Fidelity to the Geometry in Construction Program: The Geometry Class Perspective

Over the past few months I have had the privilege to interact and/or observe several Geometry in Construction programs.  Some programs have truly embraced the philosophy of connecting the Geometry with the Construction including providing opportunities for students to view geometry differently thru alternative instruction techniques. Other GIC programs are struggling because activities are ignored and the GIC lessons do not provide students a different way (learning style) to learn geometry.  These students are given worksheets of naked math (drill and kill), with little to no application to the real world.

So, how do you know if you are implementing Geometry in Construction with fidelity.  Obviously, the first benchmark to consider is the performance of all of the students. And we do mean all students, not just a select few.  Otherwise here are four key concepts to consider.

  1. On a daily basis are both teachers making direct connections with the mathematics to the construction?  Are both teachers active and engaged in the classroom?  I observed one class where both teachers were in the class but the construction teacher was doing paperwork, etc. with no interaction with the students. The team teaching model is valuable only when both teachers are active in the teaching of the math (when possible) and making connections between math and construction (when possible).
  2. On at least a weekly basis, are the students experiencing an activity where they are active in a project (other than their construction project) usually as a group of 2 – 4 students applying their math. Often times, this will involve students applying information from previous learning to a new situation using learning styles that are kinesthetic and/or visual.  As teachers, we need to provide opportunities for all learning styles.  Many of the activities will make connections between the math and the construction worlds.
  3. If someone were to ask your students how the math they are learning is used in real life, could they answer at least 75% of the time?  Remember one of the teacher’s goals is to answer the most often asked question by students in the math classroom “Where/when am I ever going to use this?”.   Initially I thought that this was not an important item in teaching.  However, I found myself asking the same question at faculty meetings and workshops,  sounding like  “I hope I can get something out of this that I can use” which is essentially the same question.  That was an eye opener for me.
  4. All teachers supplement all curriculum. I get that.  The question to ask “What percentage of the student work is supplemented?”.  If a teacher is using supplemental worksheets more than a curriculum, then are you really teaching the curriculum?  When I inquire about the amount of supplementing, teachers typically have one of two responses about why they supplement.
    1. a) Many teachers respond with, “It (drill and kill practice) has worked for me when I was in school and my students need the practice just like I did.  Yes, they need the practice but they also need to see the math applied.  Straight practice works for a small driven percentage of students of which math teachers are in that group. Questions to ask.  Were you a typical student?  Did you find math interesting?  Is that typical of your current students?  Are you supplementing because that more fits your comfort level? Are you making connections back to the real world when you supplement?
    2. b) Response 2:  I don’t have time to spend on contextualized problems.  Teachers are always short of time.  Early in teaching, I recognized that I could teach all of geometry in a matter of a few weeks.  The bigger question was and is, would the students learn it?   Are the students able to apply their mathematics?  The Mathematical Practice Standards tell us that our students need to be able to apply what they learn.  Our colleges and universities tell us the same thing.   What do the students need to be successful in future careers?   It is consistently reported they need to apply their mathematics.  Will the problem set you assign accomplish that?

The data from well implemented GIC programs have always shown superior test scores.  In addition, teachers of these programs report that their students have more “grit” than traditional students when tackling the next level of mathematics (typically Algebra 2).  That persistence is a result of seeing a variety of contextualized problems/activities.

We hope you are able to self-reflect on your teaching, celebrate victories, and adjust lessons to fit the changing face of education.  That is what good teachers do everyday.