Wednesday, June 17, 2009

WolframAlpha solves math problems

An article titled A Calculating Web Site Could Ignite a New Campus 'Math War' was posted to the math department mailing list and it got a bit of response. The author seems to suggest that WolframAlpha is going to change the way that we teach math because it can solve calculus problems and other types of math problems.

From the article:
“I think this is going to reignite a math war,” said Maria H. Andersen, a mathematics instructor at Muskegon Community College, referring to past debates over the role of graphing calculators in math education.
"I still think that anyone who is not a little scared by the changes that WolframAlpha brings hasn’t thought about it enough yet,"

I would strongly disagree with this statement even though I think that WolframAlpha is an amazing tool. If you have not seen WolframAlpha you should check it out. It is not a search engine but acts similar to one. It can solve equations and analyze data and has data-mined massive amounts of information. Try "integral sin x dx" and you will see what this web site can do for calculus.

Does this significantly change the way we teach? My answer is "no more than other tools that are out there." I think that we have not correctly adapted to the use of the internet in learning since I perceive that students are leaving high school and do not know how to write and research properly (it could be my "old fogy-ism" kicking in).

I do not think that WolframAlpha is going to change the way that students arrive at a computational answer any more than a CAS (Computer Algebra System) does and it will have less impact than graphing calculators. Perhaps the authors worry that now we have a CAS (WolframAlpha is based on Mathematica) which is freely available. We have to be aware that students have access to this tool, but we had to adapt to the way Google changed the way students do mathematics and we will have to adapt to the use of smart phones as they become ubiquitous. This is nothing new and it is a good thing that this tool increases access.

Tuesday, June 9, 2009

E-textbooks- all the rage

The budget crunch has caused some rough times for cities and municipalities in the U.S. (I don't know what it is like in Canada because Toronto, my own municipality, hasn't been able to balance its budget for years now) and this has caused some of them to teach students on the cheap. Arnold Schwarzenegger has canceled the contract with textbook companies and switched to lower cost electronic versions of textbooks. Surprisingly I haven't seen teachers and school districts in the state of California screaming. Instead the news seems to imply that schools elsewhere may use California as a model and use the same technique to lower their school budgets. We may be seeing electronic textbooks in our classrooms in a few short years if this experiment is successful.

Advantages that I can see:
(1) lower cost
(2) able to update textbooks quickly and inexpensively
(3) convenience and smaller size

(1) lower income students may have less access (its not clear how they plan to get around that one)
(2) electronic formats are WAY less convenient than their printed counterparts (what about notes in the margin?)
(3) inconvenience and larger size (a laptop or desktop is significantly larger than a textbook, but an iphone or a kindle are both smaller...which is it going to be?)
(4) there is a learning curve involved in using this technology

The NY Times also highlighted a school district in Connecticut. Connecticut District Tosses Algebra Textbooks and Goes Online. They switched from textbooks to e-books for a reason other than budgetary.

Friday, June 5, 2009

Mathematics v. Mathematics Education

I was at a day panel that was organized by Walter Whiteley in relation to the CMESG meeting that is being held at York University this weekend when I wrote this. The first talk was about the competing goals of mathematics education and mathematicians.
The speaker was Peter Liljedahl, a professor of Mathematics education at SFU who teaches mathematics to future teachers. He emphasized that you cannot truly separate math and math ed and that there are common goals but he also talked about the differences between the goals of math and math education.

Some interesting ideas that came up in this talk:
1. The first is that sometimes people who are interested in learning math education are interested in learning how to teach mathematics and not about learning the mathematics content. This can be a conflicting goal with mathematicians who tend to believe that teaching mathematics well requires that the teacher understand the subject with a real depth.

2. The other idea that I thought was interesting was he addressed how teaching courses for math teachers (for example in this program) is different than other mathematics classes. The undergraduate classes that he gives in a 'for Teachers' program do not go into depth. The courses I have taught in this MA program always keep in mind two ideas (1) the students taking the course do not have the same background as each other or even a core basis that I can assume everyone knows and (2) the content that we do teach is not required for other courses. In other graduate and undergraduate courses the purpose is to teach a subject with a depth that can only be reached by assuming the students have understood and remember the material that came before.

3. He also touched on some of the skills that we need to provide students with for them to succeed in mathematics. For him it was less about what content we teach students, but what skills we provide them with. Some examples of skills that he mentioned are: how to read a math textbook, how to recognize when a teacher is skipping steps (and why), how to approach a problem that cannot be solved in 5 minutes, etc.

From my iPhone so this may be edited later.

Thursday, June 4, 2009

Girls v. Boys now a tie in Math

A report on the state of U.S. education in the Proceedings of the National Academy of Sciences says that a performance gap between girls and boys has narrowed significantly in recent years. The researchers also found a correlation between cultural gender equality and performance by girls in mathematics. There are still some achievement gaps but this study indicates that past achievement disparity between gender is likely attributable to factors other than the popular belief that 'boys have a math gene and girls don't.'

Here's some of the buzz:
Math: It's not a gender thing
Women Bridging Gap in Science Opportunities
Culture, Not Biology, Underpins Math Gender Gap
Girls Vs. Boys At Math
Sharon Begley: The Math Gender Gap Explained
Subject: The (Math) Gap - a critique

Women in Mathematics II

Back in March I posted an article about some research on opportunities in mathematics for women. Yesterday the New York Times published a summary about a report by the National Research Council on the state of opportunities for women in science and engineering. In summary (quoting from the article):

In recent years “men and women faculty in science, engineering and mathematics have enjoyed comparable opportunities,” the panel said in its report, released on Tuesday. It found that women who apply for university jobs and, once they have them, for promotion and tenure, are at least as likely to succeed as men.