Mathematics at Sturgis: A Walk through the Math Department (Summer 2013)

By Robin Singer

The World’s Largest Graph

Why do so many Sturgis students enjoy math class and find the material relevant to life? Their parents, the department of education, and the media praise the Sturgis Math Department for preparing students well for standardized tests and for college.  But that is an artifact, not the focus of what the math teachers at Sturgis do.  Let’s walk through some Sturgis math classes to see what the math teachers do differently than many of the math teachers of the past.

When you walk into Jo Mary Pontes’ Math Studies Class, you are likely to observe the students learning something really practical.  You might walk into a lesson centered on financial math, and learn what it really costs to borrow money for college.  On a different day, you might find Ms. Pontes explaining a math topic associated with civics – how “gerrymandering” (rearranging the voting boundaries to help a given political party) is accomplished.   Ms. Pontes adds her own flavor to the IB program, in the spirit of the IB Learner Profile, which encourages teachers to help students become “Knowledgeable”.

Function Machine

Like Ms. Pontes, Ms. Singer adds her own enthusiasms to the pre-IB and IB curriculum; in her classroom she emphasizes engineering.  She builds in a “function machine” project when teaching ninth grade math and a “composite function machine” project in Standard Level Math.  Besides enhancing those IB topics,  these “engineering” projects show students how mathematical constructs can be implemented in “hardware” – that all the theoretical math they are learning can be used to build machines, machines which work according to the mathematical plan the student specifies.

You will therefore not be surprised to walk into her room and see student projects using balls, marbles, dice, boats, switches, train cars, coin combinations,  or lights going on and off  as inputs and/or outputs.  The machines might be made from Popsicle sticks, train tracks, water basins, soda bottles, paper towel rolls, or cereal boxes; the ideas come solely from the students’ imaginations.  For some students, this project has excited them about the field of engineering and given them an academic direction.

But it may not be engineering you see when you drop in on Ms. Singer – you may find her students dancing.  Well, they are not really dancing; they are acting as the vector representation of lines.  A clapping hand represents time in seconds; one student is moving according to the parametric ‘x’ equation, another to the parametric ‘y’ equation, and a third is moving as the resultant vector equation of the line.  Sturgis teachers like to add kinesthetic learning to math class.

function projects in september 2011 047Would you rather prepare for covert operations?  A trip to Ms. Sandland’s class could introduce you to the use of “codes” to send secret messages as part of the matrix unit in Algebra 2/Trigonometry class.  Matrices have long been used in cryptography, and Ms. Sandland’s students are learning some of the theory behind encryption.

Or do you prefer visual demonstrations to paper and pen work?  If you enter Ms. Sandland’s Algebra 1 class, you might find students learning the concept of slope by watching a ball roll down a two-by-four.  Such visual demonstrations help students understand the concept in a much deeper way than looking at pictures drawn on a white board.

Another activity for visual learners can be found in Mr. McKay’s room, during the unit on quadratics.  He asks the students to concentrate on his face.  He traces the shape of his face, from ear, around the chin, to ear, and shows the students how much it resembles a parabola.  He gestures the line of symmetry, which goes through his nose.  His ears are the “zeros” or x intercepts of his parabola, since he has drawn the x axis horizontally through them.  No need to bring in cheat sheets in Mr. McKay’s class; just look at his face during the test!

If you are ready for an amusement park after all this work, just amble over to Mr. Dunigan-AtLee’s Math Studies or Standard Level Math class.  Dora the Explorer and her pet monkey may be riding a tangent line roller coaster on “function tracks” and the students are raising their arms up as the car ascends the tracks and lowering their arms as the car descends.  They are learning how the slope of the tangent to a function is the first derivative of that function.  This kinesthetic and visual experience, provided by Mr. D-A’s top notch programming skills, illuminates a crucial calculus concept while they are having fun.

aaronBut it is not only his clever programming that makes Mr. D-A’s class so educational and so much fun.  He found a kinesthetic way to teach probability trees.  Called “Student Pinball”, Mr. D-A’s students roll dice and make their way to the walls of the room depending on whether the dice have even or odd results, or show prime numbers versus composite numbers.  The laws of probability are demonstrated with the students as data points, and the motions the students follow mimic the tree diagrams they will need to understand in order to solve SL math probability questions.

Math teacher John Tecklenberg found a different way of combining probability and fun.  His students learn the concepts associated with randomness and probability by throwing magnetic darts at a dart board.  Playing darts is active learning; it is known by educators that active students learn better.

Divya Johar also wants her algebra 2 students to have be active and have fun.  She plays the “I Have, Who Has” game with questions and answers on cards.    She brings out board games to teach factorizing and other crucial skills used in IB math.   The students respond with an enthusiasm for learning that is not seen when more standard techniques are used in the classroom.

And if you are hungry when you reach her class, you can hope she is teaching about exponential decay, since she uses Skittles and M&M’s to teach this concept.  By repeatedly throwing out the candies on a plate, and removing the ones with symbols sides up, her students are able to graph the trial numbers as the independent variable and the number of remaining candies as the dependent variable and produce a graph of exponential decay.

When you enter Randy Carspecken’s class, you might see just about anything!  Mr. C is known for creative projects of all kinds, some of which, like his binomial distribution board, reveal his considerable skill as a craftsman.  Golf balls can be dropped into his binomial board and natural laws bring them into a pattern known as the binomial distribution, associated with “Pascal’s Triangle” (the pattern of  values of coefficients produced when binomials are multiplied out).

World's Largest Graph

World’s Largest Graph

Mr. C develops all kinds of wonderful computer programs for student learning, he has pioneered all kinds of visually pleasing craft projects which adorn his classrooms, but one of his favorite projects for teaching statistics, is as simple as providing a bucket full of pennies, and having students sort them by date, to find out that there is a normal distribution associated with the age of the pennies, which were collected randomly.

The “World’s Largest Graph” (shown right) was a collaborative effort with students from 4 classes (Integrated Math 9 and Integrated Math 10.) This graph is a giant reinforcement of an important concept in math and science that relates scale factor and linear, area and volume relationships with implications everywhere from biology to architecture to…. If you want to take a “field trip” to Room 213, you can see the graph – all  17 feet by 9 feet of it!


Volumes of Revolution

Mr. C describes the process for creating the Volumes of Revolution image: “A standard topic in calculus is “volumes of revolution” and this year my Higher Level junior’s created a good one as shown to the left. The mathematics behind this was substantial including finding four inverse functions and entering them on a spreadsheet to determine 120 sets of measurements for the 120 “washers” that make up the 3D object created when these functions are rotated around, in this case, the y-axis. This abstract concept comes to life in this kind of activity. You are welcome to borrow our “vase” if you want as well for a bit of “show and tell.” I used an image of this volume (the opacity bumped down to save color ink on my printer here at home and also to make visible the superimposition of equations which generated it) as part of the cover sheet on the Final Exam. One of my juniors filled it with candy.”

It is known that the IB math curriculum provides a rich set of concepts and skills with an international flavor, so that students are learning at a very deep level, in a way that prepares them for life in our globalized world.   And now that you have taken a walk through the math department at Sturgis, you have seen that the Sturgis math teachers enhance the IB with their own enthusiasms and propensities for fun, thereby deepening the understanding of the material in the curriculum.

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