The Garden Project:

Over the past couple of weeks, my 3rd graders have been working with our new set of iPads on a Garden Project. Since our school has put in learning gardens this year, I thought it would be an applicable project for them.

The premise of the problem: The school wanted to build a garden with the most space to plant our vegetables. Each group was given 18 feet of fencing (18 toothpicks) to use as their perimeter. They were to design each garden, record the dimensions, and take a picture to save in their photos. After they designed all possible rectangular gardens, they had to create a presentation in Numbers to show me which garden they wanted to build.

The instruction page looked like this (Since this was our first project, I put the app pic next to each direction to help them along the way):

I…

As you’re probably aware, I’m a big believer in using stories to bring math to life. Especially when you’re teaching tricky concepts, using a story can be the “magic switch” that flicks on the light of understanding. Armed with story-based understanding, students can recall how to perform difficult math processes. And since people naturally like stories and tend to recall them, skills based on story-based understanding really stick in the mind. I’ve seen this over and over in my tutoring.

The kind of story I’m talking about uses an extended-metaphor, and this way of teaching  is particularly helpful when you’re teaching algebra. Ask yourself: what would you rather have? Students scratching their heads (or tearing out their hair) to grasp a process taught as a collection of abstract steps? Or students grasping  a story and quickly seeing how it guides them in doing the math? I think the answer is…

This will be a quick post because I have a student-posed math problem that I need some time to reason through!

Today, students found the area and perimeter of squares that increase in side length by one each time. Students used a variety of models when building their squares from Minecraft carpets, to Geoboards to graph paper. Here is the completed activity sheet from their work: I then gave them a few minutes to talk to their tablemates about things they notice in their work. Here are the answers they shared as a class and I recorded on the board:

“An even dimension by even dimension = an even area”

“An odd dimension by odd dimension = an odd area”

“The perimeter goes up by 4 every time the square gets bigger”

“The areas are square numbers.”

“The areas go up by odd skip counting: +3, +5, +7…”
I was…

This 23-year-old Chinese ‘Rain Man’ Chou Wei has IQ 46, dropped out from Primary school at age 12 because his teachers and classmates discriminated him as an idiot.

This video shows he can mentally do very complex math calculations:

The full video (in Chinese):

Today I realized something about being a tutor.

A big part of it — maybe as much as half it — involves nothing more than  …   being nice.

By that I mean being kind.

By which I mean that if someone looks at you, as a young man did today, shaking his head and saying, “It’s crazy … I don’t know what 3 x 6 is,” I don’t laugh or chuckle or say anything remotely mean or mocking. Instead I just say, “It’s o.k. Look, I tutor people every day who don’t know what 3 x 6 is. Who cares, really? Let’s just try to figure it out … or use a calculator, as long as your teacher doesn’t mind.”

Really. That is a lot of what being a math tutor is about. Being nice. Really nice. Really understanding. And being there to be accepting of people no matter…

Have you ever been befuddled by the rules for logs?

More specifically, have you ever looked at this rule:

log (v w) = log v + log w

and thought: Now why in the world is that true?! What exactly is this saying? I know that I, myself, have had that thought. And for me the desire to understand this rule never went away. Till I got it some time ago.

[By the way, keep in mind that the v and the w in the parentheses are multiplying each other, so that v w actually means: v times w]

And the good news is: I think I can explain this rule in a way so that pretty much everyone who knows basic algebra can grasp it.

O.K., first, I knew that this log rule was related to another rule, the  exponent rule that says:

(a^b) x (a^c) = a^(b…

This term I shall be giving Cambridge’s course Analysis I, a standard first course in analysis, covering convergence, infinite sums, continuity, differentiation and integration. This post is aimed at people attending that course. I plan to write a few posts as I go along, in which I will attempt to provide further explanations of the new concepts that will be covered, as well as giving advice about how to solve routine problems in the area. (This advice will be heavily influenced by my experience in attempting to teach a computer, about which I have reported elsewhere on this blog.)

I cannot promise to follow the amazing example of Vicky Neale, my predecessor on this course, who posted after every single lecture. However, her posts are still available online, so in some ways you are better off than the people who took Analysis I last year, since you will have…

I’m encountering a sporadic bug over the past few months with the way WordPress renders or displays its LaTeX images on this blog (and occasionally on other WordPress blogs).  On most computers, it seems to work fine, but on some computers, the sizes of images are occasionally way off, leading to extremely distorted and fairly unreadable versions of the images appearing in blog posts and comments.  A sample screenshot (with accompanying HTML source), supplied to me by a reader, can be found here (in which an image whose dimensions should be 321 x 59 are instead being displayed as 552 x 20).  Is anyone else encountering this issue?  The problem sometimes can be resolved by refreshing the page, but not always, so it is a bit unclear where the problem is coming from and how one might mitigate it.  (If nothing else, I can add it to the bug collection…

The Leap Forward

We are very proud to present you the new Mathist. It is a real sneak peak into the future, that allows you to easily solve and compute anything you write with a single click!

Here are some examples;

• Simplify any expression to speed up problem solving,
• Plot graphs,
• Evaluate expressions and get approximate values,
• Solve equations and inequalities (with visual representation),
• Solve definite and indefinite integrals (with visual representation),
• Crunch difficult logarithms,
• Find derivatives and much more…

You can do all of this with just one button: 

Why is this important?

Have you ever worked on a problem, that is easy to understand, but just requires too much number crunching?– So did we!

We understand that learning a million new things every day as a technology or a science student doesn’t leave too much time for crunching math. And yet in most cases you cannot solve…

What is The Mathist?

TheMathist is a very unique social math note taking application. It works on every device, and is free for everyone. You can finally focus on the math, not the software.

Do I have to know TeX or similar syntax?

There is no need to learn TeX or save the notes as pictures, they will always be available to you as regular online documents that you can edit anywhere and anytime. We have built a revolutionary simple math editor, a lot of hours went research on this. Go ahead and give it a try!

Why should I use The Mathist?

Because it is simple and straightforward to use, a true breeze… Because you already take all your notes in digital form and save them in the cloud. Because it is fast and works on all devices. It does not require any software knowledge to start, and…

After many days of discovering my HUGE learning curve with Minecraft, I am finally starting to feel relatively comfortable in Creative mode…I can build a house without flooding it, planted a few trees and I no longer have random blocks floating in the sky around my world!  My class has been staying with me during recess to teach me how to play and I am amazed at how fast and detail-oriented they are in their designs, such as putting lava rocks under the water blocks to form a hot tub and putting glass windows in their new greenhouses. I just kept thinking that I would love for them to use this same precision and perseverance in math class.

I must have Minecraft on the brain, because I as I was planning this weekend for the upcoming week (multiplying fractions w/arrays), all of the scenarios were about planting on an acre…

This week I am in San Diego for the annual joint mathematics meeting of the American Mathematical Society and the Mathematical Association of America. I am giving two talks here. One is a lecture (for the AMS “Current Events” Bulletin) on recent developments (by Martel-Merle, Merle-Raphael, and others) on stability of solitons; I will post on that lecture at some point in the near future, once the survey paper associated to that lecture is finalised.
The other, which I am presenting here, is an address on “structure and randomness in the prime numbers“. Of course, I’ve talked about this general topic many times before, (e.g. at my Simons lecture at MIT, my Milliman lecture at U. Washington, and my Science Research Colloquium at UCLA), and I have given similar talks to the one here – which focuses on my original 2004 paper with Ben…