Do We Need to Change the Way We Teach Math? A Hypothetical Exercise

The scenario is straightforward.  The online school,, is doing a better job at teaching math than your school.  Their outcomes on standardized tests are better, the retention of skills is better, and students are doing well in national math competitions.  This reality has been verified by a recent University of Pennsylvania study.  The secret to’s success is that their learning technology provides all students with their own differentiated path to success in math.  The technology adjusts itself to each learner in a way that a classroom teacher is simply unable to do.  In addition to the problem that your school is not teaching math as well as, your parents are beginning to ask uncomfortable questions as provides their education for free.  How will you respond?

This is a hypothetical scenario that I use as part of a workshop on innovation for graduate students in the School of Education at the University of Pennsylvania. The exercise challenges the group to think about innovation in the curriculum, as well as the challenges and opportunities created by new technologies like online learning.  The main point of the exercise is for participants to sort out how their school can innovate without losing what is core to their mission and culture.

Since I started doing this exercise four years ago, this hypothetical scenario has become increasingly more realistic.  Independent tuition-charging schools justify their relevance by employing great teachers, having small class sizes, offering great programs, and providing quality interaction between students and teachers.  As the product of an independent school education and an employee of one, I can attest to these qualities being true.  My own children benefit from the quality of their interaction with their teachers every single day.  The danger that lurks out there, however, is the possibility that new teaching technologies will finally live up to the hype and perform at a comparable level to traditional bricks and mortar institutions.

In the scenario, the graduate students often struggle with the idea that an online school could be better then a traditional classroom.  Their reactions mimic many of the same concerns expressed by school administrators and teachers everywhere.  Teachers, they say, have the unique ability to read the emotional cues that students give.  They point to the fact that most parents are not equipped to have children at home.  They talk about the benefit of being in the same room as other students, learning the social skills necessary for living in our world.  The idea that students would be sitting in front of computer screens is anathema to everything they believe education to be about.

While the current iteration of and websites like provide nowhere near as good an education as a great independent school, the underlying learning technology is improving rapidly.  At the heart of the improvement is the ability to tailor lessons and approaches to different kinds of learners.  And, there is a huge economic incentive to make technology-based online learning really good. is one of the leading online schools with a market cap of over $800 million dollars.  Online schools and colleges represent the fastest growing segment of the education market.  There is a lot of money being poured into developing better ways to assess, tailor, and motivate students to learn in an online environment.  The moment these online schools begin matriculating students in any numbers at top colleges, independent schools will have another hurdle to overcome in convincing families to pay their high tuitions.

Clayton Christensen, Michael Horn, and Curtis Johnson make just this argument in their book, Disrupting Class: How Disruptive Innovation Will Change the Way the World Learns.  They argue that technology will offer “the potential for customized learning in student-centric classrooms” and will alter every aspect of the way we teach and learn. (P.38) Schools that are able to “implement this computer-based technology in a disruptive fashion,” will thrive. (P.90)  Using the example of how the personal computer destroyed Digital Equipment Corporation, the authors believe that many schools will fail to see the disruption coming and will simply become irrelevant.

So what does the threat of online learning mean for independent schools?  In my view, independent schools can thrive in this new environment provided that they recognize the opportunities that new learning technologies offer and are willing to rethink the traditional classroom.  The best ideas to come from the graduate students and others who have been part of my workshop do just that. They take advantage of the differentiated learning possibilities technology provides, combine that with the best of what teachers are able to do, and wrap it in a great school community.

Here is an example using math instruction in middle and upper school.  Currently, math is taught following the Carnegie Unit, or time-based method of curriculum design, with each year defined by a specific curriculum.  Between September and June, an eighth grader taking Algebra 1, for instance, will complete a specific curriculum and, provided the student passes, will move on to Algebra 2.  So a student that gets an A moves on with the student that gets a C even though each student’s level of mastery is nowhere near the same.  A good Algebra 1 teacher is able to differentiate instruction to a certain point, but there will often be big differences in the outcomes.

By taking advantage of new learning technologies, math instruction can become untethered from the traditional Carnegie Unit method and instead each student can progress at the appropriate rate for him or her.  Instead of going to Algebra 1 during math period, students go to the math center where they are grouped according to where they are in their own progression.  The technology provides students with problems to work on and constantly assesses their progress, tailoring the lessons depending on the students’ individual needs.  The teacher will frequently gather students in groups to teach and reinforce, while also circulating around to help individuals.  The teacher gets constant feedback about student progress and can anticipate where individual and group lessons would be appropriate.  As soon as class is over, the students continue on with their day.  The hypothetical independent school that takes this approach has not necessarily changed either its mission or culture, but it has redefined how it teaches math, the role of the math teacher, and how technology is used.

There are certainly a number of issues that arise from a change in the way we teach math or any subject for that matter.  At this point, the learning technologies have not matured to the point where a wholesale shift is even viable.  What this lesson teaches, however, is the need to be open to the possibility of what may be coming very soon, what it might mean for our programs, and what it says about the viability of independent schools’ business model.


Christensen, C. M., M. B. Horn, and C. W. Johnson. Disrupting class, how disruptive innovation will change the way the world learns. New York: McGraw-Hill Professional, 2008.