When Change becomes Progress

This semester, we have more than 150 sections of Mathematical Literacy offered at colleges across the country … and these are outside of the grant-related work (such as Quantway™).  In other words, the New Life Mathematical Literacy course is now the most implemented reform math course in the United States.

Getting to this point is the result of the incredible effort of dozens of math faculty, many of whom have been members of the New Life wiki at http://dm-live.wikispaces.com/.  Our work has not involved large grants from foundations; rather, collaboration and local initiative have allowed us to create significant change.

However, change is not the same as progress.  Progress involves sustained efforts which achieve explicit goals.  We have achieved more than other efforts … but we “are not there yet”.

Where are we headed?  How will we know when we have arrived?  These are not questions for which we create singular responses and data-based conclusions; these are questions for a profession to use as standards for our work.

In the world of process and product design, one set of strategies involves having people seeing themselves in the situation that they are trying to create.  For example, we might ask 100 math faculty to imagine that the mathematics curriculum works like it is supposed to.  What does this look like?  What does it sound like?  What does it smell like?

For our work, here are some answers I would give to those questions about what we are trying to achieve:

• Students text each other about the latest exciting math problem.
• Students pass every math class unless something unexpected comes up.
• Over 10% of students major in a STEM field and over 10% of degrees are awarded in STEM fields.
• Students learn diverse mathematics, with understanding, in both pre-college and college math courses.
• Fewer students are in college-prep math classes than are in college level math classes.
• Half of the students who start in college-prep math classes change their goals to be more STEM-like.
• Math faculty are the happiest faculty on campus.

Part of our difficulty has been that we have not had a goal in mind — beyond having higher pass rates.  Higher pass rates is not a design standard; it’s a production standard (and a poor one, at that).

Progress would exist if we would judge that we are substantially closer to achieving our goals.  If we don’t articulate our goals (like the 7 statements above), we can never have progress … because we are not directing our efforts towards anything.  Change is cheap; progress is where the power is.

I started off this post thinking a next step, like getting the Algebraic Literacy course on the radar — and I still think that is very important.  Or, thinking about salvaging the college algebra and pre-calculus curriculum, which is very important.  I hope that you will be involved with one or both of those reform efforts.  Overall, however, I am concluding that we need to have more conversations about our goals.  What does progress look like?  How do we know when we are there, as opposed to where we are now?

We have created significant change.  Progress?  We’re not there yet.

The 1st National Summit on Developmental Math — Coming to a Town Near You?

In some states, the big problem is policy makers imposing a single solution on developmental mathematics.  In most states, the big problem is that math faculty are not involved with their professional organizations (AMATYC, NADE) … which means that they lack current information on solutions and options, and that they do not have a support system outside of their own college.

The 1st National Summit on Developmental Mathematics was an initial step to deal with these problems.  Most of us could not be there.  However, you can already see most of the presentations at https://sites.google.com/site/amatycdmc/national-mathematics-summit

I hope that you will take some time to look at those presentations.

Dealing with developmental mathematics is a state and/or local issue.  We need to have state and/or regional summits on developmental mathematics.  AMATYC might suggest that each state affiliate host their summit, perhaps attached to an annual state conference, and hopefully coordinated with their NADE affiliate.

These state summits can use the online presentations as a source of information so that faculty can have conversations about solutions.  As needed, these remote resources can be supplemented by one or two live experts with broad information about the possible solutions.  The costs of these summits would be minimal; those with an interest could even apply for an AMATYC mini-grant (<$750) … see http://www.amatyc.org/?page=MiniGrants  for some information.

I hope that you will be involved as this reform effort reaches more and more states.

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AMATYC Presentations about New Life Math

To see the presentations and handouts for my sessions on New Life at the 2013 AMATYC Conference and Developmental Mathematics Summit, see the page AMATYC 2013 and Developmental Math Summit 2013    [also known as https://www.devmathrevival.net/?page_id=1807]

Applications — Starting on Correlation

In our Applications course, we develop some basic statistical reasoning.  I always start key topics (like what is statistics … what is correlation) by having students work in groups on discussion questions.  I recently changed the ‘correlation’ activity, and thought other people might be interested in seeing it.

My goal with statistics in this course is to develop statistical thinking (and caution!), in ways similar to the standards in GAISE (see http://www.amstat.org/education/gaise/GaiseCollege_Full.pdf)   We use real data whenever possible, and focus on reasoning first … computation later.

In the case of correlation, I originally used a variation of the “Cereal Plots” activity like that used in Statway™.  In the cereal plots, students are presented with various nutrition values plotted against the ranking of cereals by Consumer Reports.  Conceptually, this is really nice.  However, in practice, students have too much overhead — they don’t know about rankings in general, and certainly not cereal rankings by Consumer Reports.  We ended up spending about half of the class discussion time on secondary issues.

This semester, I created my own sample of graphs.  These scatterplots deal with contexts familiar to almost all students, such as cars (price, mileage, etc).  Here is my activity for this semester

So, this was the initial part of class yesterday.  Students were in groups of 3 to 5, and answered the 10 questions on the sheet.  The context for these graphs was much better — somebody in every group knew enough about cars to provide some additional wisdom, and everybody knew enough about cars to get started.  [The last graph, on grip strength versus arm strength, is accessible to all students.]

Overall, this new activity works much better.  All of the discussion was about the graphs and statistics.

This does not mean that students magically understood what correlation is … or how to judge it from a scatter plot.  We are still working on unlearning ideas about cause & effect.  However, we did make progress on judging a linear pattern in these graphs; when I say “negative correlation”, most students can connect this to a pattern like we visualize from the phrase.

In case you are curious, the application course is pretty limited in the statistical topics included.  We include some reasoning topics (samples, population, bias, correlation, and describing distributions); we also include some displays (frequency tables, bar graphs, etc) and a few calculations (mean – median – mode, standard deviation, rule of thumb for margin of error).  We do not calculate correlation coefficients, nor do we do regressions; we do not calculate actual margin of errors, though we do calculate 95% confidence intervals (using the 1/sqrt(n) rule of thumb).  Out of 16 weeks, we spend 3 weeks on statistics; 2 weeks are spent on basic probability.

By the way, all of the graphs on the correlation activity were taken from online searches.  I was honest with the class — we do not know how valid any of them are, though I believe that they are valid.

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