high cognitive demand math tasks

Let’s talk about high-cognitive demand tasks.

First, I want to show you two different math tasks that might be presented in a 3rd grade classroom.
See what you notice about the two tasks - their similarities and differences.

Both tasks are asking students to multiply but one task is asking students to think multiplicatively. Can you see the subtle difference in complexity between these two tasks?
High cognitive demand sounds elaborate and might lead us to believe that the task has to be elaborate as well. That it must be a huge project or complicated process. This just simply isn’t true. While I do think project-based learning has it’s place in our math classrooms, high-cognitive demand tasks can take place every single day in every single lesson. And in fact, they should.

In the task above, the goal was the same: get students to multiply. Task 2 accomplishes this but also more. With task 2 students are problem solving, thinking, talking, discussing, analyzing. They will probably do some math modeling as they reach for a white board or manipulatives. With this [still simple] task, we have intrigued students and invited them to partake in solving a problem - not following a procedure.

If I observe students working on task 2, I can assess if they truly understand equal group and multiplication. With task 1 i may only be able to assess if they can do what we went over when we did “these kind of problems” before.

So, let’s define high-cognitive demand tasks. NCTM has wonderful information on this: found here.

Simply put, a high-cognitive demand task is a PROBLEM and it’s demanding. It’s authentic because it’s often the way we use math in real life - to solve a problem.

SO why use them?

1. We are required to teach the mathematical practices/processes: wherever you teach, your standards most likely have a section for mathematical process standards. The Common Core standards say things like “make sense of problems”," “explain thinking”, and “construct arguments”. If the standards require it, we need to get serious about how we are going to cover them. These type of standards cannot be done through worksheets, drills, and following steps. These practices of math are only done by doing math.

2. They engage students: We all know it is important for us to combat math anxiety, especially with young girls. We put a lot of emphasis on making reading engaging, authentic, and fun so students will be lifelong readers. We need to be creating lifelong mathematicians. The human brain loves to solve problems and look for logical patterns - and young students especially love it. You can spend time telling your students how to do the math and they may or may not get it. You can have students spend time problem solving, reasoning, explaining, and working together and insure they get it. PLUS, they will feel such ownership. The math wasn’t handed down to them, it was discovered by them - through hard work! What a sense of accomplishment. In my third grade classroom, math is our favorite time of day. It’s a comment I hear over and over again '- “HOW do you get them to love math?”. It’s confusing because our math time isn’t full of over-the-top games or art projects. In fact, most of the time my students are just solving problems (and asking for more!). There is just something to PURE MATH and it will hook you and your students!

3. Assess understanding of concepts: Sure, your students can sing the song and do the steps - but do they understand the big principles of math? Do they understand the base ten system, have the ability to manipulate numbers in their head, and explain? Do your students know the hexagon is hexagon because of its properties or because “it’s the yellow one”. Do they know that the 1 they are “carrying” is actually a 10? All these deep assessment opportunities we might miss when checking off a student paper or guiding them through steps. Because high cognitive demand tasks are very open, we can get right to the heart of the matter - not what can students do but what do they understand.

4. Differentiation: We know it’s important and we know it’s required. Unfortunately, many classrooms think high-cognitive demand tasks are for enrichment only. We have a deficit mindset, often labeling kids as low in math when they aren’t low at all. Unless students have a drastic unique circumstance, they have the ability to problem solve - they do it all the time (don’t believe me? Watch them play video games or sneak around school rules) - THEY CAN DO IT. The beauty of high cognitive demand tasks is that they are open - so you can differentiate naturally when students work with larger or smaller number, use manipulatives or mental math, etc. Students can still get to the concept but with the numbers/scaffolding they are ready for. And the best part - nobody knows that a student is working “smaller. It’s not a worksheet cut in half or a babyish assignment, it’s the same task.

I’ve used high-cognitive demand problem solving tasks in kindergarten up to third grade. My students build such a deep appreciation for math and an even deeper understanding of concepts.

Your students can too!

So how?

Well, the best way to do something is to just start! Like I said earlier, these tasks do not have to be a huge project! You can take the tasks that are already at your disposal and turn them into deeper critical tasks. Let’s take a look at some steps.

1. Take a “naked problem” and give it context. A naked problem might be just numbers (34 + 27) or might be a “too-simple” problem (I had 34 pens and 27 pencils, how many total?). Take these problems and add some context to make them real for students. Use their names, their places, and their situations. Think of real life problems/scenarios/phenomena that would intrigue them and make them want to get involved. This is a great way to bring in social justice/social studies too!

2. Avoid looking for just an answer. A correct answer is important and we want to look for it. But we cannot stop at the answer. Like I said above, a student may know the shape is a hexagon (correct answer!) but only because “it’s the yellow one” (not understanding). When creating or tweaking tasks, always think how you’re going to go deeper. Fortunately all you need is one quick phrase at your disposal -”How? Prove it.” Asking HOW a student did it and to PROVE that it works automatically ups the cognitive demand. Another good one is “is that the only solution?”

3. Get the best bang for your buck. Why give them a task that has them multiplying 2 numbers one time when you could give them a task that gets them multiplying a ton (the equivalent of a page of math facts without the crying involved with a page of math facts {please don’t give out pages of math facts}). If you want students to do a ton of math - open up your problem!

4. Don’t ask for the answer, ask for the question. The easiest and most popular way to start - a board giving an answer and asking for questions/problems.

5. Do the work. Unfortunately, high-cognitive demand tasks are no the norm in math textbooks/workbooks. It takes some time and energy to find, create, and tweak tasks to demand more! But the benefits are too great to ignore. The good news is, the more you read about high-cognitive demand tasks and study them, the easier it is to turn every small question into one!

So take a look at these tasks and determine which ones will get kids thinking, talking ,explaining, working, MATH-ing!

But for those of you starting out on your journey, I have some help for you. I have been reading, researching, implementing, and learning for years about cognitively-guided math and high-cognitive problem solving tasks. And it’s time to share the wealth and change the norm around math!

Because it’s my passion, I’ve begun creating resources ready for third grade classrooms to start MATH-ing!

Natural Math is my lesson-based resource that includes lesson aligned to 3rd grade standards. EVERY lesson has review, number sense warm-up, a high-cognitive task (hey hey!) and content practice that is built on students discussion, inquiry, questioning, and discovery! The multiplicative reasoning unit is OUT NOW and has 18 lessons included plus many bonus resources! Not sure about it, try the first lesson FREE! Look below for the freebie and scroll on for the whole resource!

But wait, THERE’S MORE!

If a whole lesson resource seems daunting, I have a GROWING monthly bundle of high-cognitive tasks for third grade. They are themed by month and include 5 tasks and 5 picture puzzles per month! They make a cute bulletin board for a math station or early finisher activity. They can also be put on Nearpod or Google for collaborative tasks - so many ways to use them and get started with high cognitive tasks! Click below to access the GROWING monthly bundle!

I hope you try some high-cognitive tasks with your students this year! Be sure to tag me on instagram (@aubreeteaches) so I can see the amazing MATH your students do!

HAPPY TEACHING!