Few things bring more joy to my life than teaching
mathematics. It might sound a little crazy, but I’ve come to embrace my
passion. And in Form 2 this past week, I was reminded of exactly why I love
teaching math…
On Monday after our uji break, I entered the Form 2
classroom, everyone stood to greet me enthusiastically, I asked them how the
uji was, they said “very nice!”, and they all sat down, opened their books, and
were ready to begin. (Seriously, I love my students)…The topic for the day was
factorization of quadratic expressions. We spend the previous week learning how
to expand quadratic expressions [for example: (x+4)(x-2) = x2 + 2x –
8]. So I began by explaining that “to factorize” is the opposite of “to
expand,” but first we must practice “how to think factorize.” Yes, sometimes my
phrases are incomplete English said in a very strange fake TZ accent that I’ve
somehow acquired, but as long as I get my point across and the students
understand, that’s all that matters…right? Anywho, when thinking factorization,
you must think about two numbers that multiply to A and add to B. For example,
what two numbers multiply to 12 and add to 7? 4 and 3 of course! We did several
example of this, eventually using positive and negative numbers, and once I
felt like the majority of the class was understanding, we moved onto
factorizing.
Example 1: Factorize the expression
x2 + 10x + 16 Madam:
“We want two numbers to multiply to 16 and add to 10”
Class: “2 and 8!”
Madam: “Ok, so now
we want to make two brackets, like this…”
( )( )
Madam: “We begin with x in both,
then we will put 2 in one, and 8 in the other, like this…”
(x 2)(x 8) Madam:
“Then, are 2 and 8 positive or negative?”
Class:
“Positive!”
Madam:
“Good, so like this…”
(x + 2)(x + 8) Madam:
“This is the solution!”
Class: a bit stunned…very
quiet…definitely unsure of what just happened…
Madam: Now, let’s check our solution.
If factorization is the opposite of expanding, then let’s do a check to see
what will happen when we expand our solution. (in case you were curious, this
is a 4 step process here at Bukiriro, and the kids are rock stars at it!)
Check: Expand (x + 2)(x + 8)
1. first terms = x * x = x2
2. outside terms = x * 8 = 8x
3. inside terms = 2 * x = 2x
4. last terms = 2 * 8 = 16
x2 + 8x + 2x + 16
Therefore, x2 + 10x + 16….
This is the moment of truth as I wait to see if they
actually understand. Within a few seconds, the entire class realizes that this
expression is where we began, and their smiles light up, a few “aha!” moments
happen, and then the whole class erupts with applause. Literally the best light
bulb moment a teacher could ever have! An applause for algebra?! YES! And I
assure you that I joined in the round of applause for the beauty of
mathematics. So much simple joy for the mere fact that
x2 + 10x +
16 = (x + 2)(x + 8) = x2 + 10x + 16
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