Sixth graders at an elementary school in St. Cloud, Minnesota, have an urgent crisis to resolve. A wounded eagle found in the woods must be transported to a veterinarian, and time is a critical factor. The dilemma generates much lively discussion, and students' motivation to participate is high-pitched. Faced with an array of alternatives, they draw on their skills in using whole-number operations, measurement, geometry, and graph interpretation to try to save the eagle's life.
Rescue at Boone's Meadow is one episode in a series of instructional videodiscs called The Adventures of Jasper Woodbury. Developed by the Learning Technology Center at Vanderbilt University, the Jasper adventures chronicle situations faced by the main character or his friends. Each 15–25 minute video-based “anchor” depicts a series of events leading up to a complex “challenge problem,” which usually requires several class periods to solve. As in real-life problems, students must distinguish relevant from irrelevant information embedded in a natural way throughout the episode.
The Problem with Word Problems
A few years ago, teachers in our school district confronted their own crisis situation: how to provide students realistic situations in which to practice solving meaningful problems. Despite calls for teachers to emphasize problem-solving activities that mirror real life, few practical ways have been offered to accomplish this objective.
Students do not associate traditional word problems found in basal series with their own experiences for several reasons. First, word problems describe situations in a textual rather than a contextual format. That is, students interpret the problem from words or a graphic on a page, whereas most real problems occur in dynamic environments that include subtleties of sight and sound. Word problems also seem artificial because key words such as “in all” or “how many more” often trigger a specific number operation—unlike real problems that offer no such clues. Finally, standard word problems usually have a single correct answer and require only a few seconds or minutes to solve. In contrast, life problems are complex and require multiple tasks. How did our teachers transform the way they teach mathematics—from using traditional word problems to simulating real-life problems in the classroom? For the past two years, community representatives, administrators, and teachers have collaborated to rewrite local learner outcomes to reflect National Council of Teachers of Mathematics standards (NCTM 1989). Many of these outcomes address the issue of problem solving. Our goal has been to break out of the word problem paradigm and focus on problem-solving situations organized around authentic tasks that relate to students' everyday lives.
Aided by a grant from the State of Minnesota, we are using “anchored instruction” to transpose rich learning contexts from everyday life to classroom settings (Cognition and Technology Group at Vanderbilt University 1991). Our primary goal is to create shared learning environments that permit teachers and students to explore together the kinds of general problem situations they encounter outside of school.
Solving “Challenge” Problems
Using the Jasper series, students and teachers are free to explore any one of 54,000 frames on the videodisc almost instantaneously. This random-access capability helps teachers accommodate student questions about details of scenes that need reviewing. Teacher and student can view scenes in any order, view details frame-by-frame, and skip sections of the episode. And, because videodisc technology is interactive, students themselves can explore meaningful sections of the video.
One of the most effective and enjoyable ways for students to use video anchors has been cooperative groups. Three or four students are assigned to each group according to teacher perceptions of their achievement. Initially, the teacher asks students to view the anchor without interruption. During the second viewing, students record in their notebooks information from scenes that depict pertinent information for solving the challenge problem. In their small groups, students compare notes, discuss possible solutions, and search the episode for more detail. The teacher or students can replay segments of the episode immediately by entering frame numbers into the remote video controller or by scanning barcodes with a barcode reader.
Deficiencies so apparent in standard word problems are not present in the Jasper videos. Video provides a rich, realistic context from which students search for relevant clues to the challenge problem. Our teachers report that students are motivated to work for several days toward plausible solutions (there are more than one) to each Jasper adventure. Most important, students gain practice in using mathematics as a tool for solving problems encountered in real-world contexts. Students actively identify features of a real-life problem situation, explore alternatives, and communicate their ideas to others in their group. Much to teachers' surprise, some students have been “caught” working on problems outside of scheduled math periods—even during recess.
We have also noted increased motivation and performance among students with a history of academic and behavior problems. In a recent study conducted with high school students who have severe learning difficulties, several special education youths earned perfect scores on an open-ended post-test that asked them to explain how they solved one of the video anchors (Bottge and Hasselbring, in press). Students commented on how much they preferred these types of problems over word problems. We expected this outcome, since most of these students were also poor readers who had found word problems extremely difficult to decipher.
Linking Instruction to Assessment
Although we were convinced that the Jasper anchors would significantly enhance our students' ability to solve the kinds of problems encountered in real-life contexts, we had no way of verifying this assumption. The next step was to design an assessment method for each of the video episodes.
To begin, we examined student problem-solving procedures from answer sheets teachers had saved the previous year. It was evident that structure was needed in student response forms in order for them to be scored reliably. However, we did not want protocols to look like worksheets that tend to “lead” students to a single correct solution. To organize student responses suitable for scoring—and yet encourage students to experiment with several logical solutions—we simply asked them to organize their procedures into steps and justify their use of each procedure.
This school year, we will begin training scorers and pilot our scoring rubric. Responses will be scored on a three-dimension, four-point analytic scale adapted from Szetela and Nicol (1992) and Psychological Corporation's Integrated Assessment System (Farr and Farr 1990). The scale will rate students' understanding of the problem, logic in procedures, and correctness of computations. Our goal is to use this scoring system both as a diagnostic tool to guide future instruction and as a descriptive way to gauge growth in students' problem-solving skills districtwide.
Preparing Students for the Real World
Both teachers and students are excited about using videodisc technology as a tool to teach problem solving in recognizable and motivating contexts. For example, each cooperative group in a 6th grade classroom in one of our elementary schools created its own complex mathematics problem complete with script and character descriptions. The teacher selected one problem to videotape. This past summer, after minor modifications to the script, the “authors” and other students acted out scenes of the episode in a grocery, a party supply store, a teacher's home, and a city park. The video is being pressed to videodisc and will be used in elementary classrooms throughout our school district.
Video anchors have motivated our students to work together toward a common goal. Reading proficiency is no longer a prerequisite to accomplishing complex mathematics tasks. Computation is no longer viewed as an end in itself but, rather, as a valuable life skill. By being able to reliably assess our students' attempts to unravel problems presented in the anchors, we hope to prepare them for the complexities of life outside the classroom walls.
