Basic Math or Pre Algebra or Nothing

What do students need before a ‘beginning algebra’ course?  Several of us (math faculty at my college) are working on this problem, with a goal of helping more students make a good transition to algebra while being aware of other expectations or demands.

My college does not have a basic math class, having eliminated that quite a few years ago.  There is still a prerequisite for the pre-algebra course (a placement test) though the cutoff is not very high, which means that one of the issues is students with extensive gaps in numeracy.  Our pre-algebra course has these components:

• variables and expressions used from the first chapter
• signed numbers start next
• solving first degree equations (some with simplifying first)
• fractions
• geometry (formulas primarily)
• units and conversions (the only math course doing this, for most students)
• percents and applications (tends to be uncomplicated)

One of the issues I see us dealing with is our own views on “what students should know”.  In our course, we designate the first part ‘calculator free’ because students “should know” their basic facts about numbers; the remainder of the course allows a calculator.  We also expect students to use arithmetic procedures for fractions, though we do not check to see if they understand ‘why’.  We cover classic percent problems, because students “should know” these.

So, what essentials are needed to help students succeed in basic algebra?  In some ways, the answer has been “do some basic algebra”; the last course revision integrated algebra throughout.  We’ve looked at the data for the progression, and it is my opinion that the alumna of the newer course have similar struggles in basic algebra compared to the older course (with less algebra).  One observation is that the students struggle with the expressions and first degree equations that they ‘had’ in the pre-algebra course, whether the algebra was integrated or covered separately.

Here is the basic need I would identify for success in basic algebra:

Students need a core of understanding about numbers and properties, and need a sound beginning on procedural flexibility.

The traditional percent material focuses on correct answers, often using memorized procedures.  I would shift to questions about equivalence and multiple solution methods … because these are core issues in algebra.  My class work and assessments would focus on creating as well as identifying alternate correct methods.  The traditional geometry work in this course also tends to have a focus on correct answers (though we do not memorize formulas).  I would instead deal with how parts of shapes relate to the whole, and concepts of perimeter/area/volume; the same focus on multiple solutions would be appropriate.

The numerical demands of a basic algebra course are quite limited; we are not going to solve a lifetime of numeracy problems in 15 weeks of a basic math course.  A pre-algebra course gains little by making the attempt.   A reasonable goal is to develop a significant set of understandings about numbers and objects, along with the flexibility that this understanding supports.  Deliberate design, sophisticated pedagogy, and faculty expertise are required for this … just as is the case for most math courses that we should place in front of our students.

One of my colleagues used to say:

The student’s fragile understanding of mathematics begins in the pre-algebra course.

We need to shift our focus.  Without understanding, any math course becomes just a barrier to student success.  Without understanding, math is that subject that everybody says they are bad at.  With a focus on understanding, we offer an honest math course that can provide real benefits for students. With a focus on understanding, we demonstrate our commitment and respect towards all students … starting from the first day of our first math course.

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3 Comments

• 

  By schremmer, September 29, 2014 @ 10:43 am

  Re:
  the basic need I would identify for success in basic algebra:

  Students need a core of understanding about numbers and properties, and need a sound beginning on procedural flexibility.

  But exactly what does this “core of understanding” consist of?

  Since it is in the pudding that the proof is to be found, here is the very first chapter in a sequence of courses intended to take adult students from where they are at, wherever that is, up to the calculus of changes, aka Differential Calculus:

  Symbolic Systems

  Since html is not precisely my cup of tea, I can only hope the link works here. Apologies in advance.

  Regards
  –schremmer

• 

  By Jack Rotman, September 29, 2014 @ 5:09 pm

  Being a blog, the goal is to general and conceptual; if I wanted to elaborate on the ‘core of understanding’, I would write a textbook (free or otherwise). 🙂

• 

  By schremmer, September 29, 2014 @ 10:04 pm

  “Being a blog” does not entail “[being] general and conceptual”. “Elaborat[ing] on the core understanding” does not entail “writ[ing] a textbook”.

  But, in the absence of any details and/or examples, I do not see what you expect your readership to do. Respond with more/other “general and conceptual”?

  I had assumed that you had the desire actually to improve a rather dire situation. I don’t see how that kind of talk could possibly do it.

  Distraught regards
  –schremmer

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