At a recent PLC meeting of the Humanities teachers at my school, we were spending some time digging into the concept of Cognitive Complexity vs. that of Difficulty. This conversation was rolled into a much deeper conversation about the ILEARN, Indiana’s new computer-adaptive assessment that all students will be taking in grades 3-8. We began talking about the differences in difficulty and cognitive complexity because we were learning that no matter what difficulty level a student fell into on the adaptive test, all students will be solving problems that are cognitively complex. So, what’s the difference between the two concepts?
When we try to define the concept of difficulty, it is considered a measure of the effort required to complete a task. In the purpose of an assessment, a problem that many students missed would be considered more difficult than a problem that everyone got right. So when looking at the difficulty of a problem or task in your classroom, the more likely it is that all students will get it correct, the less difficult it is.
As we know, all our students come to us varying levels of understanding. In his book The End of Average, Todd Rose talks about the jaggedness of people. Not only do our students walk into our classrooms with physical differences that we can all see, they walk in with different abilities in math, reading, etc. In adaptive testing, an assessment will adjust its level of difficulty based on the answers students get correct or incorrect. As one student gets a question correct, the next question will most likely be more difficult. On the other hand, a student who gets a question wrong will then see a question that is less difficult. All standards can be measured at varying levels of difficulty. Take for example the following two math problems that are working on the same skill:
Easy: Sarah planted 5 rows of 7 flowers in each row. Write a multiplication equation that shows the number of flowers in Sarah’s rectangular garden.
Difficult: Tom told Mary he planted 48 flowers in the rectangular-shaped garden. Select the correct number sentence Mary could use to describe how the flowers were planted.
As you can see, both questions require students to solve the same type of problem, using a similar level of thinking, but because of the wording, the second question would be considered more difficult.
To define the idea of complexity, we have to think about it as a measure of the thinking action, or knowledge that you need to complete a task. One way to think about this is to think about how many different ways can a task be accomplished. I think the best way to think about the idea of complexity is to think in relation to Webb’s Depth of Knowledge. DOK can be broken down into 4 different levels: Recall and Reproduction; Basic Application of Skills; Strategic Thinking; and Extended Thinking.
So basically, cognitive complexity is a way to measure how demanding of a thought process is necessary to complete a specific task. Items that simply ask a student to recall basic facts from an article they just read would be much less complex than an item that required analyzing the points of view of two separate authors and making a comparison of their purpose for writing.
So… How should an understanding of these two concepts impact our teaching in the classroom? The reality is, no matter what level of difficulty a student may be working at – whether they are reading below grade level, or working on math that is above grade level – all our students need to see the types of problems that have a high level of cognitive complexity, because no matter what level of difficulty they are working with, they need to be able to use a variety of levels of thinking in carrying out tasks in the classroom.
There are a couple of great resources that you can use to help find ways to up the level of cognitive complexity no matter what level of difficulty your students are working at.
EngageNY: A huge collection of resources for both math and language arts (and everything is FREE!!!) that will include performance tasks and opportunities for students to perform cognitively complex activities. You can search by specific topics, or seek things out based on grade level and topic.
YouCubed: A wealth of activities for math instruction, based on the work of Jo Boaler. You can seek out tasks for your students to complete, find resources for your students or parents, and so much more!
Open Middle: Another math based site that provides tons of challenging math problems. Again, you can search by grade level, topic, and more. Carrying out a problem like this a couple times a week in your classroom will up the DOK immensely!
I’m sure that there are lots of other ideas you may have to help increase the cognitive complexity within your classroom. What resources do you have? How do you make sure that all your students have opportunities to carry out tasks that are truly cognitively challenging to them? Share your thoughts in the comments below!