new formula, you have to prove that the formula will work in all cases. This requires understanding of the foundations of math - the stuff you do when you "show your work". Math follows very rigid rules and showing your work shows that you followed all the rules. If there were no teacher and no answers at the back of the book, you would still know that your result was correct because you carefully followed all the rules. Taking a math class is like going from being a cook who can follow a recipe, to being a chef who can create new recipes.

That is why math classes make you do stuff like learning the entire proof for why the quadratic formula works, instead of just having you memorize the quadratic formula.

When you're in a math class, you'll have to do things the mathematician's way - show every step to guarantee that anyone can follow it and know you haven't made a mistake anywhere. As soon as you're out of the math class, feel free to take all the shortcuts that you want.