Education ∪ Math ∪ Technology

Year: 2011 (page 24 of 28)

If you don’t ask, it can’t happen

So I’m finally able to share an interesting story which has developed over the past 3 months. It started with TEDxVancouver, which I saw Nazanin Afshin-Jam speak about her work as an activist.

Nazanin Afshin-Jam at TEDxVancouver

(photo credit: Rick Chung)

By a strange coincidence, we had a student at our school who was working on a film project about the stonings that were happening in Iran, and trying to understand the situation. Since I had just heard Nazanin talk about the same issue, I decided to look her up on Facebook. Turns out she has a public Facebook page, and she had enabled messages from anyone in her privacy settings. So I sent her a message.

Message to Nazanin on Facebook

She responded! Well, actually one of the volunteers who helps her organize and manage her Facebook responded, but he did so with Nazanin’s blessing. After several communications back and forth, and one miscommunication, we finally managed to arrange a telephone interview for today between Nazanin and my student. It took a few months, largely because Nazanin is an incredibly busy person, and travels a lot in her activist work so finding time to meet was challenging. Eventually Nazanin herself handled the last minute timing of the interview.

She called the school and I said hello, and thanked her for her time, and for the opportunity she was giving our student. I then passed the phone over to our student, because as I said, "this was her show."  We didn’t turn on the speaker phone even though we were dying to hear what she had to say, we just sat and listened to the questions our student asked, and I have to say that they were hard questions, and I really was curious to know what the responses were.

"What is the background of stoning," our student asked, after exchanging pleasantries, jumping right into the heart of what she wanted to know. Twenty minutes and 10 questions later, we had a very satisfied student in front of us, one who seemed really impressed by the conversation. My colleague, who sat in on the interview out of curiousity, said to me after our student left, "we’ll never know what Nazanin said." I agreed, "It doesn’t matter though, she obviously learned a huge amount from it. You saw her face."

You can’t help your students have experiences like this unless you ask.

Things I (almost) never use anymore

Here are some things that I either don’t use anymore, or almost never use anymore. I can remember using all of these things often, but they just don’t seem useful anymore.

The last time I burned a DVD was for a colleague at work. I think the time before that was at least a year ago.

DVDs

 

I have a calculator on my smartphone or on my computer. I do use a graphing calculator, but only at school. Why would I want a single use device?

Calculator

 

I don’t mail things anymore, or at least not often enough that I can remember the last time I did it.

Envelope

 

I don’t use pencils (and I’ve never used mechanical pencils), except for attendance, or to write a quick note when my phone is out of reach.

Pencil Case

 

This particular Yellow pages came to our apartment unrequested a couple of months ago, and we still haven’t removed the wrapper… 

Phone book

 

My paper address book is totally useless to me, now that all of my contacts are online.

Address book

 

The only reason I listen to CDs anymore is because we take car rides, and our son likes to listen to his music. Otherwise, music I listen to is on Youtube, or on my iPhone.

Music CDs

 

What’s your list of things that you’ve stopped using?

Students are like plants

My colleague just shared an interesting analogy to describe the relationship between students and teachers. I’ve heard this analogy before, but she said it so eloquently, I just thought I’d share.

"Our students are like seeds we’ve planted. We water them, we give them fertilizer, we make sure they have the right amount of sunlight, but at some point you just have to sit back and watch them grow."

So true.

Mathematics and Multimedia Blog Carnival

The Mathematics and Multimedia Blog Carnival is now accepting articles for the next issue which I will be hosting at the end of February. Although any math article might be accepted, below are the revised criteria for blog carnival selection. The following will be the characteristics of the articles that will be prioritized.

 

1. Connection between and among different mathematical concepts

2. Connections between math and real life; use of real-life contexts to explain mathematical concepts

3. Clear and intuitive explanation of topics not discussed intextbooks, hard to understand, or  difficult to teach

4. Proofs of mathematical theorems in which the difficulty of the explanation is accessible to high school students

5. Intuitive explanation of higher math topics, in which the difficulty is accessible to high school students

6. Software introduction, review or tutorials

7. Integration of technology (Web 2.0, Teaching 2.0, Classroom 2.0), in teaching mathematics

 

 

To submit an article to the Math and Multimedia Blog Carnival, click here.

The Math Teachers at Play Carnival and Carnival of Mathematics are also accepting math articles for their carnivals. Please do not duplicate submissions.

 

Why textbooks should be open source

In the past few years, there has been a push for open source content, and enough resources have been created so that schools can completely do away with the traditional textbook. However, adoption of open source content has been low, and the vast majority of schools are still relying on tradtional textbooks.

Here are some reasons besides "they will cost less" that school districts (and educators) should be pushing for open source content for schools.

  • Reduced cost for transportation if in digital form
    Schools can download the textbook and (if necessary) print it out on campus as they need it, which means they can pay for bandwidth, which most schools already do, instead of paying for shipping.
     
  • Authors paid for hours worked, not for uncertain future sales
    I’m an author of a textbook. It has not seen wide adoption, partially because it is a 1st edition, and partially because the market for the textbook I co-authored is pretty much saturated with a competitors product. I spent many hours writing this textbook, and have worked out that my wage for writing the textbook works out to about $2 an hour. In an open source model, you can release the book once it is published, and just pay the author for the time they’ve worked. Given the enormous savings to school districts after the restrictive license has been removed, this actually makes fiscal sense too.
     
  • Easier to keep updated since anyone can legally make revisions
    Textbooks can be immediately updated as soon as our knowledge of an area increases, or if an error is found in a textbook. Compare this to the speed it takes to update a typical textbook where the only incentive to update the textbook is to increase sales.
     
  • Can be provided easily in any format
    Most textbook are provided in one or two formats, meaning that once you buy a textbook, you are locked to the mode the textbook is available in, whether that is paper, or a pdf. When the textbook has an open source license, it can be legally reformated for any device.
     
  • You can be altruistic and provide curriculum to those who really need it
    There are lots of places in the world which can not afford to create their own resources for their schools. Although there are cultural implications to sending them our Westernized resources, the open source license means they can customize the content for their needs. The creation of open source content is therefore also a charitable activity.
          
  • Pick and choose what you want/remixable
    If the resource doesn’t work for you, you can fix it. You can mix multiple resources, and you can customize the content to whatever your needs are. Try doing that with a traditional textbook. This gives teachers more autonomy over the materials they use.
     
  • Redistribute resources
    Even if you print an open source textbook, the total cost of the textbook is maybe $10. You don’t really care as much what happens to the textbook if it only costs $10. You can take all of the people and resources that were involved in the storing, shipping, and tracking textbooks and use them more efficiently elsewhere.
     
  • Doesn’t need to be just paper
    A digital "textbook" could be so much more than just paper…
     
  • Collaborate between countries
    As someone who doesn’t live in the US, I certainly know how much licensing gets in the way of sharing resources across the border. So often we have to wait ages for resources available elsewhere in the world to become licensed for us in Canada. With an open source license, which much more easily be transfered from one country to another, this access barrier is dropped. Now we can collaborate across cultures and across borders much more easily than ever before. This will also allow for cross-cultural exchange. Imagine being able to download chapters about the American Revolution from the US and UK perspectives.
     
  • Less work for each district
    School districts can share the work for creating content. While some of these resources will be specific to a particular part of the world, much of what we teach in different parts of the world is almost exactly the same. Each school district can therefore do a little bit less work and focus on maintaining their own regional specific content.

 

Wheel of Fortune Game

My colleague asked me if I could find a Wheel of Fortune game he could use with his 1st grade students. I looked around for a while and found something which sort of worked here. The problem was, the code was kind of broken and needed a lot of repair. However it was the best thing I could find, so I spent a few hours and tidied it up.

You can check out what the Wheel of Fortune game looks like here: https://davidwees.com/php/wheel/

There is a "back-end" where you can add/edit the list of words, but I’m going to keep the location of it secret since my colleague is going to be using the demo version of the game with his class.

If you want to customize it further, you can download my version of the code here (note that you’ll need access to a server which runs PHP and a MYSQL database).

 

Clayton Christensen on the shortcomings of math education

"The curricular activities are designed to make students feel like failures." Clayton Christensen

When Christensen talks about designing things as an interesting activity for students, I think it’s pretty clear that this is a real world application of mathematics. This problem he talks about, where students have to first learn a bunch of mathematics before doing anything really interesting or powerful with it, is not just confined to the United States. It’s a problem here in Canada too. I’m sure it’s a problem all over the world.

We can design curriculum so that students get to work on really interesting problems. In fact, it’s been done.

(I recommend checking out a series of textbooks published by the Consortium for Mathematics and Its Applications. I’ve looked through the books, and while they won’t replace a good teacher searching for resources, they are a terrific way to start with real problems and look at solving those problems using mathematics.)

 

The relationship between family income and FSA score

The Fraser Institute released their annual "report" on the Foundation Skills Assessment (FSA, a standardized exam given to 4th and 7th grade students in British Columbia) results. As usual there have been complaints about the validity of the results, and some interesting side stories. I decided to look at the Fraser institute’s results from a particular perspective. I took the FSA data and isolated the "parent income" and available FSA results (out of 10) from the Fraser Institute data. (I could have used the data from the BC government’s education site, but the Fraser Institute data was more convenient to work with.)

After writing a script to scrape the data (download the raw data here) from the PDF provided by the FSA, throwing away schools for which either FSA results or parental income was unknown, I graphed the data.

From the graph it seems clear that there is some sort of relationship between the two variables, but it is not clear how strong the relationship is between family income and FSA scores.

So I’ve calculated a couple of regressions for a linear fit and a logarithmic fit between the two variables. The value of the correlation coefficients are approximately 0.485 and 0.517 respectively (square roots of the r2 values given above), which given the large number of data points is statistically significance, showing that there is a moderate to strong relationship between the mean family income of a school, and the mean FSA scores for a particular school.

This type of analysis has been done before for other standardized tests, most notably the SAT exams in the United States. What this type of analysis shows is that standardized exams like the FSA are better measures of the wealth of a community than the strength of the schools in that community.

The Fraser Institute rankings are a flawed comparison of schools. It is not possible to fairly rank schools of different socio-economic status because of this strong relationship between scores and the family income. What would be more fair would be to re-rank the data and break it down into different sub-classes based on socio-economic status and not try to compare apples and oranges. 

What would be even more fair would be to throw out the exams all together. What we really want to know is how effective our schools are at ensuring that our students are successful. Given the enormous complexity of this issue, and the wide variety of variables involved, finding a solution to that issue will be extremely difficult. A standardized exam is like a fast-food approach to collecting data, it is cheap and fast, but not very filling. 

Blended Learning: The Importance of Face to Face contact

Here’s a great story (shared on the Huffington post) about a student who is attending his school remotely, through a robot. Watch the video below.

The robot has become a proxy for face to face communication, and this family considers face to face communication so important, they are ignoring other, probably easier, solutions for his education. Lyndon could be going to a virtual school and learning remotely through initiatives like the Khan Academy, but he’s not. Instead he and his parents have chosen to send a robot in his stead, which Lyndon controls via his computer. 

In any blended learning model, it’s important to remember stories like Lyndon’s and remember why we would use blended learning over pure e-learning. Although e-learning has the potential to allow for a much greater degree of personalization of learning, it is a poor substitute for face to face interaction. The ability to quickly communicate a lot more than just the course content is a critical aspect of face to face learning. Lyndon has joined this school virtually because he wants the emotional contact with other people his age. He’s not just content "knowing" stuff, he wants to know it through other people’s eyes as well, hence his comment on "the other student’s point of view."

As educators, we do this too. Although we have a thriving community on Twitter, many of us will jump at an opportunity to see each other face to face. We’ll spend collectively spend vast sums of money on going to conferences like Educon and ISTE, or spend hours planning local unconferences. The online interactions are great, but nothing beats a face to face conversation.

Mumbo Jumbo

Algebra is just mumbo jumbo to most people. Seriously.

If you asked 100 high school graduates to explain how algebra works, and why it works, I’d guess that 99% of them couldn’t, not in sufficient detail to show that they really deeply understand it. Remember that I am talking about high school graduates, so these people have almost certainly had many years of algebra and algebraic concepts taught to them. Most of these people will only be able to give you some of the rules of algebra at best, and some of them don’t even remember that much.

Algebra is an amazing tool for solving problems though! Formulate a problem as an equation, and unless the equation is too complex, there is an algebraic algorithm to solve that equation, and hence the problem you formulated.

Maybe it is such a useful tool that people don’t really need to understand how it works, maybe they can get by without a deep understanding, but still be able to follow the rules of algebra and use it to solve problems. I don’t really buy that argument though, simply because people who don’t understand something are prone to make mistakes, and not be able to check their work with a reasonable level of accuracy.

Computers are also mumbo jumbo to most people. If you asked people to explain how computers work, most of them cannot. There are actually very few people in the world who can explain from start to finish how a computer works, and there is no one that can explain every single piece of a computer. Computers are still amazing tools though, and give people the ability to solve problems that would otherwise be intractable.

I think computers are a useful tool despite our lack of understanding of how they work. Like algebra, computers are a block box in which we put our inputs and get outputs and don’t understand how the inputs are related to the outputs. Given this similarity, we should look at other reasons why using a computer might be superior to algebra.

There are some significant differences between using computers to do computation, and using algebra to do computation. The first is that using a computer, the error rate is much lower. Obviously you can still press the wrong buttons, enter the wrong information, read the information the computer gives back to you improperly, so there is error, but I’d argue that this error is much less than the standard error rate for algebra. The second benefit of using computers is that they are much faster than doing even moderately complicated algebra by hand, including entering the computation into the computer. In the case that doing it by hand is faster, then I’d say you should do the calculation by hand. 

The largest difference between using a computer to do the calculation and using algebra is that algebra is a single use tool. It can only be used to turn an equation into a solution. A computer can be used for so much more.

Granted we should consider computational mathematics to be a broader tool than just plain algebra, if we want a more fair comparison with a computer, but I’d argue that all of the same problems exist with other areas of computational mathematics. As we increase the scope of computations we can learn how to use, the power of the computer becomes even more evident. It takes much less effort to learn how to compute a broader scope of problems using a computer than learning all of the individual computational methods. Witness the power of Wolfram Alpha, for example. Enter in a search phrase and all sorts of useful information comes up.

So in the consideration of using computers for solving computations, over a by hand approach, we can see postulate that the computer will produce less errors, be generally faster, and is more multipurpose than the pencil and paper model is. Furthermore, the computers can do a lot more as a tool than what you can do with algebra.

Another issue I see is that our current mathematics curriculums leave very little time to learn more important skills than computation. As Dan Meyer (@ddmeyer) points out, the formulation of a problem is more important than the actual solution. Learn how to formulate problems and understand how to verify that what you are doing makes sense, then spotting errors in computation becomes that much easier. Furthermore, I’d like to see mathematics education be much more grounded in what is relevant, than be a collection of different types of math which are taught for historical purposes or because they are the ground-work for calculus.

The question for me is, why aren’t we using computers more to do mathematics in elementary and secondary education? It can’t just be because people are scared of change, can it?