Are You There, Mr. Gates? Flip that MOOC right over, guy!

Some of us have been thinking about the influence that foundations (and rich people) are having on education.  What was once an influence of the national science foundation is now the influence of the gates foundation, with a smaller group of people making decisions based on priorities that are not open to public review or political approval.

A recent article described how Mr. Gates suggested to community college trustees that a ‘flipped MOOC’ might be a good solution — especially for developmental mathematics.  [See http://chronicle.com/article/MOOCs-Could-Help-2-Year/142123/].   I suspect that the article is misquoting the ‘doctor-not’ (Mr. Gates); an intelligent person would not use an oxymoron like ‘flipped MOOC’.  (Flipped means ‘lectures’ happen outside of class time; MOOC’s do not have class time.)

However, that minor detail (that is is not possible) will not make any difference.  Because it was Mr. Gates saying it, many of our leaders (college trustees) will be confident that it is true.  I expect to hear from my College’s trustees within a few weeks, as they wonder whether we would like to try a flipped MOOC model at our college to solve our dev math problem.

Coincidentally, I saw a very good presentation on an inverted design for instruction — a better name than ‘flipped’.  This presentation was at my state conference (MichMATYC) — a talk given by Robert Talbert (Grand Valley State University); a reference is http://scholarworks.gvsu.edu/cgi/viewcontent.cgi?article=1183&context=colleagues .  I was impressed by the amount of analysis done by Dr. Talbert to create the inverted calculus classroom; the process is much more complicated than ‘lecture outside of class time’.

To some extent, the ‘flipped MOOC’ phrase illustrates the linguistic process for the evolution of word usage: the initial use of a phrase is specific, becomes accepted, and then is applied in usage to unrelated objects in order to imply something positive (or at least ‘current’).  As educators, we have been damaged by this “phrase drift” many times over the years (mastery learning, back to basics, applications, calculator friendly, collaborative, student centered, and others).  The difference in this period is that our future is being heavily influenced by people who have less understanding of curriculum and instruction … rather than more.

There was a time when ‘trends’ in education were declared by top-level academicians and national policy heads.  These people (generally office holders of some kind) were deeply networked in the collegiate life.  No more; we are spending most of our time either agreeing with or arguing with people ‘on the outside’ — foundations in the completion agenda, philanthropists, and legislators.  It’s not that we should ignore the concerns of outside stakeholders.  The problem is that the outsiders have taken control from us; we react to them.

So, I ask:  Mr. Gates, are you there?   When do we get to have a productive conversation about the problems we are trying to solve?  We could look for problems where we agree on solutions … problems where we agree on the problem but not on solutions … and problems where we see the problem differently.  I know this, Mr. Gates — the process being used so far has put a lot of money is promising practices and technology without much sustained benefit; your return-on-investment is not so good.

When do we have a productive conversation?  Until we have real conversations with the people and groups trying to solve the problems (with the best of intentions) … until we work together, and not in reaction … until we accept both the worthy and not-so-good about the old system … only then do we have any hope of building something that will both solve problems and be capable of surviving in our world.

If you want to ‘solve the developmental mathematics problem’, Mr. Gates, I suggest you start by collecting a team of the 10 best thinkers and practitioners in the field who work with you over a 10-year period.  We want to solve problems; we strive to have students succeed and complete.  Can you recognize the need to have us as partners?

Are you there, Mr. Gates?

 Join Dev Math Revival on Facebook:

Towards a Balanced Approach

When I hear somebody suggest that we take a ‘balanced approach’, my first thought is that the speaker either does not have confidence in their judgments about what is important … or does have confidence but does not want to offend the audience.  The phrase ‘balanced approach’ is often used in reference to a reform model balanced with traditional ideas.

I suggest that we think about the phrase in a new way.  Let’s begin with the assumption that the traditional curriculum has limited value and that the reform curricula have limited value.  What would we build from a blank slate?  How would we use scientific evidence in the process?

A balanced approach looks at implementing two basic properties of human learning:

1. Understanding (connected information) results in more transfer of learning and facilitates long-term retention.
2. Repetition (deliberate practice) results in efficient recall and abilities to apply information.

Some reform curricula emphasize (1) almost to the exclusion of (2).  I have taught courses like this, and talked with my students; few of them have a good report about the experience.  We all have students who approach a math course in that fashion — the students who usually are in class, and do very little ‘homework’ because they understand what they are doing (occasionally they are correct).

As mathematicians, we are drawn to ideas with power — ideas that can represent relationships among quantities, communicate the information, and help reach conclusions about some future state of those quantities.  [We are also drawn to special cases, as well as mathematics that is aesthetically pleasing.]  Our students need the ‘basic ideas with power’ so they can handle the quantitative demands of academic and social situations.  I think we can have fairly strong consensus on the mathematics that most students need.

The balance we need is about pedagogy.  Having a better ‘table of contents’ will not help if students do not learn any mathematics.

I see this issue of balance as our basic problem over the next 5 years.  We know that our courses are going to change in basic ways.  We understand what mathematics is important for all students.  Our issue is to address both the understanding and repetition in the learning process.

Currently, an ‘understanding’ method is based on students dealing with a situation and using guided questions so that they discover the basic idea.  In some cases, this works surprisingly well.  However, discovering an idea has little connection with understanding mathematics.  Here’s an example:  By looking at a set of ordered pairs (bivariate data for a situation), students are led to the idea of slope so that they can predict another value.  This forms the beginning of understanding, not the end: understanding takes extended work with diverse views of the same idea.  Students often over- or under-generalize.  In the case of slope, students think this applies to any set of values … or that it does not matter which ones ‘go on top’ … or that slope is like an ordered pair.  Understanding is a natural human process, but does not happen spontaneously with correctness.

As for ‘repetition’, we seldom get this right.  Textbooks often confuse ‘any sequence of problems’ with ‘repetition for learning’.  Much is known about properties of practice that result in different degrees of learning — a sequence can highlight the most important idea (or hide it), a sequence can reinforce good understanding (or prevent it), and a sequence can reinforce accurate recall (or prevent it).  We somehow make the mistake that good authors can design good assignments; these are vastly different sets of expertise. We also make the mistake that computer systems provide appropriate repetition.

We can (and need to) focus primarily on the big ideas in mathematics; our courses need to match the amount of material with reasonable expectations for students learning with understanding and repetition.  With a balanced approach, we can help students succeed.  With a balanced approach, we can show policy makers that we have the professional skills to solve the problems that they are concerned with.

 Join Dev Math Revival on Facebook:

Math Lit/Applications for Living: Seeing the Power

Both the Math Literacy course and the Applications for Living course deal with two common models — linear and exponential.  I’m finding it interesting to watch how different and similar the experience is.

For both students, they have not seen exponential models in their college (developmental) courses; none of the current Applications for Living students had the Math Lit course previously.  (That will change as some Math Lit students take Applications for Living.)  In both cases, we explore models from numeric and symbolic forms; the Applications for Living course includes more variety, and also requires active graphing of exponential models.

In both courses, students have a difficult time leaving the linear world of adding and subtracting.  There is confusion about the role of slope in an adding world; during the exploring process, we take the time to show repeated adding as a multiplying, and identify the number as the slope.  When we work in exponential situations, the linear view seems to dominate.  During the exploring process, we show repeated multiplying as an exponent and learn about the role of the multiplier.  The performance learning outcomes are not what we would want; there are some differences between numeric and symbolic problems.

For example, the final exam in the Math Lit course had a doubling problem for which students needed to write the model.  Something like:

At the start, 25 people knew about the latest i-product; this number is going to double every day.  Write the exponential model for N (the number  who know) based on t (days since the start).

Another problem for the Math Lit final was a growth pattern from a numeric standpoint:

The cost of a machine is $400, and this is expected to grow by 10% per year.  Complete the following table of values.  [The table shows years 1 to 5, where the value for each year needs to be completed.]

In Applications for Living, the corresponding problems were this symbolic one:

The value of an investment is expected to grow by 6% per year.  Write the exponential model for the value in terms of the number of years.

And, this numeric one:

At 3pm, 20 mg of a drug were in the body.  At 4pm, 15 mg were in the body.  Complete the following table of values.  [The table shows hours 1 to 5, where the amount of drug needs to be completed.]

Almost half of the Applications for Living students treated the last problem as a linear one: They showed values of 10, 5, 0 and 0 (sometimes with a puzzled comment about having zero as the amount).  In class, we had done drugs in both half-life and percent decrease models; we had calculated the multiplier as well.  They did a little better on the symbolic form; part of this is the fact that this course also does work with finance formula, and one of those formulae is basically the answer for this problem.

The Math Lit students did well on the numeric problem; part of that success was the remediation we did earlier when most students had difficulty on all things exponential.  Few of the Math Lit students wrote a correct exponential model, which is noteworthy since the problem is a slight variation of a situation we used to introduce exponential models.  Most of the incorrect answers were variations on y =mx + b.

Clearly, this assessment feedback is indicating a need for an adjustment to the instructional cycles.

However, I also think that the results reflect a math curriculum that tends to treat topics in isolation.  How often do students need to deal with both linear and exponential models in one assessment?  Also, do we use the word “always” with students?  As in: “Compare the y-values; the difference always tells you what the slope is.”  Or, “If you can see how to get the next value in a table, you can always use this to complete a table.”  Or, “In a function, you can always get the next function value by adding or subtracting.”

During the instructional cycles in both courses, I can see the resistance to leaving the linear model.  It’s a bit like distributing, where students become fixated on one process.  I want students to see the power of understanding exponential models; students want the comfort of one model for all situations.

 Join Dev Math Revival on Facebook:

Algebraic Literacy: Finding a Textbook

One of the new courses coming to a college near you is “Algebraic Literacy”, a modern course that prepares students for a STEM path (and related work).  This position in the traditional curriculum is held by ‘intermediate algebra’.

For a brief comparison of these courses, see the chart below:

In this chart, “MLCS” refers to the Mathematical Literacy for College Students course (also known as Math Lit, and similar to Quantway I).

One of the issues with the Algebraic Literacy course is finding textbook materials.  Books being written for this course are not available yet.  However, there are materials available which have enough similarity to be used.

One book I have learned about recently is “Algebra: Form and Function” (Wiley publishing, 2010).  This book was written by a team connected with the calculus reform efforts, and is designated as a ‘college algebra’ textbook.  However, the book does not assume that students have the higher background; it’s quite accessible by students in an Algebraic Literacy course.  For a quick look, see this link to the Course Smart page:  http://instructors.coursesmart.com/9780471707080

You can also find more information on this text at the Wiley page http://www.wiley.com/WileyCDA/WileyTitle/productCd-EHEP000346.html

 
Join Dev Math Revival on Facebook: