Keywords: Communication
Ref: TracyA1
Author(s): Doerr, Helen; Hecht, Caroline
Date: 1995
Title: Navigating the Web
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 88, Issue 8, pages 716-719
Reviewer: TracyA
Date of Review: January 31, 2000
The internet has become a major resource in the field of mathematics. Students can use it as a tutor; teachers can use it as a resource and as a learning opportunity. The World Wide Web can be a wonderful opportunity for collaboration, communication and exploration; if you know how to use it and access the information you are looking for. Unfortunately, not everyone is internet experienced and knowledgable. Personally, I would rather have another root canal, than have to do any work on the internet. For those of you who feel the same way, this article could be a big help in getting started.
This article explains how the internet works, what a "internet address" means, and how to generally get around. It offers a variety of web site to try out and addresses for discussion groups. There were two sites mentioned that got my attention. First, The Geometry Forum. It is "built around a set of seven newsgroups for people interested in teaching and learning geometry at all levels from high school through college and graduate school" (page 717). The other site was AskERIC. This is a question-and-answer service about any aspect of teaching, learning and information about technology. This could be a great resource for a new teacher.
Personally, I found the article interesting becuase I have basically no internet experience. It offers good starting points and had almost step-by-step instructions on how to use the different search resources available on the web. For me the article was helpful, but if you have internet experience this would probably be a waste of time. I wasn't kidding about another root canal versus using the internet!
Keywords: Geometry
Ref: TracyA2
Author(s): Scher, Daniel
Date: 1996
Title: Folded Paper, Dynamic Geometry, and Proof: A Three-Tier
Approach to the Conics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volumn 89, Issue #3, pages 188-193
Reviewer: TracyA
Date of Review: February 5, 2000
There are many things a teacher needs to consider when planning a lesson. How much time is allotted for this lesson? How much knowledge do the student already have? How can this lesson meet the needs for everyone in the class, at the same time? Everyone has different learning styles; some students need hands-on experince, some comprehend through listening or reading, yet others need to see the material before they reach a level of understanding. This article explains how to teach ellipses, hyperbolas, and parabolas by using patty paper and Geometer's Sketchpad to generate proofs. The author stressed the importance of using patty paper and having hands-on experience. He said, "It is tempting to abandon the folding process and move directly to the computer. Yet Sketchpad, or any other geometric computer program cannot replace the experience of hands-on construction. .. the folding process also possesses a simplicity that stays with us after we have forgotten the speci! fics of the computer modeling" (page 192). The computer is great for moving figures around and for probing more in-depth investigations, but personal experience is still vital in the learning process.
I found this article to be very worth while and informative. I really liked ths way the author described how to use patty paper to make discoveries and conjectures about ellipses, hyperbolas and parabolas. Then he described how to verify those conjectures on Geometer's Sketchpad, followed by a BRIEF discussion about how to use this information to generate a proof. I enjoyed reading this article.
Keywords: Geometry, Technology,
Ref: TracyA3
Author(s): Izen, Stanley
Date: 1998
Title: Proofs in Modern Geometry
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 91, Issue 8, Pages 718-720
Reviewer: TracyA
Date of Review: February 12, 2000
Proofs are a very crucial element in learning and understanding mathematical concepts. Proofs can teach more than just math, they can enrich logical thinking and argumentation skills. The article, "Proofs in Modern Geometry", starts addressing the issue of computer generated "proofs". Is the information that is generated on the computer screen a mathematical proof, or is it only compelling evidence for a mathematical theorem? Are deductive proofs a think of the past? In the age of technology, what is the role of inductive and deductive proofs? Will the mathematical software available enrich the student's knowledge or will the student's "lose the math" in the graphics and computer capabilities?
If you are a math teacher who is planning on using computers in your classroom, this is the article for you. The author really explains the role of the computer and why students still need the traditional "paper and pencil" method of learning. Put your students in awe with the computer programs, but give them the insight and understadning they can only get through learning proofs.
Keywords: Curriculum
Ref: TracyA4
Author(s): Alper, Lynne; Fendel, Dan; Fraser, Sherry; Resek, Diane
Date: 1995
Title: Is This a Mathematics Class?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 88, Issue #8, pages 632 - 638
Reviewer: TracyA
Date of Review: February 20, 2000
What is your image of the Integrated Math Program (IMP)? Do you believe in the curriculum's ideas and direction? This article will try to convince you that IMP is the best thing since indoor plumbing. According to this article, students will take more math classes during high school and will graduate with more math knowledge because of the IMP curriculum. IMP is also the mathematical solution for students who think math is boring and difficult. The authors mentioned all the training required to be an effective IMP teacher. Unfortunatley, they never address the outcome of an under-trained teacher who tries to implement this curriculum. By the end, I was wondering if the authors were part of the team who created the curriculum.
I believe all students can learn math, and that math is for everyone. Not everyone will take advanced calculus, but everyone can learn! According to this article, "A major premise of IMP is that nearly all students are capable of thinking about mathematics and of understanding deep concepts" (page 635). So what happends to the students they excluded? Where do they go and how are they going to learn math?
This article did not encourage me, although it painted a really nice picture of the perfect math class. If you believe in the IMP program and would like to read about how wonderful the curriculum is, this is the article for you. If you have doubts about the system and don't think it is perfect, you would not enjoy this article. The choice is up to you.
Keywords: Geometry
Ref: TracyA5
Author(s): Barnes, Sue
Date: 1996
Title: Perimeters, Patterns, and Pi
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol, 89, Issue 4, pages 284 - 288
Reviewer: TracyA
Date of Review: March 1, 2000
Some articles are very interesting and keep your attention, and others you can't wait to finish, if you even finish at all. For the most part, this was an article I couldn't wait to finish. Don't get me wrong, there were a few good parts.
Most of the article was centered on the students discovering pi and presenting their findings to the rest of the class. That was the part I didn't care for. The way they had the students pull together the information was useful. I liked how it showed them how to organize their information, and how to logically proceed. Those are useful skills life skills everyone needs.
Unless you need organizational assistance or are interested in reading about how to generate pi, I wouldn't read this article.
Keywords: Activities, Geometry, Measurement
Ref: TracyA6
Author(s): Iovinelli, Robert
Date: 1999
Title: Discovering Optimum Networks in Triangles
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 92, Issue 6, pages 534 - 539
Reviewer: TracyA
Date of Review: March 1, 2000
This article provides a wonderful classroom activity that introduces the students to graph theory. This is an area not usually covered in high school math course. I would high recommend this article and don't want to give too much away, but here is a brief and selective summary of the article.
Here is the basic problem. "Picture three cities, each 200 miles from the other two. Each pair of cities can be connected to the others by using a total of four hundred miles of fiber-optic cable"(page 534). The students need to figure out the best way to connect the cities, using as little cable as possible. First the students are introduced to the problem on paper. Then they use a spreadsheet to solve the problem. Lastly, they use the Geometer's Sketchpad computer program to find a solution.
This is an informative article and interesting to read. I really liked how the students used so many methods to solve the "basic problem", and it had a great real life application. No on in the class would ask, "where is the math in this?" or "when would I ever need to use this in my life?" You really need to take 15 minutes to read this article, it would be worth your time.
Keywords: Activities, Games, Geometry
Ref: TracyA7
Author(s): Woodward, Ernst and Hamel, Thomas
Date: 1992
Title: Polydron, Activities in Two- and Three- Dimensional
Geometry
Journal or Publisher: J. Weston Walsh
Volume, Issue, Pages:
Reviewer: TracyA
Date of Review: March 11, 2000
Every math teacher needs to have this learning tool, even if they are not teaching geometry. Polydrom Activities in Two- and Three- Dimensional Geometry comes with an activity/Lesson booklet, a book of teacher notes, and a bag of interlocking triangles, squares, and pentagons in different sizes. This activity sets offers a wonderful way to teach Tesselations, Polyominoes, Nets, Pyramids and Prisms, and Polyhedras just to name a few.
Most students enjoy learning through hands on activities and discovery. Who wouldn't like to do a fun lesson, play with different interlocking pieces, and create cool shapes? By using activities like these in the classroom, math class will be fun and interesting for everyone present.