As mathematicians and mathematics educators, however, we often fail to notice the interaction between forces impacting our curriculum.Īt the collegiate level, the most dramatic example of such a disconnect is the course called “college algebra”. 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. 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.
Do not let ‘alignment’ lock you in to an obsolete and harmful set of mathematics courses. Do not look to MAA and AMATYC to ‘tell us’ how and when … our organizations are too fearful of offending part of ‘us’.īuild local alliances to support experimentation in modernizing mathematics in college. College mathematics could be an exciting world for our students to explore with colorful vistas combining symbolic and computational methods supported by conceptual knowledge. Advocating for alignment does not mean that people support our curricular goals they have their own agenda (not ours).īefore we worry overmuch about ‘alignment’, we had better make basic corrections to our own system. I was suggesting that much of college mathematics presented mathematics that we no longer care about as mathematicians.Īdvocating for alignment does not mean such alignment is possible it’s not. College mathematics (as known today) is a collection of obsolete tools along with a bit of valuable mathematics.Īt a CBMS meeting a few years ago, I raised the question “When are we going to question the college mathematics courses consisting of excursions into issues that we don’t care about?” Some in attendance thanked me for saying that we should change the applications in our courses sadly, that is not at all what I was saying.School mathematics was (nominally) designed to prepare students for college mathematics.The presumption is that the core of the college mathematics system is valid and that we can apply the school mathematics process to standardize the alignment.Īll of this ignores two related and critical flaws: In their view, college mathematics should be more like school mathematics where the system is well-defined operationally by a limited collection of curricular objects (‘courses’). Just as groups sought to deliberately disrupt the work of developmental education, groups using ‘alignment’ are also seeking to disrupt the world of college mathematics. In other words, the reasonable-sounding effort to create a smooth transition from one level to the next is foolish. The fact that one system is reasonably well-defined while the other is ill-defined suggests that any goal of alignment is unreasonable. College mathematics is characterized by a closed system serving history competing with components seeking to build mastery of modern mathematics.College mathematics is ill-defined with conflicting goals of historical course content and service to the discipline.School mathematics is usually characterized by a closed system focused on experiencing a constrained subset of mathematics at constrained levels of learning.
School mathematics is defined operationally by the curricular materials and accepted pedagogical practices.I hope to put some of each ‘pile’ in this post.Īs usual, a problem and its solutions are based on definitions. Some of this pondering has been pleasant reflection, while much of the pondering has been either professional regret or stimulating conjecture. 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.Īs I write one of my final posts for this blog, I am pondering history and future … and the intersection called the present. School Mathematics can NOT be Aligned with College Mathematics