Creating My Geometry Curriculum

At Arapahoe all of my students have their own computer, and so giving an assignment out of a text seems pointless.  Especially when there is Excel, Google Docs, Google sketchup, Google Earth ,the internet, Geogerba, and a host of other computer based technologies that I should be using instead.

So I set up my assessments first, based on the local, and state curriculums.  How I progress my students through my assessments came from Dan Meyer and his blog dy/dan. I hope I can work in some of his patient problem solving problems along the way and create some problems that come from good story telling.  Geometry is where I begin.  For the most part my assignments will have four main parts.  An ACT or standardized test prep question or two, a Geogebra construction problem, practice of the concept (this may include an algebra connection of some kind), and a patient problem solving problem according to Dan Meyer.  (Sorry for the oversimplification UNL) At UNL these are called Habits of Mind problems.  A problem that relates the concept of the day to mathematical experimentation.  I probably won’t do as well as Dan or UNL, but will be trying to fit problems with my students and what I feel they need to be successful citizens in the future.  The Moodle page where all of this will be slowly coming together is at Arapahoe Geometry http://moodle.esu11.org/course/view.php?id=7.  Enter and agree to terms.  I have concept 1 done, and have started on concept 2.  I will be using several texts as guides, as well as geogebra and any and all of the internet.  Most content and problems I will create myself.  But feel free to take a look and critique and add suggestions.  I just know that next year, I will feel like a total failure if we crack a book.  I want everything to come from our new digital world.  Wether I made it or organized it for them to easily find.  One down approximately 59 to go.

The Marshmallow Test For Solar Cookers

We are making cookers.  So why not cook something.  After all we are trying to make mathematics useful, and a project is never complete until we eat something.  In this case I started out small.  We cooked marshmallows.  The winning cooker was actually able to melt every marshmallow and as long as the wind stayed down and the box set stable for more than a couple of minutes. The cooker actually turned the marshmallows to charcoal.  Eggs might be in the plan for next year.

A note to self for the future, I need to make sure students create a platform that holds cooking material in the focus.  We were using wires and poking holes everywhere to get marshmallows to stay.  What I need for next year is to make them create a platform that will hold a small dish and a medium cracked egg.  This might be tough for the groups in the future, but I know it can be done.

This might be the funnest math project I have done with students.  I will have to incorporate more of these. . . but as always it is tough to give up 8 days that really do very little to prepare students for that ACT or state test . . . and I hate to say it.  It does very little to help them prepare  for success in college mathematics.  Of course I could be wrong.  Maybe there is a research project that shows that these kinds of projects help.  I know they help in sparking a students imagination.  They do not help to get the student a 30 ACT score in math.  And they do not help a student set through a 60 minute lecture five days a weak in calculus.  After all this project only addresses one of the sixty questions on the ACT.  Or one question on a college final exam.  The question on the exam might be locate the focus with respect to the vertex of the parabolic curve f(x) = (1/12)x^2.  Or this classic from the virtual math lab at West Texas A & M University.

 xample 1: Find the coordinates of the vertex of .  Without graphing, determine if the vertex is the maximum or minimum point of the quadratic function.

My interesting and relevant project might be hamstringing my entire math curriculum at Arapahoe.

Just some thoughts to feed the fire.  Next up  why I feel I should teach the way I do.

Solar Cookers A Great Project for Conic Sections

I have always been fascinated with the conic sections.  They are what makes mathematics so interesting to me.  A shape that bends and focuses the invisible.  They are almost magical.  And to some that do not understand the fundamentals behind them could be construed as some type of witchcraft.

We are done with state testing and I wanted a project that was fun, easy, and applicable to the math we were studying, so why not have students build solar cookers.  I kept my rules simple.  It has to be less than 2 feet by 2 feet.  I did not limit their depth.  It had to be made from tape, cardboard, tongue depressors, ice cream sticks and aluminum foil for the reflective surface.  It had to in some way incorporate the parabolic design.  Then I gave them eight 50 minute class periods for planning and building.

The results on a 20 degree Celsius day where nothing short of astounding for my first time with this project.  Four groups used the properties of the parabolas in their design and construction.   These groups reached temperature of  31, 76, 84, and 105 degrees at the focus.  One group did not use parabolas at all and their temperature reached 52 degrees.

When designing, three groups used geogebra to map out their parabolas so that they would have reference points to measure and cut.  Some used the projector in combination with geogerba as an overhead to draw templates on their cardboard.  In all I was pretty impressed with the designs of all groups.

The lowest temperature group had a good design (trough), but the 2 X 2 limitation I put on their trough design allowed for a very small surface area.  I think that was the biggest factor in temperature.  It was how much surface area was exposed to the sun.  The group that won had a design that fit in a 2X2X3 prism.  While the group that placed second with a temperature of 84 degrees C actually could have fit their cooker in a 2 by 2 by 2 cube.  In all groups that used the parabolic reflective surface when you reached your hand into the cooker the heat change was noticeable even the lowest temperature group (collecting heat from a long thin trough focus is hard) and when we tried to cook marshmallows it was  easy to find the focus as the marshmallow would almost light up in brightness at the focus.  Safety issue to consider for next time. . . .   They were all so bright that it was almost like watching someone weld.  Probably should have eye protection when looking into the cookers.   My eyes are still burning and had to take a pain killer to stop headache 8th hour.

Next post will be The Marshmallow Test For Solar Cookers.