Is this the end of beginning algebra?

Sometimes, we are so accustomed to seeing the world in the same ways that we can not completely process new information.

When people look at the curriculum described in the New Life model (http://dm-live.wikispaces.com) there is no label that looks like a beginning algebra course.  Does this mean that algebra is not a valid domain for developmental mathematics?

The issue here is “What are the powerful ideas of mathematics” … ideas that will help students prepare for a variety of opportunities in college and in life.  If we focus on the good stuff — ideas with power — we will find ourselves renewed and our students rewarded.

In the case of ‘beginning algebra’, we normally sort through a topic list that has phrases like ‘expressions’, ‘linear equations’, ‘graphing equations in two variables’, ‘systems of equations’, ‘exponents and polynomials’.  These phrases are so entrenched in developmental mathematics that our textbooks are almost required to use this list to create their table of contents.  If these phrases are not used, we wonder if there is any algebra involved.

Instead, think about two fundamental ideas of algebra (just to start) — proportional quantities and variables.  Proportionality is fundamental to many concepts that students either need to use or will encounter in future courses.   This includes unit conversions and dimension analysis — work that exceeds the simple mechanical conversions we often limit ourselves to.  Proportionality can be studied in various representations; the numeric level is the applied level, but we should abstract this information to the graphical level and the symbolic level.

When we look at proportionality from a symbolic viewpoint, there is an opportunity to develop a deeper understanding of variables and constants.  Students leave our existing courses convinced that any letter is something to be solved for; the power of ‘variable’  focuses on the ability to represent information and relationships in a way that communicates well.

Rather than the demise of beginning algebra, we are actually looking at the revival of algebra.  Algebra is a set of powerful ideas; the reformulated curriculum focuses on these ideas … and avoids the artificial ‘procedural’ content that has been performing an impersonation of ‘algebra’ in our curriculum.

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