Reform in Developmental Mathematics — Three Models

If you are looking for current information on reform models in developmental mathematics, here it is.

If you’d like to download this as a PDF file, click here: Summary of Three Emerging Models for Developmental Mathematics

The New Life “MLCS” course has updated information in this chart.  Specifically:  New textbooks are being published later this year (Pearson) and early next year (McGraw Hill).  The chart also now uses the Algebraic Literacy title for the second course.  In the Dana Center New Mathways information, some updates are also included.

 Join Dev Math Revival on Facebook:

Exponential Attrition in Mathematics

One of the motivations behind current reform efforts — especially in developmental mathematics — is the negative impact of long sequences of courses, regardless of individual pass rates within the sequence.  This negative impact is often summarized by the concept of exponential attrition, and is a cousin to basic probability:

The probability for a sequence of (relatively independent) events is the product of the probabilities for each event.

The probability concepts provide a more subtle way of looking at the problem.  Let’s take the simplest possible sequence — two courses.  There are three events involved:

1. Course A
2. Transition to Course B
3. Course B

Clearly, there is an event (or multiple events) prior to Course A.  However, those factors deal with systematic factors generally outside of the mathematics curriculum.  Event 2 is a retention or continuation measure, subject to impacts from within the mathematics curriculum.  However, this transition is an event with a probability less than 1.

For a two-course sequence at my college, the approximate values for the probabilities are:  .68, .75, and .55.  The product of these probabilities is about .28; approximately 28% of students starting in course A will pass course B .  In this case, the conditional probability in course B hurts; however, even if the probability in course B is equal to the pass rate of that course, the result is only a little higher — 33% in our case.

For students placed one level lower, they have a 3-course sequence with 5 probabilities:

For a three-course sequence at my college, the approximate values for the probabilities are: .65, .80, .58, .70, and .64, which have a product of about .15 — approximately 15% of students starting in this course A will pass course C.  [The ‘course A’ in this sequence is not the same as ‘course A’ in the prior sequence.]

When our department did a 3-year study following students in a 3-course sequence, we came up with a net rate of 18% (compared to the theoretical value of 15%).  The difference was caused by some additional students who repeated and passed one or more of the 3 courses.

Clearly, the primary method to reduce this net probability — the negative impact of exponential attrition — is to eliminate events in the sequence.  Some acceleration models seek to eliminate transition events — two classes combined into one semester; in some designs, this truly does produce a unitary value for the transition event (100% move from course A to course B).  However, the majority of students probably can not manage a doubling-up like this where they have 6 or 8 (or even 10) credits of math in one semester; this combination model also creates challenges for math departments — small and large.

Another approach is to eliminate the need for a given student to take course A.  In some cases, this is done by state mandate.  More professionally valid solutions involve early testing and intervention programs like El Paso Community College (see http://achievingthedream.org/college_profile/el_paso_community_college ) or boot camps.  Some of these models eliminate both course A and the transition event; most eliminate course A and still have the transition event to course B.  Some other models are described at the California Acceleration Project (see http://cap.3csn.org/ )

The New Life model seeks to eliminate courses from the general sequence and from a given student’s sequence.  A ‘typical’ student faces a 3-course sequence such as beginning algebra, intermediate algebra and then a college-credit math class.  In the New Life model, this 3-course sequence would often be a 2-course sequence (saving 2 events in the probabilities).

For more information on the New Life model, take a look at the Instant Presentations page (https://www.devmathrevival.net/?page_id=116)

 Join Dev Math Revival on Facebook:

Everything I Needed to Know About Math … Learned in 8th Grade?

Various organizations have been issuing reports critical of developmental education, and developmental mathematics in particular.  Those ‘studies’ tend to be repeated and quoted and cited … until everybody assumes that the conclusions are true.

Well, a similar thing happens with the content.  We had an ‘algebra II for everybody’ flurry, and we are starting to see the ‘algebra II for a lot less’ movement.  One recent report is being used to say that the math that students need in life is generally taught in 8th grade — fractions, rates, proportions, and simple equations http://chronicle.com/article/High-Schools-Set-Up/139105/ ).  Of course, if we read the original source for this article (see http://www.ncee.org/wp-content/uploads/2013/05/NCEE_MathReport_May20131.pdf ) the conclusions are much more subtle; the source actually says that students need conceptually understanding in general, and list ‘functions’ as a needed topic — and mentions complex measurement ideas and geometric visualizations.

In many ways, the actual source (at the National Center on Education and the Economy) is very consistent with what we found in the New Life project.  The ingredients of Math Lit (MLCS) are based on a very similar list of quantitative needs in occupations and client disciplines at the basic level.  I encourage you to read their math report (link given above at NCEE).

The worry, however, is that people will remember the articles talking about the study; that people will see that story line repeated enough that we begin to believe that it has to be true.

We need to keep our voices in the public conversation so that policy makers hear a more informed point of view, one based on professional expertise and information about what students really need in college for mathematics.

No, Virginia, students do not just need 8th grade math in life.  Many college programs will involve courses which depend on other quantitative abilities, and many occupations involve more than just 8th grade math.

 Join Dev Math Revival on Facebook:

Algebraic Literacy: Finding a Textbook

One of the new courses coming to a college near you is “Algebraic Literacy”, a modern course that prepares students for a STEM path (and related work).  This position in the traditional curriculum is held by ‘intermediate algebra’.

For a brief comparison of these courses, see the chart below:

In this chart, “MLCS” refers to the Mathematical Literacy for College Students course (also known as Math Lit, and similar to Quantway I).

One of the issues with the Algebraic Literacy course is finding textbook materials.  Books being written for this course are not available yet.  However, there are materials available which have enough similarity to be used.

One book I have learned about recently is “Algebra: Form and Function” (Wiley publishing, 2010).  This book was written by a team connected with the calculus reform efforts, and is designated as a ‘college algebra’ textbook.  However, the book does not assume that students have the higher background; it’s quite accessible by students in an Algebraic Literacy course.  For a quick look, see this link to the Course Smart page:  http://instructors.coursesmart.com/9780471707080

You can also find more information on this text at the Wiley page http://www.wiley.com/WileyCDA/WileyTitle/productCd-EHEP000346.html

 
Join Dev Math Revival on Facebook: