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Learning to calculate the area and circumference of an irregular shape
By Richard Nantel | April 23, 2007
My 13-year old daughter was doing very well in her grade seven enriched math class until her teacher fell ill for a month and was replaced with a substitute teacher. A couple of below average showings on math tests convinced the two of us that it might make sense to sit down together for an hour each week and review the material.
I don’t have any recollection of ever studying what she’s currently learning: how to calculate the area and circumference of an irregular geometric shape such as this:
I would have studied this material back when dinosaurs roamed the earth, so it’s been long forgotten. Consequently, it’s meant learning high school math all over again.
I stared blankly at a couple of sample problems for a minute and realized I didn’t have a clue how to proceed. So, I turned to the appropriate chapter in her math textbook, hoping to find the explanation.
The opening page of this chapter contained diagrams of geometric shapes and a space to enter their area and circumference. Had the page containing the explanation on how to solve these types of problems been ripped out by a previous owner of the textbook?
I turned the page. More sample problems. Still no explanation.
Finally, about four pages into the chapter, a page contained a sidebar with some tips on how to proceed. Needing more information than this, my daughter and I turned to the Web and found many helpful pages such as this one on coolmath.com.
The Gatekeepers of Knowledge
For thousands of years, people in power have assumed that providing the masses with direct access to information was dangerous. Instead, the information contained in books on topics, both religious and secular, needed to be interpreted by enlightened “Gatekeepers of Knowledge.” The same practices apparently still exist in schools today.
My daughter’s experience with the substitute teacher started making sense. The textbook was likely designed with the assumption that the teacher would provide, in class, the explanation on how to solve these types of problems. The students’ edition of the textbook contained mostly exercises. For a student to access the information he or she required to solve the problems, he or she needed to see the gatekeeper.
A good teacher would be able to explain the methodology required to solve these problems clearly. A lesser teacher, such as the substitute my daughter and her classmates endured, could not.
The immediate result was that students’ grades declined. The longer term result would likely be that children would become fearful and hateful of mathematics. What a tragedy.
It’s disturbing that the antiquated notion of Gatekeepers of Knowledge still exists in schools today. Luckily, the Web allows people with online access to circumvent the Gatekeepers and get the information they require quickly, efficiently, and often in multiple formats. With gatekeepers still around, we need to ensure that all children have access to the online learning resources they need.
April 25th, 2007 at 11:22 am
I have been exploring this in the corporate world and have a presentation to give soon which is strengthened by your thoughts. Thank you. I have been hung up lately on how we, as ‘trainers’ get in the way of employee learning - we are the corporate Gatekeepers of Knowledge. But it is a mindset that is difficult to come out of because it has been tradition and common practice. I read a great article today (http://tinyurl.com/2m2qbd) on the media, as an example, being the traditional gatekeepers of knowledge when the best news came from 2000+ writers on Wikipedia.
There is a great blog by Steve Hargadon (http://www.stevehargadon.com) that deals with what he terms “School 2.0″. There are some great implications of corporate learning in there as well.
Thanks again for your thoughts.
May 1st, 2007 at 12:24 pm
Your comment, “A good teacher would be able to explain the methodology required to solve these problems clearly. A lesser teacher, such as the substitute my daughter and her classmates endured, could not,” stuck with me as perhaps not quite complex enough. A good teacher needs to know math, and know how to teach it - I think we agree on that.
A good teacher guides the students to developing their own understandings for solving the problems rather that explaining the methodology. If your daughter is using the Connected Math curriculum, that is certainly how that curriculum is meant to be taught.
May 5th, 2007 at 9:05 am
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