DiBiano Personally Relevant Algebra Problems

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Robust Learning in Culturally and Personally Relevant Algebra Problem Scenarios

Candace DiBiano, Anthony Petrosino, Jim Greeno, and Milan Sherman

Summary Tables

PIs Candace DiBiano & Anthony Petrosino
Other Contributers
  • Graduate Student: Milan Sherman
  • Staff: Jim Greeno


Pre Study

Study Start Date 09/01/08
Study End Date 12/15/08
Study Site Austin ISD, Texas & Learnlab Site
Number of Students N = 200
Average # of hours per participant 3 hrs.


Full Study

Study Start Date 9/1/09
Study End Date 12/15/09
LearnLab Site TBD
LearnLab Course Algebra
Number of Students N = 60-90
Average # of hours per participant 1 hr
Data in DataShop n/a


Abstract

In the original development of the PUMP Algebra Tutor (PAT), teachers had designed the algebra problem scenarios to be "culturally and personally relevant to students" (Koedinger, 2001). However, observations and discussions with teachers in Austin ISD suggest that the problem scenarios are disconnected from the lives of typical urban students. This study will examine whether and the mechanisms by which cultural and personal familiarity with problem scenario context affect comprehension and robust learning. We will use the medium of Cognitive Tutor Algebra for the in-vivo portion of this study, but our aim is not to improve the quality of the software’s problem scenarios. It is instead to study how student diversity affects cognition, motivation, and learning, by using the power of a computer system that has the ability to do what classroom teachers cannot – personalize each problem to the background and interests of each individual student.

The research will begin in Fall of 2008 with a study of the cultural and personal interests of urban students in Austin ISD and at a Learnlab site in Pittsbrugh. Freshman algebra students will be surveyed and interviewed over their interests, such as sports, music, movies, etc., and the results of this study will be used to rewrite the algebra problem scenarios in one section of the Cognitive Tutor software. In the Fall of 2009 at the Pittsburgh Learnlab site the Cognitive Tutor software will be programmed to give students an initial interests survey, and then select problem scenarios that match user interests. The resulting robust learning, measured by normal post-test, delayed post-test, curriculum progress and mastery of knowledge components, will be analyzed with a 3-group design to measure the effects of the personalization.

This research will be integrated with a study in the Spring of 2009 incorporating think-aloud protocols of students solving algebra problems in familiar and unfamiliar contexts to examine how personal relevance and cultural familiarity interacts with conceptual difficulty in interpreting the problem.

Background and Significance

This research direction was initiated by the observation of classrooms in Austin, Texas using the Cognitive Tutor Algebra I software, as well as discussions with teachers that had implemented this software at some point in their teaching career. Teacher complaints were consistently centered not around the interface, the feedback, or the cognitive model of the software, but on the problem scenarios. Teachers explained that their urban students found problems about harvesting wheat “silly,” “dry,” and irrelevant. Teachers also complained that some of the vocabulary words in the Cognitive Tutor problem scenarios (one example was the word "greenhouse") confused their students because urban freshman do not typically discuss these topics in their everyday speech. It’s important to note that as part of the development of the PUMP Algebra Tutor (PAT), teachers had designed problems to be "culturally and personally relevant to students" (Koedinger, 2001). This research is designed to empirically test the claim that the cultural and personal relevance of problem scenarios affects robust learning.

Research Questions

Independent variables

This experiment will manipulate level of personalization through three treatment groups:

  • Students recieve current Cognitive Tutor Algebra problems
  • Students recieve matched Cognitive Tutor Algebra problems stripped of most contextual clues
  • Students receive matched culturally relevant Cognitive Tutor Algebra problems personalized according to student interest survey


Treatment Example Problem Received By
Problem scenarios stripped of most context A task takes 30 minutes to complete. How many times can you complete the task in 3 hours? 25-30 randomly-assigned Algebra I students at Learnlab site
Normal Cognitive Tutor Algebra problem scenarios A skier noticed that she can complete a run in about 30 minutes. A run consists of riding the ski lift up the hill, and skiing back down. If she skiis for 3 hours, how many runs will she have completed? 25-30 randomly-assigned Algebra I students at Learnlab site
Culturally relevant personalized problem scenarios (student selects personal interest in T.V. shows, cultural survey/interview shows strong interest among urban youth in reality shows)

You noticed that the reality shows you watch on T.V. are all 30 minutes long. If you’ve been watching reality shows for 3 hours, how many have you watched?

25-30 randomly-assigned Algebra I students at Learnlab site


Hypothesis

Students in the treatment with culturally and personally relevant problem scenarios will show improved performance in terms of some measures of robust learning as a result of two factors:

  • Increased intrinsic motivation (such as with the REAP Tutor study)
  • Formation of a more detailed and meaningful situation model (Nathan, Kintsh, & Young, 1992).

Dependent variables

Robust learning will be measured through:

  • Normal Post-test measuring transfer of learning to different problem contexts (including abstract problems).
  • Delayed Post-test measuring long-term retention
  • Curriculum progress and Mastery of knowledge components in the Cognitive Tutor software, including in subsequent units:
    • The students’ progress through the knowledge components in the curriculum will measure accelerated future learning by reflecting the latency in mastering knowledge components and curriculum sections that build on the knowledge components and curriculum sections affected by the culturally relevant problem scenarios.

Intrinsic Motivation will be measured through:

  • Hint-seeking and reading behavior in Cognitive Tutor software
  • Time on task in Cognitive Tutor software
  • Questionairre asking how interesting students found problems in the affected unit

Method

This experiment will begin in the Fall of 2008 with a small study of student cultural interests. An interests survey will be administered to high school classes in Austin ISD that contain a high proportion of diverse students, as well as at a Pittsburgh Learnlab. Structured in-depth interviews relating to student interests will be conducted with around fifteen of the surveyed students. Based on the results of the survey and interviews, culturally relevant problem scenarios that correspond to current problem scenarios in Cognitive Tutor Algebra I will be formulated for Section 5, Linear Models and Independent Variables. Approximately 30 problem scenarios from the selected section will be replaced, with 4-5 variations on each problem scenario that correspond to different student interests, in order to obtain personalization. I will write these problem scenarios while consulting with Jim Greeno and Milan Sherman; they will have the same underlying mathematics as the original Cognitive Tutor problems, with changes to the objects or nouns (what the problem is about) and the pronouns (who the problem is about). See the table above for an example of how these two changes might occur.

The culturally relevant problem scenarios will be reviewed by Algebra I teachers, and then by students. In a pilot study, approximately 40 Algebra I students will rate their understanding and impression of the newly created questions. Problem scenarios that students have difficulties or issues with will be reworked. Also during this pilot study, the researcher will conduct audio-taped think-aloud protocols with each student as they solve 2-3 personally relevant algebra problem scenarios and 1-2 algebra problem scenarios with unfamiliar contexts.

The new problem scenarios will then be integrated into the Cognitive Tutor Algebra software in Spring 2009 with the cooperation of Carnegie Learning. Once the new problem scenarios have been placed into the software, they will be used in an in vivo experiment at a Learnlab school site in Pittsburgh by approximately 25-30 randomly-assigned students in the Fall of 2009 semester. An additional 25-30 randomly-assigned students will receive the regular problem scenarios. A third randomly-assigned group of 25-30 students will receive a third set of problems that have the same underlying mathematics, but are stripped of even more contextual clues than the regular Cognitive Tutor problem scenarios. See table above for a description of the three treatment groups in this study.

In addition, informal interviews will be conducted with students at the University of Pittsburgh, including thinking-aloud protocols obtained as they solve word problems with texts that differ in the degree of their cultural relevance to the students. These protocols will be analyzed to identify components of students’ understanding (i.e., their situation models), and to relate these to cultural relevance and familiarity.

To summarize, the experiment will have the following progression: (1) Survey of student interests administered in Austin ISD and Learnlab site (2) Based on survey data, structured interviews with students are conducted (3) Culturally relevant problem scenarios are written by me and reviewed by teachers (4) Culturally relevant problem scenarios are tested for understanding and as part of a think-aloud protocols during a student pilot study (5) One Cognitive Tutor Algebra unit replaced at a Learnlab site with 3-treatment setup & think-aloud protocols conducted at University of Pittsburgh

Explanation

This study is situated in the new “Motivation and Metacogntion’ thrust. The foundation of this study is that relevance of problem scenarios affects robust learning during the formation situation models, defined as mental representation of relationships, actions, and events in a problem (Nathan, Kintsch, & Young, 1992), as well through intrinsic motivation (Cordova & Lepper, 1996). Our hypothesis is that personalized problems would cause students to create more detailed and meaningful situation models through enhanced problem comprehension ad implicit problem knowledge. This would in turn affect the topology of the learning event space and/or path choices, causing students to use different strategies or paths (“blue-line” vs. “red-line”) as relevant problems are more likely to help students to encode deep, relevant features and/or avoid encoding shallow, irrelevant features. Another facet of this hypothesis is that personalized problems would enhance intrinsic motivation, which would increase focus of attention on the problem, contributing both to the formation of detailed situation models as well as more general enhancement of engagement and time on task (relating to "path effects").

References

Clark, R. C. & Mayer, R. E. (2003). E-Learning and the Science of Instruction. Jossey-Bass/Pfeiffer.

Cordova, D. I. & Lepper, M. R. (1996). Intrinsic Motivation and the Process of Learning: Beneficial Effects of Contextualization, Personalization, and Choice. Journal of Educational Psychology, 88(4), 715-730.

Eskenazi, M.; Juffs, A., Heilman, M., Collins-Thompson, K., Wilson, L., & Callen, J. (2006). REAP Study on Personalization of Readings by Topic (Fall 2006). The PSLC Wiki. Retrieved June 21, 2007, from http://www.learnlab.org

Koedinger, K. R. (2001). Cognitive tutors as modeling tool and instructional model. In Forbus, K. D. & Feltovich, P. J. (Eds.) Smart Machines in Education: The Coming Revolution in Educational Technology. Menlo Park, CA: AAAI/MIT Press.

Nathan, M., Kintsch, W., & Young, E. (1992). A theory of algebra-word-problem comprehension and its implications for the design of learning environments. Cognition and Instruction, 9(4), 329-389.

McLaren, B., Koedinger, K., & Yaron, D. (2006). Studying the Learning Effect of Personalization and Worked Examples in the Solving of Stoichiometry Problems. The PSLC Wiki. Retrieved June 21, 2007, from http://www.learnlab.org