Algebraic Literacy meets Pogo (AMATYC 2016)

Pogo (by Walt Kelly) offered humor and wisdom.  That is the combination I am reaching for at my Algebraic Literacy session this week in Denver (AMATYC 2016).

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The Difference Between Mathematical Literacy & Algebraic Literacy

As more colleges implement Mathematical Literacy courses, we are running in to a point of confusion:  what is the difference between Algebraic Literacy and Mathematical Literacy?  The easy reference is problematic … comparing these courses to the traditional beginning & intermediate algebra courses; those traditional courses are at the ‘same level’ in a general way, but this fact does not help us deal with the details of new courses.

I’ve written previously on the comparison of the new courses to the old, especially Algebraic Literacy compared to the traditional course (https://www.devmathrevival.net/?p=2347 and https://www.devmathrevival.net/?p=2331 ).  However, I’ve not talked that much about the difference between these new courses that share a word in the title (“Literacy”).  That’s the goal of this post.

First, the course titles are not perfect … the word ‘literacy’ was meant to imply that the courses deal with pre-college material; ‘mathematical’ was meant to suggest that we did not start with algebra directly … while ‘algebraic’ was meant to suggest some directionality (headed towards STEM and STEM-like courses).  We have focused on the goals and outcomes documents for the new courses as a way to clarify what the courses are designed to deliver.

MLCS Goals and Outcomes Oct2013 cross referenced 2 by 2

Algebraic Literacy Goals and Outcomes Oct2013 cross referenced

Since these courses diverge from the traditional curriculum, these documents were not sufficient to clarify “what belongs in each course” for shared topics (especially algebra).

So, here is a side by side chart meant to provide some additional clarification.

The intent is not to avoid any overlap between the courses, though there is less overlap than the traditional courses (in general).  As an example, many Math Lit courses introduce systems of linear equations; the solution methods are usually limited to numeric (graphing & intersect) and some substitution.  In an algebraic literacy course, the problems would be more diverse and so would the solution methods presented.

Another example is factoring polynomials.  The classic Math Literacy course might cover “GCF” factoring only (pardon the redundancy) … though that is not assumed.  The intent is that Math Literacy avoid most factoring beyond that which is a direct application of the distributive property; Algebraic Literacy picks up most of the factoring concepts necessary.  We note that most ‘needs’ to include factoring are contrived; a deep understanding of functions (the core goal of pre-calculus) does not depend upon all the typical methods presented in the albatross “Intermediate Algebra”.

A solid Mathematical Literacy course will involve some algebraic manipulation (limited in types as well as in complexity), and these procedures would be further enhanced Algebraic Literacy.  Therefore, the distinction between Math Lit & Algebraic Literacy can not be reduced to a particular ‘problem’ being present in one course but not the other.  We really want to keep the focus on the purposes of each course; see the ‘goals’ part of the course documents listed above.

If you have questions about the distinction between the two new courses, I would be glad to provide any information I have.

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Dev Math: Where Dreams go to Thrive

In response to data showing the exponential attrition of long sequences of developmental mathematics courses, some people are using the quote “developmental mathematics is where dreams go to die”.  This phrase has been one of the most influential statements in our field over the past 5 years — not because it is true but because people (especially policy makers) believe that it is true.

This is a normal political strategy: frame an argument in a way that there is only one answer (the one that ‘you’ want).  I’ve seen leaders at my own college use this method, often successfully. … and I imagine that you’ve encountered it as well.  As teachers at heart, this style of communication is not natural for us; we respond by reasoned arguments and academic research with a goal of getting everybody to understand the problem.

The difficulty is that leaders who use the “where dreams go to die” phrase have little interest in understanding the problem.  Their goal is to remove developmental mathematics as a barrier to student success.  The next phrase after “where dreams go to die” is often “co-requisite remediation”, with claims that this solution is a proven success because of all of the data.  Of course, our view of this data is a bit more restrained than the leaders and policy makers; this is not a problem for them, as they have the answer in mind — all we have to do is agree with it.

We must do two basic things so that we can really help our students succeed:

1. Shorten and modernize our mathematics curriculum, both developmental and college level.
2. Consistently use our narrative:  “Developmental mathematics is where dreams go to thrive!”

Much of the material on this blog, as well as the wiki (dm-live.wikispaces.com)is meant to help faculty with the first goal.  The new courses, Mathematical Literacy and Algebraic Literacy, allow us to provide great preparation for college level courses within an efficient structure which minimizes exponential attrition.

“Developmental mathematics is where dreams go to thrive”:  We need to articulate this accurate view of our work, which is valid even within the old-fashioned traditional curriculum with too many courses.  I’ve posted about some of the research with a ‘thrive’ conclusion:

• The Case for Remediation  (https://www.devmathrevival.net/?p=2461)
• Research Trends in Developmental Mathematics  (https://www.devmathrevival.net/?p=1176)

Also, a great project at CUNY called “ASAP” gets a glowing external evaluation:  http://www.mdrc.org/project/evaluation-accelerated-study-associate-programs-asap-developmental-education-students#overview  The ASAP model is currently being validated at other institutions.  Please let me know of other research showing that dreams thrive in developmental mathematics.

We should add our own ‘thrive’ stories and data.  For example, at my institution, we had 6 students start in pre-algebra and the proceed up to Calculus I in a four year period … 5 of them passed Calculus I on their first attempt.  If we believe the ‘die’ narrative, you would expect zero or 1 of these to exist; I am sure that most institutions have similar results to mine where the data shows more of a ‘thrive’ result.

Our traditional courses must go; we must do the exciting work of renewing the curriculum based on modern thinking about mathematics combined with more sophisticated approaches to instruction and learning.

However, that work will generally be wasted unless we establish a ‘thrive’ attitude.    The two conditions existing together create a new system that serves students well.  Developmental mathematics is where all dreams go to thrive.

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Intermediate Algebra is NOT College Math ! :(

I actually spend a fair amount of time looking at other colleges math courses, partly from my interest in seeing how many colleges are doing New Life Project courses (Mathematical Literacy, Algebraic Literacy).  From that work, it is clear that the landscape is changing in both beginning algebra and general education mathematics.  However, two patterns are still present:

1. We continue to offer one or more courses in arithmetic focusing on procedures.  The presence of these courses is a tragedy on our campuses, since they negatively impact exactly the student groups we want to help (minority, poor).  I’ve posted on these issues earlier this year.
2. We frequently classify intermediate algebra as a college course, and commonly use it as a general education requirement.  Using a course which mimics a high school course in this way is professional embarrassment.  That’s the topic of this post.

We all know that “intermediate algebra” varies considerably between colleges, states, and regions.  In some cases, the intermediate algebra course has content at the level of the Common Core Mathematics (see http://www.corestandards.org/Math/ ) within the algebra and functions categories.  In most cases, however, our intermediate algebra courses fall below those expectations.

Intermediate algebra is a remedial course!!

The primary distinction between K-12 algebra and intermediate algebra is assessment — the college intermediate algebra course most likely requires a higher level of performance by the student in order to earn a passing grade.   It’s like “So, you were supposed to have learned this stuff in high school but NOW you are going to have to REALLY know that stuff.”

However, in many ways, our intermediate algebra (IA) courses are inferior copies of the K-12 curriculum.  Our IA courses are still descendants of copies of Algebra II from the 1970’s; much emphasis on procedures and correct answers … not much dealing with reasoning.  Given that we don’t deal with most of the discipline issues that occupy a K-12 teacher’s time, we should to better.    The K-12 content has responded to a series of standards (NCTM, Common Core) while our intermediate algebra has been standing still.

The Algebraic Literacy (AL) course is a modern system to help students get ready for college mathematics.  However, AL is still “not college math”, even though AL raises the expectations for students.

Entire states use intermediate algebra (IA) as an associate degree requirement.  In Michigan, which lacks a central governing body for community colleges, most colleges use that as one option for degrees.

We can, and must, do better.  If students do not need a course like Pre-Calculus, then we should use quantitative reasoning (QR) or statistics for their degree requirement … or even a course like ‘finite mathematics’.

Personally, I think intermediate algebra must die (and soon).  The issue in this post is whether a K-12 level standard course should be used for associate degree requirements.  Beyond the criteria of ‘expediency’, there is no rationale for that use.  IA is remedial, not college level.

Let’s MOVE ON!!

 
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