Sidebar: Generational Differences in Education

For my EDTECH 537 class we read three papers about generational difference in education, with one arguing that “digital natives,” or people who were raised with technology, fundamentally think differently than other learners (Prensky, 2001). A second paper looked at Prensky’s arguments and described in turn why each were poorly researched (McKenzie, 2007). While some of his arguments weren’t entirely logical (e.g., some video games are violent, therefore no video game could be useful for education), his arguments were far more convincing and research-backed than Prensky’s. Finally, we read an article that found that while difference between generations existed and should be understood, they were not significant enough to warrant a change to the instructional design (Reeves, 2008).

As McKenzie points out, Prensky’s unsupported arguments are often repeated and have spread quite far. However, many of these comments and arguments sound like the comments and arguments that are always leveled at the next generation:

Simply put, people always see the next generation as having a short attention span, poor conversational skills, and a lack of drive. This has always been the case, and probably always will be.

Should a colleague of mine suggest changing our content to match a generational difference, I would first listen to what they would say. For example, younger students tend to need less in the way of explanations for how to use digital tools, and some analogies (e.g., referencing the maps that used to be in phone books) no longer make sense to younger students.

If instead they were to suggest a fundamental shift in the tools or methods of instruction based solely on a perceived generational divide, I would have to disagree. Simply telling a colleague that is rarely enough to make a difference, and it shouldn’t be. After all, just saying things it what got these ideas started. Instead, I would point them towards data-backed literature like Reeves & Oh. Once they are convinced that the differences between generations are not as substantive as they thought, I would help them choose the tools they wanted to use based on the subject matter or learning theory rather than as an attempt to appeal to  “digital natives” or “digital immigrants”.

After all, kids these days aren’t as unfocused as we give them credit for.

  • McKenzie, J. (2007). Digital nativism, digital delusions, and digital deprivation. From Now On: The Educational Technology Journal, 17(2).
  • Prensky, M. (2001). Digital natives, digital immigrants part 1. On the Horizon, 9(5), 1–6.
  • Reeves, T. C., & Oh, E. J. (2008). Do generational differences matter in instructional design? In Instructional Technology Forum (Vol. 17, p. 2014). University of Georgia.

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Teachers and Math: A Guest Post

Today’s guest post is by Alan Liddell, one of the lead instructors for AcerPlacer in Ogden, Utah, a private company that teachers college math courses for its students. I asked him to write this post because of one response on an informal survey I conducted where one teacher said that they didn’t use any math because they didn’t teach it.

As a math teacher, one would think that it is obvious that I would use math in my everyday life for my career. While it is true that I do teach college-level math on a daily basis to students, my uses of math go far beyond the classroom.

For instance, I use math for statistical analysis for the company I work for. I am in charge of calculating the percentage of student test out rates and to perform statistical analysis to determine lead causes of percentage results and to predict future percentages based on previous years. I am also required to use pivot tables to compare different sets of data to determine causality and possible relationships between them.

In addition, I create spreadsheets in Google Sheets and Excel that require algebraic expressions to be inputted to auto-populate cells and columns. Although the language of Excel and Google Sheets maybe be different than traditional math, the concepts are the same.

I also use math to quickly number crunch various menial tasks around the office. I may have to make copies of a certain homework packet, so I will use mental math to determine how many copies to place into the copier queue.

As a final anecdote, I used the Pythagorean Theorem to help me at the post office for work. I was tasked with picking up boxes to ship our books to online students, and when I got to the post office, they had various sizes to choose from. The one I thought might work was a box that had the proper height, but had width and depth dimensions of 8.5 in and 1.5 in respectively. I knew that our book had a width of approx. 9.5 in, so I used the Pythagorean Theorem to determine if the book could fit on a diagonal in the box (it turns out that it could not). Using math saved me an additional trip back to the post office.

Women and Math in the Media: A Commentary

As a math teacher, one of the biggest obstacles I face when teaching students is math anxiety. Many students have it to varying degrees. Specifically, I’ve been thinking about how math anxiety tends to fall along gender lines and, of course, The Big Bang Theory [TBBT].

Before I start, I just want to be clear: I don’t hate TBBT (I actually find it pretty funny), and I certainly don’t think that it’s the cause of the problems that I want to talk about. However, I do feel that it is a very visible symptom of a larger over-arching problem. Besides, no one will have read the research articles I’ll be quoting, but most people will have seen at least one episode of one of the most popular currently-running TV shows, so it gets to be the unfortunate lightening rod for my disappointment.

For those who may have not heard of TBBT, it is a show about scientists hanging out and being nerdy. It starts out with the beautiful Penny moving across the hall from Leonard and Sheldon, two physicists doing research at Caltech. That’s a fairly straightforward sitcom setup. However, several criticisms have been leveled at the show because of its use of stereotypes as part of its humor. Penny is the beautiful, normal person. The scientists are men, socially inept, and unable to talk to Penny easily. Why is this a problem?

This reinforces some harmful stereotypes about women in science (and scientists generally, but we’ll put those aside for a moment).  Penny is often shown as completely clueless about various science and math topics and has to have them explained to her by the shows male cast members. In this, the writers cast Penny as the audience, who the writers assume know nothing about the topics on the show. For the first several seasons, there are no other female leads. This is alleviated a little bit with the introduction of Bernadette and Amy, a microbiologist and neurologist respectively. However, for their first few seasons, both are portrayed as socially awkward and admirers of Penny’s beauty. In short, it went from saying that “girls can’t do science” to “pretty girls can’t do science.” Finally, in the most recent seasons, Bernadette and Amy have taken on greater roles and shed some of their questionable character traits to become better female role models.

Maybe you’re wondering why I’m making such a big deal of an admittedly small part of the show. It’s all in good fun, right? I point it out because the way women are portrayed in media affects how girls and women feel about their abilities to perform in math and science. Multiple studies have shown that women report higher levels of math anxiety than men, and while the reason for this is up for some debate (Jameson & Fusco, 2014), studies have found that examples and role models can have positive or negative effects. For example, elementary-aged girls are more likely to have math anxiety and believe in the stereotype that boys are better at math than girls if their female teacher also has math anxiety (Beilock et al., 2010). Negativity about math is contagious, even if it is left unspoken.

On the other hand, positive portrayals of women in careers and science in magazines have been shown to help improve women’s performance on a math exam (Luong & Knobloch-Westerwick, 2017). Notice that wasn’t long-term exposure to those stereotypes, that was simply reading a few pages from a single magazine immediately before taking the exam. So if those good stereotypes helped after just a few minutes, even if that effect was temporary, imagine what constant exposure over the course of an entire TV show could do for a child?

As I mentioned, TBBT has definitely taken steps in the right direction in this regard. I am certainly not trying to get people to hate the show, but rather point to it as one of the most visible examples. However, the myths and stereotypes about women and math persist across many shows and stories in culture today. While having more positive role models of women in math and science won’t magically fix every issue faced by women in STEM fields, it could help alleviate at least the math anxiety faced by girls becoming women.

I’m not asking for anything drastic. All I am asking for are a few more Bernadettes and a few fewer Pennys.

  • Beilock, S. L., Gunderson, E. A., Ramirez, G., & Levine, S. C. (2010). Female teachers’ math anxiety affects girls’ math achievement. Proceedings of the National Academy of Sciences, 107(5), 1860–1863.
  • Jameson, M. M., & Fusco, B. R. (2014). Math anxiety, math self-concept, and math self-efficacy in adult learners compared to traditional undergraduate students. Adult Education Quarterly, 64(4), 306–322.
  • Luong, K. T., & Knobloch-Westerwick, S. (2017). Can the Media Help Women Be Better at Math? Stereotype Threat, Selective Exposure, Media Effects, and Women’s Math Performance: Media and Stereotype Threat. Human Communication Research, 43(2), 193–213.

Discussion: Algebra vs Statistics

For this discussion, we will be talking about the article Down With Algebra II! In it, the author argues that, based on a book by Andrew Hacker, algebra II should be eliminated as a required course and replaced with a class on statistics.

Let me start by saying I strongly disagree with the author that advanced algebra has little worth. If I felt that way, I wouldn’t be writing a blog to help people see how math is used. However, the discussion to be had here isn’t whether algebra is good for students to study, but rather if statistics would be better. Statistics are indeed everywhere, and many people are forced to understand things like medians or means to understand news discussions about political topics. However, is that of more worth to students than learning the abstract thinking that accompanies algebra?

What do you think? Would algebra or statistics work better as a general education course?

Matrices and Linear Algebra: A List

Linear algebra is the study vectors and vector spaces, while matrices are essentially grids of numbers used to solve some problems in linear algebra. If that sounds hard and complicated, that’s because it can be. Many colleges dedicate entire courses to the study of this one topic. However, the basics of matrices and linear algebra aren’t too bad, and can even be fun.

Here is a list of just some of the professions that need to have a knowledge of this math topic:

  1. Aeronautical Engineers – This profession designs aircraft, and matrices are incredibly important to that (assuming you want your plane to stay in the air). Some of these matrices can get fairly large (12×12, for example), and while they would be very difficult to solve by hand, they are fairly easy to solve using computers (Phillips, 2010).
  2. Computer Programmers – Speaking of solving things using computers, programmers heavily rely on matrices (though they often call them arrays). Many programming languages use them, and not just for science; most graphics are essentially matrices containing color information for each pixel.
  3. Ecologists – It may be hard to believe, but ecosystems are complicated things. To prove changes over time and distance weren’t due to random chance, ecologists often use a statistical test called PERMANOVA to test their hypotheses (“Permutational analysis of variance”, n.d.). This test relies on matrices to properly set it up.
  4. Civil Engineering – In the same way that people don’t want their planes to suddenly stop moving, most people prefer their bridges to not suddenly start. To accomplish this, each individual beam that is part of the bridge has to be evaluated for how much weight it carries, and this is most effectively done using linear algebra.
  5. Robotics – When working in robotics, it is often easier to think about multiple pieces of the machine having their own coordinate systems (Hiob, 1998). To go back and forth between them, you can use matrices.

This is just a small sampling of the different uses of matrices and linear algebra. While they may be tricky at first glance, they are powerful tools in many fields.

Now are you glad that you took the red pill and learned just a bit more about the uses of a matrix?

Hiob, E. (1998, June 11). Robotics: Using transformation matrices to change from one coordinate system to another in robotics. Retrieved July 16, 2017, from

Permutational analysis of variance. (n.d.) In Wikipedia. Retrieved July 16, 2017, from

Phillips, W. F. (2010). Mechanics of flight (2nd ed). Hoboken, N.J: J. Wiley.

Don’t Take My Word For It

Although it may be hard to believe, I am not the sole person who sees value in studying math. Before we begin with my thoughts, it might be helpful to see what others have to say.

5 Reasons Why You Should Study Mathematics – This article from The Complete University Guide talks about why you should pursue mathematics as your main focus of study. While that isn’t the main focus of this blog, it brings up some good points for how mathematics can make you more marketable.

10 Reasons You Should Study Math – In this six minute video, Danny Doucette argues for why math should be studied and touches on things such as the transferability of skills, the nature of developing industries, and the responsibilities of citizens, among others.

The importance of maths in everyday life – The author of this article from the Times of India is a math teacher. Not only do they give great reasons to study math, they also give great advice in how to teach it, especially for younger students.

Why Do We Learn Math – While the entire series of articles this is a part of is fantastic, this most directly addresses our topic at hand by taking the statement, “Math makes you think,” and explaining one way it actually does that.

6 Everyday Examples of Math in the Real World – Are you curious how math is used at home? This article focuses on math outside of a potential workplace to how it might benefit you more generally.

Examining How Mathematics is Used in the Workplace – This article seeks to examine a few studies on how math is used in workplaces from automobile production to nursing. Published by the Mathematical Association of America, it is a dense but interesting read.

Table of Examples – Tired of articles and just want to look up an example for your chosen career? Then this page is for you. Published by the Math Department at British Columbia Institute of Technology, it provides examples of problems that might be seen in various fields.

Differential Equations

When will I ever use this?

There are few questions a math teacher hears more often than when a student will ever use the math being taught. Often times if users can’t see an immediate use for a topic, they can lose interest and motivation. Teachers of adults in higher education can forget that this question hangs in the air, even if it goes unspoken. As some have argued, adult learners have a strong need to know how knowledge can be applied to their goals (Stavredes, 2011). However, taking time away from every class to explain how each and every topic can be used in the “real world” can be a source of frustration for teachers, not to mention a distraction from material that needs to be discussed. Not answering the question can be frustrating for students, who can feel like their time is being wasted.

That’s where this blog comes in.

Before we can talk about different math topics and different careers, we need to get a few general thoughts out of the way. For starters, math courses aren’t required because you will use each and every topic you will learn in each and every job you will take. Instead, you study math in order to learn critical thinking skills, problem-solving, and logical reasoning. While there is much to be gained from reading literature, studying history, or writing essays, none of them teach the same reasoning skills that math can. Even if you never use a logarithmic function again as long as you live, the experience you gained working through those problems will help you as you reason through other kinds of problems afterwards, even if you aren’t consciously aware of it.

Increasingly, young adults out of college are changing jobs or even careers, and more than half of those surveyed “thought it very unlikely they would remain with the same employer for their entire careers” (Thompson & Gregory, 2012). What this means for students is that even if the career they plan to go into doesn’t use math, a future one may. Even if they don’t retain every bit of information, having a passing familiarity with different topics in math will make students more versatile members of the workforce.

As you learn the basics of math, you become a more informed citizen. The posts in this blog will tell you how various vocations use different math topics. Even if you don’t use those topics yourself, you will have a better understanding for how others do, which will make it easier to understand news topics and issues involving those fields.

In the next several weeks. we will have the chance to explore a lot of different uses for math and hopefully help you to see how what you are learning can benefit you in the future. If nothing else, it should make for an interesting read.

If you have a suggestion for a profession or topic that you would like covered, leave a comment or go the Contact page to send your request!

Stavredes, T. (2011). Effective online teaching: Foundations and strategies for student success (1st ed). San Francisco, CA: Jossey-Bass.

Thompson, C., & Gregory, J. B. (2012). Managing Millennials: A framework for improving attraction, motivation, and retention. The Psychologist-Manager Journal, 15(4), 237–246.