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.

References:

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

I like how you compared the text between when you were in Algebra 1 and the book you currently teach. It made me chuckle as I looked back to when I was in Algebra 1 (2000) and to when I started and continued teaching it (2010-2016). The reason it made me chuckle to compare texts is because we used the exact same one, in fact each year I passed out my old book to students and told the lucky one who got it that it had special powers. So as far as content, nothing changed, as far as the teaching, a lot changed at least. I sat there in high school, my teacher would do a few problems on the board, we wouldn’t do any together, she more or less just worked them out in silence and then we were on our own. Wow, did I sure fail that year and got to take it again. Luckily, with a little bit of foundational information, the second year was a breeze and I went through the book on my own instead of sitting in a formal class. When I taught, at least there was technology for the kids to use and engage them with during class, even if the text was the same. Scientific calculators were common for using when I was in high school, however, now kids are too lazy to get out of their seats to get a calculator off the table on the other side of the room and opt out to use their phone. They probably have no idea at this point all the cool apps they could download for their phone to make math so much easier, they probably wouldn’t find them as cool as math teachers, but I try and instill how great they are in the kids (rarely does that work!).

I find it hard today to incorporate all the technology I want to and do all the fun things you can do in math with all the content we have to get through during the year. It seems like when I was in school, we could have days to explore and do fun things in math that made it interesting. Today we have a schedule and everyday has a lesson on it. There are no extra days unless the kids work really hard and get ahead of the schedule. It’s been pretty aggravating, I try and throw in fun stuff when I can, but sometimes there isn’t enough time during the period to get through what district says is imperative, but after the first semester, things seem to be going better, so my hope is it just keeps going that way.

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I agree with you about not having enough time to do some really fun stuff with technology in the math class. I do have some students interested in downloading Desmos, the graphing calculator app, onto their personal phone. What I like about it compared to a TI graphing calculator is the simplicity of just typing an equation, in ANY form, and the app will graph it flawlessly. (lines in slope-intercept, point-slope, standard, and even graph conics nicely) I used to get frustrated with TI because you had to solve for y to graph any equation…annoying! Make a mistake and you see an incorrect graph. Desmos is powerful, and I don’t know if you have used it before, but I wish our department would embrace it’s great features (use as a tool). We should get our math classmates to be in the same school building and teach math with technology, it would be great!

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I really like the “you, y’all, and we.” It’s what we do, but I’ve never heard it put that way. I still use, “I, we, you,” but there’s usually a “you’s guys” thrown in there for good measure. I also agree it gets frustrating with the way some texts approach certain lessons or concepts. A skill they need in chapter 2 isn’t really talked about until chapter 5. We are forced to either jump around, or what I do most, abandon that lesson for the day, and talk about the missing skill then and come back to the lesson the next day. This usually affords me the opportunity to talk about why they may need a certain skill, or the real world applications. It forces you to really know and understand how things are laid out in the curriculum (make good use of curriculum maps, but I only use them as a guide). A principal once asked us at a staff meeting why, after 3 years, we were finding so much success using a particular math program. She thought I was being a smart ass when I said we had finally learned how to work with it, around it, make it relevant, and how to supplement it – I was being serious.

It can also be a huge challenge for parents. I’ve had countless conversations about math and how/what we are doing. It’s usually, “I didn’t learn it that way,” “I don’t know what they are doing and I can’t help them.” Most, including myself, didn’t know or realize there is more than one way to solve a math problem. That’s what we are doing – teaching the kids how to see a problem and attack it from whatever angle they are most comfortable. The straight up algorithm isn’t the only way to solve things. It may be the fastest or most efficient way, but it’s not the only way.

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