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:
New Math Pathways General Vision 2 5 16











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  As of the first of this week, registration is still open (the event has a definite maximum).

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Developing Grit and Recognizing Grit

One of the recent emphases in education, especially college mathematics, is ‘student grit’.  Grit is what allows students to succeed when there are barriers, and we can recognize success (usually).  However, the concept of grit is not productive unless we can recognize and develop grit prior to that point.  #gritmath

The context for this post is a recent test in our quantitative reasoning course (Math119).  Our first set of topics dealt with dimensional analysis; every conversion in class was completed by that method.  Overall, students did about as well as I’ve seen.

However, some students did their work in an indirect fashion.  Take a look at this first example:




And, this example:





In both cases, many of our math classes would say “Just move the decimal point”.  I did have a few students complete the problem that way.

More importantly, many of us would tell these students that their method is wrong.  However, the first example is conceptually perfect; the error in the answer is strictly due to the rounding of the conversion facts.  The second example is also pretty good … except for the inversion of a basic conversion.

I think both students showed significant ‘grit’ in working these problems.  Although I don’t generally want students to do a problem in a complicated way when a simpler way exists, it is impressive that both students were able to salvage a problem begun in a non-standard way.

I’m not suggesting that any grit shown in these two cases is equivalent to the level needed to complete a math course.  However, I do think that developing grit is the same as developing other traits:  We start small, make it explicit, and practice.

One of the wonderful things about a good quantitative reasoning course is that there is a focus on non-standard problems.  Methods are emphasized, but we don’t focus on procedure as much as we do reasoning.  This environment lets students explore and develop in ways that traditional math courses don’t.

I suspect that our traditional math courses either discourage grit or prevent much development.  With such a strong focus on procedures and correct answers, students are often doing the ‘instructor dance’ — following steps because it will please the instructor.  Student traits can not develop in a overly structured environment.

It is important that we recognize the difference between “incorrect thinking” and “different thinking”.  Different thinking is part of trait development, like grit.  Students can not show, nor develop, grit unless I provide them opportunities to work differently.

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National Math Summit … final schedule & session information

Next month, many of us will be in Anaheim (March 15-16) for the second National Math Summit; the first summit (2013) had the word “developmental” in the title, and that is still the primary intent for this year.

The organizers have released what will likely be the finalized schedule and session information.

Sessions:  NMS Strand Presentations R for Web Display Final version 1-27-16

Schedule:  National Mathematic Summit Tentative SchR2

I’m involved with two sessions.  On the first day, there is a panel of dev math reform, where I will be joined by 3 respected colleagues (Brian Mercer from Illinois, Kim Granger from Missouri, and Laura Bracken from Idaho).  The four of us have experience with reform, and also have state policy changes to discuss.

On the second day, I am doing a brand new presentation on the New Life model for developmental mathematics.  In this presentation, I will connect this work with broader changes in college mathematics.  A highlight will be some models for implementing the courses (Mathematical Literacy, Algebraic Literacy) to fit the local needs.

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