High Cognitive Demand Math Lessons

Finding High-Quality Math Tasks Online

The internet is a fantastic resource for discovering math problems that range from easy to difficult in terms of the amount of mental effort required. Even while children in elementary school should be given opportunities to participate in activities at all levels—lower as well as higher—the focus should be on the higher level activities. Therefore, we need the ability to judge what does and does not need a high level of cognitive effort.

My co-researchers and I used a guide developed by Margaret Schwan Smith and Mary Kay Stein in 1998 called the Task Analysis Guide (TAG). This guide is comprised of four distinct levels of cognitive demand, which are as follows: memorization, procedures without connections, procedures with connections, and doing mathematics. We used this guide to determine the quality of online activities.

Learning something by heart eliminates the need for analytical thought, prevents the formation of connections that could explain why an answer is correct, and allows one to skip through steps in the process. This kind of work can look like it requires you to recall facts. Algorithms are procedures that do not make links to other mathematical concepts. In an algorithm, students arrive at a solution without making any connections to other mathematical concepts, and they are not asked to justify their work. This category contains issues that need for the solution of straightforward methods, such as utilising the United States standard algorithm for addition. Tasks that require low cognitive effort do not require a significant amount of thinking, such as memorization and procedures that do not involve connections.

In order for pupils to solve arithmetic problems that include procedures with connections, teachers may frequently show visual diagrams or manipulatives such as base 10 blocks or Unifix cubes. This gives students the opportunity to approach the problem from a variety of perspectives. Students will be able to understand why the solution is correct rather than simply knowing how to find it with the help of the processes that are used in these situations. One example of these procedures is the partial product algorithm for multiplication.

The tasks at the highest level, performing mathematics, require non-algorithmic thinking, demand self-monitoring, and allow for the application of numerous strategies; pupils are exploring mathematical concepts at this point.

According to Smith and Stein, tasks that need students to establish connections, analyse information, and draw conclusions in order to solve them are considered to have a high cognitive demand. Examples of such tasks are procedures with linkages and practising mathematics.


Elementary school teachers need to be critical consumers of the resources that are available to them in order to effectively challenge their children on a variety of cognitive levels. The following are some of the factors that assisted my coworkers and me in determining the cognitive demand of various online activities and their overall quality.

Age matters. The level of cognitive load that a challenge poses can fluctuate significantly depending on the age range of the children it was designed for. For instance, completing a worksheet with basic one-digit addition problems would be considered memorization for a fourth grader, who is expected to have them memorised (even more so if the student is being timed), whereas for kindergarteners, who are just learning what it means to add two parts to make one whole, it would be considered doing procedures without connections.

If you are seeking for tasks that require a high level of cognitive demand, you might consider a resource to be a procedure with connections if it satisfies any one of the following criteria: In order for an activity to be considered mathematical, there must be more than one way to solve the problem:

In most cases, the condition is caused by manipulatives (e.g,. 10 frames, base 10 blocks, number lines, number grids).
The students are instructed to submit explanations as to how they reached the solution, which is a requirement of the directions (through models, words, or both).
There is a significant amount of analytical thinking that must be done. Students, for instance, are required to decide how to approach a topic that can be solved in more than one manner, create links between the math and the real world, or explain their mathematical thinking.
When teachers are evaluating a math activity, they should also analyse any images that accompany the activity. Is the inclusion of an image just for aesthetic reasons, or does it serve a purpose that contributes to the solution of the problem? Clock faces, ten frames, and graphs are examples of images that serve a functional purpose. If a task has a decorative image, it is considerably more likely to be labelled as having a low level of cognitive demand; on the other hand, if the task has a functional image, it is much more likely to be interpreted as having a high level of cognitive demand. Visual attractiveness does not necessarily correlate with high levels of cognitive demand, despite the fact that an activity may be well-liked due to the presence of cute and decorative graphics. It is essential to centre one’s attention on the subject matter rather than the aesthetics.


When compared to websites such as Teachers Pay Teachers or Pinterest, which allow anybody to publish, you have a significantly better chance of discovering math exercises that have a high level of cognitive demand on websites where resources are evaluated before publication. The following websites publish various resources that have been reviewed:

For grades K–12, Illustrative Mathematics gives educators the ability to search for activities based on topic standards, either by subject or grade (free).
The English language arts and mathematics lessons included in the EngageNY curriculum were developed by the New York State Department of Education and include pre-kindergarten through eighth grade. In addition to this, it offers mathematics courses for higher grades, including algebra I and II, geometry, precalculus, and higher (free).
Students between the ages of 3 and 18 can access the NRICH library, which is maintained by the University of Cambridge in England and contains resources and curriculum-mapping papers (free).
youcubed is a website that offers high-quality math problems that can be searched for by grade (K–12) or topic. The website was developed by a mathematics education professor at Stanford University named Jo Boaler. The researchers who administer youcubed are responsible for the creation of some of the challenges, while others come from a variety of different websites, such as NRICH (free).
Illuminations is an online resource that is made available by the National Council of Teachers of Mathematics (NCTM). It contains activities for grades pre-K through 12 that are based on both NCTM standards and Common Core State Standards. Access can only be gained by becoming a member of the NCTM, which ranges in price from $49 to $139 each year.