Much of the work we will do is based on material that is available on my Web site. On most topics, there are more curriculum files available on the site than you have in your binder, sometimes many more. You'll also find teacher notes, some answers / solutions, and pedagogical / philosophical notes there. Here are some links: Henri Picciotto's Math Education Page
10cm Circle (for Slope Angles, and more) Algebra: Themes, Tools, Concepts (for sequences / series, and more) Doctor Dimension (see also a blog post on Doctor D, comparing it with "Water Line", a great Desmos activity.) Electronic Graphing (for Rolling Dice, Super-Scientific Notation, and more)
Geometry of the Conic Sections (2D, 3D)
Iterating Functions (linear and non-linear) Space (more on complex numbers, and other stuff) Teachers' Mathematics (for Staircase Sums, and more) Transformational Geometry (includes using complex numbers for computations of images) Also:Katherine's awesome complex numbers song. Chaos, by James Gleick, has many great examples of how dynamical systems are found in the real world, and a good explanation of the math in the non-linear case. When I teach this material, I have students read a couple of chapters from it. (See the link above for the Infinity elective.)Paul Foerster's books (Algebra 1, Algebra and Trigonometry, and Precalculus) are where I was introduced to modeling, in the sense of getting the formula from the data rather than vice versa. The strength of his approach to modeling is that he has many, many wonderful real-world examples. The weakness, in my view, is that the problems are overly guided, and proceed in the wrong direction, with graphing at the end. (I encourage students to start with a table and a graph.) Similarly, he presents the modeling sections after introducing the functions, while to me it makes more sense to start with an anchor modeling problem, then introduce the functions more formally, then go back to modeling problems. Nevertheless, the modeling sections in his books are a tremendous resource. |
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