In the area of mathematics education, there has been quite a few changes over the years, and this post will be comparing my high school Algebra 1 class (1979) with my current 2017 Algebra 1 class. Although the topics and content haven’t changed that much over this time frame, the way we teach it has. To begin, one drastic difference between my class in 1979 and now is the availability of electronic technology. These days we have an assortment of technology such as graphing calculators, mobile devices with apps, and computers with software and internet access. I have a classroom set of color graphing calculators that I provide my students to use on occasion, although it is not necessary to use these for most content in Algebra 1. Our current text has lessons and extension activities that utilize graphing technology to enhance learning. My students also use an online math resource with Chromebooks provided to supplement their learning and understanding. In 1979, I had no access to such tools. Although there were scientific calculators available, they had to be purchased by parents for their child if they so desired, and I didn’t have one! In fact, the graphing calculator was first introduced in 1985 (Ribiero and Akanegbu, 2012) so they were not invented until after my graduation. Everything I did in math class was through paper/pencil, and mental arithmetic. I have always felt that if I had at least a graphing calculator in my math classes, I would have had a deeper understanding of functions, variables, graphs, and other math content.
Another major difference in math education is the view that teachers need to emphasize the “why” and “how”. (Woods, 2013) I do explain the “why” and “how” in my current lessons, but when I first learned Algebra 1, the model used was “I, we, you” (Green, 2014). For example, I was taught how to multiply polynomials by watching the teacher multiply (I), the teacher asked the class to do some problems with him as we copied the procedure (we), and then the class worked on practice problems in the text for the rest of the period (you). (First text image above is similar to mine in high school.) This may be similar to current math classes, but the major difference is the explanation during the lesson why we apply procedures or methods. It’s not blind learning. In fact, many texts provide alternative ways of solving problems. There is no longer the view that there is a singular method. (Second text image above is current text.) Another pedagogy that is currently being used and is favored by educational researchers is “you, y’all, we” (Green, 2014) . The idea is that students are first exposed to a problem and try to solve it by previous knowledge (you), then as they communicate their findings to the class and collaborate with other students (y’all), they conclude the learning process by having the teacher finalize the process of solving the original problem with either a new method, or use students’ method if it is appropriate. This is very similar to what is described by Thomas and Brown in their book about the new way of learning. “The new culture of learning gives us the freedom to make the general personal and then share our personal experience in a way that, in turn, adds to the general flow of knowledge.” (2013)
This new aspect of learning resonates with me. What I seem to get frustrated with is the manner of how current texts (at least for upper level mathematics) don’t present mathematics in this way. Upper level mathematics is not very cohesive and personal. It is brand new content that needs major scaffolding to understand. For example, current Algebra 1 texts review how to create “lines of best fit” to scatterplot data (which is a real-world example of use of lines), but this content is not revealed until there are about 6-8 sections that teach about graphing coordinates, what functions are, what lines are, what is slope and y-intercept of lines, how to calculate slope (rate of change), how to find a y-intercept (and what it is), etc. The most real-world application is “hidden” until the end of a chapter, or at least until all components are taught and understood! I don’t think there is a better way to teach this concept, but it doesn’t really follow this new culture of learning that would make learning personal.
Green, Elizabeth. (2014). Why do Americans Stink at Math? New York Times Magazine. Retrieved from https://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html?_r=0
Ribiero, Ricky; Akanegbu, Anuli. (2012). Calculating Firsts: A Visual History of Calculators. EdTech. Retrieved from http://www.edtechmagazine.com/k12/article/2012/11/calculating-firsts-visual-history-calculators
Thomas, Douglas; Seely Brown, John. A New Culture of Learning: Cultivating the Imagination for a World of Constant Change (Kindle Locations 287-288). CreateSpace. Kindle Edition.
Woods, David. (2013). 10 Ways that math education is changing. Dreambox Learning. Retrieved from http://www.dreambox.com/blog/10-ways-math-education-changing