Demystifying Elementary Math (from a Secondary Perspective)

 This one's for all the parents facing the "why...?" and "how...?" and "why not...?" and "do I have to...?" questions.  And for the teachers (and parents) who are uncomfortable with admitting they aren't the omniscient geniuses we'd like our kids (and students) to believe we are.  There is a LOT of power in the word YET.  And even more power (in my opinion) in admitting you don't know. Students of all ages need to know that they don't have to know everything - and the people in their lives don't know everything either.  Try it out.        It's OK to not get it, yet.        It's OK to not know. Let's find out together. 

The last year or so has shown us all a lot about the world we live in and the people we share it with. It's interesting to see how tightly individuals may cling to ideas or beliefs that have later been shown to be inaccurate and have been updated. That's the scientific method in a nutshell - make a prediction, test it, learn something, adjust. Math works the same way, but I'm seeing that the "adjust" step is becoming harder and harder for students to make.  I had an experience in my Algebra class that sort of outlined the apparent push to reject what is proven in favor of what makes us comfortable (more about that in the video) and it got me thinking. This whole math education thing (or compulsory schooling in general) isn't about cramming kids' heads full of information. It's more about opening them up to conflicting ideas (cognitive dissonance for all you psychology/education fans out there) and giving them the tools to determine true from false, fac...

Metacognition: a buzz word that educators like to throw around Metacognition: thinking about thinking Yes, that's a real thing teachers are asked to do on a regular basis. We are expected to anticipate errors our students might make before they make them. We are constantly on the look out for students who have a different approach than their peers to a problem. And now we're seeing these "metacognition" problems showing up on standardized tests for all ages. The practice of explaining your thinking can be a tough one to wrap our heads around as adults. It feels easier to say "It just IS the answer." But we want to dig deeper into HOW or WHY you arrived at your answer because It's Not New, It's Meta

  Estimation is the one task from elementary school math that drove me CRAZY! Why would I estimate if I could just FIND the answer OR measure OR count and find the "REAL" answer.  It's taken awhile, but I've come around to appreciate this skill a bit more - check out why I think estimation is a reasonable (and important) skill for students of all ages to practice and hone to be better consumers of data.   Estimation is Reasonable What do you think? Do you estimate regularly? Do you ask your children to estimate? 

  My fellow math nerds and I may be the only people who REALLY enjoyed this show, but the opening always resonated with me. "We all use math every day: to predict weather, to tell time, to handle money. Math is more than formulas and equations. It's logic. It's rationality. It's using your mind to solve the biggest mysteries we know." "...more than formulas and equations..." that couldn't be more true for our youngest learners. While they are building the skills to add, subtract, multiply, and divide their teachers are also encouraging them to be pattern recognizers. Pattern recognition leads to deeper mathematical understanding.  Recognizing repeated addition or subtraction is the first step in recognizing linear relationships. Recognizing repeated multiplication or division is the introduction to geometric sequences and exponential growth and decay.  Ask the kids in your life about what patterns they see. Ask them to predict what comes next in a li...

That quote, is SPOT ON! I don't disagree in the least. (Bet you didn't expect that, did you??) However, I don't know any elementary school students who are sent to the grocery store to do the weekly shopping on a budget alone.  Number lines, hundreds boards, ten frames, algebra tiles, and all the other physical representations of math and numbers give students something concrete to set the stage for learning. We move away from each of them fairly quickly as students become more fluent in their math facts, but they provide a perfect physical and visual reminder for students to mentally refer back to as they learn and grow.  We all encourage our kids to try new things - consider adding new math strategies to that list! (And cheer them on, just like you would if they were trying a new sport or instrument.) 

By offering multiple ways to arrive at an answer, we are more inclusive of how students think. And in the end, who does that inclusivity hurt? (Being exposed to multiple strategies harms no one and is considered a best practice of mathematics teaching.) And who does it help? (Everyone! Our brightest students benefit from hearing alternative thought processes, and our struggling students benefit from seeing peers solve using methods similar and different from their own.) WIN WIN!