Professional Growth … Connected or Isolated?

Over on the MATHEDCC discussion list, we have been having some difficulties … which essentially are “people declaring a strong point of view, often with negative comments towards others point of view”.

In case you do not know the history of MATHEDCC, here are the basics: A committee in AMATYC (called “Technology in Math Education”, or TiME) created an email discussion list to facilitate conversations among AMATYC members.  The actual list was hosted at various servers, and is currently at the Math Forum.  However, late last year, the AMATYC Executive Board decided to discontinue the official connection between MATHEDCC and AMATYC.

I will not use this post to elaborate on the difficulties seen on the MATHEDCC list.  The purpose of that list, and of this blog, is professional development.  I wonder — can our profession make progress for the sake of our students in the absence of a community for our interaction?  Or, stated another way, does it make any sense for us to work more-or-less individually on improving our teaching and our curriculum?

For me, there is no doubt about the answers to these questions.  If we focus on individual and disconnected progress, the results will be smaller and be at higher risk of not surviving, compared to work by connected professionals.  Shared insights and progress create a change in the profession that is not possible when we are not connected.

Clearly, a discussion list is not the only way for us to be ‘connected’ in a meaningful way; we need to employ a variety of methods to work together (including conferences & blogs).  And, having a discussion list is no guarantee that we will remain connected.  At MATHEDCC, the sense of community is suffering because we do not adhere to a few basic & shared values about our interactions.  Perhaps the email list is not the best asynchronous communication tool at this time; maybe a bulletin board would be better (and there are other methodologies as well).

What do you think?  If you agree that our work needs to be connected among the professionals in our field, do we need a new place to do that (discussion list, bulletin board, etc)?  Are you motivated to help with this work?

Those were serious questions … please provide your answers.  Thanks.

 Join Dev Math Revival on Facebook:

Math – Applications for Living IV

I’ve seen the ads, often on the back of a semi-trailer, where companies say that they will pay so much per mile or so much per mile (and perhaps mention that drivers get to be home on weekends).  I can’t bring mathematics to the weekend issue for drivers, but I can  bring math to their pay system.

A typical rate of fuel consumption for the ‘big rigs’ is 8 miles per gallon (this is a little high, but is nicer for calculation!).   A truck’s speed is supposed to be 60 mi/hr in my state, and the average fuel price is $3.749 per gallon.  How much does fuel cost per hour?

    60 mi/hr * 1 gal/8 mi  * $3.749/gal  = $28.12  (rounded)

I have a problem like this on today’s test in my quantitative reasoning course (only it’s for a car, since not many of my students drive a semi).   If you are curious, a typical car would have  an hourly fuel cost of around $7 … we could get in to the cost per pound per hour, which adjusts for the much larger capacity of the semi for hauling stuff.  However, we can be sure that the average semi is loaded with far more than 4 times what a car carries.

Back to the start of this post … if a company pays semi drivers per hour, the driver has (normally) this fuel cost of roughly $30 per hour.  Now, when I see ads that say “$40 per hour to start”, I know that the real income is closer to $10 per hour.  If the pay is ‘per mile’, the calculation is a little simpler (1 gal/ 8 mi * $3.749/gal, which is something like $0.47 per mile).

Within our class, we are using problems like these to become more flexible in our proportional reasoning — a given rate can be represented in two fractions, with our choice being determined by looking at what we start from and what we need.
Join Dev Math Revival on Facebook:

Math – Applications for Living III

In class this week, we talked about ‘precision’.  Even though many of our math classes ignore this topic, students relate to it reasonably well.

One example — find the area of a rectangle that is 3.6 meters wide and 4.2 meters long.  The correct answer is ’15 square meters’, since each measurement has only 2 significant digits.  Calculating ‘15.12’ is only part of the story.  How this 15 square meters is used depends on the purpose for finding the area.  If we are estimating the amount of time needed to paint the area, it is fairly safe to work with 15 square meters … however, if we are buying the paint, we might do better with 20 square meters (1 significant digit).

Several students in class have been dealing with the concept of significant digits in their science class as well … isn’t it nice when people can see an immediate use for what we cover in math class?

The topic of significant digits is a natural whenever we cover geometry.  However, we tend to do a bad job with this; I suspect that we are too concerned about ‘keeping things simple enough’.  One of the larger errors on our part is the treatment of π.  In many books and courses, students are told to use ‘3.12’ as the value of this number regardless of the precision of the other numbers involved.  As you know, the correct process is to use all available digits and round the final answer to the appropriate number of digits.  The irony is that almost all students have access to the value of π to 10 or more digits (calculator or computer).  Let’s start doing good mathematics by having students use the built-in constant instead of the (always inappropriate) approximation.  [It’s always inappropriate because we are not supposed to round intermediate values.]

Another example from class: “A city has a deficit of 43.8 million dollars.  How much per person is this if the city has a population of 136,500?”   As a division, we can calculate any number of digits; many students would ‘naturally’ round the result to the nearest cent ($320.88), though this is not the correct value.  We often say ’round money to the nearest cent’, and this is quite appropriate with interest calculations.  However, it may not be appropriate in many other applications.

The topic of ‘significant digits’ (precision) is appropriate for most math classes, and is accessible to almost all students.

 
Join Dev Math Revival on Facebook:

New Life model – Compared to Statway & Quantway

I’m at the Statway winter institute (in Palo Alto, California), where we are getting some initial results from the Statway implementations going on this year — very encouraging, and the colleges involved have done a great job.  Makes me wish I was at a Statway institution.

I’ve also been having discussions in recent months about how the New Life model compares to the ‘Pathways’ (Statway & Quantway).   This has been addressed other places, but one aspect might help us understand a basic distinction.

First, let’s review — there are similar goals, and much common mathematics, between the New Life model and the Pathways.  The Carnegie Foundation has been gracious and inclusive in their work, which has enabled us to work on both approaches.  In both approaches, we seek to provide more appropriate mathematics for students and help them complete developmental mathematics more quickly.

So, a basic concern in Statway and Quantway is ‘recruitment’ — how do we identify the students who can take advantage of the Pathway?  The Pathways are designed to serve groups … Statway focuses on students whose ‘final’ course is an introductory statistics course, while Quantway is for students whose ‘final’ course is a quantitative reasoning-type course (with some variation in Quantway).  With the Pathways, a college has the existing sequence and then the Pathway alternative so that finding the students is a central concern.  This is especially the case with Statway, since it is a 2-semester sequence designed to be completed by each student.

In the New Life model, the vision is more general.  The first course, “MLCS” (Mathematical Literacy for College Students), is designed to connect with a variety of non-STEM college courses —  including intro statistics, quantitative reasoning, and others.  The second course, “Transitions” is used to connect to STEM-like college courses — such as college algebra, pre-calculus, and others.  The approach here provides flexibility to colleges and students.  Students identify their needed sequence of courses (hopefully 2 courses at most!) by looking at course prerequisites.

A difference between New Life and Statway is that Statway is a ‘2 semester set’ while New Life is ‘sequences for each student’ that follow patterns familiar to community college students — to take course X, the prerequisite is course A (which the student might or might not need).  Quantway is similar to the New Life MLCS, though the expectation is that Quantway students will proceed to take the quantitative reasoning course the next semester. 

In other words, colleges can build their own ‘stat path’ by implementing MLCS as a prerequisite to an intro statistics course.  Colleges can implement MLCS and Transitions as a replacement for the old courses.  Colleges can implement Transitions as a better bridge to STEM-like course; some might choose to do this for some STEM courses but not for ‘less STEM-like’ courses.  Transitions might be a better preparation for basic science courses than ‘intermediate algebra’.

New Life is all about flexibility at the local level to provide better mathematics preparation for their students.
Join Dev Math Revival on Facebook: