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
Tag: Algebra
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!
Completing the Square
New animation: a geometric representation of completing the square. In this post, I present one way to use it as part of an algebra curriculum.Many secondary school teachers figure that the derivation of the quadratic formula by completing the square can be shown to students, but have little hope of any understanding. They… Continue reading Completing the Square
the function dance!
A friend on Google+ posted this image:<a href="data:<img alt="" border="0" src="data:I have often performed "the cubic dance" (see above!) for my students. I've also often asked them to "air graph" various functions.One complication is the fact that left and right are reversed for the person watching you, and while I try to perform things "backwards"… Continue reading the function dance!
Ripples
Math curriculum ideas expand outward from their originators, like ripples in a pond. In pre-Internet days, it was great to see teachers using photocopies of photocopies of photocopies of worksheets I created, such as "Make These Designs." Nowadays, of course, people can always download and print a fresh copy. One day at an NCTM meeting,… Continue reading Ripples
More Algebra Book Fan Mail
I have some good news for the users of the online version of Algebra: Themes, Tools, Concepts (ATTC, the textbook I co-authored with Anita Wah): all the ATTC PDFs are now searchable, and many of the files are smaller than they used to be. (See below for links.)Amanda Cangelosi, a Mathematics instructor at the University… Continue reading More Algebra Book Fan Mail
The Human Unit Circle
In 2010, I wrote a series of posts on kinesthetic activities for secondary school math. I combined all of them into one page on my Web site, which I introduced thus:One way to break up the routine in math class is to have the students get up and experience some of the concepts in their… Continue reading The Human Unit Circle
area of a parallelogram
I posted a GeoGebra animation that suggests the formula for the area of a parallelogram defined by two vectors: <img alt="" height="200" src="data: <img alt="" height="200" src="data:--Henri
Middle School
I have taught grades K-5, high school, future teachers, and working teachers, but I have never taught middle school, except for a couple of summer jobs some years ago. Nevertheless, my curriculum materials are widely used at that level, and maybe half the teachers I have worked with are middle school teachers.I just started a… Continue reading Middle School
The Geometry of the Parabola
Parabolas are a central topic in high school algebra classes, but, perhaps because of the rigid separation between algebra and geometry classes in the US secondary curriculum, we do not usually treat them as geometric objects. While most teachers are aware of some of the parabola's geometric properties, few of us are familiar with the… Continue reading The Geometry of the Parabola
