A correspondent writes:We emphasize the idea that students should approach problems in multiple ways. This has caused me to wonder about patterns. For example:students might conclude that 3^0=1 because of the pattern 3^4=81, 3^3=27, 3^2=9, 3^1=1orwhen the second difference is constant, students will conclude that the function is quadraticorwhen a function is concave up, the… Continue reading Patterns
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Triangle Similarity Update
As you may remember from my previous posts on this subject, I have been thinking a lot about the Common Core approach to secondary-school geometry, specifically the logical switcheroo that makes triangle congruence and similarity a consequence of assumptions about geometric transformations, rather than the other way around. To support this change, I have started… Continue reading Triangle Similarity Update
Fathom: Free for Now!
See below for a letter from Bill Finzer, the leader of the Fathom team, dated June 15, 2014. Fathom is outstanding software for statistics, but also for basic algebra. If you are not familiar with it, I strongly recommend you check it out. It is free for the duration of this school year.Once you have… Continue reading Fathom: Free for Now!
The Lab Gear Is Back
Rethinking Triangle Congruence and Similarity
As you may know, I have discussed transformational geometry and the Common Core State Standards for Math (CCSSM) several times on this blog. This summer, I have already been a presenter in two professional development workshops on transformational geometry, and will be involved in two more. This has pushed me to move forward on writing… Continue reading Rethinking Triangle Congruence and Similarity
Doctor Dimension Returns!
In a post a few weeks ago, I told the story of Doctor Dimension, the two-dimensional scientist who spends his fictional life filling two-dimensional containers with two-dimensional liquids, and has been doing this since 1994. In the comments, two different Bay Area math teachers directed me to Water Line, a wonderful Dan Meyer / Desmos… Continue reading Doctor Dimension Returns!
World Cup Fever
The World Cup happens mostly during summer vacation, which is unfortunate, because it provides a great context for a geometry exploration.I start my book Geometry Labs with lessons about angles, starting from the very basics, and moving on to the inscribed angle theorem. (The book is available in its entirety as a free download here.… Continue reading World Cup Fever
Doctor Dimension
Twenty-some years ago, I started teaching an advanced high school geometry elective class called Space. I offered it every other year until I retired last year. Most of the course was about transformational geometry and symmetry. (That turned out to be excellent preparation for Common Core geometry. I will be presenting and co-presenting four workshops… Continue reading Doctor Dimension
New stuff on my Web site
I am busy preparing for my summer workshops, so I'm blogging less and adding more stuff to my Web site.Here's a list of recent additions:- A new Geometric Construction page, including a whole unit with a teachers' guide, plus a GeoGebra page with tools limited to straightedge and compass construction. Also an applet / file… Continue reading New stuff on my Web site
Big Fun!
In time for my summer workshops, I have a new page on complex numbers, featuring an explanation of the approach I recommend for teaching this topic, worksheets for Algebra 2 and beyond, and (big fun!) online games to introduce and practice complex number arithmetic.Over the decades, I created versions of these games in three education-oriented… Continue reading Big Fun!
Henri's Math Education Blog 