Mathematical Learning Objectives

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At my school, we’re currently in the process of identifying what we see as our essential educational objectives.  The document that emerges should help to guide all of the decisions we make in the future, including everything from an upcoming rethinking of our graduation requirements to discussions around how strongly we embrace learning experiences that happen outside of the traditional classroom setting.  I imagine this list of objectives as something to point at whenever we’re making arguments for why some practice should change (or continue, as the case may be).  It’s exciting because this has been a bottom-up approach, with input coming from all faculty, coaches, staff, and administrators as we try to discern exactly what it is that we want to instill in each and every one of our students before they graduate.

At the moment, all of the input that’s been received has been boiled down into three broad categories: dispositions, skills, and content/knowledge.  The dispositions and many of the skills are cross-disciplinary, covering things like recognizing one’s place in our global community and being able to productively work with others.  Other skills and much of the specific content tend to break out more along discipline or department lines and, as such, have been shopped out to the departments to produce lists which will then be revised and aggregated.

Ignoring for the moment the fuzzy boundary between skills and knowledge, the following list is what we’ve arrived at in the math department to describe what we see as our overriding objectives.

All of our graduates should possess:

• advanced numeracy and estimation skills as well as the ability to make sense of patterns and recognize structure in a variety of contexts;
• a well-honed aptitude for clearly communicating mathematical ideas and reasoning together with a command of techniques for effectively representing data;
• sufficiently strong foundational knowledge (i.e., conceptual understanding in algebra, functions, geometry, probability, and statistics) to facilitate: the translation of real-world phenomena into mathematical language and vice-versa, the recognition of opportunities to apply various mathematical techniques, and flexibility in the approach used to solve problems as a result of the ability to view them from multiple mathematical perspectives;
• knowledge of and facility with technology, including the discretion to recognize when (and which) technology is appropriate.

This list is fairly general and certainly not entirely math-specific;  I would expect the fourth bullet, for instance, to be useful far outside of the context of mathematics.  But I think it nicely captures what we’re trying to do.  What did we miss?  What would you add?

To push a little further toward identifying our priorities within mathematics, I played devil’s advocate and issued a challenge to the department.

Consider the following statement.  “The specific mathematical topics covered in our classes are totally irrelevant, so long as what we do leads toward our essential objectives.”  The places where you disagree with that statement – the things you think that any educated person simply cannot do without knowing – are the things we must be sure to teach.  Every other topic is negotiable.  Be prepared to defend every item on your list of essentials.

I have two goals here.  I want to separate what absolutely must be covered from everything else because I want to see us cut out some of the chaff in order to do a better job covering the non-negotiables (in more depth).   Also, I’m looking for room to insert more probability and statistics into our curriculum because I think those things are more useful for the world we live in today and studying those topics can produce the kinds of students we want just as well as (if not better than) learning how to factor cubic polynomials or utilize trig identities.  What would be on your list of absolutely essential topics in mathematics?