February 8, 2012

Motivating Students

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.

October 18, 2011

Mathematical Miseducation

This article provides commentary on the traditional mathematics education paradigm, its detrimental consequences, and evidence and reasons for shifting to current reform in primary and secondary education. Battista introduces controversial criticisms to current reform movements being made in mathematics education and how the majority of American schools still follow the traditional route when teaching students math. He explains that this route leads to failure of students to retain understanding, thus wasting enormous amounts of time and money to reteach students concepts they had been taught in previous years. After reviewing a short history of the mathematics education reform movement, Battista elaborates on the constructivist view that students must personally construct mathematical ideas as they make sense of a situation.

I think like any major change in society, the reform movement in mathematics education will take time to catch on. Scientific studies on this subject have only come into play within the past quarter-century, and in the world of scholarly research, this is relatively young. The thesis of Battista’s article is not to educate readers about mathematics education reform, but to educate readers about mathematics educators who are not educating themselves about mathematics education reform. In a way, he is “preaching to the choir.” By that I mean, his audience by definition will have already agreed with his point of view. The people he is trying to persuade are not likely aware of this article. However, I think that research about research can help, through recommendation and word of mouth. Readers of this article can recommend it to their uninformed colleagues, and every bit of awareness helps.

The more teachers that take Battista’s research into account and spread the news to fellow educators, administrators, and policymakers, the more the mathematics education community can be lead in the right direction. Soon the traditional mode of teaching will no longer be mainstream, and students will be accustomed to constructing their own understanding.


  • Battista, M. T. (). The mathematical miseducation of America's youth: Ignoring research and scientific study in education. Phi Delta Kappan, 80(6), 424–432.

Teachers' Support

A three-minute video of the student-teacher dialog

Jacobs and Philipp (2010) explore the possibilities of support that teachers can provide to students during problem solving. They discussed four basic types of support:

  1. support that focuses on the teacher’s mathematical thinking,
  2. support that focuses on the child’s mathematical thinking,
  3. support that focuses on the child’s affect, and
  4. support that includes general teaching moves.

When working with students on an individual basis, support that focuses on that student’s thinking is best. Teachers must adjust their instructional behavior to fit every individual student’s needs. In the example of Rex, this teacher said she would use what she learned about Rex’s thinking on the first two problems to help him solve the third, more challenging, one. Rex liked to use his fingers instead of the manipulatives that were available, so teachers should not push for use of one manipulative over another. In addition, children often think about math differently than adults do, and many can offer new ideas to the table. Provided the opportunity, teachers can learn from their students all the time.

That is not to say that the other three types are not appropriate. In a class discussion or lecture-type class, support that focuses on the teacher’s thinking is more suitable, since the teacher is providing content and modeling processes for the students. Students’ affect should always be taken into account, especially for struggling students; and general teaching moves are useful ‘go-to’ tools in everyday instruction.

This article would have major effectiveness in a traditional classroom. In this type of classroom, all students follow along with the teacher at the same pace, and individual needs are rarely attended to. Usually, problem solving is nonexistent because there is only one or two ‘right’ ways to solve a problem, and these ways are presented by the teacher. The students’ job is to remember how the teacher solved it and perform the same procedure on a similar problem in assessment. Rather, problem solving itself includes the task of figuring out on one’s own the method of solving the problem, and then carrying out that method. Once the algorithm for completing a task is known, the problem is no longer a ‘problem’ even if the answer is still unknown (Harvey, 2010b, p. 3).

Teachers could, and will, benefit from concentrating on students’ mathematical thinking when instructing their classes. By calling for more student involvement and keeping their classes stimulating, engaging, and fun, teachers can get to know their students and how they think mathematically.


  • Jacobs, V. R., & Philipp, R. A. (). Supporting children's problem solving. Teaching Children Mathematics, 17(2), 98–105.