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IES Grant

Title: Adapterrex: Exploring the Learning Benefits of Erroneous Examples and Their Dynamic Adaptations Within the Context of Middle School Mathematics
Center: NCER Year: 2009
Principal Investigator: McLaren, Bruce Awardee: Carnegie Mellon University
Program: Education Technology      [Program Details]
Award Period: 3 years Award Amount: $1,302,928
Goal: Development and Innovation Award Number: R305A090460

Purpose: The purpose of this project is to develop an intelligent tutoring system that helps middle school students learn mathematics. The specific focus is decimals, a subdomain of mathematical knowledge about which students often have common and persistent misconceptions. The system, called AdaptErrEx, will present students with worked examples of problems, in which each step of a problem solution path is presented for the students, along with feedback and instruction. Additionally, a unique feature of the proposed system is that students will also be presented examples of problems that contain an error, termed erroneous examples. This teaching technique is used in various fields and it is hypothesized that under certain conditions this will be conducive to learning math. This pedagogical method is intended to support the development of critical thinking, adaptive reasoning, and metacognitive strategies for evaluating and justifying solution plans.

Project Activities: The main undertaking in this project is to build an adaptive tutoring system intended to provide supplemental instruction in decimals. The system development activities will be informed and supported by empirical studies and sophisticated artificial intelligence techniques. For example, the team will design and develop a knowledge representation of correct and erroneous worked examples. The findings from this line of work will provide a basis for designing personalized help, self-explanation prompts, problem presentation, and selection of problems. The team will design and develop a student model of relevant cognitive and meta-cognitive variables, a cognitive model of help and misconceptions, and a computational architecture for adaptive erroneous example handling. Several experimental studies will be conducted to examine various aspects of learning from erroneous examples and different types of support.

Products: The products from this project will be a fully developed intelligent tutoring system focusing on instruction of decimals for middle school students. Published reports of key findings will also be produced.

Structured Abstract

Setting: The participating schools are located in urban settings in Pennsylvania, North Carolina, Texas and California.

Population: The study participants will include approximately 600 middle school students, primarily sixth graders but also seventh and eighth graders who need remedial support with decimals. A diverse population will participate, including students of varying math abilities, both boys and girls, various ethnicities, and English language proficiencies.

Intervention: The proposed intervention will be an intelligent tutoring system designed to provide supplemental instruction in decimals. Students will be presented with worked examples, both those that are correct and those that contain an error (termed erroneous examples). Erroneous examples will be attributed to a fictitious student, not the one performing the problem. Additionally, the student will be prompted to find the error and will have system-provided help available.

Research Design and Methods: Over the projects' three years, one study will be conducted each year. All studies will randomly assign students to experimental conditions and pre- and post-test measures of math performance and motivation will be collected. Additionally, all studies will implement a 3-problem sequence, where the first problem will be a correct worked example, the next an isomorphic problem to be solved (a problem with the same form but different quantities), and the last a critical problem, described below, which will vary with experimental condition. Usability and feasibility data will be collected in each study and used to inform subsequent ones.

The first study examines the self-explanation effect, where the learner must generate explanations for how presented problems are solved. Earlier research has shown a benefit when students provided explanations for both a correct and an erroneous example as compared to providing explanations for two correct examples. This study will have three conditions, which differ only in the type of third problem that students are being asked to explain: no erroneous problem (control); erroneous problem without help available; and erroneous problem with help available. The primary purpose of this study is to test whether presenting erroneous problems is an effective pedagogical tool.

The second study will examine whether various multimedia formats can facilitate instruction. For example, worked explanations will not only be textual but will also include still illustrations or short animations.

The final factor that will be examined is the effectiveness of the adaptive help system. The last study, planned for the third year, will implement an advanced adaptive help system and will examine the degree to which the system-selected features, based on the user's prior experience, improve student learning.

Control Condition: In the control conditions across all studies, students will use the intelligent tutoring system but will only be exposed to correct worked examples; they will not be exposed to erroneous ones.

Key Measures: Key measures of math performance and motivation will be collected. For example, students' abilities to detect errors will be measured by including erroneous examples in both pre- and post-test measures, and students will be asked to determine if the example presents a correct or incorrect worked example. Quantitative measures of motivation will be collected via questionnaire and measuring time-on-task.

Data Analytic Strategy: Comparisons among experimental conditions will be examined using analysis of variance techniques.


Book chapter

Isotani, S., Adams, D., Mayer, R.E., Durkin, K., Rittle-Johnson, B., and McLaren, B.M. (2011). Can Erroneous Examples Help Middle-School Students Learn Decimals?. In C. Kloos, D. Gillet, R.C. Garcia, F. Wild, and M. Wolpers (Eds.), Towards Ubiquitous Learning: Sixth European Conference on Technology Enhanced Learning: (EC-TEL-2011) (pp. 181–195). Berlin/Heidelberg, Germany: Springer.

Journal article, monograph, or newsletter

Adams, D.M., McLaren, B.M., Durkin, K., Mayer, R.E., Rittle-Johnson, B., Isotani, S., and Van Velsen, M. (2014). Using Erroneous Examples to Improve Mathematics Learning with a Web-based Tutoring System. Computers in Human Behavior, 36: 401–411.

McLaren, B.M., Adams, D. M., and Mayer, R.E. (2015). Delayed Learning Effects with Erroneous Examples: A Study of Learning dDecimals with a Web-based Tutor. International Journal of Artificial Intelligence in Education, 25(4): 520–542.


Adams, D., McLaren, B.M., Durkin, K., Mayer, R.E., Rittle-Johnson, B., Isotani, S., and Van Velsen, M. (2012). Erroneous Examples Versus Problem Solving: Can we Improve how Middle School Students Learn Decimals?. In Proceedings of the 34th Meeting of the Cognitive Science Society (CogSci 2012) (pp. 1260–1265). Sapporo, Japan: Cognitive Science Society.

Adams, D.M., McLaren, B.M., Mayer, R.E., Goguadze, G., and Isotani, S. (2013). Erroneous Examples as Desirable Difficulty. In International Conference on Artificial Intelligence in Education (pp. 803–806). Berlin: Springer. Goguadze, G., Sosnovsky, S., Isotani, S., and McLaren, B.M. (2011). Evaluating a Bayesian Student Model of Decimal Misconceptions. In Proceedings of the 4th International Conference on Educational Data Mining (EDM 2011) (pp. 301–306). Eindhoven, Netherlands: Educational Data Mining.

Goguadze, G., Sosnovsky, S., Isotani, S., and McLaren, B.M. (2011). Towards a Bayesian Student Model for Detecting Decimal Misconceptions. In Proceedings of the 19th International Conference on Computers in Education (ICCE-2011) (pp. 34–41). Chiang Mai, Thailand: Asia-Pacific Society for Computers in Education.

Isotani, S., McLaren, B.M., and Altman, M. (2010). Towards Intelligent Tutoring With Erroneous Examples: A Taxonomy of Decimal Misconceptions. In Proceedings of the 10th International Conference on Intelligent Tutoring Systems (ITS-2010). Lecture Notes in Computer Science, 6094 (pp. 346–348). Berlin, Germany: Springer.

McLaren, B.M., Adams, D., Durkin, K., Goguadze, G. Mayer, R.E., Rittle-Johnson, B., Sosnovsky, S., Isotani, S., and Van Velsen, M. (2012). To Err is Human, to Explain and Correct is Divine: A Study of Interactive Erroneous Examples With Middle School Math Students. In Proceedings of the EC-TEL 2012: Seventh European Conference on Technology Enhanced Learning, LNCS 7563 (pp. 222–235). Berlin: Springer.

McLaren, B.M., and Isotani, S. (2011). When is it Best to Learn With all Worked Examples?. In Proceedings of the 15th International Conference on Artificial Intelligence in Education (AIED- 2011). Lecture Notes in Computer Science, 6738. (pp. 222–229). Berlin: Springer.