Conversation II: Herb & Jack on the Why — Practicality of Theory

In response to a post about STEM students and the traditional developmental mathematics curriculum, Herb Gross began with this quote (from a prior talk he gave):

The music is not in the guitar.

I think Herb is saying that mathematics is not in the visible tools used, whether these tools are procedures written down or technology used to answer questions.  This is a great point, and it suggests that we question any suggestion that we limit the content of mathematics courses to just those things seen as ‘practical’.  Seeing mathematics as being bound by the practical (for STEM or non-STEM) is a self-defeating behavior; a health profession is based on continuing growth, and growth depends upon research both applied and theoretical (the two work together in surprising ways).  Our students are future policy makers — do we want them to only value mathematics that is practical NOW?  (Think University of Wisconsin budget cuts.)

The music, and the mathematics, is based on connections among concepts.  This speaks to the growth of mathematical reasoning and critical thinking.  Herb adds this comment:

So I am not overly impressed with the pass rate improving as much as I am in seeing what the effect is further down the road.  In fact one of the reasons I don’t like non-algebra/calculus based courses is that even the students who are most successful in these courses tend to know how to crunch numbers into the calculator but have little feel as to what to do when the distribution is anything other than normal.

I think Herb is speaking to a basic goal of education — the improvements retained over a longer period of time, meaning improved capabilities.  The comment Herb makes is important, and I think it applies to most algebra based courses; I also wonder about calculus based courses.  Look at this re-phrasing of a critical part of Herb’s comment:

Students tend to know how to manipulate symbols or numbers often with the use of tools but have little understanding as to what to do with mathematical concepts applied to a new situation. (JR)

Creating scalable change within an individual involves some of the same work as creating scalable change in a profession.  A more complete view of learning is required, with less focus on ‘passing’; passing is a great thing, but it can not be the core measure of our success.  We seek to create mathematical abilities, including the willingness to apply existing knowledge to new situations where this knowledge is not sufficient.

Students in STEM programs need a broad foundation in mathematics, combining procedural and conceptual fluency.  To some of us, we follow that statement with “Non-STEM students to not”; this is where we can make large mistakes.  The mathematical needs of citizens and the mathematical needs of our partner disciplines are not different in a basic way — they need procedural and conceptual fluency as well.  The difference, overall, is a matter of degree and extent.  STEM students need MORE, not so much ‘different’.

Our work in the AMATYC New Life project supports this single-source approach to mathematics — the Mathematical Literacy course serves the needs of all students.  The initial uses of the course have often been for non-STEM students; however, the outcomes of the course were designed back from the needs of all students.  I agree with the design of the New Mathways Project (Dana Center), which has a similar course serving all students.

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STEM Students and Developmental Mathematics

Pathways … Mathways … creating alternatives for non-STEM students.

The changes in pre-college mathematics are significant, and I am incredibly pleased with the work of my colleagues in dozens of institutions across the United States.  The modified curriculum for these students has dramatically increased the proportion who achieve their goals, with a significant increase in the number passing their required college-level math course (statistics or quantitative reasoning).  These gains have been achieved by putting thousands of students into a different path, wherein they avoid beginning and intermediate algebra.

We need to get over a myth about other students — the students who need at least a college algebra course, often because they are pursuing a STEM or STEM related field.  [STEM refers to Science, Technology, Engineering and Mathematics.]

Myth: STEM students are well served by the traditional developmental mathematics curriculum.

Alternate hypotheses: STEM students are ill-served by the traditional developmental mathematics curriculum.

As you may know, I have been in this work for over 40 years.  Much has changed.  However, developmental mathematics is currently bound by these constraints (which has been true for over 40 years):

Constraint 1: The pedagogy and content is limited by the preponderance of adjunct faculty assigned to developmental math courses.

Constraint 2: The content is based on textbooks reflecting a set of topics which were copied from a typical high school curriculum of 1965.

These constraints interact within our curriculum, including at my own college.  The rigor of a developmental algebra course is most often established by the complexity of the procedure students would use to solve problems; these ‘problems’ are copies or slight variations of exercises seen in the homework.  These exercises, in turn focus on the achievement of a correct answer to a well-defined problem either stated symbolically or in the disguise of a verbal puzzle (where such puzzles lack both value in the real world and value in their structure).  We have a sense of pride if OUR algebra course includes conic sections or inverse functions, based on knowing that these topics await students in their college algebra course.

Some people might wonder if I think the presence of adjunct faculty in a classroom results in lower quality; definitely not — some of my adjunct colleagues are better instructors than I am.  The constraint is based on the fact that these courses need to be ‘teachable’ by the pool of adjuncts available; the issues deal with the expectations that are reasonable for a group, rather than individuals.  Full-time faculty may, in some cases, face similar limitations in the knowledge and skills they bring to a developmental algebra course; the difference is that full-time faculty have greatly enhanced access to professional development and networking.

In terms of data, the pathways work is fueled by the low pass rates in traditional courses (50 to 55%) compared to the typical 65% to 70% seen in the reform models (Mathematical Literacy, Fundamentals of Mathematical Reasoning, Quantway I).  By saying that STEM students are well-served by traditional developmental mathematics:

We are apparently comfortable with 25% (or less) of students completing two semesters of developmental algebra.

The improved outcomes for the reform models is likely due to the fact that all 3 address both constraints — professional development for faculty AND improved content.  By saying that STEM students are well-served by traditional developmental mathematics:

We are apparently comfortable with STEM students having to survive lower quality pedagogy and outdated content.

I see other issues, as well — such as the relative lack of technology in developmental algebra courses as a basic part of the content; calculators are banned … we avoid numerical methods … and remain out-of-touch with the world around us.

Again, I say that STEM students are ill-served by the traditional developmental mathematics course.  The content is inappropriate, pedagogy is not supportive, and little inspiration is ever seen for why a student would persevere in their STEM field.  STEM students need a reformed curriculum just as much as non-STEM students; the needs of society would suggest, in fact, that STEM students have a greater need for a reformed curriculum.

Take a look at the reform curriculum; it’s actually not that complicated.  Instead of beginning algebra, use the SAME reform course as non-STEM (Mathematical Literacy, Foundations of Mathematical Reasoning, or Quantway I).  Then … replace your intermediate algebra course with a reform course.  In the New Life work, that reform course is called Algebraic Reasoning; you can see some information at https://www.devmathrevival.net/?page_id=1807 , or head over to the wiki http://dm-live.wikispaces.com/

The New Mathways project is starting their work on STEM path — take a look at this post https://www.devmathrevival.net/?p=1935

I hope to do a presentation on the Algebraic Literacy course at this fall’s AMATYC conference … as a ‘bridge to somewhere’!  I believe that the Dana Center will also be there.  I encourage you to learn more about the reform curriculum for STEM students.  The work is important, students need it, and we will find it very rewarding.

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Conversation I: Herb & Jack on the Future of Teaching

Over the past few weeks, I have been having a great conversation via email with Herb Gross, the founding President of AMATYC and long-term inspiration to many of us working in the first two years of college mathematics.  With Herb’s kind permission, I will share some of our conversations here.

Herb’s comment

In my opinion, the face of education is going to change dramatically very shortly  when we begin to use the Internet to clone “master teachers”.

Herb has a good point.  In fact, many readers will respond by saying that we are already doing just this.  Jack’s comment

Yes, the internet allows for distribution and re-use of good materials.  The issue we need to focus on is “what makes a good teacher” or a “master teacher”.

In recent years, we have seen a couple of forces that shift our focus away from a clear image of a good teacher.  One force is the “sage on the stage … guide on the side” image, where a teacher is a coach or trainer responding to students as they learn mathematics.  Another force is the huge emphasis on online learning components, which is sometimes implemented as a replacement for teaching in some redesign models.

In my view, being a good teacher is a very personal experience with a group of students.  When it works, students will say something like the following:

Thank you for a great semester.  You have been an amazing teacher.  Thank you for not giving up on any of us; you pushed me (at least) to do my best.

That is a note written to me, handed over before this student took her final exam.  She did not have the best average in class, but she did work hard and was engaged during every class.

Jack’s description of good teaching:

Good teaching involves the articulation of ideas in a way that is understandable to students, creating a learning environment that encourages learning, and inspiring students to work harder than they intended.

Only a small portion of this can be cloned, or distributed across the internet.  Herb has some great videos (like this one on You Tube:  https://www.youtube.com/watch?v=F_qX3inNCi8&feature=youtu.be); this video is part of Herb’s work on math as a language, which you can see more about on his web site http://www.adjectivenounmath.com/

One of the many things I like about Herb’s work is that he takes a lot of time.  We sometimes think that students do not have the attention span to deal with a deliberate approach; that is not generally true, and Herb gets a large amount of unsolicited positive feedback on his videos.

As good as these ‘clones’ (videos) are, they do not make a good teacher; having a master teacher articulate ideas is wonderful.  This is not sufficient to be a good teacher.  We need to provide clear statements concerning what the practice of teaching involves.  Our colleagues need this, our leaders need this, and certainly policy makers need this.

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AMATYC 2014 — Accelerate and Improve Dev Math with “New Life”

Here is the presentation file, as well as the handouts, from the November 15 session.

Presentation: New Life Accelerate and Improve Dev Math 2014 AMATYC

Main handout: References_NewLifeSession_AMATYC2014

Math Literacy Outcomes and Goals: MLCS Goals and Outcomes Oct2013 cross referenced 2 by 2

Algebraic Literacy Outcomes and Goals: Algebraic Literacy Goals and Outcomes Oct2013 cross referenced 2 by 2

Summary of 3 Emerging Models for Dev Math: Summary of Three Emerging Models for Developmental Mathematics Updated 2014

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