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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Mathematical Literacy WITHOUT a Prerequisite

Starting this Fall (August 2016) my department will begin offering a second version of our Mathematical Literacy course.  Our original Math Lit course has a prerequisite similar to beginning algebra (it’s just a little lower).  The new course will have NO math prerequisites.

So, here is the story: Last year, we were asked to classify each math course as “remedial, secondary level”  or “remedial, elementary level” or neither.  This request originates with the financial aid office, which is charged with implementing federal regulations which use those classifications.  Our answer was that our pre-algebra course was “remedial, elementary level” because the overwhelming majority of the content corresponded to the middle of the elementary range (K-8).  We used the Common Core and the state curriculum standards for this determination, though the result would be the same with any reference standard.

Since students can not count “remedial, elementary level” for their financial aid enrollment status, our decision had a sequence of consequences.  One of those results was that our pre-algebra course was eliminated; our last students to ever take pre-algebra at my college finished the course this week.

We could not, of course, leave the situation like that — we would have no option for students who could not qualify for our original Math Literacy course (hundreds of students per year).  Originally, we proposed a zero credit replacement course.  That course was not approved.

Our original Math Literacy course is Math105.  We (quickly!) developed a second version … Math106 “Mathematical Literacy with REVIEW”.  Math106 has no math prerequisite at all.  (It’s actually got a maximum, not a minimum … students who qualify for beginning algebra can not register for Math106.)  The only prerequisites for Math106 are language skills — college level reading (approximately) and minimal writing skills.

Currently, we are designing the curriculum to be delivered in Math106.  We are starting with some ‘extra’ class time (6 hours per week instead of 4) and hope to have tutors in the classroom.  Don’t ask how the class is going because it has not started yet.  I can tell you that we are essentially implementing the MLCS course with coverage of the prerequisite skills, based on the New Life Project course goals & outcomes.

We do hope to do a presentation at our state affiliate conference (MichMATYC, at Delta College on October 15).  I would have submitted a presentation proposal for AMATYC, but all of the work on Math106 occurred well after the deadline of Feb 1.

One of the reasons I am posting this is to say: I am very proud of my math colleagues here at LCC who are showing their commitment to students with courage and creativity.  We will deliver a course starting August 25 which did not exist anywhere on February 1 of this year.

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Placement for a Modern Curriculum: A Fresh Start

The college mathematics profession has been dealing with a number of criticisms of how students are placed in their initial mathematics course.  Even before recent curricular changes, evidence suggested that the tests used for placement were likely to under-place students; a modern curriculum focusing on reasoning as well as procedure increases that placement struggle.  I’ve been working on a fresh start, and I am ready to share an initial version of a new assessment that might help solve both dimensions of the problem.

First, we need to understand the legacy of the current placement tests.  The genetic background of both Accuplacer and Compass is firmly grounded in the basic skills movements of the 1980s.  Specifically, Accuplacer grew out of instruments such as the New Jersey Basic Skills test.  The primary goal during that era was “fix all of the skills that students might lack”; the only reasoning typically included was word problems, with perhaps a bit of estimation.

Our placement needs have shifted greatly since that time.  Courses like Mathematical Literacy (and siblings Quantway [Carnegie Foundation] and Foundations of Mathematical Reasoning [Dana Center]) depend less on procedural skills like those found on placement tests; rather, the issues lie in the answers to this question:

What mathematics is this student capable of learning now?

As a coincidental benefit of the New Life Project, we have information on what these prerequisite abilities should be.  In the design of Mathematical Literacy (ML) and Algebraic Literacy (AL), our teams articulated a list of these prerequisite outcomes:

• Mathematical Literacy prerequisite outcomes:
  1. Understand various meanings for basic operations, including relating each to
  diverse contextual situations
  2. Use arithmetic operations to solve stated problems (with and without the aid
  of technology)
  3. Order real numbers across types (decimal, fractional, and percent), including
  correct placement on a number line
  4. Use number sense and estimation to determine the reasonableness of an
  answer
  5. Apply understandings of signed-numbers (integers in particular)
• Algebraic Literacy prerequisite outcomes:
  1. Understand proportional relationships in a variety of settings, including paired data and graphs.
  2. Apply properties of algebraic expressions, including distributing, like terms, and integer exponents.
  3. Construct equations and inequalities to represent relationships
  4. Understand how to solve linear equations by reasoning
  5. Understand how to write and use linear and exponential functions

Using these 10 outcomes, I’ve written a “Mathematical Literacy Placement Assessment” (MLPA).  The draft 0.5 of the MLPA has 30 items, with slightly more than half on the AL prerequisites.  Here is the MLPA:

Mathematical Literacy Placement Assessment 2016 version 0.5

Note two things about the MLPA:  (1) the copyright license is Creative Commons by Attribution (you can use it, as long as you state the owner [Jack Rotman] … you can even modify it; (2) the MLPA has not been validated in any way … any use should begin with preliminary validation followed by improvements to the assessment.  In case you are not familiar with the Creative Commons by Attribution license, it allows others to both use and modify the material, as long as the attribution is provided.

The intent of the MLPA is to provide a modern assessment of students who might need a Math Literacy course.  The initial 12 items are prerequisites to that course, so a score on those 12 provides a measure (with reliability and validity to be determined) of a student’s readiness for Math Literacy.  The other 18 items are intended to assess whether the student needs the Math Literacy course; a score on those 18 items would indicate whether the student is ready for an Algebraic Literacy course (or possibly intermediate algebra).

If the MLPA has content validity, we would expect a significant but small correlation with other placement results (Accuplacer, Compass) — because the MLPA is intended to measure different properties than those assessments.  The content validity would need to be established directly, possibly by use in Math Literacy courses (as a pre-test and post-test).  Variations in the two sections of the MLPA should be highly correlated to the students’ work in the Math Lit course.

My goal in developing the MLPA version 0.5 is to provide a starting point for the community of practitioners — both mathematics faculty and companies involved in testing.  Ideally, people involved in this work would collaborate so that an improved MLPA would be available to others.  The hope is that many different institutions and organizations will become involved in developing– and using — a useful modern placement test, which would benefit both colleges and students.

If you would like an MS Word document of the MLPA, please send me a direct email; you are also free to work from the “pdf” version posted above.

Implementing Better Math Courses, Part II: Helping All Students

The traditional developmental math curriculum generally fails the mission to help students succeed in college mathematics; this failure is due to both exponential attrition (too many courses) and to an obsolete curriculum.  In this post, I will describe a specific implementation plan that addresses these problems for ALL students.  #NewLifeMath

I call this implementation “medium” because it goes beyond the low results of pathways models.  The next level of implementation involves eliminating all courses prior to the beginning algebra level … and replacing beginning algebra with Math Literacy for College Students.

Here is an image of this implementation:

This implementation means that the majority of students can have a maximum of one pre-college math course (developmental level), since most students do not need to take a pre-calculus course.  The Math Lit course was designed to serve the needs of all students — STEM and not-STEM; even though many of the initial uses of Math Lit were in pathways implementations, the course is much more powerful than that limited usage.

Doing this medium implementation results in significant benefits to students.  In order to make this work, the institution needs to address interface issues — both prior to Math Lit and after Math Lit.

Math Lit has a limited set of prerequisite knowledge that enables more students to succeed, compared to a beginning algebra course.  However, this set is not trivial.  Institutions doing a medium implementation will need to address remediation ‘prior’ to Math Lit for 20% to 40% of the population in the course.  One methodology to meet this need is to offer boot-camps prior to the semester, or during the first week.  The other method (which my institution is starting this fall) is to embed the remediation within the Math Lit course; in our case, we are creating a second version of Math Lit for 6 credits (with remediation) to run parallel to our 4-credit Math Lit course.

After Math Lit in this model, there is an interface with intermediate algebra.  At some institutions, this will work just fine … because the intermediate algebra course includes sufficient review of basic algebra.  In other institutions, some adjustments in intermediate algebra are needed.  My own institution is playing this safe for now … after Math Lit, students can take a ‘fast track’ algebra course that covers both beginning and intermediate algebra.  I don’t expect our structure to be long-standing, for a variety of reasons (most importantly, that we are likely to reach for the next level of implementation where intermediate algebra is replaced by algebraic literacy).

I suspect a common response to this implementation model is something like “this will not provide enough algebra skills for STEM”.  I would point out two factors that might help deal with this apparent problem:

1. Taking beginning algebra prior to intermediate algebra is currently associated with lower pass rates (controlling for ACT Math score).  [See https://www.devmathrevival.net/?p=2412]
2. The basic issue for STEM students is not skills — it is reasoning.  [See AMATYC Beyond Crossroads http://beyondcrossroads.matyc.org/   and the MAA CRAFTY work http://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/crafty ]

This medium implementation model is conceptually similar to the Dana Center New Mathways Project, where they follow up their adaptation of Math Lit (“FMR”) with their STEM path courses.  Like them, we have confidence based on professional work over a period of decades that this implementation model will succeed.

In a pathways model, only those students who are going to take statistics or quantitative reasoning get the benefits of a modern math course.  In the medium implementation, this set of benefits is provided to ALL students.  In addition, the medium implementation eliminates the penalties of having more than 2 developmental math courses in the curriculum, by dropping all courses prior to Math Lit.  The result is that the majority of students will have 1 (or zero) developmental math course, with improved preparation as well.

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