Wednesday, November 18, 2015

Addressing Gaps in Math knowledge

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.

My next blog will discuss preventative measures to ensure any knowledge gaps are addressed in timely manner. 

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