What to do: Intermediate Algebra Dies

What do we do when we terminate our intermediate algebra course?  A new course is necessary, with a focus on reasoning and communication — a more rigorous course (see The Rigor Unicorn).  What to do?

I’ve written before about the necessary demise of intermediate algebra as a college course (see Intermediate Algebra Must Die!! and Intermediate Algebra … the Barrier Preventing Progress).

The traditional narrative is that algebra is a barrier to college success.  Actually, the barrier is obsolete algebra courses (developmental and pre-calculus) which focus on drill more than understanding, and focus on artificial applications rather than fundamental relationships and concepts.  Mathematical Literacy forms a great starting point for a modern curriculum.  When we ‘kill’ intermediate algebra, the solution is to offer an algebraic literacy course (see Algebraic Literacy Presentation (AMATYC 2016).

My colleagues continue to show a dedication to a modern curriculum.  Within the past 5 years, we have dropped both pre-algebra and beginning algebra courses, and replaced them with a Math Lit class in two formats — regular and ‘with review’ (for students with especially weak numeracy skills).  Last month, we made the decision to eliminate our intermediate algebra course.

Temporarily, we will use a revised “fast track algebra” course.  That fast-track course has existed for 3 years, side-by-side with intermediate algebra.  However, the fast track algebra course still uses out-dated content and lower expectations.  Why?  Because there are not available algebraic literacy materials.  Actually, there aren’t any materials dealing with algebra focusing on communication and reasoning.  It’s like the books (and HW systems) are stuck in 1995 in terms of content.  [It’s only 1995 instead of 1975 because of a little bit of technology that some books incorporate.]

Our obituary sadly reads as follows:

After a long life, perhaps too long, the intermediate algebra course at ____ will be removed from life support on December 31, 2019, surrounded by many family and friends.  Intermediate algebra was preceded on the path to the math after life by basic math, pre-algebra, and beginning algebra.  Surviving are a temporary Fast Algebra course, a Math Lit course, and several college level math courses which are also on life support (although unaware of that fact).  A memorial service will  be held at some time in the future when a modern (current) algebra course can take it’s place to serve our students.

We face this change without a sense of closure.  There is some grief at the old course going away (though that was deserved), but there is a dissatisfaction with continuing the same type of algebraic work.  We are generally pleased with the learning occurring in Math Lit, and want a similar course to follow it … which might be called algebraic literacy or algebraic reasoning.

This is “our” problem, where “our” refers to faculty involved with mathematics in the first two years.  We have not written book materials to support a modern (algebraic literacy or reasoning) course.  Publishers have not pursued this, partially because of huge transitions in their “business model”.  That is, however, no excuse for our lack of movement.  There are smaller publishing companies that could undertake this work (XYZ for example) and we also have options with “OER”.

Is the lonely death of our intermediate algebra due to our disinterest?  A lack of understanding?  Are the enthusiasts for a modern course all too ‘seasoned’ (ie, old) to have the energy to write stuff?  Are the younger professionals only thinking about what they have to teach next week and next semester?  There are issues of professional involvement and responsibility behind this lack of newer materials; that is “on us”.

If you have seen value in an algebraic literacy type course, consider developing materials.  Network to find like-minded colleagues.  Collaboration and technology make the work of developing materials much easier.  Where are the people who will create the next level of new materials in developmental and pre-calculus?  Are you one of them?

Every Student Learns … Every Day!

There was a period in my teaching when the core principle was “deep assessment”.  This “Deep Assessment” idea was that every key outcome within a test would be assessed three times BEFORE the test for each student, in class … at the intro level when starting the topic, at an intermediate level after the first usage, and at a higher level as part of the review for the test.  I would tell my colleagues that I assessed the important ideas 3 times, and they seemed to think this was good … and so did I, until I thought about my observations.

Sure, it helps students to have multiple opportunities (assessments) on key ideas and get instructor feedback.  I would spend considerable time grading these assessments, and writing feedback.  This very logical structure did, in fact, work for a portion of my students.  As I thought about this, however, most of the students who benefited were doing fairly well before my class.  You know, they were mostly reviewing stuff they once knew well.

However, the ‘deep assessment’ strategy missed some of the students in the middle (of need), and missed almost all of the students with the greatest need.  Do our classes exist to serve just some students, or all?  Hopefully, you think about that question on a regular basis.  There are direct connections between that question and the posts made recently about equity Policy based on Correlation: Institutionalizing Inequity.

My current guiding principle is “everybody learns every day”.  I seek to provide some benefit to all students.

Many readers are going to be thinking … “What’s so different about that? Don’t we provide the opportunity to benefit every student in each class?”

Nope, we don’t.  Think about this … “learning” depends upon readiness and engagement, combined with communication.  We fail to address the readiness almost all of the time.  By this I am not referring to course prerequisites or placement tests; those are gross measures of overall abilities, and have very little to do with learning.

I’m referring to a thorough analysis of specific knowledge and understanding needed to learn a certain topic.  Let’s look at “basic function ideas” as you might cover in an intermediate algebra or college algebra course.  Learning basic function ideas (notation, interpretation, points) at an introductory level.  The readiness includes:

• input versus output
• simplifying expressions
• substituting values
• horizontal and vertical number lines
• ordered pair notation and meaning
• point plotting as opposed to slope

The image above shows ‘puzzle pieces’ between the person and the learning.  Vygotsky used a phrase “zone of proximal development”, which is related to what I am talking about.  [Vygotsky was primarily a developmental psychologist, so his results are indirectly related to current learning sciences.]

The ‘ready to learn’ criteria is always there.  If we ignore it, we only serve part of the students.  On the other hand, if we tell students that they need to ‘review’ something before the new stuff, we expect the weakest students to do the more complicated process without our direct support and advice.

I’m teaching developmental math, not ‘college level’, so my dive into this is really intense.  Every class day, we start with a team activity which both checks on the readiness and begins the process of learning today’s stuff.  We might spend 20 minutes doing the activity, followed by 10 minutes of reviewing it as a class; my goal is to get everybody ready, and have everybody learn every day.  Small teams (3 to 5) does a pretty good job of keeping everybody involved, and making sure that everybody is learning.

In a college level course, we could still use a team activity on readiness.  Depending on the topic, we might only need 10 minutes doing it, and 5 minutes reviewing it.  In other cases, the ‘readiness to learn’ activity might occupy the majority of the class time.

I can’t tell you that my ‘plan’ is perfect; that’s a unreasonably high standard (even for me 🙂 ).  However, I can tell you that this “everybody learns everyday” approach does wonders for attendance and participation.  My students with the greatest need still have gaps, but they are smaller.  The ‘middle’ students tend to look more like the high-quality (reviewing) students.

We know that ‘attendance’ is highly correlated with success in mathematics.  Students with greater learning needs get easily discouraged when our classes do not provide them with much learning — either due to lack of readiness (at the detailed level) OR due to our class structure not engaging every learner.  “Everybody learns everyday” minimizes this systemic risk, without harming the higher achieving students.