Saturday, August 4, 2007

A Couple of Interesting Links...

Very nice logic problem in the sidebar over at Text Savvy.
Because it involves only a few possibilities, it is a great way to open the school year without causing undue frustration. Students will enjoy the feeling of accomplishment when they solve it!

Also, I posted a comment on a fascinating piece of research over at Joanne Jacobs blog. The post is entitled No evidence for 'learning styles'.
While I agree with the researcher and the other commenters that a school district's approach that tries to match individual instruction to each child's modality is unreasonable, I take exception to research that attempts to invalidate theories by only looking at extreme cases of its application. Certainly, competent caring teachers try to create a classroom environment that is accepting of different strengths and weaknesses and attempt to provide explanations of concepts in a variety of ways. I referred to the Rule of Four in math pedagogy, a critical part of current thinking about maximizing learning in the math classroom. 'Learning styles' has become an inflammatory term that raises the hackles of most bloggers and educators in general. I expect that my comment will not be well-received and most likely will be ignored!


Mike said...


FWIW, I read your comment about learning styles and I found it useful. I had not heard of the Rule of 4, and now I will try to find out more about it. My sense is that in the blogosphere there are often people (like myself) who read and learn and don't necessarily respond all the time. The writer might think s/he is writing in a vacuum, when actually a lot of helpful information and insight is being received by others. Thank you for your work!

Jackie said...


I liked your solution to the soccer problem at text savvy - interesting approach starting with team C. I went the other route & started with team A.

I've never heard of "Rule of 4" before, although I've been doing something similar for a while now. Do you have any links to write-ups of this rule? I did a search & did not immediately find the rule to which you were referring (if I'm understanding it correctly).

Dave Marain said...

mike and jackie--
I believe that The Rule of Four (perhaps better known as Multiple Representations)emerged from the Reform Calculus movement in the 90's spearheaded by Debbie Hughes-Hallett from Ariona State and Harvard. It may have developed before then so if one of our knowledgeable readers could provide the details, I'd appreciate it. Here's a link to a talk she gave on this sometime back:

You'll have to copy and paste the link. It will probably download a PowerPoint file (depending on your browser). You may want to see if your browser can first convert it to an html file. This is a wonderful piece which describes not only the Rule of Four but the essence of the reform approach to teaching calculus (can apply to other math courses as well).

You can also go to the website, enter 'multiple representations' in their search engine and a few articles of interest will pop up.

I've mentioned the Rule of Four on my blog and other places as well, but many educators still haven't heard much about it. As I find more resources for this, I will share them and perhaps devote an entire posting to it.

Jackie said...

Thanks for the link -- when I think of multiple representations what comes to mind for me is:

table of values
verbal and written description of each and how they are related.

Huh, four things. Now I get it, I guess I'm just used to hearing/thinking multiple representations. Never heard of "Rule of Four" before.

Off to check out the link...

uhm, have you considered a separate RSS feed for comments? Just a thought/wish.

Dave Marain said...

thanks, Jackie!
I will work on the RSS feed as you suggested. Considering that the comments are the heart of this blog and the select few that respond to my posts are the lifeblood of this whole venture, I should have done this a while back.
Yes, your example of multiple representations is the classic example of the Rule of Four. I must have picked up that phrase from a presentation I heard some time ago. It makes sense for me since, if I forget any of the modalities, I can still count on my fingers to remind myself!

Also continue reading the comments on Joanne Jacobs blog regarding learning styles (there's a link on the post). I'd like to think my comment enabled some to present a more balanced view. The latest comment from passionate teacher is eloquent and puts hte naysayers and cynics to shame. The bottom lines is that educators need to consider varied 'teaching styles' to meet the needs of their learners. I'm tempted to say that most have missed the forest for the trees, but others are now saying it better than me!

Mike said...


I think the URL for Deborah Hughes-Hallett's presentation as posted by Dave was truncated, and it doesn't work as written. I think the full URL is:

And, in case it just got truncated again (!), this "tiny" URL will also get you there:

Mike said...

OK, it got truncated again, so paste the "tiny" URL, then scroll down and click on Deborah's presentation link, and you'll (we hope) be able to download a PowerPoint presentation.

mathmom said...

There's a default rss feed for comments already:

This works for me. :)

Jackie said...


Thanks! :)

Justin Aion said...

The idea of modifying teaching methods to reach each individual child is a hot button issue in teacher education courses at the moment.

As you know, it's quite a sore subject for me. My own personal beliefs stem from the concept that we must provide a safe, productive and stimulating environment for our students, however, I worry that if we modify our lessons too much, we give our students a false representation of the world. My favorite example is that there is no boss in the world who will allow his employees to give a quarterly report in the form of interpretive dance.

I know that we must be sensitive to the needs of our students, especially those with learning defficiencies,(sp?) but I fear that too much modification and adaptation does them a disservice.

This is a very fine line and I think that numerous discussions about this topic would be productive and very helpful to new teachers.

Dave Marain said...

I agree that it is unreasonable to expect teachers to accommodate every student's individual needs or preferred modalities of learning. However, at least in teaching mathematics, current research informs us that utilizing multiple representations (Rule of Four)optimizes learning for many of our students. This requires considerable training and experience for preservice teachers but it's even more difficult for veteran teachers, for some a true paradigm shift. Planning lessons that incorporate these representations is arduous work, however, once one becomes acclimated to this approach it becomes easier. I will attempt to give many examples of this pedagogy in this blog.

Your point about creating an artificial environment for students that may do them a disservice is well-taken. However, one does not have to go to extremes here. We still need to find a way to help students who do not learn by conventional methods. Ultimately, Justin, that's why we chose this profession.