Motivating students is tough. There is no explicit algorithm or formula teachers can use to get their students to show an interest in math. Despite this, Sobel (1985) suggests ten actions teachers can take to help make their math classrooms more interesting, and, quite fun. Although the article was written more than 30 years ago, many of the suggestions, or the derivatives of such, are still used today and are really effective.
Finding relavent articles in newspapers and magazines, videos on the web, and other current events can have a profund effect on students. It shows that math has a place in the real world, and it's not just a bunch of symbol manipulation.
I as a math teacher enjoy learning the origins of topics in math, even if the way they were learned and taught in the past differs so much from today. The example Sobel gives is called the rule of false position, an Egyptian method of solving equations. I believe it only works in multiplicative relationships, so it might be a cool thing for Algebra I students to explore but I wouldn't recommend teaching it. If the related history is presented then students might see the motivation behind the math.
We need not, should not, and certainly cannot show practical applications for all that we teach? (Sobel, 1975, p. 481). Why not? Does the author disagree with showing practical applications for everything, or is he simply stating that it cannot be realistically done? Granted, given the time allotted for topics in secondary school math, there is not a lot of freedom regarding exploring and investigating practical applications; but in my experience I have always seen textbooks present word problems involving real-world situations for every mathematical subject in the text. In fact, my philosophy of math education shows that there is always a practical application for any math concept. Else why would it exist?
Lab experiments are always fun for students, no matter the context. In my student teaching experience, I began the unit on Direct and Inverse Variation with two labs (one per day) in Algebra II. The direct variation is discovered through Hooke's Law, which states that the distance a string stretches is directly proportional to the weight that is applied. The inverse variation lab involved swinging a pendulum of different lengths and measuring the frequency. My students had a lot of fun collecting data, which in itself is a great use of the NCTM's Measurement standard. Another experiment I used in the same class was the visual representation of the difference of two squares. I was happy to read about Sobel's description of this because it was almost identical to the one I had used in class.
I was surprised to read the author's opinion that there is no clear indication that student discovery leads to increased learning (p. 483). Perhaps this article is too old to address the research on discovery and investigation, but if there's one thing I learned from my undergraduate and graduate mathematics education classes, it's that students learn best by figuring stuff out.
In 2004, Stevens, et al. published a study measuring affective attributes of students of different ethnicities. In two groups consisting of Hispanic and Caucasian high school students respectively, the researchers analyzed the effects of self-efficacy and motivational orientation on the students' performance and their plans to take future courses in math.
- Stevens, T., Olivarez, A., Jr., Lan, W. Y., & Tallent-Runnels, M. K. (). Role of mathematics self-efficacy and motivation in mathematics performance across ethnicity. Journal of Educational Research, 97(4), 208–221.
- Sobel, M. A. (). Junior high school mathematics: Motivation vs. monotony. Mathematics Teacher, 68(6), 479–485.