Teaching Math or Teaching Quantitative Literacy….and What About Calculators?

A couple semesters ago, I had an incident in my developmental math class that has transformed my philosophy on education.

Let’s set the stage:

Casio fx-991ES Calculator (Photo credit: Wikipedia)

This was a MAT 65 class (Beginning Algebra for those not familiar with Hopkinsville Community College’s courses).  We were getting near the end of the course.  This course is heavy in algebra manipulations (i.e. what steps do you do to get the right answer).  At the time we I was teaching the course, the departmental philosophy was to not allow calculators in the class…or at least on the common tests.  While I adhered to this rule for the common tests, I tried to do as many applications as possible during the course as appropriate.  I try to impress upon the students that the skills are nice, but the real world rarely has “nice” numbers.  Using a calculator is essential many times, so I allowed it at these times.  While most of the class was able to manage on the quizzes without the use of a calculator, I had one student who really struggled.  He had the algebra concepts down pretty good (or at least as good as the rest of the class), but when it came to taking the tests he struggled.  I eventually realized that his skills in basic addition and multiplication were his weakness.  He knew what steps needed to be done, but wasn’t getting the right numbers.

 Near the end of the course, I gave the class a project one day.

I took it from an episode of Seinfeld.  In this episode, the character Newman noticed that recycling in Michigan paid an extra 5 cents per can than in New York.  He thought that if he rounded up enough cans, he could take them to Michigan and collect a larger reward.  The character Kramer tried to convince him that the costs of transporting them from New York to Michigan would be more than the profit gained.

I gave a similar problem to my class.  I asked them to create a scenario for transporting cans from Hopkinsville to Michigan.  The algebra (at the level of the class) involved in this problem was minimal.  It was mostly some arithmetic calculations mixed in with a few geometry formulas.  I let the students use a calculator.

 What I noticed as the students got started

was that most of them struggled to get started.  They were able to find the numbers that they thought they needed, but when it came time to do the appropriate calculations, they were lost.  They would’ve known how to do the calculation, but didn’t know what to do.

Confused (Photo credit: CollegeDegrees360)

Conversely, the one student who struggled without a calculator was the “class champion” for this activity.  He immediately knew what numbers he needed to get, what do to with them when he got them, and how to get the final answer.  He easily had the best summary in the class and got it much faster than anyone else.

So here came my epiphany

….what is our job as teachers?  Are we simply to cover the material as presented so the students can be successful on the tests (teaching math in my case) or are we supposed to arm the students with the skills and make sure that they are able to know how to use them when they are called for (quantitative literacy in my case)? The results of this class activity have transformed my philosophy of teaching.  It doesn’t do me or the students much good to teach them material just so they can perform on a test.  If they don’t know why they need these skills and how to use them when asked, then I feel I have not done my job properly.

In the time since this incident I have tried to re-organize all of my classes.

Numbers (Photo credit: RichardBowen)

I am trying to minimize the use of exams and instead have created more activities/projects like the one described above.  Students will be graded on how well they can use the material that I teach them as opposed to simply memorizing it.  I am finding that this approach is working well.  As a teacher, I am less likely to teach a skill unless I have a good activity to show the students why it is relevant.  It has taken a lot of work to create activities and projects that incorporate the needed skills that can be completed in a timely manner, but I am getting there.  It also involves telling students on the spot “this isn’t right” as opposed to a number on a test paper as it is returned.

The Never Ending Math Problem (Photo credit: ddluong_)

However, I am finding that once the students realize what is expected of them they are working harder to actually learn the material.  I am also finding that the students are accepting their lack of understanding of the material.  When asked to perform on the spot, students are quick to admit that “they don’t know it”.  When these occasions happen, I find that those students have a much better attitude about learning the material for the next time.

Oh, and one final effect of this activity:

When I shared this story with my colleagues, we decided to re-visit our departmental philosophy on calculators.  We now allow calculators in the MAT 65 course since we realized that the lack of success for some students was not the conceptual ideas that we were supposed to be teaching….it was the number-crunching.  Allowing calculators, we are finding we have more time to spend on the concepts as we don’t have to continue to re-teach the arithmetic portions.

Trig or Treat

Ms. Matthews was the high school Trig teacher. She was quiet but firm—somewhat understated in demeanor with her low voice—but enthusiasm for math vibrated beneath the surface of her mildly stoic way.

One test came back with every problem wrong since I had mislabeled the sides of the right triangle that has sides of 1, 2, and square root of 3. Having drawn only one triangle to use for all of the calculations, everything depended on starting right. Reversing the two longer sides meant a moment of teen drift (which some say can grow into adult drift).

After a moment of shock, reeling from prospects of a zero test score, Ms. Matthews called me up to her desk when the class got busy on the next exercise. She had a faint, pithy smile that radiated compassion as she explained that all calculations had been performed correctly, just not using the triangle’s correct value for each of its sides. “You were consistent,” she said, “and so you made an A on the test, but be more careful next time.”

This is the moment in the course that stands out in memory. All else long ago faded, except of course Ms. Matthews the person.

Greater Winnipeg Tentative Airport Plan (1946) (Photo credit: Manitoba Historical Maps)

Twenty –five years later in 1991, during a lull at work in a lab for testing asphalt samples from trucks hauling the asphalt to Fort Campbell for construction of an aircraft runway, I noticed a book on surveying on the supervisor’s desk and looked through it. It was trig. What a late awakening to what had only left an imprint in high school as mathematical abstraction. “So that’s what they use this stuff for!”

No wonder the blue collar work force used to chide folks who only had “book learning.”

Related articles

• 5/12/13 – Happy Right Triangle Day! (MrHonner.com)
• Design Friday: Trig (ifiwereartemis.com)

Math Anxiety: Treating the Pain

Wile E. Coyote and Road Runner (Photo credit: Wikipedia)

or “MEEP MEEP!  Using the Roadrunner to distract students from the “painful” math.”

I was recently given an article to read which talks about how some students’ brains process math in the same way the brain processes pain.  The article did stipulate that similarities occurred as the student anticipated having to do math (go to a math class, do homework, take a test, etc) instead of actually doing the math.  I found this to be informative and troubling at the same time.  I knew students have (or claimed to have) math anxiety, but didn’t really know there was a physical connection in the brain.  However, knowing that this may be the case it can help to prepare students to learn math differently.

On the plus side, I think I have been trying to combat this for several years even though I didn’t realize what I might be doing.  I have known that students either didn’t like math, didn’t think they were good at it, or didn’t take an interest in it.  I can understand why.  In many cases, it has been taught in a very dry and rigid manner.  I think back to some of the math teachers I had.  Some were excellent…..but then some were so disconnected from the class that I had to wonder how anyone got anything out of the class (I barely did and I LIKE math!).  Once I became a math teacher, I dedicated myself to do what I could to try to make the class appealing to the students…..without lowering the standards.  Hopefully reading this article and how serious the issue is to some students will re-kindle my enthusiasm in this area.

So here are some of the things that I’ve tried…..

I try to get them hooked on the very first day.  Based on this study, it now appears that the first day of class causes some “trauma” for students.  I want to help dismiss that as soon as I can.  The first thing I do with each new class is give them a “scavenger hunt” to do.  They have to mingle around the class and find other students who can sign their sheet.  There are 20 items on the sheet.  Some of the things I have them look for in my College Algebra class (for example) are:

• Someone who has watched/watches Roadrunner and Coyote cartoons
• Someone who owns a horse
• Someone who has bought a hot dog from a street vendor
• Someone who has read the Harry Potter series

My hopes are that these just seem like totally random items.

Once they are finished, I let them know that all of the items on the sheet will tie back into the course at some point.  I tell them that we will be watching Coyote and Roadrunner cartoons, running a hot dog stand, etc. during the course.  As I am saying this, I can usually tell by the looks on their face that they have perked up.  If I could read their minds, it seems as if they are thinking “whoa, this sounds like it is going to be much better than I expected…..this could be fun”.  That is what I am going for.

If all they expect is the same old dry and rigid math, then why would I expect anything but the same old dry and rigid responses from students?  I have found that by using non-traditional math items, I can almost “trick” students into getting immersed in the math before they even realize it.  By the end of the lesson, they are often surprised at how much math they have learned…..especially when they didn’t realize they were being introduced to something new.

There They Go-Go-Go! (Photo credit: Wikipedia)

My advice to other teachers would be to try to find ways to tie your subject material into the everyday world around you.  Look at the things that your students ARE interested in and bring those into the classroom.  If you lead off a class with a subject, video clip, story, etc. that is not directly related to your subject and then work your subject in, you will find that your students will be more engaged.  At any rate, if the study is true that students’ brains register “pain” at the thought of having to do math, then replace their thought of impending math with a thought of another subject.  Good luck!

(*FYI for those curious…I use the Coyote and Roadrunner to cover quadratics and polynomials, the horse problem in doing maximum area problems, the hot dog problem for business applications of revenue and profit, and the Harry Potter books when covering ellipses.*)

—Pat
pleasureteam notes:  The article about math anxiety and physical pain can be viewed here.   ScienceDaily is one of our featured Super Sites.  On Friday, Anne will share a great story about the site’s influence on one of her students.

Related articles

• Math anxiety: The brain can feel the pain (eschoolnews.com)
• When people worry about math, the brain feels the pain (scienceblog.com)

Guest Blogger, Bonny Prudhomme, asks “Math just isn’t that PUNNY, or is it?”

True to self, I can’t keep bad puns and artwork out of the classroom. After all, they are a big part of my personality. Infusion of my personal style, however, has gotten more challenging lately. Our math department elected to go REDESIGN. This means that my students receive lecture via canned videos and not through me. But I still have numerous opportunities to give 1-1 help to students who are actively working on their homework in a computer classroom.

To aid in these little bursts of information sharing, I have developed handouts which focus on troublesome math topics. I pair up bad puns and free clip art to make the instruction less threatening and more memorable.

Remember the mnemonic: “Please excuse my dear Aunt Sally”? If was meant to explain the order of operations. My handout is headed by the caption: Aunt Sally should have taught me math instead of baking me cookies. It is paired with a cartoon of a grandmother rolling out dough and child watching at her elbow.

Another was designed to illustrate metric conversion. That mnemonic translates to “King Henry died by drinking chocolate milk”.  I led this handout with: King Henry should have stuck to drinking ale. A cartoon of a king in his chair was an easy find on Microsoft free clip art sites.

Bottom line is that these handouts are easy to design, personable, fun, and easily remembered by students …. especially the 2^nd time around when I encourage them to pull out King Henry for a little review.

Bonny Prudhomme is professor of mathematics at Hopkinsville Community College.  She is known for her dedication to helping students master math and for her innovative teaching style.

Pleasureteam note:   For a different take on Aunt Sally, check out: http://blogs.edweek.org/teachers/coach_gs_teaching_tips/2011/01/math_teachers_please_excuse_dear_aunt_sally–forever.html
(Warning: he is not an Aunt Sally fan!)
For King Henry, there seem to be a lot of variations.  One that we found, complete with PPT, is at :
http://freedownload.is/ppt/king-henry-metrics-15237712.html