Keywords: Technology, Calculus, Connections
Ref: LoriLa1
Author(s): Dubinsky, Ed
Date: 1995
Title: Is Calculus Obsolete?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 88, No. 2, pgs. 146-148
Reviewer: LoriLa
Date of Review: Jan. 30, 2000
In this article, the use of technology in the classroom is addressed. Technology use, in this case, is discussed through a calculus problem of analyzing a curve. The author's students want to know why they should be working out problems that can be done easily through technology. Through the illustration of this problem, the reader sees that one cannot simply plug a function into a graphing calculator for some problems without loosing some pertinent information. The author conveys the need for studying calculus, or mathematics in general, in the long-hand form. That is to say, students will benefit in seeing the "power, beauty, and subtlety" of mathematimcs by doing the somewhat grueling calculations in order to see the real methods and nature of mathematics. By the end of the article, the reader discovers that the calculus problem the author has illustrated for us, which could not be accurately described through current technology, is a problem from a chemistry tex! tbook describing the chemical reaction of a certain substance. The reaction was not described accurately through technology, and this is a problem that we would find in the real world.
The author tries to make the point that technology may not always give the best, most accurate answer. He also tries to get the point across that students need to appreciate mathematics, which is enhanced by the careful study and calculations of problems. I tend to agree with the author that technology, while being helpful classroom aide, should not be looked at as the best approach to mathematics. Students need to understand the underworking of mathematics before they accept what technology computes for them. As the author illustrates, we cannot always rely on technology because it is not always accurate!
Keywords: Technology
Ref: LoriLa2
Author(s): Hirschhorn, Daniel B.; Thompson, Denise R.
Date: 1996
Title: Technology and Reasoning in Algebra and Geometry
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 89, No. 2, pgs. 138-142
Reviewer: LoriLa
Date of Review: February 7, 200
Many mathematicians fear that students do not leave high school with an adequate understanding of the nature of proofs and their importance. The authors of the article "Technology and Reasoning in Algebra and Geometry," invite teachers to incorporate technology into their classrooms in order for students to discover the importance of reasoning and proof to the world of mathematics. With the help of technology students will be able to move to higher-level thinking and use sophisticated reasoning. They will be able to test and explore conjectures more easily. They will learn to hypothesize, or make a conjecture, and discover whether or not a counterexample exists or whether their conjecture seems suitable, urging them to pursue a formal proof of their conjecture. The authors illustrate in this article how the use of technology will speed up the testing of conjectures in algebra and geometry by processing information or tedious calculations. The authors claim that with the use of technology, students will be more engaged with the problem and more willing to discuss a proof. Technology will also enable them to easily visualize the problem. With a more hands-on aspect to mathematics, many more students may be able to understand and use the logic and techniques of reasoning and proof. I feel that the authors of this article are making a valid assertion that technology will provide an enriching avenue to mathematics. If technology is used correctly in the classroom, I believe it can prove to be invaluable to the learning and visualization process. If students are able to test conjectures with the help of technology, they are given ownership of their learning, and will be likely to use the skills learned by proving or disproving conjectures both inside and outside the mathematics classroom.
Keywords: Technology
Ref: LoriLa3
Author(s): Dion, Gloria A.
Date: 1995
Title: Fibonacci Meets the TI-82
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 88, No. 2, pgs. 101-105
Reviewer: LoriLa
Date of Review: Feb. 15, 2000
A study of the Fibonacci sequence, through the use of the TI 82, is illustrated in this article. The author believes that technology is a wonderful addition to the classroom for helping to solve problems. She says, however, because of the addition of such calculators, we have to "reexamine what we teach and how we teach." She also adds that while calculators are responsible for doing the "dirty work" of mathematics, such as number crunching, teachers are also required to be "experts" with the functions of the graphing calculator and take time in their classrooms to teach these function. With the help of the graphing calculator, the author adds that "the graphing calculator affords teachers and students an opportunity to generate data and then formulate and test conjectures, giving them a chance to do mathematics as mathematicians do." Following this statement the article illustrates her argument by providing a calculator problem concerning the Fibonacci sequence. The students are given the a variation of Fibonacci's original question of a male and female pair of adult rabbits who, placed in an enclosed pen, breed and multiply. The example brings us through various functions of the graphing calculator, using such things as the table function, the graphing function, and the sequence mode. The problem allows students to do the over-all, big picture thinking in this problem, without having to do all the foot work of making small calculations. Like the author, I think this kind of problem is invaluable to students in their mathematical career. In the real-world, students will need to be able to use and manipulate resources in order to solve problems, and this will give them good practice in generating an over-all thought process in order to solve a fairly complex problem. It will also give them exposure to the graphing calculator for possibly making their own conjectures and testing them.
Keywords: Geometry, Connections, Curriculum
Ref: LoriLa4
Author(s): Kane, Jill A.
Date: 1999
Title: A Book of Creative Geometry
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 9, pgs. 800-801
Reviewer: LoriLa
Date of Review: Feb. 29, 2000
At Indian Hills High School, the curriculum strongly enforces writing skills. Math class is no exception. Students are given journaling or creative-writing assignments in which they have the opportunity to sort through what they have learned, to expand on the ideas that have been presented in class, or to discover that they may not completely understand a concept. Teacher Jill A. Kane gives her students the task of putting their creative skills to work. Using Edwin Abbott's book Flatland as an introduction, she has them create their class Book of Creative Geometry. Students include their interpretations of geometry through computer graphics, comic strips, poems, and nursery rhyme illustrations, to name a few. All of these are made by the students and are "published" at the end of the year. Each student is given a copy as well as several administrators. The author hopes that this assignment will take the students beyond the traditional proofs, theorems, and problems of geometry to develop a sense of wonder and amazement at the relationships within mathematics and across disciplines. I personally feel that giving students creative projects in math class is a great way to grab their attention, while also providing an opportunity for higher-level thinking and learning. By giving students a creative project the teacher is tapping into hidden talents while students are making connections and discovering relationships. Chances are that the student will definitely remember what they learned and they will better understand the concepts with which they are working. This project also creates a sense of ownership with the material, as well as generating some class pride in learning Geometry.
Keywords: Connections, Assessment,
Ref: LoriLa5
Author(s): Williams, Nancy B. and Wynn, Bryan D.
Date: 2000
Title: Sharing Teaching Ideas: Journaling in the Mathematics
Classroom: A Beginner's Approach
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 2,pgs. 132 - 5
Reviewer: LoriLa
Date of Review: March 22, 2000
Many of today's mathematics educators are incorporating journal writing into their classrooms to break away from the traditional assessment approach of tests, quizzes, and worksheets. The authors of this article decided to test the waters for journaling in their classrooms and share their experiences with Mathematics Teacher readers. The authors each launched their experiments with one class. They specifically chose morning classes where the students generally held a positive attitude towards math. In the beginning, two journal assignments were given per week. One of the assignments was an affective entry, asking general questions about education, and the other was a mathematical entry, asking students to communicate their understandings of the topics in written, paragraph form. One teacher gave five minutes for journaling at the beginning of class, while the other gave ten minutes. Grading was based on a specific rubric where half of the grade was on effort and the other half on mathematical content. Initially, the authors received numerous complaints about writing for math class; however, the teachers were gaining insight into the comprehension of their students. Later, they decided to cut down the workload for the students and themselves by assigning one journal entry per week. They also decided they would give students ten minutes to work on their entries in class, since students dislike being interrupted in the middle of an assignment. By the end of their experiment, students didn't complain as much about the writing. In fact, students said that the journal entries helped their grades, they learned how to communicate mathematically more effectively, and the feedback helped them to understand the concepts. The teachers decided that the experiment went well, since the students benefited from the journal entries and they were better able to have insight into students understanding through the journal assignments. They decided they would continue this practice, but make a few suggestions: 1) Start small. 2) Only assign one journal entry per week. 3) Ask both affective and mathematical questions for variety. 4) Give students class time to work on the journals. In my personal opinion, I think that journal writing is an asset to the mathematics classroom. It enhances students ability to communicate mathematical concepts effectively and also allows them to practice their writing skills. I also think that journal writing gives a teacher immediate feedback to see whether or not the students fully understand the concepts before the teacher forges on to the next topic. I also like the authors suggestions that teachers should start small and only assign journal entries once a week. In that way, students are given some variety (without the assignment of journal writing becoming too monotonous.) Also, this gives teachers enough feedback without breaking their backs correcting journal assignments in addition to all the other work.
Keywords: Connections, Activities, Geometry
Ref: LoriLa6
Author(s): Kelley, Paul
Date: 1999
Title: Build a Sierpinski Pyramid
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol.92, No. 5, pgs. 384 - 6
Reviewer: LoriLa
Date of Review: March 23, 2000
A Sierpinski triangle is made by taking a shaded equilateral triangle and connecting the midpoints of each side to form four equilateral triangles. Then, remove the inner triangle. Repeat this process for several iterations on the new triangles. Students at Anoka High School built a Sierpinski Pyramid in conjunction with the NCTM's 75th Annual Meeting April 1997 as an extension of their work on fractal geometry. The pyramid was a culmination of the work done over a period of five years. After a few trials, they came up with a successful design, which they planned to use for next year's pyramid, which would be twice as tall. That pyramid materialized at the Minneapolis Convention Center in April, reaching a height of nineteen feet. The pyramid took eight and a half hours to construct by 30 students. The article gives instructions as to how to construct a Sierpinski Pyramid of the same nature as the nineteen-foot phenomenon constructed by Anoka High School students. (The height of the pyramid depends on the size of the template made for constructing the pyramids.) Basic materials needed are a template as shown in the article, sturdy paper, scissors, tape, and glue. (Wooden or metal reinforcements may be necessary, depending on the height of the pyramid.) I think this is an excellent display of ingenuity and problem-solving. I am impressed by the work of the Anoka High School students. Its marvelous to see students displaying their mathematical knowledge outside of the classroom. This is an activity I may want to take on with some of my math classes; however, I would probably construct it on a smaller scale!
Keywords: Connections, Geometry,
Ref: LoriLa7
Author(s): Wenninger, Magnus J.
Date: 1966
Title: Polyhedron Models for the Classroom
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages:
Reviewer: LoriLa
Date of Review: March 23, 2000
I reviewed the book entitled "Polyhedron Models for the Classroom." It is an excellent source for incorporating polyhedron models into your classroom. They are aesthetically pleasing and encourage a connection to the world of art. The also aide in acquiring skills in visualization. Students become motivated to work on math because they are constructing something that they find intriguing. Students tend to create polyhedrons with care and accuracy. Polyhedron models are also a helpful tool for discussing symmetry and congruency, not to mention adding some pizzazz to your institutional classroom. The book outlines how to create The Five Platonic Solids, The thirteen Archimedean Solids, Prisms, Antiprisms, and Other Polyhedra, The Four Kepler- Poinsot Solids, Other Stellations or Compounds, and Some Other Uniform Polyhedra. It also provides templates for some of the models, as well as outlining color schemes for your polyhedron models. Many students created polyhedron models in my high school, but I was never introduced to the concept of constructing one, or even what it was. They have always intrigued me, so therefore I believe the other when we says that polyhedron models are motivating and challenge students to take care in the accuracy of their work. I also think students will be motivated to design their own polyhedron models once they are given the background on how to construct such a fascinating geometrical shape.