Math – Applications for Living XV

Our Math – Applications for Living class is moving on to other material, much to the relief of the group.  We had more difficulty than usual this semester with our work with units and percents (the stuff on the first test). One problem in particular seemed to be more challenging:

A computer modem uses about 7 watts even when the computer is not on; the modem is left on constantly (“24/7”).  A home in Lansing pays about $0.1137 per kilowatt-hour.  For one year, how much does it cost to keep the modem ‘on’?

I know that one challenge was that the book gave the official definition of a watt (1 joule per second), which led a few students to think that they needed to calculate how many seconds in a year.  Given this, there might be a temptation to not provide that information.  However, ignorance is not good when it is by design; the course includes a variety of information that applies to life and to science, and is one of the strengths.  It does not help that the book does a similar problem by converting watts to joules (no change) then calculating the energy use for the time period in joules (for seconds in the period), and then changes the result back to watts per hour.

The correct calculation is not that complicated:

7 watts * 24 hr/1 day  * 365 days / 1 year =  61320 watt-hours per year.       This is 61.320 kw-h

61.320 kw-h * $0.1137 / kw-h = $6.97 (rounded)

A few students had the right idea, but failed to change to kilowatt-hours — they ended up with a cost about $7000 for this modem.  The “answer desperation” of students led them to record this answer, even though they could see that it is not reasonable.

This problem was similar to one we did as an example in class … the cost of leaving phone chargers plugged in constantly.  Phone chargers are a lower power drain than modems, but there are so many more of them that their energy use is an issue.  Other ‘vampire loads’ contribute to our huge appetite for electricity (most electronics have a constant power usage, even when ‘off’).

Hidden in this modem problem is a strange thing: students knew that ‘km’ is ‘kilometers’, but are stumped by ‘kw’.  This problem, I think, is caused by the mechanical way that metric conversions are presented (‘just move that decimal point as you move from the old to the new prefix’).  We connected that strategy to the standard method (dimension analysis in this class).

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MLCS — Math Literacy Textbook (Almy & Foes)

Since the start of the New Life work in 2009, the most common question has normally been “so, this is cool stuff … what textbook can I use?”  I have talked here about the general interest among publishers, who are interested in developing books for the New Life courses (MLCS and Transitions).

I wanted to give a shout-out to Kathy Almy and Heather Foes, who are getting very close to having the first MLCS book published (by Pearson).  Kathy & Heather have worked incredibly hard to develop a textbook, one that combines the content of MLCS with a design that makes learning accessible for students and teaching easier for faculty (especially adjuncts).

Recently, Kathy shared an image of the cover for their text, which is at http://almydoesmath.blogspot.com/2012/09/mlcs-book-preliminary-cover.html 
[The final bound text might have a slightly different cover.]

Congratulations to KathyAlmy, Heather Foes, and the folks at Pearson for getting the first MLCS book ready to publish.

[This is not a paid endorsement; however, my college will be using this Math Lit textbook for our new Mathematical Literacy course next semester.]

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Pre-Algebra Just In Time

In my beginning algebra classes, I made a number of changes for this year.  Some are related to pre-algebra as a prerequisite for success in beginning algebra.  For quite a while, I have concluded that a pre-algebra (or basic math) class is an inappropriate prerequisite to beginning algebra based on analyzing data; my experience this semester might provide an alternative.  Students need not spend an entire semester ‘getting ready’ for algebra.

At the start of our course, we have a chapter which reviews operations on signed numbers with a minor emphasis on very basic algebraic expressions (like terms, distributing, etc).  This chapter is essentially a typical pre-algebra course contracted down to one chapter; historically, I concluded that both experiences (a course, a chapter) did very little to enhance the readiness of students for algebra.

Instead of spending any class time on signed number operations, we spent every minute of class time on algebraic language, syntax, and concepts.  We talked about adding changing coefficients but never exponents, and about multiplying changing both (depending) … and followed this up with a variety of problems for students to struggle with.  Much time was spent on translations, but not just in to algebra: we did a bit of work on translating algebra into words; even when students remember the ‘right thing to do’ (procedure) there is often a misunderstanding about what the expression meant.

Given the equation concepts we will be studying, we covered zeros in adding and subtracting.  Take some time to interview your students about a simple problem like this:

5y – 5y = ??

When this  would come up later in the course, something like 20% of my students would report that the answer is ‘y’ — the fives cancel out, leaving the y.  Curiously, textbooks do not have problems involving zero for combining like terms, even though this is critical for later work.

Class spent a lot of time (very frustrating for students) dealing with the different uses of the ‘-‘ symbol: opposite, negative, minus.    Some of this was imbedded in the translation work, and others in procedural work.  As instructors, we are incredibly careless about reading the ‘-‘ symbol, tending to say ‘negative’ when it is ‘opposite’ (like ‘-x’).  The central issue here is often “do we have any options about how to treat this particular ‘-‘?”

To assess this change, I used the same test from prior years with some added ‘difficulty’ — 3 added questions on expressions (including the zero in adding).  The initial assessment is that the new emphasis (pre-algebra just in time) helped students with algebraic proficiency without harming numeric skills.  The average score on the somewhat harder test was almost identical to the average on the prior (easier test).  Obviously, this is not enough to assess the merits of the new approach:  if the change does not help students later in the course, then the new process is not good enough yet.  I am especially eager to see if the ‘zero’ in adding has been improved.

My belief is that we could improve the outcomes of developmental mathematics by a fairly simple change:  do not require any ‘math’ or ‘pre-algebra’ before beginning algebra, just some basic numeracy is good enough.  Some students have a direct need to know arithmetic skills for an occupation, but this is a different need than ‘algebra’.  By placing almost all students directly into beginning algebra, we eliminate a math course for a large group of students — without producing harm.  [From general data I’ve seen, the chance of success in algebra AFTER a pre-algebra course is statistically equivalent to the chance of those below the placement cutoff … and the numbers are not good for either group.]

However, I am also sure that our current algebra courses need to do much more about basic literacy issues — translations, syntax, paraphrasing, etc — as well as a more complete treatment of procedures (zero in particular, but also adding vs multiplying).  We tend to move too quickly into applications of literacy (procedures for solving equations, for example) without building the conceptual foundation required for understanding.    We need “Pre-Algebra Just In Time”!

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Webinar Recording Available — Reform in Dev Math (Treisman & Rotman)

On June 6, 2012, an AMATYC webinar was held on Issues in Implementing Reform in Developmental and Gateway Mathematics Uri Treisman and Jack Rotman; the web page http://www.amatyc.org/publications/webinars/index.html has links to view the 54 minute recording or to download it.

This webinar presented an overview of dimensions of reform (5 areas), some background on those, presented some choices in implementation, and reviewed some current reform efforts in mathematics (especially developmental).  Also included in the recording is the question and answer period based on participants’ questions.

The webinar was limited to AMATYC members, in terms of registration.  At this point, the recording is available as a professional resource to non-members as well.

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