Demystifying Elementary Math (from a Secondary Perspective)

 Just a video this time.  https://drive.google.com/file/d/1ELRiT_4YG_xy_w5gNnJifVHRxUE-Cuvb/view?usp=drivesdk

 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. 

I'm guessing that if you grew up around the same time I did, you experienced a similar progression. Master the 2 dimensional shapes and their measurements (perimeter and area) and then move on to the 3 dimensional shapes and their measurements. Throughout this process, at least in my elementary years, I'm fairly certain not a single elementary teacher I had in front of me had a degree (major or minor) in mathematics. So they did what they'd always done, show some pictures in books and talk about formulas and calculations. Once we made the leap to 3D though, my brain really struggled to "see" what was on the paper as taking up space - even with the paper nets we cut and taped into 3D objects. Do you suffer from the same affliction I do?  I can't say that my parents didn't ask me to do this often enough or not, but I certainly needed some more practice!  Don't shy away from letting your child do this kind of spatial thinking. Have them order containers s...

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...

  I hope you (and the children/students in your life) had the chance to watch the Perseverance land on Mars recently. Or see the Dragon launch last year. Every single one of the astronauts, engineers,  and technicians had years of schooling to prepare for THAT MOMENT. Every doctor or nurse has been trained through lectures, tests, and field experiences.  Something that strikes me every year around this time, as our seniors are making college decisions and our juniors are taking the ACT and beginning the application process, is that not one person in any interview I've ever had has asked me about my grades or GPA. We have tied up so much time and energy into thinking that only the best survive, but we KNOW that can't be true.  All that does is overstress our teens and lead them to believe that successful people never struggle. That is a damaging belief - especially when internalized by students who are struggling.  Here's my take on grades: 

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? 

  I ran another social media survey about math (I know, I'm a blast at parties...I swear).  This time I learned that adults - just like my students - avoid fractions! So, that got me thinking... This week's video is all about fractions (the why and how) and a little challenge to all you parents out there!  Watch and let me know what you think!! :) 

  Yet another example of adults saying "But there's a better way..."  No one would argue that you, adult, can add probably faster than an elementary school student.  We are in the process of building UP TO that speed and accuracy. By encouraging your child to imagine the groupings, you are building their imagination (draw whatever you'd like!), their math skills (count up, make 10s), and their mental flexibility ALL IN 1 PROBLEM!  Check out my NEW addition video for a little more about how this problem is VERY similar to what many adults already do! Making sense of a problem IRL isn't about having an algorithm to write out your work. Instead it's about applying what you know to a REAL situation.  This is what most adults think of when they see  an addition problem: But this is what many                                                ...

How do you do mental multiplication?  Do you encourage that same thinking in your own children? 

  Tell me if you've heard this one before...              Parent and child at the table working on child's homework.               Child becomes frustrated and begins to cry             Parent becomes equally (or more) frustrated by the tears/the                      assignment/both.           Sound familiar?            It's pretty common, but let's ask a new question - what's the upstream problem?   Not familiar with the idea of "upstream problems"? It was new to me until very recently - but the best description I've heard is this:  There's a town in which every evening a child washes up on the banks of the local river. Every day the fire department rescues the child and is lauded as heroes.  One day a new fire chief takes ov...

  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.) 

It's been hard to tell where summer break began this school year (2019-2020 into 2020-2021). And with the strange end of the year leading into and uncertain new one, you and your child can be practicing math. Not with worksheets or computer programs, but in 5 or 10 minutes of conversation a day.  I bet you'll find that all those connections your student was learning at school are still there.  Fostering that learning at home will help ensure your child is safe from summer slide AND fall falter!

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!

Ah yes, I'm sure we've all seen this or similar postings around the internet - the famous "too smart for elementary school" parent who's really "showing those teachers". The problem I see here is a parent who despite his MANY years of education, failed. He failed to read directions. He failed to answer the question being asked. Without knowing what grade level this problem is aimed at (I'm assuming 1st or 2nd grade), the problem here is not that "math has changed". The problem is that the problems have changed. This highly educated parent (and many of those educated as much or less who see and share this) all fail to see that the question is NOT 427-316 = ??? Instead, the question is demonstrating a method of subtraction (more on that strategy here ) and asking what went wrong for the student. It's about error analysis. I bet if Mr. Engineer Dad had seen the problem labeled Error Analysis his chest would've puffed with p...

                                              I know it's not exactly the most comforting advice to adults who have been through a lot of change, but 1 thing I know for sure is that no school, no teacher, no administrator, no aide wants any child to be poorly educated.  Instead those teachers, administrators, aides, and school officials all know that there is a building process from Kindergarten (or 4K) through senior year of high school.  There is a progression that they've spent (countless) hours working to align so that every topic is covered, every concept is given time to develop, and every student has access to the material when they're ready. The long and short of it is that there is a well thought out process - please trust it.  While it may be frustrating for you at times, remember that you have all the "keys to the castle" as an adult who's be...

Drawing a picture is one way to envision a fraction problem, but it certainly isn't the only way.  Another strategy for dealing with fractions is to utilize a number line. A number line is really the school version of a tape measure - and every carpenter or contractor knows their tape measure fractions!  If we expose students to the number line early and often, then as they start to investigate negative numbers the concept will be clearer. We aim for students to be flexible and nimble in their thinking, so if one pattern or strategy doesn't work they don't give up - instead they have another tool in their tool box (perhaps a tape measure?) to use.

Fractions - another one of those things that send shivers down the spines of adults who never EVER have to see them again, right?   Well, sure. Unless you use a measuring tape. Or cook or bake - especially if you decide to double or *gasp* halve a recipe.   I think we can all agree that fractions HAVE a place in the real world.  So why in the world do we allow our students to hate them so much? Fractions are seen earlier and earlier in elementary math these days and for good reason: we don't need to hide concepts from kids. Every single child understands what half a sandwich looks like (and can probably tell you if their brother just got the "bigger half"...which can't be a thing, but I digress...) What do you, as a parent or tutor or homework helper, need to know about fractions in elementary school? I'm going to explore a few different strategies for fraction work in a series of videos. Starting with pictures.   If you're out ther...

Ah...division.  The 4th and final fundamental operation of elementary math. But I bet when I said that more than a few people were sent back to the days of long division being brutal. I think just about everyone can agree, long division was a HIGH hurdle of elementary school. While division is the partner to multiplication (more on that later), for whatever reason it's also Cinderella's ugly stepsister that nobody wants to acknowledge is really there. Division is incredibly applicable though - need to give each of your kids an equal number of cookies from what's left in the package so nobody fights? Or do you need to figure out how many more glasses of wine you can get from what's left in the bottle...  Either way, division is real life. Luckily, instead of pushing students to just memorize more number facts (which is useful - to a point) we teach multiple ways for students to arrive at their answers, giving them some number dexterity. Your student probably has a...