## Sorting Mathematical Tasks

**Instructions on Sorting Tasks:**

-When sorting tasks, always begin by thoroughly reading the problem. The key words in the problem should give you a good idea of where the task may go.

-When a problem contains few words and simply asks students to solve a simple algorithm, the task is probably low cognitive demand task. Memorizing or reciting an algorithm that was previously learned is not very cognitively demanding. The number of words does not always give away if a problem is high or low, but it can sometimes be an indicator.

-If the task uses the phrase, “explain your answer,” or some version of this, it should be grouped as a high cognitive demand task. When students are asked to explain, they must demonstrate a deeper understanding of the mathematical concepts.

-In order to separate low cognitive tasks into the two subcategories, “Memorization” and “Procedures without Connections,” you must examine what the task is asking students to do.

-If the task is asking students to recite a fact they have memorized, for example, multiplication tables, the task is grouped as “Memorization.”

-If the task asks students to use an algorithm and requires students to follow the steps of a procedure without needing to understand the mathematics behind it, this task would be grouped as a “Procedures without Connections” task. These tasks can involve all sorts of algorithms, as long as they do not require the student to understand the mathematical concepts. These tasks enable students to mindlessly perform algorithms and successfully complete the problem.

-In order to separate high cognitive tasks in to the two subcategories, “Procedures with Connections” and “Doing Math,” you must also examine what the tasks are asking students to do.

-If the task is asking students to use an algorithm or procedure, but dig deeper, it would be grouped as “Procedures with Connections.” These tasks can use algorithms but usually require the students to use the algorithms in different ways or represent their answer or problem in different ways. These problems require students to find connections or relationships between different mathematical concepts.

-If the task is asking students to think using extremely high cognitive demand, includes no algorithms, and requires students to make connections that show they deeply understand the material, it would be grouped as “Doing Math.” "Doing Math" tasks require students to analyze other students' work, their own work, and explain how and why they did certain procedures or strategies. "Doing Math" tasks are the most difficult tasks and can frustrate many students if the task is above their developmental level.

-When sorting tasks, always begin by thoroughly reading the problem. The key words in the problem should give you a good idea of where the task may go.

-When a problem contains few words and simply asks students to solve a simple algorithm, the task is probably low cognitive demand task. Memorizing or reciting an algorithm that was previously learned is not very cognitively demanding. The number of words does not always give away if a problem is high or low, but it can sometimes be an indicator.

-If the task uses the phrase, “explain your answer,” or some version of this, it should be grouped as a high cognitive demand task. When students are asked to explain, they must demonstrate a deeper understanding of the mathematical concepts.

-In order to separate low cognitive tasks into the two subcategories, “Memorization” and “Procedures without Connections,” you must examine what the task is asking students to do.

-If the task is asking students to recite a fact they have memorized, for example, multiplication tables, the task is grouped as “Memorization.”

-If the task asks students to use an algorithm and requires students to follow the steps of a procedure without needing to understand the mathematics behind it, this task would be grouped as a “Procedures without Connections” task. These tasks can involve all sorts of algorithms, as long as they do not require the student to understand the mathematical concepts. These tasks enable students to mindlessly perform algorithms and successfully complete the problem.

-In order to separate high cognitive tasks in to the two subcategories, “Procedures with Connections” and “Doing Math,” you must also examine what the tasks are asking students to do.

-If the task is asking students to use an algorithm or procedure, but dig deeper, it would be grouped as “Procedures with Connections.” These tasks can use algorithms but usually require the students to use the algorithms in different ways or represent their answer or problem in different ways. These problems require students to find connections or relationships between different mathematical concepts.

-If the task is asking students to think using extremely high cognitive demand, includes no algorithms, and requires students to make connections that show they deeply understand the material, it would be grouped as “Doing Math.” "Doing Math" tasks require students to analyze other students' work, their own work, and explain how and why they did certain procedures or strategies. "Doing Math" tasks are the most difficult tasks and can frustrate many students if the task is above their developmental level.

(Smith & Stein, 1998, p.348)