Blog Posts
Links to the most recent posts on my Math Education Blog, and some old favorites.
Disciplinary Learning
A frequent refrain from would-be educational reformers is a complaint that secondary school learning is siloed in departments. The argument goes something like this: the real world is not divided into departments, and schools should be organized to reflect that. And yet, attempts at interdisciplinary programs rarely last more than a year or two. In my view, it's not a big loss. Effective interdisciplinary projects have to be founded on a solid disciplinary foundation. I discuss how to do this right in a blog post: Making Connections.
Habits of Mind
Most of our students will not find a use for the quadratic formula or the Pythagorean theorem in their future personal or professional life. So why do we ask them to spend so much of their schooling in math class? One reason is to keep open the possibility for some of them to pursue studies and/or careers in STEM — and we can't tell in advance who that will be. But another reason, which applies to all students, is the development of habits of mind. Chief among those are problem solving and argumentation. Frank Cassano and Anya Sturm, along with their high school math department, have developed a strategy to make this explicit and achieve student buy-in. They share this in two guest posts: Integrating Problem Solving Seamlessly, and Integrating Argumentation Seamlessly.
Story Tables
Back in the 1970's, I came across a powerful representation of algebraic expressions, based on inserting additional columns in the usual input-output tables (known by some as "t" tables). I believe this was pioneered by someone in Oregon. Unfortunately, I promptly forgot about it. Much more recently, I was reminded of this representation by Shira Helft who rediscovered it, named it (story tables), and took it a lot further. (See these posts on my blog: 2018 | 2019.) Shira recently launched a Substack home for story tables. If you teach math in middle school or high school, I strongly encourage you to subscribe — I am sure that she will share many useful applications of this multipurpose learning tool.
Your Post Here!
Shira, Frank, and Anya are not the first to share their ideas on my blog. As you can see here, my blog and website include material from quite a few math educators. I'm happy to incorporate your contributions, as long as they come from a philosophically compatible point of view, and are not commercial pitches for products I know nothing about. (I get a lot of spam from businesses offering "content" for my site.) I'm especially interested in feedback from users of my materials, responses to my blog posts, and reviews of my book(s) or website. To propose a topic for a guest post, just reply to this email.
MathEducation.page
Visit my website!
Old But Excellent
A selection of launch pages on my website:
- Lab Gear: This is a powerful manipulative for algebra, which can be used from middle school to Algebra 2. It is vastly more versatile, effective, and popular with students than algebra tiles. The Lab Gear is supported by classroom-tested curriculum materials based on an engaging problem-solving approach. Teacher-prep videos are free on my website.
- Applets: Those are small, single-purpose computer programs, accessed through a browser. I built them using GeoGebra, with the goal of making various secondary school mathematical ideas more visual and more interactive. As you can see below, some are among the most popular items on my website.
- Fractions: The Well-Chosen Rectangle is a grid-paper approach to fraction arithmetic, presented there in text, graphics, and video. It is an extremely accessible tool with many uses, a big idea to complement any other techniques. Also, for students (and teachers!) who can add fractions: the Egyptian Fraction Challenge, a great extension.
There Is No One Way
In addition to sharing a vast amount of curriculum materials, I've been known to philosophize about math education. For example, read these articles:
- Reaching the Full Range: Students learn math at different rates. Everyone knows this. Can something be done about it? Yes! I suggest practical strategies to address this challenge.
- Taking Notes vs. Doing Math: Students cannot do both at the same time.
- Big-Picture Planning: Lesson planning is key, but it resides in a context. I share ideas on planning units, courses, and entire programs.
These articles are now improved, extended, and embedded in the book I co-authored with Prof. Robin Pemantle: There Is No One Way to Teach Math: Actionable Ideas for Grades 6-12.
More Links!
- Most-visited pages in the last six months, in order:
- Virtual Grid Paper
- Virtual Pentominoes
- Virtual Geoboard
- Geometry Labs
- Geometric Puzzles (many links)
- For a Tool-Rich Pedagogy (many links)
- Geometry of the Parabola
- Proving Pick's Formula
- Manipulatives (many links)
- My books
- Virtual Base-Ten Blocks
- Some pages I tweaked since the last newsletter:
- π
- Recognizing Functions (many links)
- The Assessment Trap
- Nothing Works
- Proof (many links)
- Teaching (many links)
- There Is No One Way
- Pentominoes Home Page (many links)
- Infinity
