This blog is officially ‘inactive’ as far as new posts and comments are concerned.  This ‘prologue’ post is my final commentary. Goals and intentions: When the three major professional efforts to change developmental mathematics began in 2009 (AMATYC’s New Life Project, Carnegie Foundation’s “Quantway & Statway”, and the Dana Center’s “Math Pathways”) people in the profession of developmental mathematics were facing a unique combination of opportunities and external forces.  This blog was begun with a goal of supporting fellow faculty members in their adaptations and challenges.  The word ..read more

What SHOULD we teach?  How SHOULD we teach? Those questions underlie discussions of professional standards.  In fact, AMATYC had a new project in the early 1990s with the acronym “CPR” — Curriculum and Pedagogical Reform for the first two years (sometimes listed as “CPR-MATYC” to emphasize the AMATYC connection).  The leaders of this work were knowledgeable professionals at the forefront of college mathematics who wanted to provide a set of standards that would help lead the practice of teaching college mathematics across the country.  The leaders knew that some elements of such standards woul ..read more

My department has been discussing the concept of ‘rigor’, which usually invokes some variant of ‘mathematical reasoning’.  Definitions of either concept often involve communication and flexibility, though our practices may not encourage any of this as much as we would like. In general, if a learner is simply showing the same behaviors (and mathematical analysis) that have been described … justified … and demonstrated during the class then I do not see much rigor.  Building mathematical reasoning involves exploring something new, and sometimes shows in failed attempts to solve a problem Of cour ..read more

How do we help students become ready for college mathematics?  How do avoid students earning credit for learning that should have occurred before college?  Perhaps our conceptualization of these problems is flawed in fundamental ways. As I write one of my final posts for this blog, I am pondering history and future … and the intersection called the present.  Some of this pondering has been pleasant reflection, while much of the pondering has been either professional regret or stimulating conjecture.  I hope to put some of each ‘pile’ in this post.           [Here, “common core” is a place-hol ..read more

We like to believe that taking a mathematics class (or statistics) will improve a student’s ability to solve ‘problems’ with quantitative properties.  A basic flaw with this belief is that most of us (as math educators) do not like to present actual problems to our students — a problem is a situation where the solution is not just to be remembered.  There is a basic element of “have not seen this before” in a problem situation; at one extreme we have exercises (where memory can retrieve exactly what needs to be done) and the other extreme we have non-standard problems (where the presentation i ..read more

People in the profession of education — including mathematics education — are prone to exhibit some common modes of reasoning.  We tend to value linearity within learning, compliant students, and evidence which supports our current outlook.  Until we overcome this bias in evidence, there is no hope to make real progress for our students.               A concept used in social science research (which is what education is) is ‘confirmation bias’.  Although the image above refers to ‘facts’, for our purposes the word ‘evidence’ might be a better fit (and I also include the phrase “established sc ..read more

When a person approaches the end of a job or career, whether as a transition to a new position or as a retirement, it is natural to examine and ponder what was accomplished.  Perhaps there were awards received, new products introduced (‘courses’ in the college world), or new processes developed (‘pedagogy’ in the college world). As I approach my ‘inflection point’ (retirement), my thoughts have been on similar matters.  However, I have a great colleague who asked an excellent question: What is YOUR legacy?           Most of us would like to reflect on a set of positive accomplishments, and mi ..read more

A few years back, my dean informed me that returning adult students wanted to know how their learning would be applied to their lives as opposed to understanding theory.  I was quite surprised by this statement, given all I’ve learned over the years; I had reached the conclusion that the more ‘seasoned’ students wanted to understand the why as well as the how and when.  This cognitive dissonance resulted in a non-discussion as the Dean would not believe my statements.  Of course, these generalizations (hers and mine) are seldom true over a broad range of situations.               This idea of ..read more

We are all familiar with ‘predictions’ based on societal trends which are seldom validated by reality — whether it is flying cars, Facebook’s “population”, or economic stability.  Predictions are often based on a presumption of continuity within the determining forces; people attempt to apply modeling concepts to an open (or semi-open) system.  As mathematicians and mathematics educators, however, we often fail to notice the interaction between forces impacting our curriculum.               At the collegiate level, the most dramatic example of such a disconnect is the course called “college a ..read more