A Conversation with the Director
Andrew Engelward is the director of the Graduate Program in Mathematics for Teaching.
Q: What is the focus of the Extension School’s Graduate Program in Mathematics for Teaching?
A: We’ve created a program that encourages middle and high school teachers to revisit and explore the math that’s necessary to be effective in the classroom. Math teachers need to know more than just the results and the formulas that come up in math classes. They need to know why things work the way they do, where the formulas come from, and what properties are involved in proofs of mathematical results.
By covering math from these angles, our degree candidates find more than 1 correct way of solving a given problem, helping them explain complicated topics to students who come at problems from various perspectives and may otherwise get lost, frustrated, and confused. One of our candidates explained the program to his friends by saying that he was “studying familiar topics from a sophisticated point of view.”
Q: Who is this program for?
A: Most candidates in our program are teachers with several years of experience. But we welcome people who are considering the profession. Our candidates benefit from studying a range of mathematical topics and exploring these subjects from a student’s perspective. Through our program, aspiring and experienced teachers expand their mathematical confidence in the classroom and are ultimately made more effective as math teachers.
Q: What are some of the benefits of the math for teaching program?
A: First, besides the obvious benefit of rediscovering critical math topics for teaching, you get to connect with other professionals in the classroom. You also benefit from becoming a student again—directly experiencing those issues related to learning mathematics to develop a more empathetic approach in your teaching. Courses allow you to once again experience the thrill of mathematical discovery, and inspire you to try to get the same “aha!” response from your students. One of our recent graduates wrote that she “so missed going to class,” having really enjoyed the classroom atmosphere and the inherent excitement in the learning process—these are hallmarks of our courses.
In addition, a master’s degree in math for teaching is a critical requirement for professional licensure in Massachusetts (the top tier of licensing for those in the mathematical teaching profession), and often helps teachers gain an increase in salary.
Q: Is there a networking potential?
A: A lot of candidates get a kick out of meeting other teachers in the program—not just because of their interaction in the classroom but also because they often find out about interesting job possibilities when talking with 1 another.
Q: What are some of the foundational courses in this program like?
A: In our math for teaching courses, we revisit standard middle- and high-school topics in a more detailed way than you’d experience in a traditional math course. Our classes often feature discussions and activities based on familiar themes, peeling apart the math to consider fundamental details that are hidden behind the scene.
For example, in MATH E-300 Math for Teaching Arithmetic, we tear apart the notion of base 10 number systems, look at how place value works—note that the 2 numbers 12 and 21 both involve the same digits, but obviously have different meaning—and explore the standard algorithms to find out why, for instance, the associative property is needed for carrying.
In MATH E-301 Math for Teaching Number Theory, we explore the mystery of the primes while building up number sense through a series of simple games you can then share with your own students.
In MATH E-302 Math for Teaching Geometry we go back to Book One of Euclid’s classic text, The Elements, and spend time revisiting the Pythagorean theorem to appreciate some of the different approaches people have taken to prove this monumental theorem.
Q: What topics beyond standard middle- and high-school math are covered?
A: In addition to courses in number sense, geometry, probability, precalculus, and calculus, we also offer several classes in nonstandard mathematics topics such as graph theory and game theory. In these, the burden is placed on participants in the classes to discover and invent much of the math content and how it applies in the classroom. These courses encourage inquiry-based learning, allowing current and aspiring teachers to consider firsthand how these approaches work and how they can incorporate elements in their own teaching.
Joining the math for teaching program also opens up a host of interesting elective courses, from classes in education psychology to basics of website design. We try to let students tailor their class selection to the topics they’re most interested.
I encourage you to set up a time to talk or meet with me so I can answer any questions you might have about the program or about our courses. My e-mail is engelward@dcemail.harvard.edu. I hope to see you in 1 of the classes soon.