Q Who else advocates a multi-step problem-solving process?
A Examples appear below.
Illinois
Just as Texas gives its students the TAKS test, Illinois has their own test, the ISAT—the Illinois Standards Achievement Test. The School of Education at Chicago ’s Loyola University produces a TV call-in show called Countdown. Below is a sampling of some Quick Time movies offered by their Web site. Although Illinois students use graphic organizers other than “The Big Q,” they are learning a strikingly similar approach to problem-solving.
Some links connect to video clips that require QuickTime Player.

# |
Title of Quick Time Movie |
Summary |
1 |
Problem Solving Checklist |
The host displays a page titled “Math Detectives” and directs the caller through a list of actions to be completed when solving a problem. The list is divided into three sections—The Plan, The Explanation, and The Math. |
2 |
Extended Response Frame |
The host provides the caller with guidelines about his written responses, which should include a topic sentence, details, and a conclusion. A specific format prompts the student to compose a thorough response. |
3 |
Graphic Organizer |
The host goes through a flow chart of rectangles, a graphic organizer titled “ISAT Math: Extended Response Prompts,” which leads the student through a multi-step approach to problem-solving. She emphasizes that the word “because” must appear in the response for the student to get full credit. |
4 |
Rubric |
The host takes the caller through a series of questions that appear on a green-colored card titled “Can the problem-solver explain the solution to the problem?” and a salmon-colored card titled “Did the problem-solver do the math?” using an example of high-scoring student work. |
5 |
Evaluating the Plan |
The host covers questions found on a blue card titled “Did the problem-solver have a plan?” which addresses the various components making up the problem-solving process. |
6 |
Evaluating the Explanation |
The host uses her green-colored card to review a student’s explanation paragraph written as part of the problem-solving process. She guides the caller in verifying that the example student explained both what he did to solve the problem and why he solved the problem that way. |
7 |
Evaluating Math Knowledge |
The host uses her salmon-colored card to review an example response. She guides the caller in evaluating whether the example student got the correct answer, used correct math terms, and made no errors in computation. |
National Assessment of Educational Progress (NAEP)
Excerpts from the NAEP 2003 Mathematics Report Card are shown below (Figure 1.3 from page 8). View Chapter 1 of the document here.
Achievement Level |
Fourth-grade students
performing at this level should… |
Problem-solving Portion of Description |
Basic |
…show some evidence of understanding the mathematical concepts and procedures in the five NAEP content strands. |
….Their written responses are often
minimal and presented without supporting information. |
Proficient |
…consistently apply integrated procedural knowledge and conceptual understanding to problem solving in the five NAEP content strands. |
….Students performing at the Proficient level should employ problem-solving strategies such as identifying and using appropriate information. Their written solutions should be organized and presented both with supporting information and explanations of how they were achieved. |
Advanced |
…apply integrated procedural knowledge and conceptual understanding to complex and nonroutine real-world problem solving in the five NAEP content strands. |
…. These students are expected to draw logical conclusions and justify answers and solution processes by explaining why, as well as how, they were achieved. They should go beyond the obvious in their interpretations and be able to communicate their thoughts clearly and concisely. |
National Council of Teachers of Mathematics
Because problem-solving is such an important component of the NCTM standards , the majority of K-12 mathematics programs throughout the U.S. employ some approach to the teaching of a formal problem-solving process. |