Sharing Teaching Ideas Research Articles

Sharing Teaching Ideas: Bulletin Boards In Mathematics Class

Could you use a few bulletin-board ideas? Here are some that have been consistently popular in my high school classroom.

Sharing Teaching Ideas: Preparing Posters Promotes Learning, Some Interesting Sums and The Radian Walk

Sharing Teaching Ideas: Preparing Posters Promotes Learning, Some Interesting Sums and The Radian Walk

Sharing Teaching Ideas: Folding Perpendiculars and Counting Slope

During the study of coordinate geometry, students are told that the slope of a line and the slope of a perpendicular to the line are negative reciprocals. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) calls for “active involvement of students in constructing and applying mathematical ideas.” This activity will encourage inductive thinking and allow students to discover this relationship for themselves. Students should have previously computed the slope of a segment by counting squares and using the rise-over-run format.

Sharing Teaching Ideas: Very Special People, Mathematically

For several years the Oak Ridge Schools have observed “Very Special Person (VSP) Week” during Valentine's Day week in February. This five-day period is specifically intended to remind administrators, teachers, and students that acts of kindness toward each other enhance the school environment. As a mathematics teacher, I think that the most special thing I can do for my own students is to offer continual challenges and excitement in mathematics. It occurred to me, however, that I meet less than 10 percent of the high school population in any year and that many other students and teachers may not share my enthusiasm for mathematics. Thus I was determined that my Very Special Person project for 1990 would reach every classroom — in fact, every teacher and administrator — in the school.

Sharing Teaching Ideas: A Celebration in Honor of Isaac Newton

Many of us wish we could find cause to celebrate the coming of winter break with our students as our foreign-language colleagues do by cooking and sharing festive foods. For those of us who teach calculus to high school students, Isaac Newton presents a wonderful opportunity for a celebration

Sharing Teaching Ideas: Discovering the Law of Sines

Before my precalculus students derived the law of sines, I wanted them to explore the relationships between the angles and sides of a triangle. In particular, I wanted them to develop a conjecture about the proportionality between the sines of the angles of a triangle and the lengths of the sides opposite the angles. After they perceived a pattern in several triangles, my goal was to get them to predict the law of sines before moving to a formal proof.

Sharing Teaching Ideas: Earthquakes and Black Coffee

Logarithms were once taught to simplify calculations, but with the invention of the calculator, that rationale for motivation is no longer sufficient. Today's curriculum stresses the importance of the integration of subject matter. We can integrate the study of logarithms with investigations in the fields of geology and chemistry, thereby motivating our students to learn and appreciate the application of logarithms.

Sharing Teaching Ideas: MTV in Your Classroom

The idea for this article came to me when I decided to have my algebra students prepare and play the game of “Jeopardy.” They groaned and told me that everybody plays “Jeopardy.” So I asked them what game we could play, and the idea of MTV's “Remote Control” was suggested.

Sharing Teaching Ideas: Improving Students' Understanding of Geometric Definitions

As middle school mathematics teachers work to restructure a mathematics curriculum that now contains little in the way of new ideas or concepts (Flanders 1987), careful attention must be paid to pedagogical ideas that enhance and facilitate the attainment of newly developed curricular goals. In particular, even as a greater amount of class time is spent considering geometric topics, care must be taken to employ activities that help students attain higher levels of geometric understanding (Crowley 1987; Talsma and Hersberger 1990).

Sharing Teaching Ideas: Giving Meaning to Volume in Calculus

Sharing Teaching Ideas: Giving Meaning to Volume in Calculus

Sharing Teaching Ideas: Area and Perimeter are Independent

Sharing Teaching Ideas: Area and Perimeter are Independent

Sharing Teaching Ideas: The Gymnasium—A Dynamic Classroom For Teaching Slope

During our after-school gymnastics program, a student-gymnast commented that the inclined mat that we use for spotting had a slope. Having discussed slope in prealgebra class that morning, I asked the gymnasts to estimate the slope using a folding mat (fig. 1). We had discussed many times that estimates must be made from the materials at hand. I saw the moment and seized it for a great lesson. The following day I brought the students from my seventh-grade prealgebra class to the gymnasium for alesson whose objective was to help the students estimate and calculate slope. I assigned students to find slopes for the beams, the bars, and the braces on the gymnastics equipment (fig. 2). The students gathered the materials needed to measure and calculate the results: tape measures, calculators, pencils, and papers.

Sharing Teaching Ideas: Collaborative Writing of Mathematics Problems

The NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) calls for opportunities for students to use mathematics as a tool for the communication of ideas. In this project, students in any level of mathematics, working in a cooperative, active setting, can develop their understanding of mathematical concepts through the collaborative writing of word problems. In so doing, they see mathematics from the inside out, as creators rather than mimickers; they are “doers” of mathematics, reflecting on and clarifying their own thinking about mathematical ideas in specific situations. Additionally, projects of the type described here can give teachers valuable information on which they can base further instructional decisions regarding the development of students' ability to communicate effectively using the language of mathematics.

Sharing Teaching Ideas: Princess Di, Spaghettios, and M & Ms

What do the items in the title have in common? Well, read on.

Sharing Teaching Ideas: “Modeling” In The Statistics Classroom

When teaching a beginning statistics course two years ago at a small midwestern women's college, I encountered an enormous amount of anxiety and lack of confidence, both on the part of the students and within myself. To the students, this course had bad public relations and a reputation for difficulty that far exceeded the actual level of mathematical skills involved. On my part, I faced the challenge of overcoming students' antipathy and fear-a task that sometimes seemed overwhelming.

Sharing Teaching Ideas: A Conceptual Approach to Solving Equations

I have developed a technique for solving equations that gives algebra students an intuitive grasp of this fundamental process while dispensing a healthy dose of graphing and computer experience

Sharing Teaching Ideas: Writing Study Cards for Understanding

How often have you heard your students say, “I understand that but I just can't explain it”? Nonsense! If they really understood they could explain it, and furthermore, requiring them to explain it in complete sentences helps them to understand the informat ion. Here is a technique that really helps students to identify and learn important mathematical concepts.

Sharing Teaching Ideas: Discovering a new Algorithm for area

During a recent discussion in my Advanced Placement calculus class regarding the area bounded by two curves, one of my students, Jon Brod, noticed that certain results occurred with great frequency.

Sharing Teaching Ideas: Seven Ways to Find The Area of a Trapezoid

We all want to get away from rote teaching, from students' memorizing and repeating to the teacher what the teacher has told the class. This struggle is particularly apparent in mathematics, in which much teaching is directed toward the mastery of formal tools of thought.

Sharing Teaching Ideas: The Legend of Soh Cah Toa

When I first learned of the mnemonic SOH CAH TOA, I was told that a legend went along with it. Every year, when introducing trigonometric ratios in my precalculus classes, I searched to find such a story in an effort to anchor the acronym. I finally decided to create one myself. The result is the Trigonometric Review's exclusive story on the origin of SOH CAH TOA.