Project Activities
This study built on the researchers' past work by examining the relative effectiveness of EAI for improving students' mathematics achievement. EAI uses a mix of video-based problems delivered on CD-ROM (called anchors) and hands on projects (e.g., building skateboard ramps, compost bins, or hovercrafts). Each anchored problem consists of several sub-problems embedded in a realistic and motivating context. Anchored problems require considerable time to solve, usually five to ten 60-minute class periods. Students must first define and understand the EAI problem, locate the relevant pieces of information for solving it, and then integrate this information into a solution that makes sense. In previous work, students have been found to identify with the video's main characters and to work hard on helping them solve their problem. The additional practice the applied projects afford students appears to help them understand the importance and benefits of learning math.
This project tested EAI in two conditions. In the first condition, basic skills such as computation of whole numbers and fractions were explicitly taught before and during EAI as planned units of instruction. In the second condition, these same skills were taught informally as they are needed in student efforts to solve the mathematical problems presented during EAI. The researchers carried out this study with classrooms of students including both average achieving students and low achieving students, many of whom are likely to have LD or emotional disabilities (ED) disability classifications.
The participating middle and high schools serve diverse ethnic and socioeconomic student populations. In the study, 30 classrooms of students were randomly assigned to receive EAI with either explicit or informal teaching of basic skills. The researchers tested students' mathematical achievement before and after the instruction to measure how much they learn from the EAI instruction. Additionally, attitude surveys and classroom observations were used to study the student learning process as students attempt to solve complex problems. Using this information, the researchers refined EAI to make it a more effective instructional approach for low-achieving students.
Key outcomes
First, the project developed a new set of instructional modules called “Fraction of the Cost.” These modules addressed multiple skills and concepts stated in the NCTM middle school math standards, including several within the categories of Number and Operations, Geometry, Measurement, Problem-Solving and Communication. The team demonstrated both feasibility and usability of the modules with teachers and students with a range of abilities.
As part of this process, they also developed and tested the validity and reliability of a computer-based version of the paper and pencil measure that had been developed to test learning within EAI. A study comparing the use of the computer and paper and pencil version found that the computer version was as valid as the paper and pencil version. In addition, the team gathered additional information that helped them understand how learners were navigating through the assessment, revealing that the low-achieving students were able to navigate the test, spent about the same amount of time solving the sub-problems as the more advanced students, and made use of the learning scaffolds.
The second goal was to gather a set of empirical data that tested the effectiveness of embedding direct instruction of basic skills in the curriculum. The project team completed two randomized experiments carried out in schools testing the effects of participating in these different curricular variations. A total of 478 students participated and they have complete data on all of them. Analysis of these data indicated that the low-achieving students in particular performed well on both computation and problem solving. Indeed the combination of media-based instruction with concretized instruction seems to have been an important step to take to help low achieving students master fractions. For the low achieving students, the data also indicated that the formal fractions instruction did improve their fractions computation skills.
Finally, the team gathered detailed data derived from the videotape analysis describing how students in each of the EAI + ET, EAI + IT, and Comparison conditions. A total of 368 whole class periods were observed during the implementation of the two studies. The analysis of the videotapes was ongoing at the conclusion of the project period.
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Products and publications
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Journal articles
Bottge, B.A., Grant, T.S., Rueda, E., and Stephens, A.C. (2010). Advancing the Math Skills of Middle School Students in Technology Education Classrooms. NASSP Bulletin, 94(2): 81-106.
Bottge, B.A., Rueda, E., Grant, T.S., Stephens, A.C., and LaRoque, P.T. (2010). Anchoring Problem-Solving and Computation Instruction in Context-Rich Learning Environments. Exceptional Children, 76(4): 417-437.
Bottge, B.A., Rueda, E., Kwon, J.M., Grant, T., and LaRoque, P. (2009). Assessing and Tracking Students' Problem Solving Performances in Anchored Learning Environments. Education Technology Research and Development, 57(4): 529-552.
Cho, S.J., Bottge, B.A., Cohen, A.S., and Kim, S.H. (2011). Detecting Cognitive Change in the Math Skills of Low-Achieving Adolescents. Journal of Special Education, 45(2): 67-76.
Cho, S.J., Cohen, A.S., and Kim, S.-H., and Bottge, B. (2010). Latent Transition Analysis With a Mixture Item Response Theory Measurement Model. Applied Psychological Measurement, 34(7): 483-504.
Stephens, A.C., Bottge, B.A., and Rueda, E. (2009). Ramping up on Fractions. Mathematics Teaching in the Middle School, 14(6): 520-526.
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