https://youtu.be/ejqH1ofSx8U
While scrolling Facebook, I caught a glimpse of this video (briefly) and the caption, "This is why the kids are doomed." As a lover of math, I couldn't help the burning desire to draft up a piece in efforts to stand up for and defend mathematics!
While I understand why parents and even educators (who learned the traditional algorithm) feel as if students are "doomed" for having to learn this "new math" (which actually isn't new math at all); there are so many misconceptions that have formed these thought patterns.
Now if you're like me and you've sat in front of hundreds of students who have been taught the traditional algorithm, you would concur that several students are guilty of making one or more of the following misconceptions and mistakes in this learning process:
Mistake #1 - forgetting to place the "place holder" zero on the second partial product (2nd row).
Mistake #2 - recording an incorrect answer; either because of mistake #1 or a computational error (multiplication or addition).
Mistake #3 - not regrouping appropriately or at all.
Mistake #4 - not realizing their product is incorrect (as a result of mistakes #1, 2 or 3).
As a teacher, however, the natural inclination is to get frustrated with the student and resort to fussing and/or giving MORE homework problems so they can "practice makes perfect" their way into the correct process.
However, that is a reactive approach based on a lack of understanding of appropriate progression. It's like trying to teach a kid to swim, who has a fear of water. Or trying to teach a kid to walk who has not yet developed the motor skills for crawling. Both can be done with practice. But both are not within a developmental cognitive progression. A student who learns how to embrace water in their face and floating is cognitively & thus developmentally ready to embrace the steps and strokes of swimming. A toddler that has worked through the natural motor skills needed to crawl, roll and pull up is cognitively and thus developmentally ready to conquer placing one foot before the other. And furthermore has the foundational skills to "know how" to recover when they have fallen from their attempts at walking.
So why can't we (as educators) provide the same deep foundations for students by being proactive (rather than reactive) through conceptual instruction (the why) coupled with abstract (the how) instruction?
- Why can't students know the reasons behind why the Constitution is so meaningful to our country?
- Why can't students understand and learn how and why storm clouds form?
- Why can't students learn when to appropriately use the homophones: to, too and two?
- Why can't students learn how to mentally build answers for accuracy?
I would agree that students ARE doomed...but not because they learn models such as the video on the left. Students are doomed because processes like the one on the right are forced down their brains without a rhyme or reason. They are taught to JUST DO IT (because I taught it to you) and are left with a system of steps (that can easily be forgotten, or simply incorrect) without an ability to justify whether their answer makes sense. I would argue that this is the same reason why students (as young adults) stand behind cash registers and cannot tell you whether the amount of change they are giving you is correct or incorrect (they just hope and pray they typed the right numbers into the machine).
NO NUMBER SENSE!
NO ABILITY TO REASON!
Here's what students learn with each approach!
Conceptual Approach Abstract Approach
- Place Value Concepts - Memorization of steps
- Connection to why - Rote processes
- Partial Products - How to get an answer
- Why the answer is correct - Lower level of thinking
- Reasonableness
- Deeper level of thinking
I take great pride in being a part of the paradigm shift occurring in mathematical education. I love that the conceptual components of math (that were left out when I was a student) are now evident in the TEKS. The instruction that we as educators are now able to provide students can better equip them to be problem solvers, reasoners, thinkers and developmentally appropriate mathematicians (or just productive citizens in our society, for that matter).
