Keywords: Communication, Technology
Ref: AndreaB1
Author(s): Dick,Thomas; Kubiak, Evelyn
Date: 1997
Title: Issues and Aids for Teaching Mathematics to the Blind
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 90, No. 5, P. 344-349
Reviewer: AndreaB
Date of Review: 01/31/00
The purpose of this article is to help mathematics teachers learn how to communicate with visually impaired students. An example used is, "if the expression is meant to be (x+3)^2, then the teacher should say, 'the quantity x plus 3 [pause] squared' rather than 'x plus 3 squared,' which sounds like x+3^2." The article explains some common learning challenges for visually impared students. Because the much of the language of mathematics relies on visual cues, it will take a blind student much longer to grasp a concept. The article gives suggestions for teachers. One suggestion that surprised me was to have a conversation with the student or parents to find out the visual limitations of the student. Another suggestion is to reduce the ammount of homework. The homework should be carefully selected to insure the student will keep up with the class. This is done because the time it requires for a visually impaired student to complete an assignment can be 1.5 to 2 times longer than their classmates. Helpful resources are listed, such as textbooks in braille, taped versions of textbooks, calculators with large displays or talking calculators and graphing and drawing aids.
I thought that the article had a lot of useful information. Learning the sight experience of a student can give the teacher insight in to how to explain a concept. The talking calculator is a great idea. I hope that, the problem of a useful graphing calculator for the blind has been resolved. There is a list of suppliers that sell the graphing and drawing kits. If you have a visually impaired student in your class I would recommend reading this article.
Keywords: Technology
Ref: AndreaB2
Author(s): Watanabe, Tad; Hanson, Robert; Nowosielski, Frank D.
Date: 1996
Title: Morgan's Theorem
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 89, No. 5, p.420 - 423
Reviewer: AndreaB
Date of Review: 02/06/00
This Article is a wonderful example of what can happen while using technology. It began with an assignment to rediscover Walter's theorem. Walter's Theorem states: If the trisection points of the sides of any triangle are connected to the opposite vertices, the resulting hexagon has an area one-tenth the area of the original triangle. The class was using the software GeoExplorer. One ambitious ninth-grade student wanted to know what happened when the sides of the triangle were broken up into more than three pieces, perhaps n. We will call this "n-secting". Using The Geometers Sketchpad, this student discovered that when n was odd, a pattern emerged. Using regression on a calculator, he discovered that the ratio of the inner hexagon to the original triangle was (9n^2 - 1) / 8 to 1. The teacher was unfamiliar with this conjecture and took it to the mathematics department of Towson State University. The teacher and student were invited to present their findings at a colloquium. There are a couple reasons that they were invited. First, the students work involved significant mathematics. Second, they were unable to find an equivalent theorem in the existing resources. Third, technology made this discovery possible. Without the use of Geometers Sketchpad, this exploration would have been difficult, if not impossible. The icing on the cake was that when scholars offered the student proofs to this theorem, the student declined them because he wanted to prove it without any help.
I absolutely loved this article. It shows that with the use of technology there are going to be many more discoveries in the field of Mathematics. Opportunities are out there for anyone, even a ninth-grader in high school, to discover something new.
Keywords: Activities, Geometry,
Ref: AndreaB3
Author(s): Van Dyke, Frances
Date: 1995
Title: A Visual Approach to Deductive Reasoning
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 88, Issue: 6, p. 481-484, 492
Reviewer: AndreaB
Date of Review: 2/14/00
This article describes activities that can be used to introduce students to three patterns of reasoning in inferential logic. Using Ven Diagrams and p-q symbolization, students explore direct reasoning, indirect reasoning, and transitive reasoning. Students find valid and invalid conclusions for each type of reasoning. There are five activity sheets for use in classroom. Group activities are built into the lesson plan.
Proving conclusions from a visual perspective can be helpful in today's modern classroom. I really found this article helpful because when I studied logic and deductive reasoning there was no attention was paid to students who learned visually.
Keywords: Algebra, Manipulatives, Geometry
Ref: AndreaB4
Author(s): Forringer, Richard S.
Date: 2000
Title: (A + B + C)^3
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 93, Issue 1, p. 6-8
Reviewer: AndreaB
Date of Review: 2/22/00
This article connects algebra to geometry. Many of us are familiar with representing (x + y)^2 with a square of length x + y, and the resulting squares. This article uses the same approach with the equation (A + B + C)^3. This approach allows students to see that a cube with side length of (A+B+C) is composed of smaller blocks, and that the faces look much like the square from (x+y)^2.
I found this article very enlightening. I am a visual learner, but had never seen this approach. This approach is much clearer than algebraic expansion of (A + B + C)^3.
Keywords: Geometry, Activities, Manipulatives
Ref: AndreaB5
Author(s): Malloy, Carol E.
Date: 1999
Title: Perimeter and Area Through the Van Hiele Model
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 5, Issue 2, p. 87-90
Reviewer: AndreaB
Date of Review: 02/27/00
This article summarizes the Van Hiele levels and applies them to the study of perimeter and area. An activity is provided, along with the responses from three students. Each of these students were at different levels. Guiding questions and extensions are included.
I have studied the Van Hiele levels and believe I have a decent understanding of them. However, this article was enlightening because it not only included activities and questions, but it also showed how your students might go about solving the same problem in different ways.
Keywords: Technology, Geometry,
Ref: AndreaB6
Author(s): Purdy, David C.
Date: 2000
Title: Using The Geometer's Sketchpad to Visualize Maximum-Volume
Problems
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 93, Issue 3, p. 224-228
Reviewer: AndreaB
Date of Review: 3/5/00
This article shows how to explore the Maximum-Volume problem for a box made from a square piece of paper using Geometer's Sketchpad. It can be used in conjunction with a graphing calculator and actual construction of boxes. It is not recommended as a stand-alone activity.
I really liked the way this introduced an interactive aspect to the problem of Maximum-Volume problems. This is also gives a new way to solve an old problem using Geometer's Sketchpad.
Keywords: Proof, Geometry, Problem Solving
Ref: AndreaB7
Author(s): Fidler, Mark
Date: 1999
Title: Chipping away at Proofs: A Cooperative Approach
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, Issue 7, p. 565-567
Reviewer: AndreaB
Date of Review: 03-12-00
This article describes one teacher's method to teaching proofs. He started with a cooperative learning idea, and tailored it to fit what he wanted. Although his grouping method does not fit with the heterogeneous groups called for by cooperative learning, it seems to work well in his class. In this class students describe working on proofs as challenging, intense, exciting, and fun.
This method could do wonders for many geometry classes. Making math fun yet challenging is a great goal. In a class of my own, I would like to see if this approach works better with the heterogeneous groups recommended by cooperative learning leaders such as Professor Johnson.