Steffen's Article Reviews, 2008

Keywords: Equity/Diversity, Activities, Teaching Strategies
Ref: Steffen1
Author(s): Winsor, Matthew S.
Year of publication : 2007
Title: Bridging the Language Barrier
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 101, No. 5, p. 372-378
Reviewer: Steffen
Date of Review: February 18, 2008

This article discusses possible teaching strategies for use in ELL mathematics classrooms (or any mathematics classroom where students have first languages other than English). The author compares those methods by which people best learn mathematics and second languages in order to use what is shared by both to create effective teaching methods. The author discusses those methods he found to work best, namely journaling and communicating about the material, utilizing group work, and applying the course material to real-world contexts. Ultimately, the findings and conclusions were suggestive at best, but the outcome definitely encourages teachers to give the "MSL" strategies a try.

I was glad I got to read this article, because I have a strong interest in ELL education; I have often had aspirations to go into bilingual education for my strong background in Spanish. It was interesting to read how many key teaching strategies apply to both mathematics and second-language acquisition, because I knew the strategies applied to both but had never made the connection to the context of teaching mathematics in a second language. What especially struck me was the discussion of real-world applications, because as much as some math teachers will cling to the idea that applications aren't necessary, there is no argument that can be made to dismiss the fact that real-life application is NECESSARY for second-language acquisition. I think that has strong implications for ELL mathematics classrooms.

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Keywords: Connections
Ref: Steffen2
Author(s): Petras, Richard T.
Year of publication : 2001
Title: Privacy for the Twenty-First Century: Cryptography
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 94, No. 8, p. 689-692
Reviewer: Steffen
Date of Review: February 20, 2008

This was a brief but dense discussion of one particular system for cryptography, called public-key cryptography. The author asserts that the internet age has brought forward a new, desperate need for safe systems of information transfer, and so cryptography has become something of a hot area in the last couple decades. The algorithm presented here is one such example of a cryptographic method to come out of this growing need.

I've always been fascinated by cryptography and code systems, so I chose this article. Some of the mathematics behind it were admittedly dense and tough to follow, but it was interesting to see one method that spawned as a result of growing consumer skepticism about internet security. Given the article was written in 2001, I'd be interested to read if there have been any more recent discoveries in the area, or if this is still a convention widely used today.

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Keywords: Representations, Problem Solving
Ref: Steffen3
Author(s): Peterson, Blake
Year of publication : 2006
Title: Counting Dots and Measuring Area: Rich Problems from Japan
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 12, No. 4, pg. 214-219
Reviewer: Steffen
Date of Review: February 25, 2008

This article discusses the methods used by student teachers and experienced teachers in Japan teaching mathematics. The article discusses several different specific problems used by the teachers, and also elaborates on several student approaches that were used. The problems draw heavily on pictorial representations, modeling how students can think differently about a problem using graphical displays. The main focus is on the title problems: counting dots and finding areas.

These sorts of articles are very helpful for me. As a proponent of mathematics, it's always good to absorb several different ways to attack certain problems, because it definitely adds to my personal arsenal for when I am a teacher in the future. It is helpful to gain some prior insight into different ways of thinking that students might be coming from, particularly with respect to the ways in which students represent a problem, both in their head and on paper.

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Keywords: Proof
Ref: Steffen4
Author(s): Askey, Richard A.
Year of publication : 2004
Title: Fibonacci and Related Sequences
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 97, No. 2, p. 116-119
Reviewer: Steffen
Date of Review: February 27, 2008

This article is basically a lesson or review in mathematical induction using Fibonacci numbers. The author proves that (F_(n+2))(F_n) - F_(n+1) = (-1)^(n+1) by induction, and then connects the proof to several other applications and proofs, including geometric explorations. The author suggests a couple problems for students (or the reader) to prove themselves. By the end, the author introduces Lucas numbers and shows how several results proved for Fibonacci numbers are analogous for Lucas numbers.

I found this article interesting for its value in giving me some food for thought, but not necessarily as a tool for teaching. To be honest, I never learned induction before college, so I have a hard time picturing it in the secondary classroom. Still, the problems presented in the article can be interesting even viewed without knowledge of induction, but it's hard for me to imagine getting kids really excited about these problems unless they were fairly self-motivated in mathematics.

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Keywords: Number and Operation
Ref: Steffen5
Author(s): Miller, Catherine B. & Veenstra, Tamara B.
Year of publication : 2002
Title: Beautiful Patterns, Beautiful Mathematics
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 5, p. 298-305
Reviewer: Steffen
Date of Review: March 10, 2008

This article delves into a very common topic used to introduce numbers and patterns: Fibonacci numbers. The article suggests an exploratory set of lessons that can be used for middle schoolers. The introduction talks about Fibonacci as found in nature, in structures like pine cones and so forth. The latter part contains potential worksheets and activities for students to explore. These activities deal heavily with exploring patterns and odd facts about the sequence.

Despite having worked with Fibonacci numbers an obscene number of times, I was surprised to find this article had explorations I had never seen before. I think the discussion of nature is obviously something that can get a lot of kids interested, but I feel the worksheets would need some work to get kids excited about them. While I'm perfectly happy to find patterns in the Fibonacci sequence all day, some kids might need a little extra help with the "why am I doing this?" piece. All in all, I thought this was a useful tool in suggesting some possible work with patterns and number operations, but it might take some extra adaption for really effective and successful classroom use.

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Keywords: Problem Solving
 Ref: Steffen6
Author(s): Hodgson, Ted R. & Burke, Maurice J.
Year of publication : 2005
Title: Tennis, Anyone?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 98, No. 9. p. 586-593
Reviewer: Steffen
Date of Review: March 17, 2008

This article addresses a problem very close to my heart: tennis! The games of tennis can be easily represented by different mathematical structures like tree diagrams and other probability models. In this article, the problem is simple: given a player has an n% chance of winning a point, what is the probability he/she will win a game? The problem is addressed from a number of different angles, both graphical and theoretical. The article discusses five strategies: simulation, algebra, matrices, and calculus.

I really enjoyed this article, particularly because it gives a discussion of how to use the problem in the classroom at the end of the article. I also think (and I am admittedly a little biased here) that tennis is a great avenue to illustrate things like tree diagrams and examples of situations revolving around probability. (It's also a great way to demonstrate how a situation can be approximated probabilistically.) I would definitely recommend this article as an idea for a problem to use in the classroom during a probability unit or something connected.

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Keywords: Teaching Strategies
Ref: Steffen7
Author(s): Various
Year of publication : 2001
Title: Classy Tips
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 94, No. 1, p. 464-467
Reviewer: Steffen
Date of Review: March 31, 2008

The focus of this particular article is on how to effectively start the year, which is probably one of my greatest anxieties when it comes to my future teaching. Most educators I've talked to say that the first day is probably the single most important day of class, and a bad slip on day one can hurt you for months out of the year. Some of the suggestions touch on how to arrange seating, how to go over classroom guidelines, and how to initiate dialogue with parents.

If I'm being honest, I didn't find anything incredibly groundbreaking in this article. Some of the suggestions were fairly bland, and I thought some bordered on painfully corny. Some, though, were useful and sounded like reasonable approaches to me. I particularly liked the idea of having students write to the teacher on the first day, and then having the teacher respond thoughtfully to each student's concerns and questions. I know I personally love to have established a dialogue with the teacher right away, since it lets me know he/she is approachable for help. My biggest complaint about this article, though, is that it wasn't terribly math-specific. Many of the entries from different teachers had mathematical tints, but most of them were, I thought, stretches, and I definitely never found a good answer to the whole "how do you make kids want to be in your math class?" dilemma. After all, motivation in mathematics is probably the hardest battle, and that question was left f! loating with this article. Worth a read, but not essential.

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Keywords: Statistics, Activities
Ref: Steffen8
Author(s): Groth, Randall E. & Powell, Nancy N.
Year of publication : 2004
Title: Using Research Projects to Help Develop High School Students' Statistical Thinking
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 97, No. 2, p. 106-109
Reviewer: Steffen
Date of Review: April 2, 2008

This article describes projects given to an AP Statistics class to help students develop an understanding of how to find, analyze and interpret data. The projects are granted its significance by noting the ever-increasing need for statistical literacy in a society that uses data more and more to support and explain things. The authors describe the projects, and then provide insights they gained regarding students' misunderstandings. They offer possible suggestions for improvements based upon these observations. They also discuss the specific methods they used in class to help foster statistical understanding. Specific descriptions are provided, along with the rubrics used to evaluate students' work.

I was interested in this article because I never encountered statistics in high school. The first time I encountered regression was my junior year here at St. Olaf, and even now I struggle with the concept, so it's always interesting to me that they are teaching kids in high school how to work with linear regression. I think this article is a useful starting point for teachers interested in teaching statistics in the future. The teachers identify some specific points of weakness they encountered with students when working with the interpretation aspect of regression, which is useful in order to anticipate questions and confusions. I was disappointed that I have never worked with the computer program they mention, called Fathom, but this only detracted slightly from my understanding of their discussion. Overall, a worthy read.

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Keywords: Number and Operation, Connections, Representations
Ref: Steffen9
Author(s): Garland, Trudi H.
Year of publication : 1987
Title: Fascinating Fibonaccis: Mystery and Magic in Numbers
Journal or Publisher: Dale Seymour Publications
Volume, Issue, Pages: 100 pp.
Reviewer: Steffen
Date of Review: April 7, 2008

This book has eight chapters. Most of them focus on the prevalence of fibonacci numbers in the real world, including topics in art, architecture, nature, music, literature, and medicine. The book also offers a historical perspective on the Fibonacci sequence, noting its power across time.

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Keywords: Geometry.
Ref: Steffen10
Author(s): Soto-Johnson, Hortensia & Bechthold, Dawn
Year of publication : 2004
Title: Tessellating the Sphere with Regular Polygons
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 97, No. 3, p. 165-167
Reviewer: Steffen
Date of Review: April 9, 2008

This article introduces a possible way to approach geometry with tessellations across a sphere. (The best example of this concept is a soccer ball tessellated by pentagons and hexagons.) Almost the entire article talks about the mathematics behind the tessellations -- why a square is able to tessellate a flat plane, for example. It concludes with diagrams that graphically explain the idea of sphere tessellation.

This article strikes me as a great way to approach geometry, but it's also a very difficult topic. At the same time, it sort of covertly dabbles in subjects not usually seen until college -- some of the math in this article delves into non-Euclidean geometry with its spherical explorations. I think some students, particularly those who excel in geometry, would find this exploration fascinating -- the idea that, on the surface of a sphere, two lines can make a polygon, for example. That's the main thing that stuck out at me -- that students are being introduced to non-Euclidean ideas without really realizing it. Definitely a great idea for a class topic, but also one that is difficult and would need either serious consideration or adaptation.

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Keywords: Activities, Geometry, Gifted
Ref: Steffen11
Author(s): Juster, Norton
Year of publication : 1961
Title: The Phantom Tollbooth
Journal or Publisher: Random House
Volume, Issue, Pages:
Reviewer: Steffen
Date of Review: April 14, 2008

This is a little bit of a stretch, but I had to include this in a review. The Phantom Tollbooth is easily my favorite book ever, and it played a huge role in my mathematical development during my childhood. (This class also gave me a great excuse to read the book again.)

The book follows the adventures of Milo, a boy whose dull interactions with life often leave him bored and listless. One day, though, a tollbooth arrives in his room, and, with nothing better to do, he ventures into a world that will soon change his outlook forever. He journeys through strange lands, meeting characters along the way who introduce him to all the wonderful doors that knowledge can open for him. Of particular interest for this class are the sections where Milo encounters the beauty of mathematics. He meets the Dodecahedron, whose twelve faces--and in this case, they truly are faces--are used to represent his different moods. He also encounters the Mathemagician, whose "magic staff"--otherwise known as his pencil--unlocks incredible insights. Milo discovers the concept of infinity and wrestles with cryptography.

I. Love. This. Book. When I was in fifth grade, my teacher read this book to us, and we did a whole unit on it. The Phantom Tollbooth is that unique work--one that is both ceaselessly entertaining and academically invaluable. Still today, during my 53rd reading of the book (literally), I will learn things I hadn't caught last time. Even now, the mathematical sections are a great reminder of the two ends of the subjects--from the maniacally simple to the devastatingly impossible to understand. As a kid, I loved to learn vocabulary like "dodecahedron," and now, as an adult, I love to struggle with the idea of infinity.

The book provides countless activity ideas for the classroom. Many of the possibilities are better for lower-age kids, if for no other reason than they are the book's intended audience. Still, there's no reason the book can't be adapted to an older group. For example, one of the central arguments in the book is one we still encounter as college students: which are more important, numbers or words? The book has countless opportunities for map-making, diorama-building, number exploration, and so on. Norton Juster surely penned a work of genius when he wrote The Phantom Tollbooth.

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Keywords: Geometry, Measurement, Activities
Ref: Steffen12
Author(s): Pagni, David & Espinoza, Larry
Year of publication : 2001
Title: Angle Limit -- A Paper-folding Investigation
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 94, No. 1
Reviewer: Steffen
Date of Review: May 11, 2008

This article uses basic origami to discover an interesting property. If you begin by folding a piece of paper to create a crease, and then continue to make folds based upon the creases you create, the angles formed by the paper and the creases becomes closer and closer to sixty degrees. (This is easier to understand given the diagrams in the article.) The authors end with a proof of the concept using a symbolic argument.

I've always loved origami, and I remember doing a project in my high school geometry class where I presented origami and its relationship with math to my class. I've always been interested in using it as a means to introduce topics in a future geometry class because it's a great way to bring in all kinds of connections -- art, history, culture, and so on. This is one example of how it can be challenging to answer the "why?" of how such a thing works. One can also make different shapes, like regular pentagons, out of origami and try to figure out why certain folds make things work. This article doesn't specifically offer an activity to use in the classroom, but it would be a great starting block for some ideas.

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Keywords: Connections, Equity/Diversity
Ref: Steffen13
Author(s): Lamb, John F. Jr.
Year of publication : 2000
Title: A Chinese Zodiac Mathematical Structure
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 2
Reviewer: Steffen
Date of Review: May 5, 2008

This article delves into the Chinese Zodiac system, which is traditionally trivialized into a simple system of 12 animals and their associated cycles. The actual system, however, is much more complicated and can reveal several interesting mathematical applications. The article begins with an explanation of the system itself, noting that the Zodiac is indeed split into twelve animals. Each person is assigned an animal based on his/her year of birth. There are two other cycles, however -- namely the elemental and age cycles. There are five elements (wood, fire, water, earth, wind) and two ages (younger and elder). Immediately we have an application of least common multiple, since it takes 60 years (LCM of 12, 10 and 2) to return to the same age, element and animal year again. The article goes on to examine many interesting patterns in the Chinese Zodiac, such as relating the compatibility of certain animals with one another to the Chinese superstition surrounding the number!

I love this article because it's a great example of something that is so lacking in our classrooms today. With all due respect to their accomplishments, I get tired of learning about White European Male X and his contributions to mathematics. The Chinese had a beautiful understanding of mathematics as well, and this is just one piece of evidence. I think this is the kind of exploratory stuff that kids can really get excited about, especially since it starts by asking the question, "which sign am I?" It makes the exploration personal, and gives the kids a reference point to look back to throughout the whole investigation. Definitely recommended.

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Keywords: Calculus, Assessment, Curriculum
Ref: Steffen14
Author(s): Perrin, John Robert & Robert J. Quinn
Year of publication : 2008
Title: The Power of Investigative Calculus Projects
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 101, No. 9, p. 640-646
Reviewer: Steffen
Date of Review: May 5, 2008

This article discusses a particular project approach for high school calculus classes. The author, wanting to take advantage of the insight of his students, decided to let students investigate problems of their own creation as part of the calculus curriculum. (The article begins with an example exploratory question: "why is the derivative of the area of a circle its circumference, but the derivative of the area of a square is not its perimeter?") The project is designed to address several suggestions made by the NCTM, such as the use of nontraditional assessment. The "rubric" for this project is provided.

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Keywords: Geometry, Communications, Problem Solving
Ref: Steffen15
Author(s): Gole, Andy M.
Year of publication : 2003
Title: Sherlock Holmes, Geometry Proofs, and Backwards Reasoning
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 8
Reviewer: Steffen
Date of Review: May 5, 2008

This article talks about backwards reasoning, which is a method that can be used for solving proofs (in this case, geometric ones). Traditionally, students are taught to look at their list of given information and plow forward from there until they can reach the desired conclusion. In backwards reasoning, a student looks at the desired result and tries to reason: "what information do I need in order to achieve that result?" So, for example, if I am to prove that AC is congruent to BC, I might note that I could prove this by finding that I have a pair of congruent triangles. From there, again, I try to think of what information I need in order to prove I have a pair of congruent triangles, and so on, until I already have the information I need. Once this process is complete, the proof is essentially written.

I was excited to find this article because it addressed an approach that I used often in high school but was never taught. I was lucky to have had a rich math background that allowed me to deduce some techniques for myself. But I think backwards reasoning is a skill that ALL students should be taught -- it's a great tool for solving more difficult proofs, and also certainly extends beyond just geometry. It can be applied to both other mathematical subjects and also non-mathematical life in general (if such a thing exists!). The read is pretty easy and informal, so it's worth giving this article five minutes of your time, especially if it's something you hadn't considered.

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Keywords: Geometry, Puzzles
Ref: Steffen16
Author(s): Barr, Stephen
Year of publication : 1964
Title: Experiments in Topology
Journal or Publisher: Dover Publications, Inc.
Volume, Issue, Pages: 209 pp.
Reviewer: Steffen
Date of Review: April 27, 2008

This book is a sort of Topology 101 course. It starts with an introduction (aptly titled "What is Topology?") and then goes on to investigate some of the problems that topologists are interested in. The book is clearly written to both educate and entertain—chapter 10, for example, titled "The Trial of the Punctured Torus," is written entirely as a conversation as if a mathematician is on trial to prove a rather odd topological feat. The book also poses small riddles and puzzles for the reader; as an example, I stopped to figure out how to draw a Venn Diagram for four groups (rather than the usual two-group ones we are taught in school).

I think this is a great read for a teacher looking for some activities and thought puzzles, especially for students who are quick to understand everyday material. I have to admit that, having not taken a topology course before, my understanding of some parts was fragmented at best, but many of the concepts were easy to work out. Many of the problems were also very familiar to me—Venn Diagrams, the Bridges of Koenigsberg, map coloring, etc. I do think one would need to have had an at least mildly formal introduction to topology in order to understand and fully appreciate everything, but the book is definitely worth a peek for some ideas.

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This article outlines a teacher's struggles to get his students motivated after having passed back a particularly demoralizing test. He discusses his beliefs on subjects like note-taking, studying, test-taking, and general academic practice (from a student's perspective). In particular, the author makes the case that students need to view homework as less of a chore and more of a tool for understanding.

I have to admit that I took issue with this article. The teacher clearly has good intentions, but he announces these "necessary changes" as if the responsibility lies solely with the student -- as if the teacher has no responsibility him or herself to foster this motivation. I know as well as many how frustrating it can be to work with students whose motivations lie anywhere but with your class, but the simple fact of the matter is that some students have so much going on in their lives already that to ask them to shift their priorities overnight is not only fruitless, but also offensive and insensitive, especially when it's presented in a "fix yourself, and then we'll talk" type manner. I believe the TEACHER is responsible for student engagement with homework. If you know why you gave a particular assignment, but your students don't, then that's a problem -- after all, they're the ones completing the assignment (hopefully), not you. I feel similarly about his arguments about note-taking, etc. -- his intentions are good, but I can't agree that the burden lies solely with students. As teachers, we have a responsibility to act in the best interests of our students' learning, even if that means going beyond the "hey, you should do your homework" lecture.

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Keywords: Probability, Activities
Ref: Steffen18
Author(s): Canada, Dan & Goering, Dave
Year of publication : 2008
Title: Deep Thoughts on the River-Crossing Game
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 101, No. 9, p. 632-639
Reviewer: Steffen
Date of Review: May 20, 2008

This article discusses a game of probability that two students play against each other. Players each place twelve chips on their own sides of a river that contains eleven spots, numbered 2 through 12. Players take turns rolling a pair of dice, and if they roll a number on which they've placed a chip, they may move that token to the other side of the river. The first player to cross all of his/her chips wins the game. The article discusses some winning strategies for this game, as well as applications of technology that can be used to illustrate them in the classroom. The vast majority of the article involves mathematical reasoning in order to find the best solution.

I was so glad to find this in the most recent edition of Mathematics Teacher because I'm always looking for new probability games. I can only play Pig for so long! In particular, I think this is a great game in order to judge students' pre-knowledge about probability. If you used this game as an introduction to a unit, and asked students to arrange their chips in the way they think would work best, it will allow you to get a sense of how familiar students are with probability. (If a student just places one chip at every number versus placing more chips on 7, etc.) All in all, I've always believed that students will learn more about probability if they can dig into it, and the subject lends itself so well to hands-on activities and chances for students to engage the material. I was glad to add this game to my repertoire, so it's worth a read in order to consider it for a future probability unit. I can see this working in both the middle school or high school.

Keywords: Probability
Ref: Steffen19
Author(s): Bright, George W., et. al.
Year of publication : 2003
Title: Navigating through Probability: Grades 6-8
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages: 140 pp.
Reviewer: Steffen
Date of Review: May 20, 2008

The Navigation series takes the PSSM standards and digs into them with respect to specific topics. In this case, the book begins with a very brief overview of the NCTM standards for data & probability, and the rest of the book is a very specific look at what those standards mean with reference to specific concepts, ideas and activities. The vast majority of the book is filled with lesson ideas that highlight different topics in probability, complete with possible worksheets and other materials. The book is very much the practical companion to the more abstract PSSM and would likely be the one pulled off the shelf when the need for a lesson idea arises.

These Navigation books were sort of what I was waiting for. The PSSM standards offer a great way to organize objectives and structure goals, but offer very little practical substance. This book provides a lot of great lesson ideas — specifically designed so that a teacher can appropriately adapt them for his/her class rather than design one completely from scratch. The book actually reminds me a bit of the IMP books I've taught from in the past, minus the cohesive strain of thought running through the entire thing. Many of the activities are either discovery learning or very hands-on, though I'm not certain if that's because probability tends to be a hands-on unit or if all of the Navigation books are specifically made to be that way. All in all, these are definitely resources that teachers should have on their shelf.

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Keywords: Geometry
Ref: Steffen20
Author(s): Coxford, Jr., Arthur F., et. al.
Year of publication : 1991
Title: Addenda Series Grades 9-12: Curriculum and Evaluation Standards for School Mathematics: Geometry from Multiple Perspectives
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages: 72 pp.
Reviewer: Steffen
Date of Review: May 20, 2008

This book is almost like a mini-textbook. Like the Navigation series, the Addenda series begins with a very brief overview of what the NCTM says broadly about geometry standards and why students should learn it, and then goes on to discuss many different ideas for lessons about different topics. This particular book is divided into chapters, providing a suggested sequencing of material and grouping activities by common thread. The activities are heavily spatial for the most part — the book is full of diagrams and pictures to accompany the lessons.

As far as I can tell, the Addenda series is just the old version of Navigations. The two books are similar. I was surprised by how non-traditional the Addenda activities were—it covers a lot of topics that I think are generally reserved for "enrichment" activities in schools these days. For example, I wasn't introduced to Frieze patterns until I got to college, but this book uses them to talk about polygons and their properties. The Sierpinski triangle is another topic that isn't usually brought up unless it's just to mention something cool in class. I really appreciate that the book makes an effort to bring in some of these topics in order to teach "normal" geometry—I think it makes it more fun and meaningful for kids. Again, a resource that any teacher should probably have on the shelf.

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