Difference between revisions of "DiBiano Personally Relevant Algebra Problems"

From LearnLab
Jump to: navigation, search
Line 1: Line 1:
 
== Robust Learning in Culturally and Personally Relevant Algebra Problem Scenarios ==
 
== Robust Learning in Culturally and Personally Relevant Algebra Problem Scenarios ==
  ''Candace DiBiano, Anthony Petrosino, Jim Greeno, and Milan Sherman''
+
  ''Candace Walkington (DiBiano), Anthony Petrosino, Jim Greeno, and Milan Sherman''
  
 
=== Summary Tables ===
 
=== Summary Tables ===
 
{| border="1" cellspacing="0" cellpadding="5" style="text-align: left;"
 
{| border="1" cellspacing="0" cellpadding="5" style="text-align: left;"
| '''PIs''' || Candace DiBiano & Anthony Petrosino
+
| '''PIs''' || Candace Walkington & Anthony Petrosino
 
|-
 
|-
 
| '''Other Contributers''' ||  
 
| '''Other Contributers''' ||  
Line 15: Line 15:
 
| '''Study Start Date''' || 09/01/08
 
| '''Study Start Date''' || 09/01/08
 
|-
 
|-
| '''Study End Date''' || 12/15/08
+
| '''Study End Date''' || 4/15/10
 
|-
 
|-
| '''Study Site''' || Austin ISD, Texas & Learnlab Site
+
| '''Study Site''' || Austin, Texas & Pittsburgh, PA
 
|-
 
|-
| '''Number of Students''' || ''N'' = 200
+
| '''Number of Students''' || ''N'' = 125
 
|-
 
|-
 
| '''Average # of hours per participant''' || 3 hrs.
 
| '''Average # of hours per participant''' || 3 hrs.
Line 27: Line 27:
 
'' Full Study ''
 
'' Full Study ''
 
{| border="1" cellspacing="0" cellpadding="5" style="text-align: left;"
 
{| border="1" cellspacing="0" cellpadding="5" style="text-align: left;"
| '''Study Start Date''' || 9/1/09
+
| '''Study Start Date''' || 9/1/08
 
|-
 
|-
| '''Study End Date''' || 12/15/09
+
| '''Study End Date''' || 4/15/10
 
|-
 
|-
| '''LearnLab Site''' || TBD
+
| '''LearnLab Site''' || Hopewell High
 
|-
 
|-
 
| '''LearnLab Course''' || Algebra
 
| '''LearnLab Course''' || Algebra
 
|-
 
|-
| '''Number of Students''' || ''N'' = 60-90
+
| '''Number of Students''' || ''N'' = 125
 
|-
 
|-
| '''Average # of hours per participant''' || 1 hr
+
| '''Average # of hours per participant''' || 3 hr
 
|-
 
|-
| '''Data in DataShop''' || n/a
+
| '''Data in DataShop''' || Yes - Personalization Hopewell 2010
 
|}
 
|}
 
<br>
 
<br>
  
 
=== Abstract ===
 
=== 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|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 – [[personalization|personalize]] each problem to the background and interests of each individual student.
+
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 familiarity with problem scenario context affect comprehension and [[robust learning]].  We will use the medium of [[cognitive tutor|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 – [[personalization|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|Cognitive Tutor]] software.  In the Fall of 2009 at the Pittsburgh Learnlab site the [[cognitive tutor|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]].   
+
The research began in Fall of 2008 with a study of the personal interests of urban students at an "Academically Unacceptable" school in Austin, TX (75% free/reduced lunch).  Freshman algebra students were surveyed and interviewed over their interests, such as sports, music, movies, etc., as well as how they use mathematics in their everyday lives. Students were also asked to solve a number of cognitive tutor problems, rewritten to have varying levels of "relevancy," while thinking aloud. Results of this study were used to rewrite the algebra problem scenarios in one section of the [[cognitive tutor|Cognitive Tutor]] software, Section 5, "Linear Models and Independent Variables." In Fall of 2009 at the Pittsburgh Learnlab site the [[cognitive tutor|Cognitive Tutor]] software was programmed to give students an initial interests survey, and then select problem scenarios that match user interests.  The resulting [[robust learning]], measured by ''delayed post-test'', ''curriculum progress'' and ''mastery of knowledge components'', will be analyzed with a 2-group design (experimental vs. control) to measure the effects of the [[personalization]].   
 
+
This research will be integrated with a study in the Spring of 2009 incorporating [[think-aloud data|think-aloud protocols]] of students solving algebra problems in familiar and unfamiliar contexts to examine how [[personalization|personal relevance]] and cultural familiarity interacts with conceptual difficulty in interpreting the problem.
+
  
 
=== Background and Significance ===
 
=== Background and Significance ===
Line 56: Line 54:
 
=== Research Questions ===
 
=== Research Questions ===
  
* How will [[robust learning]] be affected when [[personalization]] through culturally relevant problem scenarios is implemented instead of the current problem scenarios in the [[cognitive tutor|Cognitive Tutor]] Algebra I software?
+
* How will performance and time on task be affected when [[personalization]] through relevant problem scenarios is implemented instead of the current problem scenarios in the [[cognitive tutor|Cognitive Tutor]] Algebra I software?
* How will [[robust learning]] be affected when current problem scenarios in the [[cognitive tutor|Cognitive Tutor]] Algebra I software are stripped of many of their contextual clues?
+
* How will [[robust learning]] be affected when [[personalization]] through relevant problem scenarios is implemented instead of the current problem scenarios in the [[cognitive tutor|Cognitive Tutor]] Algebra I software?
  
 
=== Independent variables ===
 
=== Independent variables ===
  
This experiment will manipulate level of [[personalization]] through three treatment groups:
+
This experiment will manipulate level of [[personalization]] through two treatment groups:
 
*Students recieve current Cognitive Tutor Algebra problems
 
*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
 
*Students receive matched culturally relevant Cognitive Tutor Algebra problems personalized according to student interest survey
 
<BR>
 
<BR>
 
{| border="1" cellspacing="0" cellpadding="5" style="text-align: left;"
 
{| border="1" cellspacing="0" cellpadding="5" style="text-align: left;"
 
| '''Treatment'''|| '''Example Problem''' || '''Received By'''
 
| '''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
 
| 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 [[personalization|personalized]] problem scenarios || (student selects personal interest in T.V. shows, cultural survey/interview shows strong interest among urban youth in reality shows)
+
| Relevant [[personalization|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?
 
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
+
|| 110 randomly-assigned Algebra I students at Learnlab site
 
|}
 
|}
 
<BR>
 
<BR>
Line 81: Line 76:
 
=== Hypothesis ===
 
=== Hypothesis ===
  
Students in the treatment with culturally and [[personalization|personally relevant]] problem scenarios will show improved performance in terms of some measures of [[robust learning]] as a result of two factors: <BR>
+
Students in the treatment with [[personalization|personally relevant]] problem scenarios will show improved performance in terms of some measures of [[robust learning]] as a result of two factors: <BR>
 
* Increased intrinsic motivation (such as with the [[REAP_Study_on_Personalization_of_Readings_by_Topic_%28Fall_2006%29|REAP Tutor study]])<BR>
 
* Increased intrinsic motivation (such as with the [[REAP_Study_on_Personalization_of_Readings_by_Topic_%28Fall_2006%29|REAP Tutor study]])<BR>
 
* Formation of a more detailed and meaningful situation model (Nathan, Kintsh, & Young, 1992).
 
* Formation of a more detailed and meaningful situation model (Nathan, Kintsh, & Young, 1992).
Line 95: Line 90:
 
*Hint-seeking and reading behavior in Cognitive Tutor software
 
*Hint-seeking and reading behavior in Cognitive Tutor software
 
*Time on task in Cognitive Tutor software
 
*Time on task in Cognitive Tutor software
*Questionairre asking how interesting students found problems in the affected unit
 
  
 
=== Method ===
 
=== 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|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|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.
+
This experiment began in the Fall of 2008 with a study of student interests. An interests survey was 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 were conducted with around 29 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|Cognitive Tutor]] Algebra I were formulated for Section 5, Linear Models and Independent Variables.  Approximately 27 problem scenarios from the selected section will be replaced, with 4 variations on each problem scenario that correspond to different student interests, in order to obtain [[personalization]].  I wrote these problem scenarios  while consulting with Jim Greeno and Milan Sherman; they will have the same underlying mathematics as the original [[cognitive tutor|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 data|think-aloud protocols]] with each student as they solve 2-3 [[personalization|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|Cognitive Tutor]] Algebra software in Spring 2009 with the cooperation of Carnegie LearningOnce 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|Cognitive Tutor]] problem scenarios.  See table above for a description of the three treatment groups in this study.
+
The culturally relevant problem scenarios were reviewed by two master Algebra I teachersIn a pilot study, 24 Algebra I students participated in [[think-aloud data|think-aloud protocols]]  where they solved five story problems with varying degrees of relevancy, that were based on Cognitive Tutor problems. Problem scenarios that students have difficulties or issues with will be reworked.   
  
In addition, informal interviews will be conducted with students at the University of Pittsburgh, including [[think-aloud data|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.
+
The new problem scenarios were integrated into the [[cognitive tutor|Cognitive Tutor]] Algebra software in Summer 2009 with the cooperation of Carnegie Learning.  Once the new problem scenarios were placed into the software, they were used in an [[in vivo experiment]] at a Learnlab school site in Pittsburgh by approximately 50-55 randomly-assigned students during the 09-10 school year. An additional 50-55 randomly-assigned students received the regular problem scenarios. See table above for a description of the two treatment groups in this study.
  
To summarize, the experiment will have the following progression:  
+
To summarize, the experiment had the following progression:  
(1) Survey of student interests administered in Austin ISD and Learnlab site
+
(1) Survey (paper & online) of student interests administered in Austin ISD and Learnlab site
(2) Based on survey data, structured interviews with students are conducted
+
(2) Based on survey data, structured interviews on students' out-o9f-school interests were conducted
(3) Culturally relevant problem scenarios are written by me and reviewed by teachers
+
(3) Based on interest interview, 24 students participated in think-alouds where they each solved 5 problems with different degrees of relevancy.
(4) Culturally relevant problem scenarios are tested for understanding and as part of a [[think-aloud data|think-aloud protocols]] during a student pilot study
+
(4) Relevant problem scenarios for Section 5 were written by Candace Walkington & Milan Sherman and reviewed by 2 master algebra teachers
(5) One [[cognitive tutor|Cognitive Tutor]] Algebra unit replaced at a Learnlab site with 3-treatment setup & [[think-aloud data|think-aloud protocols]] conducted at University of Pittsburgh
+
(5) One [[cognitive tutor|Cognitive Tutor]] Algebra unit replaced at a Learnlab site with randomized control (in-sequence) setup
  
 
=== Explanation ===
 
=== Explanation ===

Revision as of 15:36, 26 July 2010

Robust Learning in Culturally and Personally Relevant Algebra Problem Scenarios

Candace Walkington (DiBiano), Anthony Petrosino, Jim Greeno, and Milan Sherman

Summary Tables

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


Pre Study

Study Start Date 09/01/08
Study End Date 4/15/10
Study Site Austin, Texas & Pittsburgh, PA
Number of Students N = 125
Average # of hours per participant 3 hrs.


Full Study

Study Start Date 9/1/08
Study End Date 4/15/10
LearnLab Site Hopewell High
LearnLab Course Algebra
Number of Students N = 125
Average # of hours per participant 3 hr
Data in DataShop Yes - Personalization Hopewell 2010


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 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 began in Fall of 2008 with a study of the personal interests of urban students at an "Academically Unacceptable" school in Austin, TX (75% free/reduced lunch). Freshman algebra students were surveyed and interviewed over their interests, such as sports, music, movies, etc., as well as how they use mathematics in their everyday lives. Students were also asked to solve a number of cognitive tutor problems, rewritten to have varying levels of "relevancy," while thinking aloud. Results of this study were used to rewrite the algebra problem scenarios in one section of the Cognitive Tutor software, Section 5, "Linear Models and Independent Variables." In Fall of 2009 at the Pittsburgh Learnlab site the Cognitive Tutor software was programmed to give students an initial interests survey, and then select problem scenarios that match user interests. The resulting robust learning, measured by delayed post-test, curriculum progress and mastery of knowledge components, will be analyzed with a 2-group design (experimental vs. control) to measure the effects of the personalization.

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

  • How will performance and time on task be affected when personalization through relevant problem scenarios is implemented instead of the current problem scenarios in the Cognitive Tutor Algebra I software?
  • How will robust learning be affected when personalization through relevant problem scenarios is implemented instead of the current problem scenarios in the Cognitive Tutor Algebra I software?

Independent variables

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

  • Students recieve current Cognitive Tutor Algebra problems
  • Students receive matched culturally relevant Cognitive Tutor Algebra problems personalized according to student interest survey


Treatment Example Problem Received By
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
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?

110 randomly-assigned Algebra I students at Learnlab site


Hypothesis

Students in the treatment with 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

Method

This experiment began in the Fall of 2008 with a study of student interests. An interests survey was 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 were conducted with around 29 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 were formulated for Section 5, Linear Models and Independent Variables. Approximately 27 problem scenarios from the selected section will be replaced, with 4 variations on each problem scenario that correspond to different student interests, in order to obtain personalization. I wrote 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 were reviewed by two master Algebra I teachers. In a pilot study, 24 Algebra I students participated in think-aloud protocols where they solved five story problems with varying degrees of relevancy, that were based on Cognitive Tutor problems. Problem scenarios that students have difficulties or issues with will be reworked.

The new problem scenarios were integrated into the Cognitive Tutor Algebra software in Summer 2009 with the cooperation of Carnegie Learning. Once the new problem scenarios were placed into the software, they were used in an in vivo experiment at a Learnlab school site in Pittsburgh by approximately 50-55 randomly-assigned students during the 09-10 school year. An additional 50-55 randomly-assigned students received the regular problem scenarios. See table above for a description of the two treatment groups in this study.

To summarize, the experiment had the following progression: (1) Survey (paper & online) of student interests administered in Austin ISD and Learnlab site (2) Based on survey data, structured interviews on students' out-o9f-school interests were conducted (3) Based on interest interview, 24 students participated in think-alouds where they each solved 5 problems with different degrees of relevancy. (4) Relevant problem scenarios for Section 5 were written by Candace Walkington & Milan Sherman and reviewed by 2 master algebra teachers (5) One Cognitive Tutor Algebra unit replaced at a Learnlab site with randomized control (in-sequence) setup

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