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Archive of posts filed under the Technology category.

Making Math with Scratch — Scratch Ed

Scratch Ed, an organization at the Harvard Graduate School of Education that supports teaching and learning with Scratch, recently profiled some of my work teaching mathematics using Scratch.

The article, Making Math with Scratch, highlights a Math for America workshop I ran for teachers that centered on approaching mathematical concepts through the lens of coding and computer science.  Several projects I use in my classroom are featured, and I also discuss why I like teaching with Scratch and how it’s become a valuable part of my approach to teaching math.

The purpose of the workshop and Patrick’s classroom activities are to demonstrate the power of bringing mathematics and computer science together. “Ultimately the goal is to show how math and computer science are great partners in problem solving. And Scratch provides a terrific platform for that.” 

I’m excited to share the work I’ve been doing with math and Scratch over the past few years–including talks and workshops at conferences like Scratch@MIT, SIAM ED, and the upcoming NCTM Annual meeting–and I really appreciate this nice profile from Scratch Ed.

You can read the full article, Making Math with Scratchat the Scratch Ed website.

Regents Recap — June 2016: Still Not a Trig Function

I don’t know exactly why, but fake graphs on Regents exams really offend me.  Take a look at this “sine” curve from the June, 2016 Algebra 2 Trig exam.

2016 June A2T 33

Looking at this graph makes me uneasy.  It’s just so … pointy.  Here’s an actual sine graph, courtesy of Desmos.

2016 June A2T 33 -- desmos graph

Now this fake sine curve isn’t nearly as bad as these two half-ellipses put together, but I just don’t understand why we can’t have nice graphs on these exams.  It only took me a few minutes to put this together in Desmos.  Let’s invest a little time in mathematical fidelity.

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Scratch@MIT Conference, 2016

Scratch MIT logoI’m excited to be participating in this summer’s Scratch@MIT conference.

The conference, held at MIT Media Labs, brings together educators, researchers, developers, and other members of the Scratch community to share how they use Scratch, the free, block-based, web-based programming environment, in and out of classrooms.  The theme of this year’s conference is Many Paths, Many Styles, which aims to highlight the value of diversity in creative learning experiences.

I’ll be running a workshop on Mathematical Simulation in Scratch, which will introduce participants to some of the ways I’ve been using Scratch in my math classes.  I’m looking forward to sharing, and learning!  And I’m grateful to Math for America, whose partial support has made it possible for me to attend.

The 2016 Scratch@MIT conference runs from August 4th through 6th.  You can find more information here.

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Using Mathematics to Create — Geogebra

Geogebra Student Work -- TriangleOne of my guiding principles as a math teacher, as I articulate in this TEDx talk, is to provide students with tools and opportunities to create with mathematics.  Few things are as aligned with that principle as well as Geogebra, the free, open-source, dynamic geometry environment.

I’ve integrated a lot of Geogebra work in my Geometry class this year.  I use Geogebra assignments to assess basic geometric skills, to connect old ideas to new, and to explore geometry dynamically.

But much like geometry itself, once you master a few elementary rules in Geogebra, you can create amazing and beautiful works of mathematics.

Below is an example of some wonderful student work from this year.  After an introduction to polygons, students were given two simple ideas for creating new objects from polygons:  constructing diagonals and extending sides.  I gave students some technical tips on how to color and polish their final products, and invited them to be creative.  As usual, they did not disappoint.

Geogebra Student Work -- Combination

Students, and teachers, need more opportunities to create with mathematics.  We’re fortunate to have technologies like Geogebra that offer us those opportunities.

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How Many Circles Pass Through Two Given Points?

The impact of technology on education is often overstated.  However, some applications of technology are unequivocally transformative in mathematics teaching.

The question “How many circles pass through two given points?” is a wonderful prompt for a geometry class.  It’s simple, it provokes debate, it can be explored in a variety of ways, and it connects to many important geometric concepts.  And in the end, it requires some imagination on the part of the student to truly comprehend the answer.

And after all that classroom work, it is so powerful and satisfying to see something like this.

circles through two points


A simple demonstration that elegantly captures the essence of the problem, and leads to new compelling questions.  That shows students that mathematics is beautiful and inspiring.  And that takes just a few moments to put together in Geogebra.

And what’s truly transformative is how easy it is to get students using technology to create their own mathematics like this!  This is the real promise of technology.

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