Content Analysis of Tasks

Low Cognitive Demand Tasks

 

• Memorization, as we all know, is the lowest on Bloom’s Taxonomy of thinking skills. In math it requires only that students regurgitate information we have given them in the form of definitions, formulas, algorithms, etc. At the memorization level, a student uses no procedures and makes no connections to math concepts. Memorization has no positive impact on helping a student create number sense.

 

• Tasks that involve Procedures without Connections mainly rely on students using algorithms to produce one correct answer following one selected route of achieving the answer. Students demonstrate little to no understanding of the math involved in solving the problem. This is old school mathematics. It’s the task that requires students to do numerous problems that follow the same procedure over and over again so that the algorithm is engrained in their heads. It requires no connection be made to math concepts that are integral to developing number sense. Oftentimes we might think we have increased the cognitive demand by asking students to explain these types of problems but in reality students are only explaining the procedure – not the math behind it.

 

High Cognitive Demand Tasks

 

• Tasks that involve Procedures with Connections begin to help us make our way past the bottom rungs of Bloom’s ladder of thinking skills. In these types of tasks students are required to make connections to mathematical concepts which will deepen their understanding of the underlying concepts involved in the task. Although a procedure is used, students are required to demonstrate an understanding of what makes the procedure useful for the assigned task. Students may be asked to represent their thinking in numerous ways – using manipulatives, models, diagrams, etc. This type of task is time-consuming for the teacher to develop and for the student to work through but the learning payoff far outweighs what can be gained from the low cognitive demand tasks.​

 

• Doing Mathematics should be the ultimate goal in our math classrooms. These types of tasks rely totally on a demonstration of number sense. Students must impose their own structure and procedure oftentimes using manipulatives, models, drawings, etc. They will attach meaning to their work by referring to the representations they produced to explain each step of how they arrived at a particular quantity. This process helps build connections to mathematical meanings and concepts. There is no relying on memorized algorithms and procedures. When we develop these types of problems students attain a deeper understanding of the interconnectedness of math concepts involved in a task. In setting up these experiences teachers need to consider the students past experiences with these types of problems. Students will probably encounter anxiety with these problems because of the length of time required to work through the task and because they simply are not used to combining multiple previously learned math concepts to produce an outcome or to complete an open-ended task. These are the types of problems that students will often wear down the teacher with questions of how and where to start. When the teacher gives in and starts offering procedural directions the task begins to lose cognitive demand. Instead teachers need to provide the scaffolding of student thinking and reasoning that will be required to make this level of cognition successful.