It started with an unassuming bunny that hopped along a number line.
In 2011, our team at KCP Technologies released Sketchpad Explorer for the iPad, making it possible for teachers and students to interact with desktop Sketchpad models on their iPads.
We were thrilled to bring the iPad’s … Continue Reading ››

Four years ago, my colleague Scott Steketee and I began brainstorming new Sketchpad activities for a National Science Foundation grant called Dynamic Number. Our goal was to use Sketchpad to make ideas from number, operation, early algebra, and algebra come alive through interactive models that emphasized conceptual understanding.
Continue Reading ››

In my previous two posts, I listed some of the new Dynamic Number project activities (for grades 2-5 and grades 5-8) that engage students in manipulating and investigating dynamic mathematical objects from day … Continue Reading ››

In the Dynamic Number project, one of our goals has been to create activities in which students actually experience mathematical objects by creating them, manipulating them, and investigating them. (George Lakoff and Rafael Núñez describe, in Where Mathematics Comes From, how students' abstract mathematical concepts are grounded in … Continue Reading ››

As an 18-year veteran teacher in Philadelphia public schools, my initial reaction when I first saw Sketchpad was “This would have completely changed the way I taught geometry.”
I phrase it differently today: “This would have completely changed the way students experience mathematics.” a perspective that differs in two important details.
First, I now understand that the … Continue Reading ››

As a fourth-grader in 1977, I had a love-hate relationship with my Addison-Wesley textbook. Its contents overflowed with arithmetic problems, but every so often an entertaining brainteaser appeared to break the monotony of drill practice. These puzzles were clearly marked: Each appeared in a box set aside from the main text and featured a bespectacled … Continue Reading ››

Like other enthusiasts of mathematics, I’m captivated by the way that mathematical ideas can explain things in the physical world around me, and by the way that I can carry out mathematical thought experiments in my mind and then apply the results to control my external physical environment.

Functions are hard for students.
Students seem to master various families of functions – linear, polynomial, exponential, trigonometric, and so forth. They can graph them, evaluate them, transform them, and answer a variety of questions about them. But ask even our better students a question that’s out of the ordinary and we’re likely to be taken … Continue Reading ››

As an author of Sketchpad activities, I like to think that I can pose good problems for students to solve. But as I visit elementary classrooms and watch students use Sketchpad, I realize that a large part of the enjoyment they derive from using our software comes from creating their own problems and sharing them … Continue Reading ››

A quick quiz: How many fractions are there?
This may sound like an absurd question, but in the context of elementary mathematics curricula, it makes a lot of sense. Think about it: Children encounter fractions like 1/2, 3/4, and 2/6 all the time, but do they ever see 1/100, 31/90, or 499/500? Unlikely. No brave soul … Continue Reading ››