For almost all of my classes, which range from 7th grade pre-algebra to BC Calculus, I find myself using the Harold Jacobs book, Mathematics: A Human Endeavour. It is very clever.
For several classes, but specifically geometry, I recommend the manipulatives called "Polydrons." These are durable but expensive plastic polygons which snap together to make 3-D models. They last forever, so you can accumulate a collection of them over time. I keep giving them away as house-gifts to people I stay with when I do workshops, which is *not* a good way to accumulate a collection.
Also for geometry, the book Discovering Geometry is a good resource--some nice big pictures where you try to calculate angle measures all over the place. Also I recommend that you read, to stimulate your thought processes, the book Creating Miracles by Chip Healy. This is short and readable and is about Chip's experiments with a course he calls "Build-a-Book" in which the students write the textbook.
Since I'm relatively new to teaching in an academic situation, I don't have many resources yet. But here are a few.
For my HS Geometry Class we use McDougal-Littell Geometry. I have the Teacher Resource Book. It reviews Algebra concepts throughout the course and develops Two-column proofs really well. For PreCalulus I use Larson & Hostetler's Precalculus: A Graphing Approach. It's a new book that has programs and descriptions of programming for the TI-8X Graphing Calculators. For a good Texas Instruments Educational Source, There is a Mail List "Graph-TI". I'm not sure of the complete address but I will get it later today.
I teach Advanced Placement Calculus (AB) and will use Larson & Hostettler's Calculus with Analytic Geometry, 5th edition, 1994. I have only looked at the materials so far but haven't used it. I was given a lot of resources from the AP Calculus for Teacher's Class given at the Univ of South Carolina, but I did not bring them with me. I'll be happy to post them later.
Some of my favorite geometry resources include:
1. patty paper -- using hamburger patty paper to do geometric constructions. (Michael Serra)
2. origami -- paper folding using L.L. Bean catalog paper instead of expensive origami paper.
3. using New England Math League problems on geometry as a challenge.
4. using graphing calculators to find Pythagorean triples.
5. using graphing calculators to show that the limit of the perimeter of a regular polygon, as the number of sides increases, is the circumference of a circle with the same radius.
As I work with teachers in developing hands-on activities, I always go to Michael Serra's Patty Paper book of support activities.
How do you get the students to quickly remember the ratio for the 30-60-90 triangle? Well, I recommend that the students use the last 3 fingers as an aid to keeping the ratios in order. The pinky represents the shortest side, the middle finger the hypotenuse, and the ring finger the side opposite the 60 degrees. On most people the middle finger is usually twice as long as the pinky--and therefore the hypotenuse is twice as long as the short side. Therefore the side opposite the 60 is the one that uses the measurement for the short side and radical 3. This usually works unless the student's fingers are all the same length :-). There is also other finger method for the 45-45-90 triangle which you can have for a small fee. ;- ) Pax, Howard
My favorite resource is the "math teacher" because it gives a variety of ideas that can be used in the various classes.
On GSP, I like to construct the orthocenter, set trace, and then animate one of the vertices along a segment. If you don't know try it this afternoon.
If I had to pick a single math resource, I would pick The Joy of Mathematics. This is a book that illustrates numerous classical math ideas and puzzles. There is a followup called More Joy ... that I recommend as well.
I like this book because it emphasizes building things. I believe with Piaget that in order to understand something some building is required. I believe this is especially true with regard to children. However, I think Papert advanced Piaget in claiming that all learning requires a concrete operational stage regardless of one's age. The building one does in The Joy of Mathematics is as fun as it is illuminating, and this fact recommends it above all others.
This year I used Discovering Geometry from Key Curriculum Press. There are some great paper activities, Logo activities, Geometer's Sketchpad type of activities, as well as sample problems, quizzes, and great word problems.
I like to use Discovering Geometry from Key Curriculum Press.
Hi All! I just got a preview copy of Discovering Geometry and it has a lot of interesting problems and activities in it. It's published by Key Curriculum Press. I just got a copy of Sketchpad and am looking forward to implementing it this year.
The "Problems of the Week" and "Problems of the Month" on the forum are very good resources. I only got involved in doing them with my classes at the end of the school year but am looking forward to using them more in my classes this year.
Two of the best books I've read is Making Every Minute Count in Your Math Class and Making Minutes Count More by Dave Johnson. He has many good ideas on classroom management.
My geometry classes are all required to read Edwin Abbott's Flatland. They all balk at this in the beginning but wonderful discussions are generated from the readings and in the end, they all are glad they've read it.
Most of the ideas I get are from going to local and state math workshops. Also, "Mathematics Teacher" is a wonderful resource.
As I have explored ways to become a better teacher, I have identified my own learning style. I have discovered that I am right brain dominant and have been instructed predominantly by left brainers. I now understand why I am drawn to color, shapes, sound, M.C.Escher, origami, Donald in Mathmagicland, Penrose tiles, packing space, John Conway, tessellating the plane.
As I free myself from my left brain orientation, I am compelled to all things visual.
This year I had a lot of fun with tesselations that began with a hexagon. Geometry classes as well as calculus classes participated. Angels, devils, fish and fowl as well as lots of others designs decorated the halls and my classroom. The students had a great time and I loved seeing their creations.
I hope to continue discovery through origami. I look forward to learning more. I am a novice; I hope to engage my students to help me. I have a number of resource books that hopefully will point me in the right direction.(no pun intended)!
The Geometer's Sketchpad was a welcome addition to my repertoire of visual resources. My geometry students really enjoyed using elecronic construction after having tried traditional construction.