Monthly Archives: January 2012

The Beef Taco Dilemma

This is a problem that I wrote for my statistics class.  The objectives for this problem are as follows:

1.  Compute percentages.
2.  Compute the arithmetic mean.
3.  Critically think about whether or not Joe had enough tacos to meet the ‘average’ demand.

 

What I found was some students had a hard time computing the percentages and some also had a hard time keeping straight how many beef and how many chicken tacos Joe ordered on each day.

FOIL is for BAKED CHICKEN

Here is why I believe that the FOIL method for multiplying two binomial expressions should NOT be used:

The underlying premise of the FOIL method is that students must first be able to identify a binomial.  However, most instructors do not seem to stress enough that the FOIL method can only be used to multiply two binomials.   We can only speculate on the reason for why they might not do this – Maybe they only teach multiplying binomials so they do not need to make any distinction or maybe whey wrongly assume that students will be able to identify a binomial.  However, in my opinion, if a student cannot identify a binomial, then they should not even be using the FOIL method.

Either way, what worries me the most is that fact that a student will get to a problem that involves multiplying expressions that are not binomials and will not know what to do.  If I would have taught the student the distributive property that can be used in every case, rather than the FOIL method that can only be used in the special case of multiplying two binomials, wouldn’t that have been a better use of class time?  

I have also had students who have asked me if they can use the FOIL method to multiply two trinomials and I, of course, tell them that they cannot.  But then the student objects because they  have just multiplied two trinomials using the FOIL method and want to show me that their answer is correct.

Even in the cases when the student has shown correct work and has arrived at the correct answer, I still have to cringe at the fact that the FOIL method involves the student multiplying four times and multiplying two trinomials involves the student multiplying nine times, but the student still wants to argue about the fact that he can use the FOIL method on every problem.  There is a big difference between four multiplications and nine multiplications.

I honestly believe that students would benefit more if we simply dropped the FOIL method and instead taught them the distributive property along with a review of counting properties by asking them to count how many different multiplications must be done before they even begin.  It is definitely one way that we could help increase ‘number sense’ in our students.

And ultimately, FOIL is for baked chicken, NOT for multiplying binomials.

PEMDAS is NOT a Word

Here is why I believe that the PEMDAS method for remembering the order of operations should NOT be used:

1.  PEMDAS is not a word.  In general, I believe that for mnemonic devices to have the greatest impact, they should be easy to remember words.  PEMDAS is not easy to remember and PEMDAS is not even a word.

2.  PEMDAS implies to students that there are six steps in the order of operations:  Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction, when in fact, there are only four steps in the order of operations.   How can we expect students to properly remember the order of operations if we are providing them with such a misleading mnemonic device?

3.  PEMDAS should not be used simply because it is the way that students want to be taught.  One student told me the other day that he was confused by the way that I was doing the order of operations simply because I was not using PEMDAS.  I told this student that he could continue to use PEMDAS if he wanted to, but he would continue to get incorrect answers (He is one of the students who thinks that PEMDAS has six steps).

4.  PEMDAS simply does not work.  If PEMDAS worked, wouldn’t students actually understand the order of operations?  The fact of the matter is that PEMDAS does not help students understand the order of operations.  PEMDAS did not work for students when they were in elementary school, why should it work for them in college?

I truly believe that my position as a college math instructor requires me to present the material differently than the students saw the material the first time that it was taught to them because whatever they were taught the first time obviously did not stick long term.  Although my ultimate goal is to help students refresh their memory, why should I refresh someone’s memory about something that is misleading and simply does not work?

Below is an example of the Order of Operations using the GEMS Procedure.  I prefer the GEMS Procedure because GEMS is actually a word and GEMS implies that the order of operations actually has four steps and not six steps.

Gems1

To further prove my point, here is an example of a problem that is incorrectly done using PEMDAS versus a problem that is correctly done using the GEMS Procedure. 

Gems2

I know that the GEMS Procedure is not going to become ‘mainstream,’ but I can hope, right?

Upcoming Conferences in Michigan

One of my biggest pet peeves is when I hear instructors complaining about the lack of professional development activities.  There are plenty of conferences to attend, wherever you live (I happen to live in Michigan).  I honestly believe that one of the keys to a successful teaching career is attending conferences, networking, and building a personal learning network.  To that end, I have compiled the following list of upcoming conferences in Michigan.  I hope to see you there (At this point, I plan to attend all of these).

January

Macomb Community College Math and Technology Workshop

February

Math in Action 2012

March

2012 Michigan Association for Computer Users in Learning (MACUL) Conference

Michigan Developmental Education Consortium (MDEC) Conference

April

Society for Industrial and Applied Mathematics (SIAM) Great Lakes Section Meeting

May

2012 Michigan Mathematical Association (MAA) and MichMATYC Meeting

June

2012 Michigan Joint Education Conference

August

Michigan Council of Teachers of Mathematics (MCTM) Conference

2012 Muskegon Community College Math and Technology Workshop

October

Meaningful Play 2012

MichMATYC Fall Conference

November

Detroit Area Council of Teachers of Mathematics Fall Conference

New Games, Activities, and Projects

In this post, I want to talk about a few of the projects that I have been working on over the break to use with my students in the upcoming Winter 2012 Semester.

Imag0220

1.  Electrifying Truth Table – This is an activity that a friend of mine got from Pete Wildman during the 2011 AMATYC Conference in Austin, TX.  The idea is for students to build multiple different circuits to model truth tables in different situations.  The one in the picture above is the AND Circuit since both switches (sets of paperclips) must be closed for the light to turn on.  The biggest pain in getting this activity up and running was getting the proper supplies.  It seems that in Michigan where I am from, there is no ‘one stop shopping’ for these supplies.  However, the activity is a good activity.  And I do have permission from Pete to share the activity with anyone who contacts me.  So, just ask if you want it. 

Imag0219

2.  Hedbanz Game – If you have kids, you may have already heard of the Hedbanz Game.  But did you also know that there is a Hedbanz Adult Game?  I only found this out because I was in Toys ‘R’ Us looking for the game, but they were sold out.  So, the salesperson asked me if I would like to buy the Adult Version instead.  The main difference between the kid and the adult version is that the kids’ version has pictures on it.  This got me thinking that I could use the vocabulary words and concepts from my classes to do a math version of the game.  The picture below shows me wearing a headband with the word ‘calculators’ that I am trying to ask yes or no questions to answer.  If you want a copy of the game rules, just ask. 

Img_2690

3.  Indian Mathematician Project – My school is really big on Multi-Cultural initiatives and one of the college-wide activities for the upcoming semester is a display about India at the library. So, I have decided to have my classes participate in the upcoming Library Fair by creating tri-fold posters about a famous Indian Mathematician or Indian Statistician.  A couple of my students last semester created a prototype of a poster for me.  Thus, I really have a good idea of what level of work that I am expecting from my students this semester.  I encourage all of you to think of one way this semester that you can implement a Multi-Cultural initiative within your own classroom.  I believe it is a really good way to raise awareness among our students about the importance of diversity. 

Imag0221

4.  Prime Number Tiles:  Revisited – If you have visited my blog often enough, by now, you know my frustration with teaching students about the Least Common Multiple and the Greatest Common Factor.  I have always wanted to use these Prime Number Tiles, but it did not seem worth the trouble or the expense to me to buy the scrabble tiles or cut out the paper number squares.  But I have found a solution that I really am happy with.  I am going to write the numbers on the backs of dominos that I got from the dollar store, which is 40.5% cheaper than using the Scrabble Tiles

 

Taking the Fun Out of Enjoyment

Last weekend I cleaned out my apartment over a period of three days.  I was even called a hoarder on Twitter.  Anyway, three days and multiple bags of trash certainly give a person a lot of time to think and reflect.  The majority of what I was throwing away was papers from when I used to teach at other schools as a part-time instructor.  I had to keep the papers at home because I never had an office.

What struck me as odd though is looking through all of the student work I had kept from over the years and realizing that I used to have fun in my classes.  I used to have students do in-class presentations on famous mathematicians, create games and puzzles related to the unit we were studying, and do a lot of other fun paper-based activities when I first started teaching.

But now that I am trying to create more games, activities, and projects for my classes, I actually feel like my classes are less fun than they used to be.  The students still think that the classes are fun.  I am just saying that my own perspective has changed.  Does this mean that I am headed in the wrong direction and that I am headed for doom?  Or does it just mean that I am not as naïve as I used to be and I am more focused on the specific objectives of each game, activity, and project?

I go into every semester thinking that it will be different, that I will have lots of games and activities for my students to do throughout the semester.  But somehow it always turns out that after the first few weeks I begin to get buried in grading and the usual junk that always comes my way as the semester gets underway.  I am not sure how to prevent this from happening, except by better planning on my part.

So, what I can I do differently to ensure I will have fun in class, as well as my students?  Do not get me wrong, I really enjoy teaching.  I tell that to my students all the time.  I make sure that my students are very aware that I enjoy and like what I do for a living.  But I feel as if I have come to a point where I have taken the fun out of enjoyment.  Is it really possible to enjoy something without having fun?  I really hope that I am wrong and that I am not headed for doom.

First Day Policies and Activities

Below is a list of rules that I plan to give to my students on the first day of class to try to prevent some of the behaviors that bothered me last semester from occurring again during the upcoming semester.  If the tactics in the handout seem a little extreme, good, I mean them to be.  I want students to realize that certain behaviors have consequences, both for the low achieving students and the high achieving students, both at school and at home.  I know that I will not get through to every student, but if you like my handout, feel free to tell some of the stories in your own classroom.

The_Rules.pdf
Download this file

As for how I am going to present the rules on the first day of class, I am going to use the grid below.  The students will be given a blank version to fill out while I am giving an overview of the course policies.  I plan to give this to the students before I even pass out the syllabus.  So, the first piece of paper the students will receive from me is a sheet of paper that they have to take notes on.  I hope that this will instill in them the importance I place on taking notes in class, as last semester I had way too many students who did not take notes and then when they did not understand how to do a problem, wanted me to redo the entire examples for them.  By the way, I got the idea for the grid from Dan Meyer’s First Day Wiki.  He has example of one that he uses in a high school geometry class there.   

Syllabus_Grid_Version_web.pdf
Download this file

Another thing that I am going to do on the first day of class is the coin problems that are listed below.  I got this idea from last year’s MichMATYC Fall Conference.  The idea is to give students logic problems to work on in small groups on the first day of class so that they can get a feel for working in groups in a less intimidating setting.  I hope that this activity will help instill in my students the importance that I place on group work and participation in class.  I really believe that students learn the most when they are given the time and opportunity to explain the material to each other during class.  And for your convenience, the answers to the problems are on the second page if you want to use them in your own class.  I actually got my selection of five coin problems from a website of multiple coin puzzles. 

Coin_Problem.pdf
Download this file

For those of you teaching statistics, you may be interested in Sugar Coated Statistics or this blog post from the Sage Statistical Blog on Starting it Out Right.

I hope you enjoy your semester!

Review of ‘GridPaper’ iPad App

Picture

GridPaper is an iPad App that recognizes handwritten mathematical symbols.  You can use this App to perform operations and to solve equations.

During the Fall 2011 semester, I evaluated GridPaper to see if I would like to use it with my students.  All of my students who saw me using this App really thought that it had the potential to be a great learning tool.  They liked that the App uses handwriting recognition software, but I honestly do not believe that the like of this App went any deeper than just the ‘wow factor.’

For me, the most frustrating thing about using GridPaper is that it did not come with instructions.  When you open the App, there are a few instructional diagrams, but no words explaining what everything does.  So, everything I know about the App now came from trial and error.  I still have trouble writing certain numbers using the App, pi being one of them.  My advice is to write all of the numbers that you want to use first (see the top of the Screenshot above) and then pull them down to do the operations.

If you are interested in trying some of the advanced features of GridPaper, such as using variables or pi, you will definitely want to check out the three screenshots provided on the GridPaper Preview Page.  I would not have been able to figure out how to write certain characters without the Screenshots.  And it took me two months to figure out that those Screenshots were even there since they are not accessible from within the App.

Overall, except for the ‘wow factor,’ there I do not believe that GridPaper is a good choice.  It could be made better if there were proper documentation and examples that could be accessed from within the App, but without it, the App is just too frustrating to use.  I cannot ask students to spend hours upon hours just to learn how to write pi. 

I would give this App 1 out of 5 stars.

 

Reflections of Former Part-time Instructor

Last semester (Fall 2011) was my first semester teaching full-time.  As such, I have learned a lot of lessons about what bothers me and what does not bother me.  However, the biggest thing I noticed is that when certain behaviors bother me now, I actually want to do something to prevent them from happening again in the future.  But during my eight years of teaching part-time, I never did anything about it.

That got me thinking about why if those behaviors bother me so much, why I never did anything about them in the past, as a part-time instructor.  Here are a couple of my thoughts on why part-time instructors might be less likely to take action:

1.  They are scared.  First of all, they are scared about losing their job.  Many part-time instructors have multiple positions at multiple schools because they actually need the money.  So, if they tell students not to do something, it is quite possible that the students might complain.  And the fear among a lot of part-time instructors is that if there are too many student complaints against them, they will be fired.

2.  Lack of support.  Many colleges I have taught at in the past seemed to have supportive administrators until I actually needed to enforce the rules.  When I started to enforce rules, the administration started complaining about the increase in students in their offices due to my enforcement of the rules.  Several times, in fact, I was told to just to be quiet and give the students the grades that they wanted.  After a while, I just got fed up and just gave up.

3.  We’ll never see those students again.  As a part-time instructor, I generally taught the same developmental math classes every semester.  So, it was very rare that I would ever have a person as a student more than once.  Thus, if there was a student who really bothered me one semester, it was very likely that I wouldn’t have that student again since the student would be moving on the next class that I would not be teaching.  Problem solved, right?  Until the next batch of students arrived.

I know I am probably stating the obvious.  So, what can we do to change the classroom environment for our part-time instructors?  I honestly believe that we need to reach out to them and share our ideas about what has worked for us in the classroom and what has not worked for us in the classroom.

I have to say, every semester the first day of class becomes more and more scary for me.  I now know it is the most important day in terms of setting the tone for the semester.  The very first semester I taught, I was nervous on the first day of class, but not scared.  There is a big difference between being nervous and being scared.  But none of this means that I have to come to class every day for the next sixteen weeks dealing with behaviors that I should not have to put up with in the classroom.