Math Applications for Living I

I’ll be sharing some applications that you might find interesting from the Math119 class that I am teaching this semester.  The title of this class is “Math – Applications for Living”, and that will tend to be the title of the post; this is number I in this ‘series’.

Here is the problem:  You are figuring out if it makes more sense to take a bath or take a shower, in terms of conserving money or energy (or both!).  The approximate dimensions of the bath tub are 6 feet by 3 feet by 2.5 feet, and you guess that it is filled halfway.  Your shower head, according to the manufacturer, has a flow rate of 1.75 gallons per minute; you guess that you take 10 minutes with the shower with the water running. 

A key step in solving the problem is being able to convert from cubic feet to gallons (or the reverse).  In our class, we focus on flexible use of fractions — proportional reasoning.  For this problem, we have the fact listed that there are 7.5 gallons in one cubic foot.  If you want the values, this bath scenario uses about 170 gallons of water while the shower uses about 17.5 gallons.  [We have not covered precision and significant digits yet, so I did not worry about whether they rounded the bath volume correctly.]

   0.5 * (6ft * 3ft * 2.5ft) = 22.5 ft³;     22.5 ft³ * (7.5 gal/1 ft³) = 168.75 gal  [Bath]           10 min * (1.75 gal/1 min) = 17.5 gal

The students were a bit surprised by the magnitude of the difference, and they seem to be getting more skilled at using these fractions.  We will see how they do next week when I give them a more challenging follow-up problem.

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Is Algebra Bad?

Today was the first meeting of my favorite class — Math119 is called “Math – Applications for Living”, which follows beginning algebra in our curriculum as one of the options for an associate degree.  Math119 is a mathematical reasoning or literacy class.

At the start of the class, I asked the group “Why did you take this class … it is not required specifically of any student?” 

The first answer:  “Because it is not algebra!!”  This got nods of agreement, and several students supported the comment.  These students — some accomplished, some challenged to pass — were taking a course that is essentially all word problems to avoid taking an algebra class.  Of course, I was honest and told them that I would be sneaking in some algebra in this class (which got some people laughing).

Why does ‘algebra’ have a bad reputation among some students?  Some readers will be sure that this is because we teach algebra without making it relevent for students, that the situation would be much improved by basing an algebra course on contexts that the student can identify with.  My conversations with students leaves me with the conclusion that this is quite untrue, for the majority of the general population; those students only interested in a quick path to an occupation based on training are the main exception.

No, I think the problem lies much deeper than ‘context’.  Our algebra courses cover topics in a disconnected manner, with unnecessary (and sometimes outlandish) complications in the problems … because we focus so much attention on procedures and correct answers.  It’s also true that we avoid applications of algebra that might involve ‘weird’ numbers or (gasp!) problem solving skills.  Most of our algebra courses, especially at the developmental level, are not respectful of human intelligence (including those at my institution).

I hope to share other experiences from this Math119 class; may you enjoy the stories!

 
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Pathways Webinar — January 24, 2012

Our friends at the Carnegie Foundation for the Advancement of Teaching are offering a webinar on January 24, 2012 on the “Pathways”.  See the information at http://www.carnegiefoundation.org/spotlight/webinar-updates-carnegies-work-in-developmental-math

This webinar has 5 topics listed: an update on student and faculty experiences, explanation of how faculty are contributing to the materials, the role of “productive persistence”, the use of analytics to plan, and how to get involved with this work in the future.

If you have been curious about the Pathways — Statway™ or Quantway™ — this is a great opportunity, and provides an early look at how to become involved in the work.

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Online Homework … Research

We’ve been talking, as a profession, about online homework systems.  To some, some of these systems are the ‘best thing since sliced bread’.  On the other hand, some basic ideas from learning theories suggest that the benefits may not be uniformly positive.

A general source, summarizing various research, is the MDRC report  Unlocking the Gate: What We Know About Improving Developmental Education  http://www.mdrc.org/publications/601/full.pdf  .  On page ES-7, the report states:

                     Little research has been conducted on these strategies despite their popularity, and the research that exists shows mixed results.

In general, we can trust that a report from the MDRC is valid and reliable.  I thought I would look for some additional research, in case you are interested.

http://editlib.org/p/32318

Laurie Lenz
“This study compares student outcomes in multiple sections of a required mathematics course. The sections differed only in the homework delivery method: WBH, PPH, or a combination of the two. Among other results, it was found that students were more likely to attempt and to receive higher homework grades with WBH than with PPH. However, the study found no significant difference between the exam grades of students in the WBH sections and the students in the PPH sections.”
[WBH means web based homework; PPH means paper & pencil homework]

http://www.editlib.org/p/33222

David Shane Brewer, Kurt Becker

“This research compared the effectiveness, in terms of mathematical achievement, of online homework to textbook homework over an entire semester for 145 students enrolled in multiple sections of college algebra at a large community college. A quasi-experimental, posttest design was used to analyze the effect on mathematical achievement, as measured by a final exam. The control group completed their homework using the textbook and the treatment group completed similar homework using an online homework system developed by the textbook publisher. All class sections followed a common syllabus, schedule, and homework list and completed a common, departmental final exam. The results of the research found that while the treatment group generally scored higher on the final exam, no significant difference existed between the mathematical achievement of the control and treatment groups. When students were divided based on incoming math skill level, analysis showed that low-skilled students who used online homework exhibited significantly higher mathematical achievement than low-skilled students who used textbook homework. Exploratory analysis also showed that more students with low incoming skill levels and more repeating students received a passing grade when using online homework than did their higher-skilled, first-time counterparts, although the differences were not significant.”

http://iisit.org/Vol6/IISITv6p285-298Buzzetto556.pdf

Nicole Buzzetto-More and Ojiabo Ukoha

“The results of this study were mixed and marked by high levels of neutrality; however, the findings did indicate that most students felt that the system was easy to use, a valuable learning tool, successful at having helped them to learn course concepts, and an aide that helped them to perform better on their assignments. At the same time, most student responded that they were not satisfied the system. The analysis of the student performance data noted a significant decrease in student withdrawal rates and a marked increase in pass rates for the course under consideration.”

 As you may have discovered, this research is not easy to find.  If you search online for research for online homework systems, most of what you see will be marketing materials from publishers of such systems with an occasional ad-hoc summary of what happened in a class or course — which is not research.  Research strives to answer a question in a way that can be duplicated and validated, and the marketing & ad-hoc reports do not qualify; they might raise valid points, but do not show what the results are relative to online homework systems.

Here is a list of online articles for this research:

http://jolt.merlot.org/vol7no4/baugher_1211.htm                              

 http://editlib.org/p/32318                                                       

 http://coe.ksu.edu/jecdol/Vol_6/pdf/theeffect.pdf

http://academics.georgiasouthern.edu/ijsotl/v4n1/articles/PDFs/Article_DoornJanssenOBrien.pdf                     

http://jolt.merlot.org/vol5no4/hodge_1209.htm

http://iisit.org/Vol6/IISITv6p285-298Buzzetto556.pdf                     

http://www.editlib.org/p/33222                                        

http://www.ifrnd.org/JEVR/1(3)%20June%202011/Enhancing%20the%20Study_of%20Business%20Statistics.pdf

http://www.math.umt.edu/tmme/vol3no2/TMMEvol3no2_SaudiArabia_pp176_183.pdf

 
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