Clarifying the Curricular Vision of the New Life Project

The ‘map’ showing how the New Life Project courses (Math Literacy, Algebraic Literacy) fit into the collegiate mathematics curriculum has been updated.

Here is the version intended for mathematics professionals:

We also have a ‘simplified’ version, intended for those outside of mathematics departments:

These new versions continue the same concepts.  The clarifications involve (A) the eventual use as replacements for the traditional developmental mathematics courses (from 3 or more, down to 2)  and (B) placement into algebraic literacy (more than can go into intermediate algebra).

 Join Dev Math Revival on Facebook:

Too Many Math Courses!!

Have you got course(s) in … basic math … arithmetic … pre-algebra … fraction modules … decimal modules … etc??  Although some colleges and a few states have eliminated courses at this level, the vast majority of colleges still have one or more.  One is too many!  #acceleration #FinancialAid

Federal financial aid guidelines prohibit a course to count for enrollment levels unless it is at least at the high school level; courses below high school (K to 8) can not be used.  See https://ifap.ed.gov/fsahandbook/attachments/1415Vol1Ch1.pdf

My institution is currently going through a process (intensely so) dealing with our single course at that level (pre-algebra).  Our department has been asked (about every 10 years) to classify developmental courses as ‘high school’ or ‘below high school’.  The most recent request resulted in our best answer at this time: pre-algebra is at the K-8 level.  That was mostly true 10 years ago, and the answer is even clearer when the Common Core standards are considered.

Does your college follow this rule?  You might know already, but be aware that all institutions can be subject to a financial aid audit; violations can result in financial penalties up to and including loss of all federal financial aid money.  Fines are the most common penalty, from what I’ve heard.

Do you have 3 or more courses below intermediate algebra?  Two of these are likely to be ‘elementary level’ (non-federal financial aid), and one ‘high school’ (beginning algebra).  Three courses at that level creates a practical problem for students (completion), a financial problem for your institution (financial aid audit), and a moral problem as well.

The Math Literacy course is designed to have a minimal prerequisite (basic numeracy).  Some colleges use Math Literacy with a lower placement cutoff than beginning algebra; some offer Math Literacy without any math prerequisite at all.  To me, this is a situation where co-requisite remediation makes a lot of sense.  The prerequisite knowledge is a fairly small set, and the range of ‘gaps’ is therefore more limited than it would be in a higher-level course.

For some of us, ‘arithmetic’ is the most common placement level for new students in our college.  I’ve heard up to 36% in that placement, with my college’s rate a little lower.  In all of the research I’ve seen over the years, one thing has been consistent:  courses before beginning algebra do not benefit students in terms of passing subsequent math courses (in general).  Our instruction and learning is often the least sophisticated at this level, and student motivation tends to be pretty low.

Let’s agree that eliminating courses below Math Literacy (and beginning algebra) is a really, really good goal.  The problems have other solutions within our reach, and our students deserve better than they are getting now.  The federal financial aid rules provide an added incentive; however, we have sufficient rationale from other considerations.

 Join Dev Math Revival on Facebook:

How to Recognize an Algebraic Literacy Course

The next AMATYC journal will have an update on the New Life Project (over 100 colleges, over 800 sections, and something like 16000 students this fall semester).  In order to prepare that update, I spent a lot of time searching various web sites and following up leads.  That detective work led me to a number of colleges using “algebraic literacy” as a course title … when the course was just ‘intermediate algebra’; I also found some courses titled ‘intermediate algebra’ that were closer to algebraic literacy. #AlgebraicLiteracy #MathLit #NewLifeMath

This post is a brief “field guide” to help us recognize an algebraic literacy course.  Algebraic Literacy (the course) is one of the New Life math courses (AMATYC Developmental Mathematics Committee) developed in 2008 to 2010, based on the professional work from the last two decades.  The material below comes from our wiki (http://dm-live.wikispaces.com/Algebraic+Literacy ).

GOALS and FOCUS:

The Algebraic Literacy (AL) course prepares students for mathematics pathways which include college algebra, pre-calculus, and other courses requiring a background beyond the Mathematical Literacy (MLCS) course.

This is similar to an intermediate algebra course … on the surface.  There is a fundamental difference, however:  intermediate algebra is a derivative of an earlier “Algebra II” course from K-12, while Algebraic Literacy is engineered to meet the mathematical needs of college mathematics (backwards designed).

The focus of the AL course is on building understanding of mathematical systems with a dual emphasis on symbolism and application. The Algebraic Literacy course includes quantitative topics from areas besides algebra, which supports the needs of both STEM (Science, Technology, Engineering, and Math) bound students and other students.

A typical intermediate algebra course is heavily symbolic, with applications playing a minor role (and often using trivial applications with little payoff for preparing students).  The Algebraic Literacy seeks a balance between procedural fluency and higher level skills.  For some Algebraic Literacy courses, the applications form the context within which the mathematics is developed; for others, the mathematics begins first with applications integrated.  In considering applications, the Algebraic Literacy course includes problems with numeric solutions which would be solved symbolically in calculus.

PREREQUISITES

Basic proportional reasoning and algebraic reasoning skills, and some function skills, are required prior to the Algebraic Literacy course.

We do list 5 specific areas of prerequisite skills following this general statement.  However, the Algebraic Literacy course is designed to allow ‘co-requisite remediation’ at the appropriate level: Building on basic algebraic reasoning skills, for example, we aim for deeper understanding and solid symbolic skills.  By contrast, the typical intermediate algebra course presents a conflicted approach: students must show higher levels of symbolic mastery before enrolling but then intermediate algebra reviews many of those skills (without directly dealing with the development of reasoning directly).

More students are able to begin an Algebraic Literacy course than a typical intermediate algebra course.

CONTENT

1. Numbers and Polynomials
2. Functions
3. Geometry and Trigonometry
4. Modeling and Statistics
The content is intended to be integrated and connected.

In the Algebraic Literacy course, we would not see a chapter on “radicals and rational exponents”; we might see a section dealing with fractional exponents in an early sequence dealing with functions, including an application in half-life models … and a later section working on radical notation focusing on domain and range, followed by a section on translating between radical and exponential forms.  Either of these sequences of topics might also include geometry and/or trigonometry, and modeling concepts such as parameters.  Almost all topics will be presented as connected to one or more other topics, both conceptually and in terms of applications.

For most intermediate algebra courses, the content is usually 9 to 12 ‘chapters’ of material arbitrarily divided up … and separated.  A minimum of connections are made to other ‘chapters’.  Overall, the intermediate algebra course does not tell any story; the intermediate algebra course is a long series of vignettes only loosely connected by ‘category’.

By contrast, the Algebraic Literacy course tells a story of mathematical reasoning with both symbolic and application dialogues.  The design of the Algebraic Literacy course is based on being the first step along a path which includes calculus and/or other significant mathematics.  We seek to build covariational reasoning, a step up from Mathematical Literacy, on the path towards a good pre-calculus experience.

This field guide would not be accurate without  emphasizing a fundamental difference: Algebraic Literacy supports other STEM fields in addition to those needing the traditional Calculus Path.  This is primarily a distinction for the two-year college situation, where our programs often include mid-skill to high-skill fields (manufacturing technology, engineering technology, health careers, electronics, computer science, etc).  This inclusive approach is why Algebraic Literacy is not just algebra … geometry, basic trig, and statistics are included.  Most intermediate algebra includes some non-trivial geometry (right triangles, for example); however, you can recognize an Algebraic Literacy course by the presence of non-trivial geometric reasoning and symbolic representations, trig functions at a basic level, and enough statistics to interpret models developed from data.

Recognizing an Algebraic Literacy course involves multiple factors — goals, prerequisites, content, and the nature of the ‘story’.    A instinctive evaluation is based on this:

As a mathematician, can I get excited about teaching this course … is the focus on good mathematics, with the goal of developing abilities as opposed to “Algebra II all over again”?

We will see colleges move in this direction; I hope that you will consider joining the work!

 
Join Dev Math Revival on Facebook:

Acceleration, Pathways, and the Forum on the First 2 Years of College Mathematics

I will be posting more about the actual “CBMS Forum” (Conference Board of Mathematical Sciences) held earlier this month in Reston, Virginia; several of the talks made relevant points about our work.

One of the breakout sessions was a one-of-a-kind: A single session covering all three models for pathways and acceleration (Carnegie Pathways, Dana Center New Mathways, and AMATYC New Life).  You can view the slides for that session here CBMS Pathways to Success Oct 2014 or at the “Instant Presentations” page (https://www.devmathrevival.net/?page_id=116).   The three of us (Bernadine Fong of Carnegie, Uri Treisman of the Dana Center, and myself) were impressed by the standing-room only crowds at both of our sessions.

Much of the motivation for faculty and colleges falls under the heading of ‘acceleration’, which is fine.  However, my own view … and much of what I heard at the Forum … dealt with the nature of the mathematics courses we offer (developmental and ‘college’ mathematics).  Issues surrounding the curriculum will be the focus of my comments-to-come in response to “Forum 5”.

 Join Dev Math Revival on Facebook: