Wednesday, February 15, 2012

Mathematics education in the technological age

      There has been a lot of buzz  about Silicon Valley’s role in mathematics education.  Computers and the Internet have provided a new outlet for people to share their knowledge.  You can find thousands of videos on nearly every subject on youtube.  Surprisingly, many of these videos are actually very informative.  There are many people out there with a significant amount of knowledge on the subjects they discuss in their videos.  Not all of them are educators; many of them are normal everyday people who simply have a passion and understanding for a particular subject.  Mathematics is a difficult subject for a large number of people, and that is why we see so many mathematics videos on youtube.  Included are many videos from the now controversial Khan academy.  The common argument we see is that the definition of mathematics changes as the medium it is placed in changes.

Here is a quote from Dan Meyer on his blog at

YouTube videos, digital photos, MP3s, PDFs, blog posts, spoken words, and printed text are all different media and they are all suited for different messages. When you attempt to distribute mathematics through any of these media, it changes the definition of mathematics.

To read the full post go here
            So basically the use of technology to explain mathematics has changed its meaning. I have two questions I am going to propose. 

First: Is redefining mathematics truly hurting people’s capacity, ability, or willingness to learn?

     To answer this first question let’s look at khan academy.  I just looked them up 5 minutes ago, and on their youtube channel they have 8.3 million channel views and 121,000,000 total upload views. Now according to the U.S. census bureau in 2010 there were approximately 83 million people age 3 and older in school.  This “implies” that, there are more views than the number of students in the U.S.  Now the total views do not represent the total number of unique views. It does however show a significantly increased interest to learn mathematics.
     Khan academy isn’t the only source of videos on mathematics circling the internet. It just seems to be the most “popular”.  Many individuals and other groups all post their knowledge of mathematics in different formats.

Second: If this were true for printed text, how did the printing of the very influential “liber abaci” in the 1800’s change its meaning from the original hand written manuscript?
  The use of the Arabic numerals 0-9 and place value are the universal standards today. Without the use of new technology and new mediums the Liber Abaci would have not have half the impact it did.
Did this in anyway hurt students’ ability to learn or understand mathematics? Or did this make it easier to understand and share this knowledge with the world.

      Now let us look at today’s technology. The computer and the internet have made a huge impact on the distribution of knowledge. (Just as the printing press did when it was invented.) The only difference is now with computers we can share our knowledge with the world nearly instantly. Mathematics has always been about analyzing and understanding the world around us. The sharing of knowledge has never changed that definition. It has only enhanced how many people are able to use mathematics for whatever they wish to analyze or understand.

    What role do educators, parents, and students have in education?

Degree holding, certified educators seem to have or desire to have a complete control over how students are educated.  I agree that educators who have spent years of their life studying their craft deserve a certain level of respect. However, we need to ask are they all still living up to the respect that their “title” deserves, or is the title “all” that accredits them. ( I am not saying that all teachers “hide” behind their title. I am just simply saying that it sadly does happen) Parents and teachers both are missing the most import factor that controls a students learning. That is the students themselves. Students learn from each other and from all of their experiences combined, more than they learn from schools.
     When you look at other countries that surpass the U.S. in math and science scores, most would wonder what they are doing differently.  In general U.S. students (k-12) are punished for discussing, disagreeing, or criticizing problems offered during class. (This is a generalization that does not “always” happen in “all “classrooms, but it unfortunately does happen)
In Japan, for example, we see a complete opposite practice.  The students there are encouraged to discuss and criticize the material in order to gain a full understanding of all ways to look at a problem.

To better explain this here is a quote from a case study from the National Institute on Student Achievement, Curriculum, and Assessment prepared by Angela Wu.

“ While students look to teachers for comprehension and evaluation in American classrooms, students look to each other in Japanese whole-class instruction classrooms. The teacher asks the class to evaluate individual students' solutions to math problems.”

The original report can be found here
 Group focused learning is teaching students to teach themselves, and each other. When we look at this we can wonder, how this relates to the flood of tutorial videos and other online media for teaching and learning.  The group learning mentality has evolved past the students in one classroom or even one country learning from each other. It has evolved into individuals who are not educators, but are more knowledgeable on a subject than their target audience. These individuals share their knowledge in the best way they can, to reach as many people who can benefit from it as possible.  The individuals that provide their knowledge for free should be given as much respect as any other educator whether they just teach the mechanics of a subject or teach the philosophy behind it.
 Do Silicon Valley and regular classrooms actually tell students the same thing?

Rote memorization and mechanical repetition of tasks is exactly how the “majority” of educators teach mathematics. It is a sad truth, but it is the truth. (I am sure a lot of educators would completely disagree with me on this, but even if I get 1000 emails/comments on this that number will still represent the minority of educators.)  

     A lot of the individual video tutorials found on the internet also provide this type of instruction. The big difference is that Silicon Valley or computer based instruction is available to everyone at any given time.

To quote Dan Meyer once again

“On the one hand, Silicon Valley tells students, "Math is a series of simple, machine-readable tasks you watch someone else explain and then perform yourself." Our best classrooms tell students, "Math is something that requires the best of your senses and reasoning…”

 To read the full post go here

This statement implies that there is a separation between Silicon Valley and the “…Best classrooms…” Although this may be in part true, the number of the “best” classrooms is not a big number.  I do completely agree with Dan’s last statement    "Math is something that requires the best of your senses and reasoning…”
Math does require your senses and reasoning. That is why I feel there should be a prerequisite class on logic and critical thinking prior to taking any math class pre-algebra and above.  After taking the prerequisites, logic and critical thinking should be merged into the rest of the mathematics instruction.  Additionally, the online resources such as Khan Academy and others should be used to supplement the limited time teachers have for instruction in classes. A certain amount of repetition and memorization is needed in mathematics, but neither approach should be the "only" way to educate.


  1. "Parents and teachers both are missing the most import factor that controls a students learning. That is the students themselves."

    And why on earth is this so hard to see?!?

    Thanks so much, John.

    1. "And why on earth is this so hard to see?!?"

      In some cases, teachers place themselves so far above their students they forget the "human" side of teaching. We are not educating infants. We are educating children and young adults. The same is true with parents. We don't have to be "Friends" with students, but they do deserve the same respect that we expect them to show for others.