National Math Summit — Final Program

The final program has been set, for the National Math Summit next month (March 15-16, 2016 … Anaheim).  Summit Program 2016 feb 11 2016

If you are curious … I am part of a panel on the first day, and also am doing a session focused on the New Life Project at 8am on the second day.  That New Life session will include some specific implementation models for the first time.

Making Up For Twelve Years

How can we make up for what students did not get from twelve years of math?  Is it possible to have just one or two pre-college math courses, regardless of the entering level of students in a community college?  This is the big issue of our era, and the truth lies in a deeper understanding of the problems we face.  #CoRequisiteMath #NewLifeMath #CollegeMath

The origins of remedial mathematics, which formed developmental mathematics, are in the “college student” concepts of universities.  Being a college student meant that you had a solid high school academic background, and (almost coincidentally) meant that you could register for college algebra.  If a student could not show this high school background, remediation was used to fill it in.

This “college student” approach was originally based on the K-12 curriculum, which has never been very standardized in the USA.  Even with the recent Common Core, great variations exist.  The remediation provided, in mathematics, was usually a package that estimated the most common content as measured by topics and procedures.  We often referred to developmental courses as the “same as high school, only faster and LOUDER”.

In a basic way, remediation was done to estimate the desired college readiness measures (ACT, SAT); those measures, do correlate with placement in to college algebra.  The studies I’ve seen show correlation coefficients between 0.2 and 0.4; significant and meaningful, although these values indicate that only 5% to 15% of the variation is explained.

Meanwhile, we have no validation that the K-12 content as identified by topics and procedures has any causative connection to college mathematics success.  The entire set of them correlates somewhat, but we lack the professional validation of what members of the set (or a different set) are necessary.

Now, all of this means:

K-12 mathematics has a vague connection to readiness for college mathematics.

The conjecture we are exploring, in the current reform efforts, is that only some members of the K-12 math set are needed along with some members of another set (not taught in K-12).  [The reforms are the New Life Project, Dana Center New Mathways, and Carnege Pathways.]

In other words, the issue is not “making up for twelve years”.  The issues involve the particular abilities needed for success in specific college math courses.  Perhaps it really does not matter if a student can not tell me what 8*9 is, or what -4 + (-2) is; perhaps it is more important that students can reason about numbers and quantities at a level necessary for the college course.

In the current reform work, we in the New Life Project have identified some prerequisite learning outcomes needed before our first course (Math Literacy).  Here is what our document states:

Prerequisites to MLCS Course:
Limited quantitative skills are required prior to the MLCS course. Students should be able to do the following prior to this course:

• Understand various meanings for basic operations, including relating each to diverse contextual situations
• Use arithmetic operations to solve stated problems (with and without the aid of technology)
• Order real numbers across types (decimal, fractional, and percent), including correct placement on a number line
• Use number sense and estimation to determine the reasonableness of an answer
• Apply understandings of signed-numbers (integers in particular)

The New Life Project recommends that students be provided any needed instruction for these areas in either a short-term format (‘boot-camp’) or just-in-time (within the course).

These outcomes are vague, because we did not engineer down to the details.  My college is about to begin this process for a new version of our Math Lit course; our initial estimate is that we will need something like 20 hours of class time (perhaps 30) to help students develop the necessary abilities.  We do not have a goal of making up for twelve years … that goal is both unrealistic and not productive.  Instead, we will work on the much smaller set of “what does the student need to succeed in THIS course”.

The same conjecture would extend to other levels.  Whether it is Algebraic Literacy or Intermediate Algebra, what abilities does the student need?  The New Life Project suggests that the Math Literacy course is a good match.  For college algebra needs, the Algebraic Litercay course was designed to provide the abilities needed.

“Covering twelve years” is a bad solution to the wrong problem.  Student readiness for particular math courses is not a matter of ‘twelve years’ … it is a matter of specific abilities, and dealing with those is much more efficient.

Do not confuse these comments with support for “co-requisite remediation”.  Co-requisite remediation takes the extreme step of saying that essentially all students can start a college math course with enough support.  My position is that some portion can do this (more than we might think) … but taking the extreme position of co-requisite remediation is foolish and lacks the professional judgment that we are supposed to apply to our work.

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Skills, Abilities, and Readiness

So, I’ve been thinking about “replacing them all” (a recent post here), and wondering what types of reactions that idea would receive.  Do the old courses have something valuable?  Would we harm students by getting rid of them?  #NewLifeMath #SaveMath

Not all implementations of arithmetic, pre-algebra, beginning algebra and intermediate algebra are equivalent to other implementations of those courses.  Certainly, some instructors (and perhaps some institutions) deliver a course that is qualitatively different from the accepted norms for those courses.

However, the norms for those 4 courses essentially define the courses as:

The student will use n procedures to get correct answers in the topics ________.

The courses are designed to maximize the value of n, often while maximizing the list of topics.  Our textbooks reflect these priorities; in fact, many of our courses are set up so that there is no textbook — just the class and the online homework.

Part of this set of norms is a fact that the New Life Project has focused on since the beginning.

Most commonly, developmental mathematics is taught by adjunct instructors.

The problem here is not the employment status of adjuncts.  The biggest problems deal with support for adjuncts and expectations — adjunct faculty do not receive the same level of support as full-time, and adjuncts are expected (in general) to follow the normal expectations.  For us to make any significant improvements, this pattern needs to be broken.

As long as we offer the traditional courses, there will be a very strong trend towards doing exactly what we’ve been doing — focus on skills, measure by correct answers, and avoid reasoning.  The traditional dev math courses produce completers who are the same as the starters, except for a finite number of specific skills which tend to be forgotten before they can be used again.

The reform dev math courses (all similar to the New Life courses at this basic level) focus on student abilities (reasoning in particular) along with a focus on strategically chosen skills.  The courses are qualitatively different in several ways.

Adjunct faculty can certainly teach Math Literacy and Algebraic Literacy.  However, in most cases, this will require an increase in institutional support in professional development.  Our hope is that this will become “the new normal”, which will tend to integrate adjunct faculty more completely into the math department.

We’ve approached “readiness” as a check-list of skills … frequently including far too many ‘skill’s … with no emphasis on reasoning abilities.  Skills can be quickly reviewed, as needed — IF the student has the reasoning to support it.  Reasoning is the ability that can not be ‘reviewed’.

The traditional dev math courses, with their focus on skills, provide such a limited benefit to students that we can safely replace them.  This is especially true if their replacements are engineered to develop a healthy combination of reasoning and skills, which the New Life courses do.

This change from ‘old’ to ‘new’ is more of a problem for us, than our students.  Are we ready to offer math courses which focus on central ideas and reasoning?  Can we give up the ‘easy’ path of doing the same old stuff?  This change issue is true for all college mathematics in the first two years; external forces are causing us to start with developmental courses, though pre-calculus and calculus courses will go through similar changes.

We are not changing “for changes sake”.  We are changing for the sake of our students … we are are changing to save mathematics.

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Time to Replace Them All (dev math courses)

My college is undertaking a major change, motivated in some ways by applying the federal financial rules about remediation with integrity:  courses need to be at least at the high school level in order to be included in a student’s financial aid load.  I’m also getting ready for the National Math Summit (next month, Anaheim).

When we began the New Life Project back in 2009, the core group working on the curriculum stated that there was no need for a course prior to Math Literacy … that Math Literacy can replace beginning algebra for ALL students (STEM and non-STEM) … and that Algebraic Literacy can replace intermediate algebra.  Since that time, more has been understood about the college algebra/pre-calculus curriculum and problems.

So, here is an updated curricular map that puts this together:

The small box at the start of this image represents a non-course preparation for Math Literacy.  My college is exploring the other option — including the needed prerequisites within the Math Literacy course.  We have not made any decisions, though we are going to do something along these lines.  At this point, we will not offer any arithmetic nor pre-algebra course.

One of the changes in the map is the courses after Algebraic Literacy.  The original map made reference to reform college algebra (for general education).  However, the recent discussions have focused more on revising pre-calculus to be a modern course … so the map uses that terminology, and maintains the college algebra ‘box’ for the non-calculus paths.

Several colleges are known to be ahead of my college on this path — some have totally replaced their dev math sequence with the Math Lit and Algebraic Lit courses.  More have replaced beginning algebra with Math Lit, and would consider replacing intermediate algebra with Algebraic Literacy if the materials were readily available.

I want to remind all of us that one of the goals of our Project was to replace the old courses for all students.  STEM-bound students deserve the good stuff in Math Literacy.

In my presentation at the National Math Summit, I will be sharing data on how (poorly) the beginning algebra course serves students.  The data on this question is glaring, and should encourage more of us to walk down this path of ‘replacement’.  The data on intermediate algebra is also consistent with the goal of replacing the old courses (though the data is not as ‘bad’).

The up-to-date information on the National Math Summit is available at http://www.nade2016.net/math-summit.html  As of the first of this week, registration is still open (the event has a definite maximum).

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