Show Me What You Know

I was recently reading a blog where a debate raged regarding the validity of a math activity.  The debate, as I saw it, is between:

Side A:  Proponents of math activities that contain a minimum amount of given information so that students must hypothesize, test, and conjecture in order to arrive upon a reasonable conclusion.  And, conclusions may vary but must be justifiable.

Side B:  Proponents of math activities in which mathematics as a precise science is emphasized.  Activities where ambiguity is allowed are of diminished quality because the student’s interpretation is not a measure of their mathematical understanding and skills.  Correct answers are singular, precise, and unambiguous.

These two sides will never see eye-to-eye because they don’t even agree as to what counts as mathematics.  Side A would likely agree that the mathematics activities valued by Side B is a subset of math.  But, Side B sees information or context that obscures the mathematical representations and precise conclusions as obstacles to student understanding and not mathematically relevant.

I believe the math wars have already taken too much time and depleted the energy of too many invested educators.  Therefore, I do not want this blog entry to become another “flare-up” of this war.  I do want to use this entry to advocate for an educational activity that I believe can bridge this divide.

It is time that all high school graduates be required to complete a Capstone Project.

If we are asking that students graduate “College and Career Ready,” then we should require students to synthesize their educational experience into a project that relates to their upcoming endeavors.  This self-chosen project will allow students to dive more deeply into an area of interest and apply the math they have studied.  For example, if a student plans on being a:

Teacher:  their project should include an analysis of the achievement gap including an analysis of their own school’s data.

Auto mechanic:  their project could include an analysis of how transmission and differential gear ratios affect a car’s performance and fuel usage.

A classics major:  their project could include an algebraic modeling of the economy of ancient Greece.

A math major: their project could consider applying the four-color theorem to congressional districts in the United States.

A capstone project requires students to show us what they know, or can figure out, about a topic they see as their next step in becoming a contributing member of society.  And, it should be valued by both sides of the math wars.  By its nature, the task does not give students information; students are required to seek out and analyze relevant information.  Additionally, it allows students who prefer the unambiguous world of pure and precise mathematics to show us what they know.

As students approach their 18th birthdays and high school graduation, I think we can all agree that we should give them the opportunity to show us what they know through a medium of their choosing, not ours.


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