Here are links to posts on my Math Education Blog that you might find interesting.
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Technology in Math Education
It no longer makes sense to prioritize speed and accuracy in numerical computation or algebraic manipulation — if it ever did. The underlying concepts continue to be essential, but focusing on memorized techniques does not help students understand the math. Quite the opposite! Those techniques are intended to serve as a substitute for understanding. The endless practice required to be fast and error-free is not only pointless given today's technology, but it is also terribly boring. I discuss all this, and share some alternatives, here.
We Need to Review!
Most students do not learn important and difficult ideas the first time they come across them. Thus the need for review. But it is not a good idea to reteach the same ideas the same way. It is a waste of time for the students who already get it, and not very helpful to the others. It is especially problematic to start a course or a unit with review. In this post, I discuss the when and the how of review in math class. (For more on the need for extended exposure, and how to achieve it, see Reaching the Full Range.)
Polyarcs in the Classroom
In the late 1980's, I came up with polyarcs, a geometric puzzle in the tradition of polyominoes. I introduced them to the world on my website, but never managed to make them part of my teaching. Meghan Lee may well be the only teacher to have used polyarcs with students. In this guest post, she shares how they fit in her geometry class.
Making a GeoGebra Slide Show
I've used interactive geometry software for more than 30 years, and have shared my ideas on the Web for almost as long. However, I've only recently started to record videos for my site. So far, I've managed to do it without specialized video software or equipment. Instead, I've used whatever video camera and software is available on my computer. In this post, I share how GeoGebra can provide a way to make a presentation consisting of slides and geometric animations. See A New Path to the Quadratic Formula for the result of that experiment. (The "new path" is a derivation of the quadratic formula that involves neither parabolas nor completing the square.)
New, newish, and old on my website.
Lab Gear Videos / Lab Gear Q and A
Between 2007 and 2021, I offered summer workshops for math teachers. My most frequent topic was Visual Algebra, and in fact that workshop almost always had the largest enrollment. Part of it was dedicated to the Lab Gear, the algebra manipulative I designed. This summer, in lieu of a workshop, I created eleven videos about how to use the Lab Gear, and correlated them with pages in the Lab Gear books. I also suggest pages appropriate for teachers' professional development, and offer links to slide shows teachers can use in their pre-algebra and algebra classes. Find all this here.
Additions, Updates, and Tweaks...
...since my last newsletter:
- I added Parisa Safa's Python program for the iteration of "dome" functions to the Chaos section of my Infinity page. (Infinity is a post-Algebra 2 elective. The site already included instructions for a GeoGebra approach to those iterations.)
- I tweaked the Complex Numbers page.
- I added Boxer: A Teacher’s Experience, an overview of my long involvement with this computer language.
- I added links between A New Path to the Quadratic Formula, Constant Sums, Constant Product, and Parabolas and Quadratics.
According to Google, these were the ten most-visited pages on my website since the last issue of this newsletter:
- Virtual Grid Paper
- Math Education.page (the home page)
- Virtual Pentominoes
- A Graphical Path to the Quadratic Formula (an approach based on moving a parabola)
- Lab Gear home page
- Geometric Puzzles
- Geometry Labs (dozens of hands-on activities)
- Geometry of the Parabola
- How to Get Some of My Publications
- Algebra Manipulatives: Comparison and History (a rather technical overview)