letters to my class

2 November 2011

November 2nd, 2011

Dear Chemists,

Lately, we’ve been talking about chemical reactions. We’ve learned that chemical reactions form new substances. Today we’ll talk about what must always stay the same in any chemical reaction: the amount of matter. This is the law of the conservation of mass. Scientific laws are different than societal laws because they can never be broken.

Scientists have long known about this law. The ancient Greeks knew that “nothing comes from nothing,” but it took many centuries before scientists were able to use the law of conservation of mass to create the field of chemistry. Through experiments, close investigations, and communication of their results with others, scientists in the 1600 and 1700s uncovered entirely new insights about the transformation of substances after chemical reactions.

Isn’t it comforting to know that despite all the changes and transformations going on, there’s at least one thing that stays the same? It sure makes the world a whole lot easier to study and understand.

Sincerely,

Mr. H
1 November 2011

November 1st, 2011

Dear Polygon Creators,

The difference between knowledge and a hunch is how well it’s explained. Often, we look at things and know what it is, but what we’re really doing is quickly recognizing the properties that make it what it is. Learning isn’t about knowing what a thing is. Learning is about observing, investigating, and explaining the properties that make it that thing.

So before you call something a square, stand on a little better authority and say, “It’s a square because it has 4 equidistant sides that all meet at 90 degree angles.” A square isn’t something that we draw on paper: it’s the idea of those properties. And ideas lead us to imagine things that were previously unimaginable.

Sincerely,

Mr. H
31 October 2011

October 31st, 2011

Dear Pumpkin Carvers,

Today we’ll use all of our thinking skills to find ways we can know about a pumpkin. Where did the pumpkin come from? Why does it look the way it does? What other things is it like? What things is it totally unlike? Pumpkin farmers are always trying to grow the biggest pumpkin (The current world record holder is over 1800 pounds). What is it about the pumpkin that allows it to grow so big?

By posing these questions, we learn not only about pumpkins, but we learn about the world that the pumpkin is woven into. There’s nothing really all that special about the pumpkin. It’s just an orange gourd that happened to spring from the bush of life in North American a few thousand years ago. While there’s nothing universally true about the answers we get about the pumpkin, there is something universally true about the questions we ask.

How do we know about the pumpkin? What properties and information can we discover about the pumpkin that allows us to communicate its essence to other human beings? These are the questions that last, and these are the questions we use to discover everything we know about the world and our place in it.

Sincerely,

Mr. H
4 October 2011

October 4th, 2011

Dear Calculators,

Before we had electronic calculators and computers, human beings created ingenious methods for calculating large numbers. Only recently have electronic calculators become cheap enough that anyone can have one. Before that, humans used mechanical calculators or simple devices to help them calculate. The abacus is one example that you’ve all seen. Today, we’ll create another calculating device called Napier’s Bones. You will notice that Napier’s Bones look a lot like the lattice method of multiplication. That’s because Napier borrowed that algorithm from people in the Middle East who had been using it for hundreds of years.

If you’re patient in the construction and use of Napier’s Bones, they will not only help you calculate multiplication problems, but they will also help you better understand what exactly multiplication is and what it does.

Sincerely,

Mr. H
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
29 September 2011

September 29th, 2011

Dear Geometers,

Archimedes was one of the greatest mathematicians of all time, but when he died as an old man, he was still drawing circles in the sand. Circles are an endless mystery: they are an enclosed space with infinite sides. Unlike many other shapes, circles appear in nature–ripples in a pond, craters in the moon, the eye of a hurricane, the face of a sunflower. Ancient people studied these circles and from them created the field of geometry.

Today, we’ll create circles using one of the geometer’s best friends–the compass. With this simple tool, we’ll be able to create beautiful, intricate designs. As we’re doing it, look for patterns, look for symmetry, and be prepared to be amazed.

Sincerely,

Mr. H
27 September 2011

September 27th, 2011

Dear Statisticians,

Numbers become data when we collect them and analyze them. For our data to be good, we have to go about collecting it in accurate, reliable, and precise ways. For our data to be meaningful, we have to use it to draw conclusions. The world is full of data. Some of it is good, some of it is bad. Some of it is reliable, some of it is not. Your job is to find the good data, analyze it for meaning, and use it to say something true about the world.

One tool for analyzing data is landmarks: median, maximum, minimum, range, mode, and mean. These landmarks help us make sense of data. Today we’ll collect data, organize data, and analyze data using landmarks. Then, we’ll use it to try to say something true about the world.

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
26 September 2011

September 25th, 2011

Dear Satellite Dodgers,

Did you see the news about the falling satellite? It weighed six tons and was the size of a school bus! When it re-entered the atmosphere, it broke into smaller pieces, but scientists said it had a 1 in 3200 chance of landing on a person. What do you think the odds were that it would have landed on you?

This week we’ll talk about probability. When you learn to think probabalistically, the world lets you in on its not-too-well-hidden secrets, you make better choices, and you don’t waste precious time worrying about 6-ton satellites falling on your head.

Look at the globe or the map. Where do you think the satellite probably landed?

Let’s have a great day.

Sincerely,

Mr. H.