Content Analysis of Tasks

Memorization: Task K, Task E

   Memorization is the lowest cognitive level; it is simple memorized facts used in mathematics. Task K is an example of this because it’s a simple addition problem that students don’t need to alter in any way. By not asking and in depth questions with this problem, students will answer it quickly, and move on. Smith and Stein list one of the demands of memorization as a task that “Cannot be solved using procedures because a procedure does not exist, or because the time frame in which the task is being completed is too short to use a procedure.” (Smith & Stein 1998, p. 348)

   Another example of Memorization tasks is the basic multiplication table; students do not need to do any math work to solve simple multiplication problems because most have it memorized.In task E students must solve a subtraction problem that includes fractions 3 5/6 – 1 1/6. Although this may seem intimidating to students since fractions are involved. The problem is actually memorization; the denominators are the same so the problem actually ends up being 3-1 and 5-1; the answer being 2 4/6.

 

Procedures without Connections: Task F, Task G, Task H

   The tasks F, G, and H are all procedures without connections. All of these problems require a certain amount of work, but nothing past creating and solving algorithms. Both Task G and H are word problems that require the student to take given information, create the proper algorithm, and solve the problem. Doing this student’s are taking memorized math facts, using them to create a procedure, which helps them solve the equation, with very little creative freedom.In Task F students are asked to solve a subtraction problem where the minuend and the subtrahend are both fractions. Although this problem is very similar to task E, there is a difference. Task F’s denominators are different from each other which requires students to use a new procedure to solve the problem.

 

Procedures with Connections: Task A, Task B, Task D, Task I, Task J, Task L

  Tasks that are Procedures with Connections require students to not only solve a problem, but also explain the work around it. Often times in this concept students need to explain someone else’s thought, like in task L. This connects math to problem solving, making each equation more than a quick procedure. In task A students are asked to create a real life situation that describes a math problem. By doing this, they are connecting math to way scenarios make sense to them. Many of these tasks give problems that could be considered procedures without connections, although these problems ask the student to explain, which requires higher cognitive effort. Examples of this can be found in tasks B, I, and J. In task D the student is asked to solve a problem more than one way, in this task students are given creative freedom to play with the equation in multiple ways. 

 

Doing Mathematics: Task C

  Doing mathematics is the highest cognitive level. Solving problems in the doing mathematics category will be much more advanced then working through an algorithm. Doing mathematics will “Require students to explore and understand the nature of mathematical concepts, processes, or relationships” (Smith & Stein 1998, p. 348). An example of doing mathematics is Task C, in this task the student is given two equations, and asked to explain the differences between addition and subtraction. To do this work students need to know the algorithms for addition and subtraction, they also need to have a firm grasp of both of these concepts. They need to know enough to compare and contrast elements of both problems. This deep thought requires a full understanding of these mathematic concepts well enough to reiterate their work to someone else.