Thinking Allowed

Math students explain problem-solving out loud as they talk through their thinking

Ms. Franklin teaches first grade at a suburban elementary school. The school uses an inclusion model for special education in the early grades; nine of her 25 students have learning difficulties of some kind. A teaching assistant provides additional assistance during and after the math class.

Franklin taught her students math problem-solving strategies in a systematic way during the first part of the school year. They learned to interpret and solve problems by making a picture or model; acting it out; making a systematic list; guessing, checking, and revising; looking for a pattern; and eliminating possibilities. In the spring she wanted to assess students' abilities to problem solve. One strategy would be to get them to summarize what they were doing as they were engaged in the process.

Implementing Research-Based Strategies

• When asked to give a summary, students must analyze information at a fairly deep level to decide what information to delete, what to substitute, and what to keep (Anderson, & Hidi, 1988/1989; Hidi & Anderson, 1987).


• Having students use "think-aloud" strategies makes their tacit knowledge more explicit (Hayes & Flower, 1980; Smith & Wedman, 1988).

Franklin's students used the "thinking aloud" process in reading class and when they read in other subjects, such as social studies. When guided to "think aloud," students would read, pause, check for understanding, and summarize in their own words what they read.

Franklin built on this understanding by modeling the thought processes that she wanted students to engage in when solving a math problem. She presented a simple word problem and then solved it, describing aloud her thinking at each step. She talked as she highlighted text; made diagrams, lists, and pictures; and wrote calculations as she worked through the problem. Students heard her ask herself:

• What am I trying to solve? I am trying to figure out...
• The important information is... (and at times: THIS information isn't important)
• What strategy will I use to solve the problem? The strategy I will use is..
• I am going to think aloud each step of this strategy: First... next... and finally...
• Does this answer make sense if I read the problem over again?

She made a poster of these think aloud steps for students to refer to as they began their own work.

• The more a person is aware of an explicit structure, the better he or she can summarize information (Meyer, 1975; Meyer & Freedle, 1984).

Students practiced "think aloud" summarizing strategies as a class. Then they tried it with a partner, using easy problems they were familiar with. Taking turns, partners used paper, pencil, and manipulatives to solve problems, talking as they went. They referred to the chart to structure their thinking, as Franklin and the teaching assistant monitored and guided their efforts.

Technology Supporting Success

When Franklin tried to use a rubric to assess individual students as they demonstrated their processes, she was frustrated. Finding time for a 10-minute demonstration by each child just wasn't practical in a class of 25.

As a form of performance assessment, she decided to capture their work on video. Not only would she be able to assess their processes at her leisure, but she would also create an important artifact to add to the children's digital portfolio. She reserved the school's digital video camera. With a tripod and the camera power supply cord, Franklin set up a temporary filming station in her classroom.

Franklin first asked the students to record her as she demonstrated the process. Next, she showed students the rubric for assessment, and together they graded her performance against the rubric. Then she captured a digital record of each student solving a math problem, and they reviewed them together with the rubric, increasing the students' understanding of the learning goals.

Videos provided a more robust sample of student work than she had ever had before. Reviewing the videos gave her greater assurance that students were learning, along with a permanent record that could be used to determine and document student progress.