A Little Social Justice Education

In my Geometry class we are deviating from our normal Geometry studies to learn about statistical representations.  I chose to use real world data from the US Census Bureau to investigate the wage gap in America.  I had the students break up into pairs to compare/contrast the data distributions of the median income of Americans based on Race or Gender.  I’ve included a link to the assignment at the bottom of this post.  Hopefully, we will get to have some interesting conversations based on the students results.  I had them exclude Puerto Rico and Washington D.C. from their projects due to that they were large outliers in the data set.  This should be part of the conversation and was used in our pre-project discussion.


Wage Gap Project Description and Data

Teaching Trigonometry

I decided to try a new approach to teaching trigonometry this spring.  In the past I have used a scaffolding approach by reviewing my students knowledge of right triangle trig from geometry.  Then I extend their knowledge slightly by finding trig values for non-acute angles and negative angles.  Next, I would introduce Radian measure as length of an arc on the unit circle.  Then finally leading into trig on the unit circle.  Again, the mentality of this was to make connections with previous knowledge to maximize long term retention.

This year I changed it up and jumped right into using the unit circle for all my trig definitions and worked back towards their geometry knowledge using the EngageNY curriculum.  So far, this has been a tremendous success.  My students have a much better understanding of Trig, than they have had in the past.   I’m crediting this to not only the sequencing and mindset created from the curriculum, but also the student centered explorations presented in the curriculum.  I would not rank this curriculum as the best out there, but it is better than many.  When you add in the free price tag, EngageNY is a great resource.


Engage NY

One of my personal teaching goals has been to incorporate more student centered and exploratory learning to my lessons.  There are a lot of these lessons available for free on the internet.  The problem with this approach is that they do not follow a single theme, strategy, or approach to learning.  This results in confusion for the students as they have to adapt to new styles, notations, expectations, etc.  Much of the time learning focuses on learning each lessons nuances than the activity itself.  My department has also been looking at the Core Plus and Interactive Mathematics Program.  So far, both these programs seem to fit my students needs and my goals, but implementing a new curriculum is costly and requires approval from many parties.

The solution may be in EngageNY.  This is a curriculum put forth to meet the common core standards for the state of NY which features student based explorations and multiple representations.  I have used a few of these modules in my classroom with a lot of success.  Many of these modules meet my courses scope and sequence requirements.  Yet, the lessons create a broader understanding of concepts than my current curriculum affords.  Also, its free for use.  So far the only drawbacks I have found include: not enough kinesthetic learning opportunities, lack of support materials for extra practice or absent students, assessments that are publicly posted, and large amounts of material that need to be printed for student use.

This spring I plan on replacing my trigonometry units with the modules from the EngageNY curriculum.  I will post my results in May concerning this.

Patriots “Inflate-gate”

I wish to thank the NFL and the New England Patriots for giving all of us STEM teachers an opportunity to help teach some science.  During the AFC championship game, the New England Patriots were found to have been using balls during the game that were under inflated.  I’m not going into the football or controversy behind this, the press is all over this.  Go and run an internet search for these kind of details.

I’m interested in the Physics here and the opportunity to teach students some relevant classroom curriculum. Much of the media and fan rantings is that when the ball is inflated in a warm area and then brought out to the cold field it will decrease in pressure.  OK this makes sense.  Let’s check out the Math(eek, not Math!!)

According to the Ideal Gas Law.  Gas (like air) has a relationship spelled out as PV=nRT.
P is the pressure of the gas
V is the volume of the gas
n is the number moles of gas there are (how much air)
R is a constant for used for the gas
T is the temperature of the gas.

The balls weighed before and after the game have things that will not change such as Volume of the ball, number of moles of air in the ball, and the constant of the air.  So the only variables are the pressure and temperature.

First, this law is used with SI units.  So we need to do some converting.  According to NFL rules all balls to be used in the game are to be inflated to between 12.5 and 13.5 PSI of pressure.  Using Google to convert the units that’s 86,184.4662 to 93079.2235 Pascals of pressure in each ball at game start.  For argument’s sake, let’s say the room temperature the ball’s were checked pre-game was at 72 degrees Fahrenheit.  Again, using the wizardry of the internet, this converts to 295.372 degrees Kelvin.  Game start temperature was reported to be about 51 degrees Fahrenheit.  But, the ball issue didn’t become apparent until the third quarter, it had gotten colder out.  Let’s say it got to about 40 degrees Fahrenheit (the temperature it was on my way home after the game.)  This converts to 277.594 Kelvin.  Much of the conversation I have found on the internet has failed to convert the numbers to SI units making some pretty odd results.

Going back to the formula, we will be looking at the on field pressure at 40 degrees Fahrenheit.  The balls would drop to between 87997.2 and 87476.9 Pascals of pressure or 11.7 to 12.7 PSI.

So, yes, the cold weather would make a difference in the pressure of the balls used in the AFC game.  But, the NFL reported the balls used by the Patriots were under inflated by over 2 pounds per square inch.  The cold could not have accounted for this much pressure drop.  I’m not claiming the Patriots knowingly cheated, there are too many people involved in the handling of those balls.  But, I do claim that the under inflation was not due to weather alone.

self learning

The most important job I have as an educator, in my opinion, is to leave my students with the ability to teach themselves.  After all, once they leave our schools they will have a lifetime of learning to acquire.  Most of which without a formal teacher.  I’ve been introducing lessons which make the students use manipulatives, software, and internet resources such as Kahn academy and web quests to learn math skills.  All I’ve been getting from my students is, “I don’t get it”, “how do I do this”, or the usual blank stare of daydreaming.  I know they can give more than i’m seeing, but laziness and unwillingness to think for themselves takes presedence.  Research may state open ended and student centered lessons create better thinking and greater learning outcomes along with higher levels of engagement.  Yet, many of my students will just sit there and do next to nothing unless I hold their hands throughout the exercise.  It has been an uphill battle I have made very little gains with, but I refuse to give in.  Any thoughts on turning this classroom culture around would be greatly appreciated.  Grades are not a motivating factor.  Most of these students have come accustomed to failing and D’s are welcome surprises.

Technology in the classroom

So, I’m currently introducing cloud technology and geometry software into my classroom. Following the state common core standard of using technology to make geometric constructions, I have decided to use geogebra software this week to teach the students about parallel lines and angle pair relationships. I had blocked off two days with the computers to do this. In addition to using the software the school has set up all students with Google accounts so we may share files through Google Drive.

First, we had to set up the google drive accounts, then link the accounts with Geogebra’s chrome app. With the various levels of technology exposure and some students not yet setting up their accounts, we experienced much frustration and time consumption not learning anything related to Math. But, in the end, we persevered and got to the geometry program.

Next, we started using Geogebra’s graphical tools to make parallel lines and angles. Again, this led to much frustration and time consumption as students learned to navigate the environment. In the end, I believe students reached the learning outcome. I’ll know later this week with added assessment.

Many students were frustrated using this approach to learning. I tried to emphasize that cloud computing, computer based collaboration, and exploration is where commerce and education is moving towards and will be a part of a successful career. Also, I hope that with this trial and error and self learning, students will have greater retention than with traditional lecture methods. I just hope the learning doesn’t get lost in the frustration of learning the software.

Also, I hope the time used in this experiment is worth it, it took 3 class periods to finish. I could have taught this lesson in just one class period using other methods (such as patty paper geometry or lecture/discussion). I will continue teaching through Geogebra throughout the semester and hope that students will enjoy this more once the initial learning period is completed. Any thoughts, comments, or suggestions are greatly appreciated. I will continue to discuss our progress in this endeavour.

Here is a copy of the instructions I gave my students:
Parallel lines exploration

Exponential Growth Lab

There is a lot on the web for students to model and explore exponential growth patterns. A quick web search pulled up a lot of options for me. I really liked this one: m&m lab. Just be warned you need a lot of m&m’s. Some groups had populations over 400. I placed the students in pairs or groups of 3. Any more than this I feel would be very unproductive for some members. This was a great way to demonstrate how the growth pattern was produced by a constant (or near constant) multiplicative change as apposed to a constant additive change brought by linear growth patterns. I will emphasize this again as the class moves towards learning about sequences and series.

e and natural logarithm

Over the past few years I have been teaching exponential an logarithmic functions as part of my course load. A student teacher I was working with found this great website which explains many Math topics in easy to grasp visual and contextual ways. I really like the authors explanation on compound and continuous interest as it leads to the famous (1+1/x)^x formula. I use this explanation with a little hands on activity in the classroom and it really helps.

The website is betterexplained.com

Music and Acoustics in the Mathematics classroom

I am currently teaching a hybrid algebra 2/trigonometry course this year. I know there is a ton of acoustics material that relates directly into my curriculum. In particular I am looking at exponential and logrithmic models (i.e. fret placement on string instruments) and modeling sound with trigonometric functions. I have a few online resources, but not enough to create an entire unit of study. Any help in this endeavor would be greatly appreciated.

Direct Variation Using Virtual Lab

I recently gave a lesson on direct variation. I normally do an informal exploration using Hooke’s law to demonstrate this. This year I found a website with virtual science labs through the University of Colorado. This website has a ton of awesome interactive activities. I think the lab lost something when I took away the physical Hooke’s law devices, but the simulation gave me a lot more avenues to explore. I look forward to expanding this lesson in the years to come.

Link to the PHET website:


Link to my activity worksheet:

hooke’s law (word document)