High-Cognitive Demand: More than just..."more"

I Remember from my own days in school...

I was in First Grade...I had homework, basic addition, 100 problems on a page. The teacher said we needed 100 problems because "the more you do, the better you get". 

Technically, yes, but actually, no!

I was six years old and I remember crying that night at the kitchen table, it took me two hours to do that worksheet. Worst part about it was, that was a very low-demand, low-value task. One that made me detest math work well into the third grade, where, thanks to a dedicated teacher and a change of heart on my part, math and I made amends.  

So what would have been more effective than 100 addition problems? Well, first of all, the word "problem" is problematic. But that was the last post, for this one, I have to rave on about cognitive demand! Why is "more" actually "less"?

Let's introduce the work of Dr. Bloom and company:

(HelpfulProfessor.com, 2022)

This is Bloom's Taxonomy. Most educators are familiar with it. Effectively, Bloom's Taxonomy organizes cognitive demands of certain tasks based on demand level. Higher demand tasks reside at the upper portion of the taxonomy, i.e. "high on the mountain", while lower-demand tasks are towards the bottom. Repetition is a low-demand task. Simply repeating the same thing over and over doesn't make the math more demanding...it just makes the math more nauseating! If we want to make something higher demand, we have to change the mission a bit. Simply scribbling away at basic math isn't going to accomplish much. 

Remember those third graders who needed help with subtraction? Those kids liked Pokemon cards. Most teachers consider Pokemon cards to be the bane of their existence, but I saw an opportunity. The third graders wanted to go outside...but we had math to do and a limited time to do it...so I told them we'd have to compromise. We'd go outside...mathematically!

A quick explanation for those who are unfamiliar, every Pokemon card has a few important numbers on it...HP, or Hit Points, are at the top, and are effectively the "health" of the Pokemon on the card. Under the picture of the Pokemon is a list of "moves" or attacks, with a number next to them showing the amount of damage each one does. If you're thinking what I was thinking...

I decided we'd play a math game. Each student was given three Pokemon cards, ones I'd selected ahead of time in the interest of fairness. (Some HP numbers are in the low 200s, others are in the upper double-digits, attacks vary wildly too). Students would count down from three, then they turned their cards over at the same time. They had to read their opponent's HP number, subtract their attack number from it, and get the correct answer. First one to get their answer correct was the winner. I'm fully aware that this is absolutely not how the card game is played, but we're learning math at the age of eight, so it's fine! All of the math was done in sidewalk chalk outside on the blacktop, which only served to make the game more engaging. 

This was a higher-cognitive demand task than simply repetitive subtraction within 200. My students had to apply their knowledge of subtraction problem set-up, execute the operation, and all while their opponent was attempting to do the same. Application is higher demand than simply repetition. Plus, we got to play outside with Pokemon cards during school! To elevate this further, if we had time, I would have these students tell me, for each combination of cards, if the Pokemon took turns attacking, which one would win, and how many turns would it take? Now they would have to do two "chains" of alternating subtraction, until they reached zero, all while also keeping track of the number of steps in the chain. Unfortunately, we ran out of time, the weather never cooperated again, and I couldn't bring myself to do Pokemon without the chalk. It didn't feel right!

Obviously, every task cannot be a high-cognitive demand task. However when we're teaching kids we need to be aware that we're not doing them any favors when we fall into the trap of "more is better". 

"Better" is better. "More" is only more. 

Can you think of another high-cognitive demand math task to use with these students? What makes it higher demand?

For another awesome blog entry with a lot more detail than this one, visit the link below:

https://www.aubreeteaches.com/blog/high-cognitive-demand-math-tasks

References:

HelpfulProfessor.com. (2022). Bloom’s Taxonomy. https://helpfulprofessor.com/wp-content/

        uploads/2022/09/blooms-taxonomy-1024x617.jpg 

 

The Haunting of our Classrooms, a.k.a. How Do We Make Kids Afraid of Math?

Scared of Math? Kids aren't Scared of math!

Well, of course they are!

The simple way we frame mathematics to kids scares them off before we even begin to teach the "hard stuff" (read: abstract) like trigonometry or calculus. I firmly believe that everyone has a story from their childhood where some adult or older kid they knew told them "math is hard" or "I'm no good at math". Before we even set foot in a classroom with complex mathematics on the syllabus, we've developed a predisposition. 

"Adults I trust think it's hard."

"Adults I trust think it's scary." 

Kids mirror the thoughts of the adults in their lives. 

Then, these young students arrive in our classrooms. We put papers in front of them. We call them "worksheets" or a "workbook". Kids don't want to work, they want to play! On the worksheet, the one we tell them is full of problems, we tell them to show all of their work.

From their perspective, it looks like everything the adults told them is true. Work, Problems, papers, lots of writing...what seven-year-old wouldn't be afraid? 

It's not just the young kids though. Math Anxiety is a real thing, and it affects adults and teens too! Often times, this anxiety can start as early as first grade, and the processes we use in our classrooms can absolutely make it worse.

But we don't have to make it worse. Words are powerful things, especially in the concrete and literal mind of a grade-school child. And fortunately it's completely free to switch up the ones we use!

Instead of introducing math to our youngest kids as "problems", exchange that word for a neutral or positive phrase. It's not a problem, call it an equation if there's an equal sign present, or if not, just a "number sentence". 

For harder math (according to age, ability, and grade level), get more positive to counteract the perceived difficulty. It's a challenge or a quest for an explanation! Kids love challenges!

One of the most influential notes I've taken during my undergrad is how much I hate the word "work" in math. Math is about critical thinking, not work. Replace the word "work" with "thinking" in any place, it's not about just doing work...it's about thinking! So have the kids demonstrate their thinking! 

Outside of language, a little bit of unconventional can elevate even the mundane to a more interesting level. While doing intervention on subtraction with a group of third graders, I decided that the standard algorithm was a bit too boring all on its own...so we decided to practice it "by the campfire" instead. I present to you: Torch Subtraction!

(It's an LED lantern, no actual fire was produced in the school building)

These kids loved every minute of this. Mind you, this was an intervention group...some of these kids came to me at the beginning struggling to count backwards from 20 to 0. One of them got teary-eyed when faced with subtraction with two digit numbers! We built our way up in basic skills, then when it came time to re-introduce the standard algorithm, we called it the "Capture the Algorithm Challenge" and since "the Standard Algorithm for subtraction is afraid of bright lights, third-graders, and pineapple on pizza (last one was their words, not mine), we had to be sneaky and work by firelight, lest it runs away!" We practiced this exactly the same way we would have under fluorescent lights. The lesson itself was no different. The atmosphere was what set the tone for the day. Not one student was stressed out or overwhelmed, they had a blast doing basic math, and all that was different was the tone and atmosphere. The math was scared of them!

Words and methods do matter to the kids, it's not that hard to adjust and have fun with it! We can't control what kids hear from other people, but in the classroom, we can cultivate a math-positive mindset, starting with how we talk about math!

What routines, words, and processes in your math instruction are scaring the children? Can you think of other ways to cultivate a Math-Positive Mindset in your classroom?

For additional information on Math Anxiety from the American Psychological Association, visit the link below:

https://www.apa.org/monitor/2023/10/preventing-math-anxiety

Introduction!

Hello there! Let's TACO BOUT TEACHIN' MATH!

Thanks for stopping into my corner of the internet! You've just discovered (or been directed to) the landing page for all of my eccentric mathematical musings and antics in Early Childhood Education! The purpose of this blog is for me to share creative ideas I've found successful (or unsuccessful) while working with Elementary math students. By no means am I an expert, nor am I claiming to know everything. Each student is unique, and your mileage may vary with each of these concepts.

Some of these ideas will be targeted to a small group or individual instructional setting, others will be more of a whole-group idea. All of them will be more interactive and interesting than any worksheet you'll find or make anywhere!

Here's a synopsis of my philosophy on Math Education in the Elementary years, each summarized in their own posts which are linked below:

1. Kids are scared of math, and it's all our fault!

2. High-Cognitive-Demand is NOT the same as "too challenging" or "more work"!

3. Kids love math, they just don't know it yet (and usually it's in a very good disguise)!

A bit about me: I'm an undergraduate student at Kent State University in Kent, Ohio. My expected graduation date is in May of 2025, with a B.S.E. in Early Childhood Education. The ideas I share here have been implemented in instruction with real-life kids, students of mine through fieldwork, classwork, and work outside of my collegiate environment. Any photographs of minors are shared anonymously or with express written permission of the parents or guardians. I hope you find this page at least somewhat entertaining, if not useful! Thanks for stopping by!