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The Pillars of Math Teaching
Muneer Mohammad Al Wadi, Teaching Assistant of Math, Foundation Program
Effective teaching requires the ability to
communicate effectively. George Bernard
Shaw stated that “[t]he single biggest
problem in communication is the illusion it
happened”. Ultimately, communication is
at the heart of learning, and teaching
mathematics requires the ability to com-
municate effectively. In his TEDx talk enti-
tled
5 Principles of Extraordinary Math
Teaching
, Dan Finkel describes mathe-
matical best-practices as the following: 1.
Ask questions; 2. Let students struggle; 3.
Say ‘yes’; 4. Don’t be the answer key; 5.
Explore. These five ideas contribute to the
ability of being able to communicate effec-
tively.
Firstly, motivational teachers ask ques-
tions and encourage students to follow
suit. Launch your lessons with questions
and allow students to formulate their own.
Later, you can incorporate their questions
to guide classroom discussions. Remem-
ber, not all questions need answers. More
importantly, students must learn to ‘think’
creatively and out-of-the-box; this begins
by considering questions as empowering,
rather than a sign of ignorance. Moreover,
good questions are exciting and keep the
classroom active, engaged, and full of
surprises.
Secondly, empowering educators allow
students to struggle. Students learn by
grappling with mental obstacles and over-
coming them. When you interfere to solve
problems, students don’t learn. This is not
to say you should not be involved in their
speculative/learning processes. However,
you must differentiate between being
’productively stuck’ (i.e., unable to answer
the question but still making progress),
and being ’unproductively stuck’ (i.e., giv-
ing in to despair). Productively stuck stu-
dents need encouragement, while unpro-
ductively stuck students need help scaf-
folding the problem by rephrasing the
question. For both, time is critical: priori-
tize giving students the time to let their
curiosity flourish.
Third, an emboldening instructor says,
“yes” to students’ ideas. Doing math re-
quires making connections between dis-
tinct concepts, translating knowledge into
new contexts, and making intellectual
leaps into unexplored territory. These are
the hallmarks of creative thinking. Howev-
er, when that effort is received with nega-
tivity, it demoralizes. You should not disal-
low the exciting process of student con-
ceptualization. Rather, allow your students
to come up with ideas and follow them,
even down rabbit holes, to see what they
can discover.
Fourth, impactful tutors understand that
they are not the answer key. Most stu-
dents will avoid hard work if they suspect
that there is an easier way. Often this is an
efficient strategy for handling a complex
world with an abundance of information.
However, by always providing answers,
students can be discouraged from devel-
oping higher levels of cognitive curiosity.
Rather, the teacher should be an orches-
trator, setting up learning opportunities,
where students take ownership of their
knowledge through grit. Instead of show-
casing your own knowledge, encourage
students to reference their own under-
standing of the mathematical problem. If
they don’t have the conceptual models at
hand, help them build what they need.
Lastly, great teaching involves exploration.
The educator is in many ways a master
storyteller who guides students through a
shared journey of discovery. One must
encourage student participation, say,
“yes” to their ideas, but, also, be careful
not to disallow their struggle or readily
provide answers. Instead, encourage stu-
dents to test out their ideas for them-
selves. Say “yes” to their creative act and
respond, “I don’t know; let’s find out to-
gether”.