Joy in the Struggle

By Sharon Weldy, Principal and Rhetoric School MathTeacher

If you were to take a peek into Covenant’s honors geometry class, you might be surprised to see students working without textbooks, lists of formulas, or lecture notes.  Instead, the students in this class are taught using a curriculum developed over decades by faculty members at Phillips Exeter Academy in New Hampshire.  This curriculum is problem-centered, meaning that the primary mode of learning for the students is through active engagement with complex problems.  There are no lectures given.  The teacher does not provide students with a dogmatic procedure for solving a particular type of problem and then ask the students to complete a set of problems using that procedure.   (As we know, in the real world, problems seldom come with a set of attached procedures to follow!) Rather, the teacher merely provides guidance and helps to steer the students’ thinking as they struggle with rich and engaging questions.  These exercises are designed to integrate numeric, algebraic and geometric principles and to deepen the students’ understanding of these concepts.  The need to apply a particular mathematical concept arises organically as the students reason through the problems.  

Students are frequently surprised at how concepts they had learned in previous years are seen in a new light and with more depth once they discover the need to apply them without having been told to do so.  There are almost always several different ways to approach each problem, and it is always a great joy to compare approaches and see the creativity employed by the students.  After many years of teaching, I have seen that this type of curriculum creates more joy, enthusiasm, curiosity, comprehension, retention, and ingenuity than any other I have used.


The following are testimonials from our own students regarding their experiences in this class:

  • “In previous math classes we were given an equation, and you just had to go through the steps.  We didn’t really learn why a problem works the way it does.  With this math curriculum, we figure out for ourselves why a problem works the way it does.  The most exciting thing for me is that I can know how to solve a problem without having to memorize a theorem.  This class is fun, but still challenging.  It’s basically geometry + logic - memorization = pretty cool stuff.” 

  • “With this class we are encouraged to find the answers ourselves using previous knowledge, and by doing so it is so much easier to remember the procedure.  Getting the right answer is always a victory.”

  • “This class has challenged me to take different routes to find the answer. It teaches us how to think for ourselves and teaches tenacity in solving problems.”

  • “This class has caused me to grow in my understanding of math concepts, as I use logic to truly solve problems.  Many times [in the past] I have been taught all about a concept and how to use it, and this makes it much easier to ‘solve’ problems (if one can ever call it ‘solving’ since we just use steps to safely find a solution).  However, that is not nearly as challenging and gives no opportunity for finding out for ourselves.  Being told how to solve a problem is like being told the ending of a mystery story.  It’s not fun anymore.  We all like having the chance at playing detective.”

  • “Struggling with solving problems provides many benefits.  When I use logic and analysis to work through a word problem, not only is it easier to grasp the math concept because I really understand the work behind it, but there is a sense of satisfaction.  It’s as if we are doing the great work of the philosophers who originally came up with the math concepts and are uncovering the concepts for ourselves.”

  • “This class is like none other in the teaching style.  These problems are not simple.  They are quite challenging and often contain new vocabulary that is explained to us, but we are never given a clue as to how to solve the problems.  It is frustrating but wonderful that logic is being applied.  The next day, everyone discusses how they solved the problem, and you can’t be afraid to be wrong.”

Below is an example of the types of problems that Covenant’s students grapple with.  
How would
you choose to solve it?  




To learn more about Covenant's Rhetoric School, please visit the following:
Rhetoric School Curriculum

To R.S.V.P.  for our Rhetoric school Open House, please email: [email protected]