Never be afraid to get dirty, but be sufficiently sure-footed to avoid the abyss of contamination.

I’d Rather be a Hammer…

I took shop class in middle school. While I can’t recall specific lessons about using tools like a jig saw, sander, set square, etc., I do remember using them to build a tote box and other items. Middle school was also when I took the Algebra I and II sequence. I remember learning how to use a lot of mathematical tools, but we only applied them to figure out when trains would meet up in Chicago. Following this sequence, I took Geometry and Trigonometry. Aside from learning a lot of interesting properties about circles, lines, and polygons, we learned how to construct mathematical arguments like proofs.

What would happen if shop class were taught like math was? Maybe a year would be devoted to to the hammer and screwdriver. I can picture projects like hammering a bunch of nails to a piece of wood. The next year would cover saws. This type of teaching style might allow students to really get a solid feel for each tool and its purpose, but it would also risk losing the big picture. It might be difficult to construct a tote box after just Hammers I and II.

I heard about Robert Moses‘s Algebra Project from a workshop at MSRI. Moses originally gained prominence during the civil rights era when he worked to end Jim Crow laws in Mississippi. Since the late 1960s, he has been working to improve education in the inner city and rural areas. One of these efforts has been the Algebra Project, which he started with money from his MacArthur “Genius” Award.

The Algebra Project takes the novel idea that students will get a better sense for mathematical concepts if they understand why someone might want to think mathematically. The Trip Line lesson series is one example of how this is accomplished. Looking at the first lesson alone, in which students are asked to prepare for a “field trip”, one might question whether this has anything to do with mathematics. However, after the students make observations from the trip, they eventually learn to distinguish different types of observations and identify structure. This structure eventually paves the way for actually learning the concepts one might see in a pre-algebra course.

Teaching shop like a math class sounded ridiculous, so one might ask whether this approach, which appears to teach math like a shop class, is equally ridiculous. When the Algebra Project was started in Jackson, Mississippi, the passing rate on corresponding standardized tests was significantly larger for students in the program. While I expressed concerns in an earlier blog that placing too much emphasis on standardized tests might have negative consequences, these concerns arose from forcing students to learn to take these tests rather than learn the material. While the Algebra Project covers the same material one might find on such a test, the absence of multiple choice questions and other elements from its curriculum suggest that it does not suffer from this flaw.

Should other schools abandon current teaching methods for the Algebra Project? A potential downside of applying the Algebra Project universally is that it might reduce the number of tools covered in a course. However, for those students that are not mathematically inclined, it would be more useful to know why people use mathematical tools in the first place. I doubt current graduates of Algebra II will be asked when two trains meet in Chicago until their children take the class.


3 responses

  1. Des

    This is very interesting. You probably didn’t know this, but I failed my Physics curriculum miserably. Part of it was due to the fact that I couldn’t understand why you would need to use the TOOLS I was being taught. Thus, when I was taking “Mathematical Methods for Physicists,” I was too busy trying to figure out why you would need to use a Green’s function or a Bessel function, that I neither mastered the functions nor could understand them. I think my math career has been mostly like that, because I’ve been learning Hammers I and them Hammers II, etc. without knowing why anyone would ever want to use a hammer. In a sense, I was trying to build a toolbox which would eventually have to hold the tools that built it, but I couldn’t recognize what a toolbox was since I had never seen one.

    August 7, 2006 at 4:39 pm

  2. Krish

    I remember that I got through my Microelectronics class in college using the “plug and chug” method, and unfortunately, I didn’t get much out of it. I did not pursue this are of engineering further in part because I could not see the big picture of when to use these tools.

    August 9, 2006 at 6:48 am

  3. Pingback: Past Posts « Dirty Hands

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