AMATYC 2017 Conference “Guide”

I am thrilled to be able to do 2 presentations at this year’s AMATYC conference (San Diego, Nov 9-12).  As usual, there are more sessions we’d like to attend then anybody can attend.

I am hoping that you (if you are attending) will consider both of my sessions.  Information on each is provided below.

“Using Data to Improve a Curriculum”  (S116, Friday at 2:55 pm)
This session focuses on two key issues in our curriculum: the transition to pre-calculus, and equity.  We will look at how to use data to help understand the issues and then monitor for program improvement.  You will learn about methods and variables that can be used at your campus.
Preview:  Using Data to Improve a College Math Curriculum and Equity S116 Preview

“45 Years of Dev Math in 50 Minutes”  (S137, Saturday at 11:55am)
The goal will be understanding our history and the current issues sufficiently to see the path forward.  Dev Math has been nudged, prodded, and attacked in the last few years, and some of us are dismayed; it may be difficult to see where we are headed.  By the end of this session, I hope to show you how we can move forward … towards a goal we can be excited about.  Do not come to this session to hear whining; come to hear a positive message focused on what we can (and should) do.
Preview:  Forty Five Years of Dev Math in 50 minutes Preview

As many of you know, this will be my last AMATYC conference.  In one way, the ’45 years’ session is my farewell … and my thanks … to AMATYC.  [If you are curious, I will be teaching for another year or two.]

 Join Dev Math Revival on Facebook:

The Bad Part of Dev Math

This past weekend, I was at our state affiliate conference.  MichMATYC has a long history (relatively), and we have had a number of AMATYC leaders from our state (including three AMATYC presidents).  We’ve been heavily involved with the AMATYC standards (all 3 of them).  However, you can still see some bad stuff among our practitioners.

One of the sessions I attended focused on lower levels of dev math — pre-algebra and beginning algebra.  The presenter shared some strategies which had resulted in improved results for students; those improved results were (1) correct answers and (2) understanding.  That sounded good.

However, the algebra portion was pretty bad.  The context was solving simple linear equations, and the presenter showed this sequence:

• one step equations (adding/subtracting; dividing)
• two step equations (two terms on one side, one on other)
• equations with parentheses, resulting in equations already seen

All equations were designed to have integer answers; the presenter’s rationale was that students (and instructor) would know that a messy answer meant there had been a mistake.  All equations were solved with one series of steps (simplify, move terms, divide) — even if there was an easier solution in a different order.

When asked about the prescriptive nature of the work, the presenter responded that students understood that it was reversing PEMDAS (which, of course, makes it even worse for me).

The BAD PART of dev math is:

1. Locking down procedures to one sequence
2. Building on memorized incomplete information (like PEMDAS)

As soon as students move from linear equations taught in this way to any other type (quadratic, exponential, rational) they have no way to connect prior knowledge to new situations.  In other words, the student will seem to ‘not know anything’ in a subsequent class.

To the extent that this type of teaching is common practice, developmental mathematics DESERVES to be eliminated.  Causing damage is worse than not having the opportunity to help students.  When we offer a class on arithmetic (even pre-algebra), the course is very likely to suffer from the BAD PART; offering Math Literacy to meet the needs in ‘pre-algebra’ and ‘basic algebra’ will tend to avoid the problem — but is no guarantee.

All of us have course syllabi with learning outcomes.  Those outcomes need to focus on learning that helps students, not learning that harms students.  Reasoning and applying need to be emphasized, so that students seldom experience the BAD PART.

 
Join Dev Math Revival on Facebook:

Students at the Center of Learning

“Teaching and Learning” … a phrase often used in professional development for us teachers, as well as in titles of articles and books.  Perhaps a better phrase would be “Learning and Teacher Behaviors”, or “Learning … Teaching without getting in the way!”

I am thinking about how well our Math Literacy course is doing in the Math Lab format.  The Math Lab format creates a learning environment by establishing assignments and a structure for students to work through those assignments.  The instructor ‘stays out of the way’ as long as learning is successful.  This format has been used with very traditional content, and is now being used with a modern developmental course — Math Literacy.

Although some students struggle longer, and do not initially ‘get’ new ideas, the vast majority of students in the Math Lab Math Literacy course have been successful with:

• identifying linear and exponential patterns in sequence
• using dimensional analysis for unit conversions
• identifying the type of calculation for geometry (perimeter, area, volume)
• writing expressions for verbal statements

What’s been tougher?  Anything dealing with percents — applications, simple & compound interest, etc.  Of course, these are weak spots for students in any math class; over the years, I have not seen anything that ‘fixes’ these in the short term; the fix involves unlearning bad or incomplete ideas, and this takes time and long-term ‘exposure’ to errors (along with support from an expert).  Direct instruction or group activities have limited effectiveness against the force of pre-existing bad knowledge.

The instructional materials form the basis for the learning in this Math Lab format.  If the ‘textbook’ is focused on problems to do, contexts to explore, with the expectation that the instructor will provide ‘the mathematics’, then the learner centered approach requires that we use specialized processes in the classroom.  The classroom becomes the focus, and we spend resources & energy on tactical decisions such as ‘homogeneous groupings’ or ‘group responsibilities’ or ‘flipping the classroom’.  The materials we use in this course are well crafted to support learning; the authors ‘expected’ the classroom to be the focus, though our Math Lab ‘classroom’ is working quite well with the materials.

What if we could offer a true “student at the center of learning” design?  Seems to me that this goal would lead us to use methods like our Math Lab, where students interact with the learning materials without an instructor mediating (as much as possible).  Students in our Math Literacy course have been successful in learning new mathematics with decent reasoning skills in this format.  Although initially confusing to students, the classroom is lower stress than a ‘regular’ classroom; there are no artificial social processes used to ‘facilitate’ the learning.  Think of it as being more like a student as an apprentice, where direct engagement with the objects of the occupation is the key for learning.

Of course, we are not normally able to offer all math courses in this format of active learning.  For me, the approach is to design my ‘lecture’ classes to be more like workshops.  In a 2-hour class, I might deliver 45 minutes of very focused presentations (direct instruction) distributed in a deliberate manner through the class time.  The length of ‘lecturing’ is varied according to the course and somewhat according to the needs of the students in a given class.

The point of this post is …

Stay out of the way of learning.

Students can learn by interacting directly with the learning environment.

We want students who are independent, and able to learn without a special structure.  Prepare your students for the real world by creating learning environments where they develop those skills while they are learning mathematics.

 Join Dev Math Revival on Facebook:

What Does the Future Look Like? College Mathematics that Works!

We live in a transition time, for college mathematics.  Developmental Mathematics is shifting away from the traditional curriculum, with an over-use of “prerequisite remediation” in the short term.  At the same time, both of the primary professional organizations for our work (MAA and AMATYC) have been calling for basic shifts in both what we teach and how we teach within the ‘standard’ college level mathematics courses.  What does our eventual ‘target’ look like?  Can we anticipate where we will end up?

In a basic way, the answer to the last question is ‘yes’, due to the fact that all of the forces shaping the future are known at the present time.  We don’t know precisely which forces will have a larger influence, and that is fundamental since the forces are not operating in the same direction.  Imagine yourself in an n-dimensional force field where you can see the vectors around you.  Although the wind varies over time, some types of vectors dominate your environment.

These vectors around us originate from power sources.  Professional standards (MAA, AMATYC, etc) send out vectors in the direction of higher levels of reasoning, modern content, more diverse content, and more sophisticated instructional methodologies.  The K-12 educational system, the Common Core in particular, send out vectors in very similar directions.  Policy influencers, higher education provosts and chancellors, and state legislators send out vectors representing forces in different directions from those in the prior lists.

In the short term, this latter set of forces will dominate … because some of the individuals involved have sufficient decision making power that they can impose a set of practices on portions of our work.  However, these practices will not survive long term except to the extent that they support the prevailing set of forces around us.  As the people in authority change faces, the practices will tend to revert … either to the pre-existing conditions (bad) or to a condition making progress in the direction of the prevailing forces.

Here is a description, a picture, of where we will be in 10 to 15 years.

• Remediation will be smaller than in the past, but still normally discrete (not combined with college courses as in co-requisite models).  Arithmetic will be ‘taught’ but never as a separate course and never will be a barrier to a college education.  Content will focus on the primary domains of basic mathematical reasoning — algebra, geometry, trigonometry, statistics, and modeling.  No more than two remedial courses will ever be required of students, regardless of their ‘starting condition’.
• “College Algebra” will not be used as a course title.  Similar courses for non-STEM majors will have titles such as “Functions and Modeling in a Modern World.  The content of this course, never used as a prerequisite to standard calculus, will be from the same domains as remedial mathematics — algebra, geometry, trigonometry, statistics, and modeling.
• “Pre-calculus” courses will be replaced by a one-semester “Intro to Math Analysis” course which focuses on the primary issue for success in calculus: reasoning with flexibility supported by procedural understanding.  This course will have a very strategic focus in terms of objects and skills involved, with a shorter topic list than prior courses … taught in a way which results in a true readiness for calculus.
• “Calculus” courses will be re-structured to focus on a combination of symbolic and numeric work.  The first semester of the two-semester sequence will include derivatives and integration for basic forms, as well as an introduction to scientific modeling using matrices such as those encountered in the client disciplines; this eliminates the need for our client disciplines to teach basic quantitative methods, and provides modern content to serve those disciplines.  The second (and final) semester calculus course focuses on multi-variable processes combined with a more complete approach to scientific modeling — appropriate for students who may eventually conduct their own research in a client discipline
• “Liberal Arts Math” and “Quantitative Reasoning”  will have merged in to a new QR course at most institutions.  At some institutions, these courses are replaced by the “Functions and Modeling” course (which is fundamentally a QR course).  Where QR exists as a separate course, the ‘practical’ content will be de-emphasized relative to today’s courses, with an increase in symbolic mathematics. The primary distinction between QR and Functions and Modeling is that QR does not include as much trigonometry.
• “Intro Statistics” will exist with similar content to the best of today’s courses.  The primary change will be a relative decrease in the number of students taking a Stat course to meet a degree requirement, as program planners realize that their mathematical needs are more diverse than statistics … and that requiring statistics should not be based on just a desire to avoid college algebra (which does not exist in this ‘now’).
• Students will become inspired to consider a major in mathematical sciences by the diverse quality content along with the effective methods used within the courses.  Instead of a focus on weeding out students not ‘worthy’ of majoring in mathematics, we will focus on including all students on the mathematical road to maximize the distance covered.

I see an exiting future, once we get past the relatively short-term impacts of changes imposed from outside.  In the long-term, nothing can stop us from achieving a desired goal … except for our own doubts and lack of clarity.

My hope is that you see something in this image of the future to get excited about, something that plays the role of a beautiful sunrise in the forest.  If you can SEE where you want to go, you can get there … and it is a lot easier to survive temporary struggles along the way.

 Join Dev Math Revival on Facebook: