The purpose of the Self-Explanation study is to investigate whether prompting students to explain problem-solving steps made by themselves would facilitate tutor learning. In the proposed learning environment, 8th grade students will be prompted to explain the reasoning behind their tutoring activities when teaching SimStudent. The proposed learning-by-teaching environment is designed for Algebra students to learn two major types of knowledge, namely: procedural skills to manipulate algebraic expressions and solve equations; and conceptual knowledge to justify skill applications when solving problems. The research question is: Does asking students to provide explanations for their reasoning behind the tutoring activities facilitate tutor learning? The hypothesis to be tested is: If students provide explanations on their reasoning behind the tutoring, then the effect of tutor learning will be facilitated. Students will be randomly assigned to one of the two experimental conditions: the treatment condition where the students will be prompted to provide explanations on their tutoring activities; and the control condition where the students will use the base-line Learning-by-Teaching environment. Pre- and post-tests will be used to measure students' learning achievement in conceptual and procedural knowledge. Student comparisons using the learning gain as the dependent variable will be the focus of analysis.
The study focuses on Algebra I linear equation solving, which is a critical area in the middle school algebra curriculum as indicated in both the Principles and Standards for School Mathematics (PSSM) publication of the National Council of Teachers of Mathematics (NCTM) and the more recently released document Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It is well known that prompting students to self-explain facilitates learning both when they are asked to explain correct worked-out examples and when they are asked to explain errors made by others. The study tests the hypothesis that self-explanation is also effective in tutor learning. Students will be asked to explain: correct steps when they demonstrate steps to their SimStudent; incorrect steps when they catch SimStudent making an error and want to indicate why the step is wrong; and 3) their choice of problems to teach to SimStudent, for instance, based on the observation on what mistakes SimStudent make when given a quiz.
The goal of this project is to investigate cognitive and social theories of learning by teaching. There is ample evidence in the literature that both a tutor and a tutee benefit from peer learning, especially even when the peers are at the same proficiency levels. However, the underlying cognitive and social theory of tutor learning has yet to be investigated. To achieve the project goal, we have developed a synthetic peer, called SimStudent, by applying an artificial intelligence (machine learning) technology. SimStudent learns skills to solve problems when tutored. We then developed an online, game-like learning environment, APLUS—Artificial Peer Learning environment Using SimStudent, in which students learn to solve Algebra linear equations by teaching SimStudent. APLUS is equipped with a set of quiz problems. The goal of the student using APLUS is to tutor SimStudent well so that it passes the quiz. APLUS also has resources for students to learn about Algebra equations to better prepare for teaching SimStudent. To advance theory of learning by teaching, we have conducted four classroom (in vivo) experiments each to test a specific hypothesis. These hypotheses included (1) the engineering hypothesis that conjectures that our software intervention would be robust enough for a classroom study with expected effect in students’ learning, (2) the self-explanation hypothesis that conjectures that tutor learning would be facilitated when tutors were asked to explain their tutoring decisions and activities, (3) the motivation hypothesis that conjectures that tutor learning would be facilitated when students were more engaged in tutoring, and (4) the meta-tutor hypothesis that conjectures that tutor learning would be facilitated when tutors were provided scaffolding on how to tutor. All four classroom studies were randomized controlled trials conducted in one private and four public schools. Study sessions were placed as part of each participating school’s normal Algebra I class activities. Students used APLUS for three days, one classroom period per day. Students took pre- and post-tests before and after the intervention. The tests were designed to measure proficiency to solve equations (procedural skill test) and understanding of basic algebraic concepts (conceptual knowledge test). Highlights of the study results include following: (1) The first hypothesis, the engineering hypothesis, was supported. All four classroom-studies have successfully demonstrated that our technology intervention (APLUS and SimStudent) is robust and reliable enough for classroom usage. It has been also demonstrated that our technology allows us to collect detailed process data that, when combined with learning outcome data (i.e., test scores and questionnaire responses), facilitate theory development. (2) The second hypothesis, the self-explanation hypothesis, was supported with an insight into future study. The data showed that the amount of "deep" responses for SimStudent questions had a statistically reliable predictive power for the post-test scores. In the classroom studies, SimStudent did not actually process students’ responses, but merely acknowledge it. Therefore, only about 20% (N=2008) of students’ responses were "deep" responses. These findings suggested further extension of the SimStudent’s questioning module so that it understands students’ input and provide follow-up dialogue (e.g., "Hmm, I still don't understand -- could you explain this to me in more detail?"). (3) The third hypothesis, the motivation hypothesis, was partially supported. The data showed that the introduction of the competitive Game Show, in which a pair of SimStudents competes each other by solving challenging problems and students observe the competition, increased students’ engagement tutoring, measured by the amount and depth of students’ response to SimStudent’s questions. However, the tutoring engagement showed no correlation with post-test scores. It turned out that once students entered in the Game Show, they did not switch back to tutoring SimStudent to make it more proficient, but stayed in the Game Show and strategically selected weak opponents for an easy win. The result suggested that the Game Show must be redesigned so that the learning goal (i.e., to tutor SimStudent better) and the Game Show goal (i.e., to win the competition) are better aligned. (4) The fourth hypothesis, the meta-tutor hypothesis, was supported. The meta-tutor’s scaffolding on how to select problem positively affected students’ decisions on what problems to be used for tutoring, which further affected tutor learning. The data showed that the more advanced the type of equations tutored were and the quicker the transition from easy to advance types of problem occurred, the higher the post-test scores were. The broader impact of the project includes (1) the advancement of the cognitive and social theory of learning by teaching, (2) the wide dissemination of the developed online learning environment that are freely available on our project web site, and (3) the shared data we have collected from classroom studies (through the PSLC’s DataShop -- www.learnlab.org) for secondary analyses.
