Tag: problem solving

12 March 2013

March 12th, 2013

Dear Problem Solvers,

After spending lots of time around the same people, sometimes problems crop up. Sometimes people do things that we don’t like and sometimes we do things that others don’t like. One of the most important skills we can teach you at school is how to handle these conflicts in a healthy and productive way.

It’s important that you learn these conflict resolution skills because conflict is something you will have to deal with for the rest of your life. Unless you end up on a deserted island in the middle of the Pacific, you will have interpersonal conflict. When that happens, we have a choice: we can deal with it in ways that show respect for ourselves and our fellow human beings, or we can deal with it in dangerous, unsafe ways. I hope you choose the first.

At school we’re trying to help you build the skills you need to be capable, self-reliant, and confident people. That means we learn how to solve math problems and it also means we learn to solve interpersonal problems.

Sincerely,

Mr. Heimbuck
February 4, 2013

February 4th, 2013

Dear Problem Solvers,

“If I had an hour to solve a problem I’d spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.”–Albert Einstein

We’re going to continue to talk about problem solving today. We’ll review strategies and talk about methods, but mostly we’ll just talk about problems and the things that make them interesting. As Einstein’s quote implies, if we want to find a meaningful solution, we need to really know the problem.

Anyways, our bigger goal is to come up with our own problems. That’s the purpose of math: to pos esolveable problems that might reveal something interesting about the world.Often, the solutions to such problems are incomplete, fleeting, and up for debate, but the problems themselves last a long time.
January 15, 2013

January 15th, 2013

Dear Problem Solvers,

Math really is only about solving problems. We often use numbers to solve those problems because they let us do it more efficiently, but we could solve almost any problem by drawing a picture. Many times, such a picture takes a very, very long time to create, so numbers are more efficient, but the job of math is solving problems.

You’ve been solving problems your whole life. In many cases, you probably used math to solve these problems and didn’t even know it. Our goal in math class is to give you the tools to solve problems more efficiently and more creatively. And after you get practice solving problems, you start making up problems of our own to which math is almost perfectly suited to solve.

We’ll spend a lot of time the rest of this year thinking of problems, solving problems, and talking about our mathematical methods of doing so.

Sincerely,

Mr. Heimbuck
September 24, 2012

September 23rd, 2012

Dear Problem Solvers,

Over the past few days, we’ve practiced our addition and subtraction algorithms. I hate to tell you, but that’s the easy part. Today, we’ll do the hard part: figuring out when to use those algorithms to solve real world problems.

The real world will never hand you a sheet of addition and subtraction problems and ask you to solve them without a calculator. Instead, the world will ask you to figure out how much money you’ve spent so far in the month and how much money you have left. The world will ask you to keep track of bowling scores and fantasy football points and batting averages. The world abounds with numbers, and our job is not just to crunch those numbers, but to really figure out what they mean.

Today we’ll practice that skill by solving number stories, and we’ll learn some great methods, tips, and tricks for solving those number stories. That’s really what math is all about: giving us the tools and mindsets for more efficiently and effectively solving everyday problems.

Let’s have a great day,

Mr. Heimbuck
3 October 2011

October 3rd, 2011

Dear Rectangle Makers,

This week we’ll learn a few different algorithms for multiplication. While these step-by-step processes might look a lot different, they’re really all just the same. When we multiply, we’re making rectangles. One factor is the base. The other factor is the height. The product is the area. The different algorithms are just different methods for counting up the pieces of that rectangle.

The algorithms we’ll learn are the methods that people throughout history have devised to solve problems. We learn all of the algorithms because there’s never only one right way to solve a problem. Also, it’s a lot of fun to play with numbers.

Sincerely,

Mr. H
30 September 2011

September 30th, 2011

Dear Estimators,

Math is like horseshoes–most of the time, close enough is good enough. Usually, an estimate will give us the information we need. Sometimes, however, we have to be precise. Good mathematicians have to know how to do both. More importantly, good mathematicians have to know when estimates are appropriate and when it’s time to calculate precisely. As always, math thinking is about creating a method for solving a problem, not just doing the arithmetic.

Today, we’ll make magnitude estimates for products. The orders of magnitude are the powers of ten–1, 10, 100, 1000, 10,000, etc. By estimating the magnitude of the product, we’ll not only be able to check our calculations, but we’ll learn about the wonders of our number system. That’s really what it’s all about.

Sincerely,

Mr. H
26 September 2011

September 26th, 2011

Dear Problem Solvers,

When we do math, we’re learning how to think. More importantly, we’re learning how to solve problems. In the “real world,” no one actually does arithmetic, but those who know how to are better at solving problems because they’ve had lots of practice and they have a powerful method for doing so.

You’re going to have to solve problems every day of your life, numerous times, almost constantly. What should I believe? What is true? What is the good life? What kind of toothpaste should I buy? Those are the types of philosophical problems that math prepares us to tackle in analytic and truthful ways.

So when you’re doing your math today, spend less time worrying about your answers and more time thinking about your thinking. The most important thing you learn from math can’t be written on the other side of an equal sign. It’s in your head.

Sincerely,

Mr. Heimbuck