At the Altar of Alignment

The answer to all questions is “42” (see Hitchhikers Guide).  The solution to all problems is “alignment”.  Academic leaders, government officers, and policy makers are using the word “alignment” in attempts to address many perceived failures in academia.  Alignment is not even a necessary property, and is certainly not sufficient, for an academic system to be successful.

At the micro-level, people tell us to align course outcomes.  If course A is a prerequisite to course B, then the outcomes should be “aligned”. In cases where our goals are strictly operational (just the doing, not the understanding nor the reasoning), we can align courses.  I’d suggest that this is a very weak methodology for a mathematics curriculum, since aligning outcomes directs our attention to the fine levels of granularity as opposed to the basic story line of a course.  A stronger design is to focus on mathematical abilities being developed over time … both within a course as well as across courses.  Alignment is often counter-productive in mathematics.

At the mid-level, we are told to align the mathematics required with the needs of the student’s program.  In other words, if the primary quantitative need of an occupation is the consumption of statistics, then the mathematics required for the program should be a statistics course.  As attractive as this alignment might be … the practice is based on two unfounded assumptions — (1) that a student KNOWS what they plan to become when they begin college, and (2) that this plan is relatively stable over time for each student.  Unless we plan to return society to pre-global, pre-fluid periods for occupations, alignment is a dis-service to many students.   Instead of alignment, we’d be better served by offering a good mixture of valuable mathematics, not specialized.

At the macro-level, we try to align K-12 mathematics with college mathematics (or, vice versa).  The unfounded presumption here is that K-12 mathematics exists primarily to prepare students for college mathematics. And, there is an assumption that this ‘alignment’ (whatever it means in this context) will make a significant difference.  Like aligning course outcomes, aligning levels of education tends to push our attention down to small details —  in other words, alignment is based on focusing on insignificant details while ignoring larger concerns.  For this level alignment, think about what would be more powerful:

• Students have mastered skills A1 to A5, B1 to B7, C1 to C4, and D1 to D8 which logically can be followed by A6 to A9, B8 to B12, C5 to C10, and D9 to D11.OR
• Students develop learning and academic skills (including mathematics) to develop reasonable proficiency as well as an ability to learn in a variety of situations using different tools.

We spend time at the altar of alignment, working on ‘solutions’ which have little chance of helping students.  Education is much more than the sum of a finite series of detailed objectives … education is much more than learning just the mathematics needed for an expected occupation … education is more than a series of steps which present a surface logic but lack power in a person’s life.

Our time would be better spent in seeking a vision and some wisdom on educating students, educating them for capacities and success.  The checklist success of alignment is worthless compared to the benefits of education done well.

 Join Dev Math Revival on Facebook:

“Envisioning our Future” launched … Mathematics in the First Two Years

I am developing a new page on this blog … ‘envisioning the future’, devoted to where we are (or should be) going with mathematics in the first two years.  See Envisioning Our Future

The rationale for putting a focus on this ‘envisioning’ is simple — too much of our effort is currently invested in either defending our traditional curriculum OR in responding to demands to change in specific ways.  We need to focus on where we want to go in the long term, instead of coping with demands resulting in short term changes.

Progress means that we are closer to our goals on this path called ‘college mathematics’.  Our strategies should place this progress at the center of our work whenever possible.

I hope that you will find some useful ideas, and perhaps even some inspiration in this content.

 Join Dev Math Revival on Facebook:

The Envelope, Please!! The answer is …

The next AMATYC Webinar will be April 3 (3pm EDT).  My goal in doing this webinar is to provide some answers to help you deal with the present … and the future.  See http://www.amatyc.org/events/EventDetails.aspx?id=1084248 for details.

In order to understand the present and future, we need to gain some understanding of the past.  Therefore, the first part of the webinar will present a fast-paced summary of where developmental mathematics has been in the prior 40 to 50 years.  We will see that some of the current trends had their origins in past practices in the profession.

The second portion of the webinar deals with the present, responding to the primary current theme … “minimization” (pathways & co-requisite remediation being specifics).  I will share our current curricular structure at Lansing Community College — providing a template which any college can implement, without depending on grant money nor on external directives.  You will see modern curricular standards in practice.

The third portion, somewhat intertwined with the second, deals with the future … what is a viable structure for both ‘developmental mathematics’ and college mathematics in the first two years?  You may discover that the current all-purpose ‘solutions’ are not projected to be a central component of our future mathematical landscape; co-requisite remediation has a role in the future, just not primarily as math avoidance.

Throughout the webinar, we will keep the focus on mathematics — good mathematics for ALL students, opening doors previously closed and allowing every student access to upward-mobility.  Embracing mathematics will be our goal, and that includes the scourge of Complete College America — “ALGEBRA”.  Not your grandmother’s algebra … not your father’s algebra … but algebra as part of an education resulting in better lives for our students.

I hope that you are able to participate in this webinar; feel free to invite non-AMATYC members to view with you.  I am especially interested in academic leaders and policy makers/influencers being a part of the process.  I am working hard to make this webinar enjoyable, helpful and possibly inspiring.

The webinar link is http://www.amatyc.org/events/EventDetails.aspx?id=1084248

 Join Dev Math Revival on Facebook:

Anti-Algebra College Mathematics: What are we DOING?

Much “cool-aid” has been distributed in recent years (as in “he/she has drunk the cool aid” … become a ‘convert’).  Our institutional leadership cadre sing the praises of ‘alignment’ and pathways, and celebrate the emphasis of non-algebraic courses in college curricula.

Of course, the word ‘algebra’ itself has multiple meanings. In this post, I am referring to polynomial algebra along with the reasonable connections to geometry, trigonometry, and modeling at the curricular level of first year of college.  The delivered curriculum in ‘algebra’ has degraded to the point that the primary student outcome is ‘survival’ that qualifies them to take another course.

This is not the same discussion as “Algebra II for All” in the K-12 world; we could debate the pros and cons of that issue, though in most ways that train has left the station.  Our interest is in college mathematics in the first two years.

At the  highest level, an observation is that the enrollments in STEM-enabling math courses is declining based on increased enrollments in courses aligned with programs (by which I mean statistics and quantitative reasoning [QR]).  As a general education course for students in non-scientific programs I think a rigorous QR course is the best option.  Such a rigorous QR course includes a significant focus on algebra and algebraic reasoning.  We probably don’t reach that goal very often in QR courses.  In any case, the STEM-enabling math courses are declining in enrollment.

Why?  Why does our leadership consider these non-algebra options to be superior?  Is it because they have conferred with us about the mathematical needs of students within the context of their programs and the issues of the 21st century?  Have some of us taken on the anti-algebra mantle to the extent that we encourage excessive emphasis on statistics and QR?

Sometimes, algebra has been used as a filter to weed out students who “can’t make it”.  Let’s be honest — that is not the nature of algebra, only the nature of algebra courses used to weed out students.  A positive … and accurate … conception of algebra is this:

• Algebra provides a set of tools for representing scientific and technical knowledge
• Algebra provides a framework for dealing with quantitative problems which are not primarily computational exercises
• Algebra encourages precise communication

If students do not need to deal with scientific or technical knowledge, AND will not need to deal with quantitative problems, then the emphasis of QR and statistics is not inappropriate.  As mathematicians, we value the precise communication aspect of algebra, and we might even make the case that this type of communication is just as foundational as the ‘regular’ communication areas (writing, speech, etc).  That rationale is probably insufficient to require students to take an algebraic STEM-enabling course.

Let’s just consider the first feature of algebra — representing knowledge.  Take a look at the occupations with the best employment prospects (above minimum wage), and I think you will find primarily scientific and technical fields (including health careers).  Some of the very best employment prospects are in highly quantitative professions.

We don’t need all of our students to declare a STEM major (though we can always dream of what this would be like).  However, I wonder if the rush to completion is putting a large portion of our students in programs for which they are either not prepared for the jobs available OR not prepared to handle the quantitative demands of those jobs.  That statement might not be clear; here’s an example of the latter condition: students in an associate degree nursing program take a statistics class to meet their math requirement, but they are not prepared to deal with problems requiring algebraic representations or algebraic reasoning.

The ‘elephant’ in the room is how poorly we have been delivering algebra-based courses in college.  In spite of fundamental changes in both the mathematics profession and in K-12 mathematics, we still emphasize courses which might be called “death by algebra” … which serve to weed out students rather than prepare students.  How could we, in good conscience, suggest to our leadership that these algebra courses should be used instead of the QR or statistics course?

The changes in college mathematics, so far, have been at the edges — developmental mathematics reform and co-requisites (usually for QR or statistics).  I believe that the external pressure will come to our algebra-based STEM-enabling courses:  either we make fundamental changes to those courses OR the leadership will make curricular changes that take our courses out of the normal set of student programs.  Within 10 years, we could be dealing with a situation in which the only students taking STEM-enabling math courses are those in ‘high’ STEM fields (physics, engineering, perhaps a few math majors).

What’s the future you want to see?  What’s the role of STEM-enabling math courses in your vision?

 
Join Dev Math Revival on Facebook: