In Where Mathematics Comes From, cognitive scientists George Lakoff and Rafael Nuñez assert that our understanding of abstract mathematical concepts relies upon our sensory-motor experiences:
“For the most part, human beings conceptualize abstract concepts in concrete terms, using ideas and modes of reasoning grounded in the sensory-motor system. The mechanism by which the … Continue Reading ››
Shiva Gol Tabaghi obtained her PhD degree in Mathematics Education from Simon Fraser University in 2012. This guest post is based on her doctoral dissertation research. Presently, she is involved in teaching undergraduate mathematics courses at Simon Fraser University. She enjoys using dynamic geometric diagrams to influence students' ways of thinking about mathematical concepts.
If you’ve taken linear algebra, chances … Continue Reading ››
In my Advanced Methods class at Penn’s Graduate School of Education, my students are working in groups to create shared lesson plans using an inquiry approach. For a number of reasons it can be challenging for these pre-service teachers to identify appropriate topics for student inquiry, but sometimes the brainstorming they do turns into something … Continue Reading ››
In the 1970s, my childhood friend Tim owned an Activision console and a variety of game cartridges. Tim was the envy of our block, but no matter how much I enjoyed a rousing game of Pong, I knew that my electronic toy was even better. No, I didn't own the rival Atari game system: I … Continue Reading ››
Take a look at the interactive model below (and here). Most of the numbers in the array are shaded orange, but several are blue. What is special about these blue values? They are the factors of 32, the largest number in the array.
Try dragging the red point to change the dimensions of the array. … Continue Reading ››
Yesterday, I led a webinar that demonstrated how Sketchpad and Web Sketchpad can be a powerful tools for exploring Common Core algebra topics. My examples included solving for unknowns with a pan balance, exploring the slopes of lines, maximizing the area of a fixed-perimeter rectangle, and graphing trigonometric functions. I touched only briefly on each example during the … Continue Reading ››
I recently got a question from a question from a user about how to line up text objects. The question was both about lining up objects on a page, and about lining them up from one page to the next, so that when you switch pages things are in the same place on every page.
As … Continue Reading ››
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 ››
Harry Parker died this summer, two weeks after coaching the Harvard rowing team to yet another sweep of all four races (varsity, JV, freshmen, and spares) against Yale and two days after accompanying his 1980 Olympic … Continue Reading ››