New Life Project presentation at National Math Summit (March 2016)

The New Life session (at the 2nd National Math Summit) involves these materials.

• Presentation slides:  AMATYC New Life Project NADE Math Summit March 2016
• References:  References NewLife NMS 2016
• Implementation Maps and curriculum:  Implementation Maps AMATYC New Life Project 2016
• Math Literacy Learning Outcomes:  MLCS Goals and Outcomes Oct2013 cross referenced 2 by 2
• Algebraic Literacy Learning Outcomes: Algebraic Literacy Goals and Outcomes Oct2013 cross referenced 2 by 2

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Discovery Learning versus Good Learning

As people look at improving mathematics courses in college, we tend to look at some methodologies as naturally superior to others; we often fall in to the trap of criticizing faculty who use “ineffective” methods (traditional ones).  Some of my discomfort with the current reform efforts in developmental mathematics is the focus on one category of teaching methods … discovery learning.  #CollegeMath

At the heart of the attraction for discovery learning (and it’s cousins) is a very good thing — an active classroom with students engaged with the material.  It’s no surprise to find that research on learning generally concludes that this type of active involvement is one of the necessary conditions for students learning the material (in any discipline).  We can find numerous studies that show that a passive learning environment results in low learning results for the majority of students.  One such study is “The Effects of Discovery Learning on Students’ Success and Inquiry Learning Skills” by Balim (http://wiki.astrowish.net/images/e/e1/QCY520_Desmond_J1.pdf). In this study, the control group was (perhaps intentionally) very passive; of course, discovery learning produces better results.

It feels good to have our students engaged with mathematics.  By itself, however, that engagement does not produce good learning.  Take a look at a nice article “Correcting a Metacognitive Error: Feedback Increases Retention of Low-Confidence Correct Responses” by Butler et al (http://psych.wustl.edu/memory/Roddy%20article%20PDF’s/Butler%20et%20al%20%282008%29_JEPLMC.pdf) The role of feedback is critical to learning, but most implementations of discovery learning suggest that the teacher not intervene (or even correct errors).

Good learning does not happen from constantly applying one teaching method; teaching needs to be intentional, and modern teaching tends to be diverse to the extent that our work is research based.  I can see the benefits of incorporating some discovery learning activities within a class, along with other teaching modes.  See a study of this for college biology “The Effects Of Discovery Learning In A Lower-Division Biology Course” by Wilke & Straits (http://advan.physiology.org/content/25/2/62)

I use some discovery learning activities in my classes, and have found that I need to be very careful with them.  Here is my observation:

When students are asked to figure something out, they tend to apply similar information they have (correct or erroneous) and the process tends to reinforce that prior learning.

For example, I use an activity in my intermediate algebra class to help students understand rational expressions at a basic level — focusing on the fraction bar as a grouping symbol and on “what reduces”.  The activity provides a structured sequence of questions for a small group to answer.  Each group tends to use incorrect prior learning, even when the group is diverse in terms of course performance.  Even the better students have enough doubts about their math that they will listen to the bad ideas shared by their team; the only way for me to avoid that damage is to be with each group at the right time.

So, I have taken the discovery out of this activity; I now do the activity as a class, with students engaged as much as possible.  Even when done in small groups, students tend to not really be engaged with the activity.

I notice that same self-reinforcing bad knowledge in our quantitative reasoning course.  I use an activity there focused on the basics of percent relationships — percents need a base, and percent change is relative to 100%.  Many students do not understand percents, and the groups tend to reinforce incorrect ideas.  I continue to use that particular activity, as the class tends to be a little smaller; I am able to work with each group, during the activity.

Some of the curriculum used in the reformed courses are intensely discovery learning (often with high-context).  We need to avoid the use of one methodology as our primary pedagogy.  Do not confuse the basic message of replacing the traditional math courses with the pedagogical focus used in some materials.  To achieve “scale” and stability, our teaching methods need to be more diverse.

 
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Avoiding the Beginning Algebra Penalty

The most commonly taken math course in two-year colleges is beginning algebra; if we select a math student at random, there is a 21% probability that they are enrolled in a beginning algebra course.  On average, taking a beginning algebra course either does not improve the odds of passing intermediate algebra … or actually decreases the odds of passing.  #NewLifeMath #MathLiteracy

According to the 2010 Conference Board of Mathematical Sciences report (CMBS, http://www.ams.org/profession/data/cbms-survey/cbms2010-Report.pdf) about 428,000 students enrolled in a beginning algebra course at community colleges, compared to a total of 2.02 million enrolled.  The next most common enrollment was intermediate algebra (344K) followed by college algebra (230K) and pre-algebra (226K).  These extreme enrollments in courses in a long sequence have got to stop … see other posts on ‘exponential attrition’.

The main point today is this:

Evidence suggests that students incur a penalty when they enroll in a beginning algebra course.

Progression data is difficult to obtain, at the cross-institution level.  When the progression data is available, the format is often an overly simplistic comparison of those who placed at level N compared to those who took course N-1 then course N.  These summaries provide little information about the results of course N-1 (beginning algebra in this case).  At my institution, for example, those taking beginning algebra prior to intermediate algebra have a slightly higher pass rate in intermediate algebra compared to the course average.

However, this data is not research on the impact of beginning algebra.  Fortunately, our friends at ACT routinely conduct research on various components of the college curriculum.  In 2013, ACT released a research study on developmental education effectiveness (see http://www.act.org/content/dam/act/unsecured/documents/ACT_RR2013-1.pdf).  This ACT study used a regression discontinuity method, with a very large sample (over 100K), to examine the impact of taking certain courses with ACT Math score as a basic variable.  Since most two-year institutions do not use ACT Math as a placement test (at this level), their sample included large numbers of students at varying levels … a portion of which took beginning algebra first then intermediate algebra, and a portion which took intermediate algebra only.

The results were strong and negative:

The ‘dashed’ lines are students taking beginning algebra prior to intermediate algebra.  The upper set of lines represents ‘receiving a C or better in intermediate algebra.  For all ACT Math scores, the data suggests that students would be better served by placing them in to intermediate algebra (6% or higher probability of success, regardless of ACT Math score).

This is not what we want, at all; our personal experience might suggest that reality is different from this research study.  I believe that the research study is accurate, and that our own perceptions are misleading about generalities.

What strikes me about this research is that the results form a consistent pattern even though we lack a standard for what is ‘beginning algebra’ and what is ‘intermediate algebra’.  In some states, this is defined by a governing body; overall, though, we have operational definitions — beginning algebra is a course called beginning algebra, using a book titled beginning algebra.

Both courses (beginning and intermediate algebra) are heavily skill and procedure based,  organized around discrete chapters and sections.  In practice, intermediate algebra involves enough complexity that some understanding is required … while beginning algebra tends to reward memorization techniques.  To me, the research findings make sense

We need to avoid the beginning algebra penalty by replacing beginning algebra with a modern course that builds reasoning (like Mathematical Literacy).  Students are ill-served when we ‘keep it simple’ … students are not prepared for the future, and we also reinforce negative messages about mathematics (“I am not a math person”).  As long as we teach beginning algebra, we harm our students — we help some, but harm a larger group.

The beginning algebra course is beyond rescue; no amount of tweaking and micro-improvements will result in any significant improvement.  It’s time to start over.

At my institution, we are expecting that our beginning algebra course will decrease over the next few years while Math Literacy grows.  [We also expect to move away from intermediate algebra, but that might take longer.]  I know of other institutions, like Parkland College in Illinois, which have gone further on this path.

What is your plan for getting rid of beginning algebra at your institution?

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What is Co-Requisite Remediation?

Several posts here have involved a critique of “Co-Requisite Remediation”, which usually results in questions of “what do you mean by co-requisite remediation?”  Let’s take a look at what is usually meant by the phrase.  #CCA #Corequisite #SaveMath

The first thing to know about corequisite remediation is that it is a new and ill-defined phrase.  Before about 2011, corequisite remediation was a micro strategy — to help with specific weaknesses, a course would include focused remediation within a limited portion of the class.  Most math faculty do remediation within courses, and this initial use of the phrase ‘corequisite remediation’ seems to have been an effort to focus on this work to support collaboration across institutions.

Within the past 5 years, the phrase “corequisite remediation” has been almost exclusively being used by Complete College America (CCA) and their co-conspirators.  The methodologies they suggest are goal-driven, which means that the actual practice is ill-defined.  That goal is:

Place students directly into college-level courses instead of developmental course(s) followed by college-level.  http://completecollege.org/tag/corequisite-remediation/

The CCA agents have been very effective at using their rhetoric to support this ‘method’; unfortunately, for us practitioners, corequisite remediation is implemented in such diverse ways that we have small probabilities of interpreting the results in practical ways.  Further complicating our interpretation is the fact that the CCA agents will report that the “results are in” and “data supports” co-requisite remediation.

Sadly, we find  ourselves in the situation where almost all supporters of corequisite remediation are policy makers or administrators, while the majority of practitioners are skeptical or ‘non-believers’.  Neither side can convince the other, as long as the problem is ill-defined and we lack practical research on various methodologies used.

Like I said, corequisite remediation is a goal statement, not a single method.  Here are some common implementation patterns:

• Students in gen ed math (statistics or quantitative reasoning) who did not place at that level are required to register for a second class — a class providing the remediation.
• Students in gen ed math who did not place at that level are required to register for special sections of the course which incorporate additional time for the remediation.
• Students in gen ed math who did not place at that level are required to complete a remediation workshop (before the semester, during the first week or two).

In general, (1) The methods for remediation are not uniform and often not shared, and (2) pre-calculus is almost never used.  And, although I use the tag “quantitative reasoning”, the course is sometimes liberal arts math or an everyday-math type.

So, the corequisite remediation targets college-level math courses which tend to have a smaller set of prerequisite abilities.  Intro statistics is a course widely believed to have minimal requirements on the behalf of students; the liberal arts math course is often very similar in the demands for ‘skills’.  In most cases, the prerequisite was intermediate algebra or comparable test level.  Therefore:

Co-requisite remediation is often used for courses which have had an artificially high prerequisite in the past.

Separate from the remediation issues, we should correct our prerequisites for college math courses.  AMATYC has a position statement on this … see http://www.amatyc.org/?page=PositionInterAlg

I suspect that we will begin to see presentations at our conferences (AMATYC and affiliates) documenting the practices and results of co-requisite remediation; that will help the rest of us make an informed judgment on any possible validity.  I do not expect any “gold standard” research in this area (randomized, controlled studies which can be replicated), due to the politicized context.

Perhaps this has helped a little.  I remain a skeptic of the rhetoric surrounding corequisite remediation.

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