As a tutor, I often had students come to me
and tell me they needed help to study for this next test (coming up very
shortly) because their mark was low in math. As I work with the student I work
through the material slowly and I ensure to stop on concepts that a student
does not understand, ensure they understand it, and then progress to the next
level with the ultimate goal to get them ready for the test. It is very
possible that a student understands the topic but needs some extra help on
specific item in that unit. We cover the concepts and topics, ensure
understanding, and the student is good to write the test in confidence.
But what happens when the student does not understand
the current topic because they don’t understand the previous related topic, and
in some cases the previous one to that and so on?
That is exactly how students become
discouraged in math. It’s because they went down a path without full
understanding of a concept/topic and now they are so far down they are lost in
the unknown. This is where a good teacher shines. You see, you must keep on
going ‘back’ in concepts that are related, until you find the root cause (the
beginning of) the students’ confusion.
And you begin there.
Test or no test looming, you must start
from that point or you don’t stand a chance in helping this student understand
this particular math concept, and in some cases, math in general.
Allow me to give you a practical example. A
grade 9 student doing a geometry unit – specifically on congruent triangles.
They may need to prove that two triangles are congruent. But these triangles
are embedded inside other triangles and/or a parallelogram with additional
information provided. For this exercise
they will need to do some deductive work. Meaning, figure out what they do know
and how to find the rest of the unknowns to ultimately get them to prove the
triangles are congruent.
They may need to know some theorems (e.g.
Pythagorean), rules such that all angles always add up to 180 degrees in a
triangle, definitions, or trigonometric functions, depending on the nature and
complexity of the question.
It is one thing to help a student ‘deduce’
the answer when they understand how it was deduced. In that case the student
can practice their deduction skills. But what if a student did not understand the
deduction steps? Then you need to backtrack their knowledge line and see where
the breakage happened. Do you need to review the geometric rules? Do you need
to review the trigonometric functions concepts? If yes, do you need to go back
all the way to definitions of adjacent side, hypotenuse, opposite sides of a
triangle? Do we need to review the SAS, SSS, ASA congruence rules? Figure
out how far back to we need to go …and go there.
On a simpler level, how about a child
learning how to add double digits and re-grouping? If they don’t understand –
do you continue or do you pause and try to figure out what it is they don’t
understand? In this case you might need to go back and review single digits.
You might need to review the concept of ones and tens and what does it mean and
do some related exercises. You may need to break the number up into ones and
tens and manipulate the numbers slightly differently if a child understands it
a certain way. In other words, go back as far as necessary and stay there as
long as necessary until the concept is well grasped. Then move forward. This may
require a few sessions depending on how far back you had to go and the age of
the student.
The effort is well worth it.
Because once you fill in the knowledge gaps
for the student, suddenly everything makes sense. Math makes sense. Confidence
returns and math results improve.
You may find me sprinkling this topic
throughout my blogs going forward, as I truly believe this being the number one
reason why kids fall behind in math – they develop knowledge gaps that are not
resolved.
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