Effects of Curricular Change Effects of Curricular Change in a Freshmen College in a Freshmen College
Applied Algebra Course Applied Algebra Course
Dr. Robert MayesDr. Robert Mayes
Director of theDirector of the
Institute for Mathematics Institute for Mathematics LearningLearning
Crisis in Mathematics Crisis in Mathematics EducationEducation
Business Higher Education Forum (2005) Business Higher Education Forum (2005) American Diploma Project (2005) American Diploma Project (2005)
Percentage of ninth grade students in the U.S. Percentage of ninth grade students in the U.S. who graduate from high school is 68%who graduate from high school is 68%
40% of these same ninth graders start college40% of these same ninth graders start college 27% of them persist through the second year27% of them persist through the second year 18% earn a degree18% earn a degree 22% of college freshmen are not ready for the 22% of college freshmen are not ready for the
entry level mathematics course and require entry level mathematics course and require remediation remediation
Crisis in Mathematics Crisis in Mathematics EducationEducation
MAA Task Force on the First College Level MAA Task Force on the First College Level Mathematics Course (Kime et al, 2000) Mathematics Course (Kime et al, 2000) College enrollments are increasing, calculus College enrollments are increasing, calculus
enrollments are stagnantenrollments are stagnant 9% of students matriculate into calculus9% of students matriculate into calculus Majority of first year students’ first college Majority of first year students’ first college
mathematics course is either remedial, liberal mathematics course is either remedial, liberal arts, or college algebraarts, or college algebra
Failure and withdrawal rates in before calculus Failure and withdrawal rates in before calculus courses are often dismal, with numbers courses are often dismal, with numbers between 40% and 60% commonbetween 40% and 60% common
Institute for Mathematics Institute for Mathematics LearningLearning
Reform in before calculus courses Reform in before calculus courses over the past 5 yearsover the past 5 years Liberal Arts Mathematics, Applied College Liberal Arts Mathematics, Applied College
Algebra, College Algebra, College Algebra, College Algebra, College Trigonometry, Precalculus, and Applied Trigonometry, Precalculus, and Applied Calculus Calculus
Subsequent Course SuccessSubsequent Course Success Fall 2004-Spring 2005 students successful Fall 2004-Spring 2005 students successful
in a subsequent course 80% if A or B in in a subsequent course 80% if A or B in IML course, 50% if C in IML courseIML course, 50% if C in IML course
Success Rates Success Rates Fall 2004-Spring 2005 Fall 2004-Spring 2005
Course Success Rates (A, B, or C grade)
Liberal Arts Mathematics 65.9%
Applied Algebra 63.3%
College Algebra 58.6%
College Trigonometry 63%
Precalculus 64%
Applied Calculus 68%
Applied College Algebra Applied College Algebra StudyStudy
Theoretical FrameworkTheoretical Framework Curricular RevisionCurricular Revision MethodMethod Pilot Study – Fall 04Pilot Study – Fall 04 Full Study – Spring 05Full Study – Spring 05 DiscussionDiscussion
Theoretical FrameworkTheoretical Framework Constructivist theory of learning Constructivist theory of learning Curriculum and Evaluation Standards Curriculum and Evaluation Standards
(2001) (2001) Achieving Quantitative Literacy Achieving Quantitative Literacy
(2001)(2001) CUPM Curriculum Guide for CUPM Curriculum Guide for
Undergraduate Courses in Undergraduate Courses in Mathematical Sciences (2003)Mathematical Sciences (2003)
A Collective Vision: Voice of Partner A Collective Vision: Voice of Partner Disciplines (2004) Disciplines (2004)
Theoretical FrameworkTheoretical Framework Tapping America’s Potential: The Tapping America’s Potential: The
Education for Innovation Initiative Education for Innovation Initiative (Business Round Table, 2005) (Business Round Table, 2005)
A Commitment to America’s Future: A Commitment to America’s Future: Responding to the Crisis in Responding to the Crisis in Mathematics and Science Education Mathematics and Science Education (Business Higher Education Forum, (Business Higher Education Forum, 2005) 2005)
American Diploma Project (Achieve, American Diploma Project (Achieve, Inc., 2005) Inc., 2005)
Theoretical FrameworkTheoretical Framework Liberal Studies Program goals Liberal Studies Program goals
Introduce the great ideas and Introduce the great ideas and controversies in human thought and controversies in human thought and experience, in this case the function experience, in this case the function concept.concept.
Develop the ability to reason clearly, Develop the ability to reason clearly, communicate effectively, and understand communicate effectively, and understand major influences of society.major influences of society.
Develop critical thinking by requiring Develop critical thinking by requiring logical inquiry to evaluate decisions, logical inquiry to evaluate decisions, question posing, problem formulation, question posing, problem formulation, and interpretation of results.and interpretation of results.
Incorporate a writing componentIncorporate a writing component
Theoretical FrameworkTheoretical Framework Cognitive science Cognitive science
Lyn English (1997) views reasoning as Lyn English (1997) views reasoning as embodied and imaginative embodied and imaginative
Learner Centered Instruction movement Learner Centered Instruction movement Treisman’s Model (1992)Treisman’s Model (1992)
Collaborate on challenging problems in an Collaborate on challenging problems in an environment of high expectations environment of high expectations
Weekly collaborative learning sessions in small Weekly collaborative learning sessions in small groups with student mentors groups with student mentors
Rather than remediate - engage in challenging Rather than remediate - engage in challenging mathematics that is engaging and meaningfulmathematics that is engaging and meaningful
Faculty sponsorship in development and Faculty sponsorship in development and management of the coursesmanagement of the courses
Curricular RevisionCurricular Revision
Computer enhancedComputer enhanced Vista WebCT course management Vista WebCT course management
software, web sites, and interactive Java software, web sites, and interactive Java applets to provide access to course applets to provide access to course materials, implement assessment, materials, implement assessment, communicate with students, engage communicate with students, engage students in exploring and discovering students in exploring and discovering mathematics, and manage the course mathematics, and manage the course grades grades
Grapher Grapher
Curricular RevisionCurricular Revision 10 online quizzes, four on-line chapter 10 online quizzes, four on-line chapter
reviews, four on-line exams, and an reviews, four on-line exams, and an on-line gateway pre-assessment to on-line gateway pre-assessment to determine student mathematical determine student mathematical deficiencies deficiencies
Computer laboratory componentComputer laboratory component Students are peer mentored while they Students are peer mentored while they
engage in explorations of mathematical engage in explorations of mathematical concepts and apply mathematics to solve concepts and apply mathematics to solve real world problems real world problems
Curricular RevisionCurricular Revision Active student learning and student Active student learning and student
accountability, implementing teaching accountability, implementing teaching strategies that engage students and strategies that engage students and provide informal formative feedback on provide informal formative feedback on their progresstheir progress
Personal Response System (PRS) Personal Response System (PRS) Implement 22 classroom participation activities Implement 22 classroom participation activities
that allow students to respond and receive that allow students to respond and receive immediate feedbackimmediate feedback
Power point slides guide the course discussion, Power point slides guide the course discussion, serve as student lecture outlines, and provide serve as student lecture outlines, and provide instructors with real world data problems as well instructors with real world data problems as well as a guide to key conceptsas a guide to key concepts
Curricular RevisionCurricular Revision Supplemental Instruction (SI) Supplemental Instruction (SI)
Fall 2004 - paper worksheets focusing on Fall 2004 - paper worksheets focusing on selected skills or applicationsselected skills or applications
Spring 2005 grounded in programmed Spring 2005 grounded in programmed instruction (McHale, Christenson, and instruction (McHale, Christenson, and Roberts, 1986) and implemented with PRSRoberts, 1986) and implemented with PRS
Two versions of SITwo versions of SI Algorithm SI focus on basic skills without Algorithm SI focus on basic skills without
contextcontext Application SI used real world applications Application SI used real world applications
to motivate the need for learning basic to motivate the need for learning basic skillsskills
Curricular RevisionCurricular Revision Students assigned to SI based upon performance Students assigned to SI based upon performance
on Pre-assessment. on Pre-assessment. Taken after a week of reviewing college algebra Taken after a week of reviewing college algebra
prerequisitesprerequisites Students who scored below 80% on the first attempt Students who scored below 80% on the first attempt
were required to attend an SI review session and then were required to attend an SI review session and then retake the Pre-assessment within a week. retake the Pre-assessment within a week.
If the student failed to attain an 80% or higher mark on If the student failed to attain an 80% or higher mark on the Pre-assessment on either attempt, then they were the Pre-assessment on either attempt, then they were required to attend SI for the remainder of the semester required to attend SI for the remainder of the semester (designated Required) Students who scored above 80% (designated Required) Students who scored above 80% were encouraged to attend SI, but their attendance was were encouraged to attend SI, but their attendance was not required (designated Optional)not required (designated Optional)
Optional students whose performance on one of three Optional students whose performance on one of three subsequent tests was less than 70% were then required subsequent tests was less than 70% were then required to attend SI until they earned at least 70% on a later test to attend SI until they earned at least 70% on a later test
MethodMethod Class randomly assigned to receive either Class randomly assigned to receive either
Algorithm SI or Application SI Algorithm SI or Application SI Retired version of the standardized ACT Retired version of the standardized ACT
Mathematics exam as Pre- Post-testMathematics exam as Pre- Post-test Mathematics Attitude Inventory (MAI), Mathematics Attitude Inventory (MAI),
developed by Mayes (2004) developed by Mayes (2004) Analysis of impact of supplemental on Analysis of impact of supplemental on
student outcomes within course student outcomes within course components, including exams, components, including exams, laboratories, on-line homework quizzes, laboratories, on-line homework quizzes, and overall grade. and overall grade.
MethodMethod Nonequivalent Control GroupNonequivalent Control Group Quasi-experimental Quasi-experimental
research design research design
O1 O2 O3 X1 O4 O5 O6O1 O2 O3 X1 O4 O5 O6--------------------------------------- --------------------------------------- O1 O2 O3 X2 O4 O5 O6O1 O2 O3 X2 O4 O5 O6
O1 - O4 : Pre- and Post-Math Attitude Inventory O1 - O4 : Pre- and Post-Math Attitude Inventory (MAI)(MAI)
O2 – O5 : Pre- and Post-ACT ExamO2 – O5 : Pre- and Post-ACT Exam O3 : Pre-assessment of basic skillsO3 : Pre-assessment of basic skills O6 : Final ExamO6 : Final Exam X1 : Algorithm SIX1 : Algorithm SI X2 : Application SIX2 : Application SI
MethodMethod Analysis was conducted using Analysis was conducted using
quantitative methods, including quantitative methods, including univariate and repeated-measures univariate and repeated-measures analyses of variance (ANOVA) and analyses of variance (ANOVA) and correlations. Significant main effects correlations. Significant main effects were further analyzed with pairwise were further analyzed with pairwise comparisons using a Bonferroni comparisons using a Bonferroni adjustment. adjustment.
Research QuestionsResearch Questions What are the plausible effects of a What are the plausible effects of a
Supplemental Instruction program Supplemental Instruction program targeted at students at risk of targeted at students at risk of failure?failure?
Does Application SI or Algorithm SI Does Application SI or Algorithm SI have the greatest impact on student have the greatest impact on student cognition and affect?cognition and affect?
What is the impact of the reformed What is the impact of the reformed Applied College Algebra course on Applied College Algebra course on student cognition and affect?student cognition and affect?
Pilot Study Fall 04Pilot Study Fall 04
ACT Pre- Post Analysis ACT Pre- Post Analysis 2 x 2 repeated-measures ANOVA with a 2 x 2 repeated-measures ANOVA with a
between-subject factor of SI Requirement between-subject factor of SI Requirement (Required or Optional) and a within-subject (Required or Optional) and a within-subject factor of Test (ACT pretest and ACT factor of Test (ACT pretest and ACT posttest) posttest) No significant difference between the cohorts on No significant difference between the cohorts on
overall ACT score overall ACT score Significant main effect of ACT, Significant main effect of ACT, FF (1, 283) = (1, 283) =
335.695, p < .001, with the posttest scaled 335.695, p < .001, with the posttest scaled scores (scores (MM = 19.86, = 19.86, SDSD = 3.02) exceeding the = 3.02) exceeding the pretest scaled scores (pretest scaled scores (MM = 15.71, = 15.71, SD SD = 3.11) = 3.11)
Pilot Study – ACT AnalysisPilot Study – ACT AnalysisCohort N Pre-test
MeanPre-test Std.
Dev.Post-test
MeanPost-test Std.
Dev.
Optional Earned 1-5
9 13.00 3.39 17.89 3.48
Optional Earned 6-9
38 15.18 2.95 19.34 2.76
Optional Earned 10-11
123 15.80 3.04 19.98 2.95
Required Earned 0
17 15.41 3.20 19.06 3.67
Required Earned 1-5
30 16.10 2.81 19.80 3.22
Required Earned 6-9
36 16.44 3.45 20.14 3.32
Required Earned 10-11
37 15.76 3.08 20.57 2.44
Pilot Study – ACT SubscalesPilot Study – ACT Subscales
Subscales of Pre-Algebra and Subscales of Pre-Algebra and Elementary Algebra (PAEA) and Elementary Algebra (PAEA) and Intermediate Algebra and Coordinate Intermediate Algebra and Coordinate Geometry (IACG) Geometry (IACG) All Optional cohorts made significant All Optional cohorts made significant
gains on both subscalesgains on both subscales Required cohorts made significant gains Required cohorts made significant gains
in both subscales when they participated in both subscales when they participated in SI over 50% of the time in SI over 50% of the time
Pilot Study – ACT SubscalesPilot Study – ACT SubscalesCohort Mean Gain in
PAEAStd. Dev. In
PAEAMean Gain in
IACGStd. Dev in
IACG
Optional Earned 1-5
1.857* 2.93 2.143** 2.179
Optional Earned 6-9
2.478*** 3.082 2.957*** 2.675
Optional Earned 10-11
2.415*** 2.985 2.468*** 2.659
Required Earned 0
-0.333 4.163 3.667 3.055
Required Earned 1-5
2.200* 2.300 1.600 2.875
Required Earned 6-9
2.969*** 3.290 2.031*** 2.456
Required Earned 10-11
2.774*** 3.074 2.355*** 2.374
Pilot Study - Final Course Pilot Study - Final Course AverageAverage
Univariate ANOVA indicated a significant effect of Cohort on Univariate ANOVA indicated a significant effect of Cohort on final course average, F (6, 398) = 6.970, p < .001. final course average, F (6, 398) = 6.970, p < .001.
Pairwise comparisons using a Bonferroni adjustment Pairwise comparisons using a Bonferroni adjustment indicated that both the Required and Optional 6-9 cohorts indicated that both the Required and Optional 6-9 cohorts outperformed the Required 0 cohort, p <.05. outperformed the Required 0 cohort, p <.05.
Required and Optional 10-11 cohorts outperformed the Required and Optional 10-11 cohorts outperformed the Required 0 cohort, p < .001.Required 0 cohort, p < .001.
No significant differences were found between Required No significant differences were found between Required and Optional students who earned the same number of and Optional students who earned the same number of points for SI. points for SI.
There is also overwhelming evidence that the more you There is also overwhelming evidence that the more you attend SI, the better you do in the course. attend SI, the better you do in the course. A Required student attending SI 6 to 9 times has a course A Required student attending SI 6 to 9 times has a course
mean equivalent to an Optional-Earned 6-9 studentmean equivalent to an Optional-Earned 6-9 student A Required student attending 10 to 11 times actually had a A Required student attending 10 to 11 times actually had a
higher mean than an Optional-Earned 10-11 student.higher mean than an Optional-Earned 10-11 student.
Pilot Study - AffectPilot Study - Affect
Statistically significant drop in overall Statistically significant drop in overall students’ attitudes from the students’ attitudes from the beginning to end of the semester beginning to end of the semester Paired-samples t-test (t (459) = 11.92, Paired-samples t-test (t (459) = 11.92,
p< .001).p< .001). Required SI students had a significantly Required SI students had a significantly
poorer attitude at the end of the poorer attitude at the end of the semester then their Optional SI semester then their Optional SI counterparts counterparts
Pilot Study - AffectPilot Study - Affect
Optional Required
Mean Std. Deviation
Mean Std. Deviation
Attitude Survey 1
3.03 .81 2.91 .93
Attitude Survey 2*
2.32 1.40 2.00 1.43
Full Study – Spring 2005Full Study – Spring 2005
PRS in Supplemental Instruction and PRS in Supplemental Instruction and offering Algorithm SI and Application offering Algorithm SI and Application SI at distinct times in large lecture SI at distinct times in large lecture classrooms, allowed more control classrooms, allowed more control over tracking students. The question over tracking students. The question of which type of SI was most of which type of SI was most effective could now be addressed. effective could now be addressed.
Full Study – Spring 2005Full Study – Spring 2005
A 2 x 2 x 2 ANOVA with between-A 2 x 2 x 2 ANOVA with between-subjects factors of Section (Application subjects factors of Section (Application or Algorithm) and SI Requirement, and a or Algorithm) and SI Requirement, and a within-subjects factor of Test was used within-subjects factor of Test was used to analyze the data. to analyze the data.
ThereThere were no significant differences were no significant differences between the Application SI and between the Application SI and Algorithm SI sections on the ACT pretest Algorithm SI sections on the ACT pretest or posttest or posttest
Full Study – Spring 2005Full Study – Spring 2005 Significant main effect of Test, Significant main effect of Test, FF (1, (1,
205) = 180.471, p < .001, such that 205) = 180.471, p < .001, such that performance on the posttest (performance on the posttest (MM = = 20.15, 20.15, SDSD = 2.47) was better than on = 2.47) was better than on the pretest (the pretest (MM = 18.42, = 18.42, SDSD = 2.64) = 2.64)
Significant main effect for SI Significant main effect for SI Requirement, Requirement, FF (1, 205) = 11.973, p = (1, 205) = 11.973, p = .001, with the Optional group (.001, with the Optional group (MM = = 19.875) outperforming the Required 19.875) outperforming the Required group (group (MM = 18.89). = 18.89).
There were no significant interactions.There were no significant interactions.
Mean scaled ACT scores and standard Mean scaled ACT scores and standard deviations by section and deviations by section and
Supplemental Instruction requirementSupplemental Instruction requirement Section Supplemental
InstructionRequirement
ACT Pre Mean
ACT Pre SD
ACT Post Mean
ACT Post SD
Algorithm Optional 19.44 2.91 21.93 2.35
Required 18.09 2.34 19.26 2.10
Application Optional 18.61 2.49 20.37 2.45
Required 18.14 2.92 20.16 2.51
Three Subscales of ACTThree Subscales of ACToverall effect overall effect
PAEA subscale: post-test (PAEA subscale: post-test (MM = 16.82, = 16.82, SDSD=3.21) =3.21) exceeding pre-test performance (exceeding pre-test performance (MM = 14.66, = 14.66, SDSD = 3.67), = 3.67), FF(1, 205) = 85.067, p < .001(1, 205) = 85.067, p < .001
IACG subscale: post-test (IACG subscale: post-test (MM = 8.44, = 8.44, SDSD = 2.69) = 2.69) exceeding pre-test performance (exceeding pre-test performance (MM = 6.63, = 6.63, SDSD = 2.64), = 2.64), FF(1, 205) = 97.903, p < .001(1, 205) = 97.903, p < .001
PGTRG subscale: post-test (PGTRG subscale: post-test (MM =7.54, =7.54, SDSD=2.83) =2.83) exceeding pre-test performance (exceeding pre-test performance (MM = 6.29, = 6.29, SD SD = 2.64), = 2.64), FF(1, 205) = 43.40, p < .001(1, 205) = 43.40, p < .001
Three Subscales of ACTThree Subscales of ACTby SI Type by SI Type
PAEA subscale: Optional SI (PAEA subscale: Optional SI (MM = = 17.615) outperformed Required SI (17.615) outperformed Required SI (M M = = 15.12), 15.12), FF(1, 205) = 28.974, p (1, 205) = 28.974, p < .001< .001
IACG subscale: Optional SI (IACG subscale: Optional SI (MM = 8.69) = 8.69) outperformed Required SI (outperformed Required SI (MM = = 7.155), 7.155), FF(1, 205) = 18.442, p < .001. (1, 205) = 18.442, p < .001.
PGTRG subscale: Optional SI (PGTRG subscale: Optional SI (MM = = 8.02) outperformed Required SI (8.02) outperformed Required SI (M M = = 6.545), 6.545), FF(1, 205) = 16.319, p < .001(1, 205) = 16.319, p < .001
ACT Subscale by SI TypeACT Subscale by SI TypeSubscale Section SI
requirementACT Pre Mean
ACTPre SD
ACT Post Mean
ACTPost SD
PAEA Algorithm Optional 16.35 3.35 18.42 3.10
(24) Required 14.21 3.49 16.36 3.26
Application Optional 16.50 3.52 19.19 2.12
Required 13.90 3.69 15.93 2.92
IACG Algorithm Optional 7.13 2.60 9.88 2.42
(18) Required 6.32 2.42 7.98 2.91
Application Optional 7.50 3.25 10.08 2.33
Required 6.44 2.60 7.87 2.19
PGTRG Algorithm Optional 7.77 2.76 8.27 2.43
(18) Required 6.07 2.64 7.76 2.86
Application Optional 6.88 2.72 9.15 2.84
Required 5.79 2.36 6.39 2.50
ACT by CohortACT by Cohort
Optional 0 students outperformed the Optional 0 students outperformed the Optional 1-5, Optional 11-13, and all Optional 1-5, Optional 11-13, and all Required cohorts on the ACT. Required cohorts on the ACT.
No other cohorts were significantly No other cohorts were significantly different from one another. different from one another.
This supports the previous findings that This supports the previous findings that while the overall course influenced ACT while the overall course influenced ACT posttest scores, SI had little impact posttest scores, SI had little impact
ACT by SI AttendanceACT by SI AttendanceCohort N Mean ACT SD
Optional 0 27 21.204 .429
Optional 1-5 30 19.017 .407
Optional 6-10 17 19.882 .541
Optional 11-13 10 18.850 .706
Required 0 28 19.268 .422
Required 1-5 37 19.338 .367
Required 6-10 28 19.036 .422
Required 11-13 32 17.922 .394
Final Course Average by Final Course Average by CohortCohort
All Optional cohorts outperformed both All Optional cohorts outperformed both the Required 0 and Required 1-5 the Required 0 and Required 1-5 cohortscohorts
Required 0 cohort was outperformed by Required 0 cohort was outperformed by all other Required cohortsall other Required cohorts
No other cohorts were significantly No other cohorts were significantly different from one another different from one another
This indicates that SI had an overall This indicates that SI had an overall course impact for Required students course impact for Required students who attended at least 50% of the timewho attended at least 50% of the time
Final Course Average by Final Course Average by CohortCohort
Cohort N Mean Course Avg SD
Optional 0 34 75.032 22.507
Optional 1-5 39 73.509 16.575
Optional 6-10 18 79.099 9.394
Optional 11-13 12 80.728 8.362
Required 0 67 36.764 31.540
Required 1-5 63 53.094 26.436
Required 6-10 46 59.960 23.722
Required 11-13 37 66.403 14.392
Exam Average by CohortExam Average by Cohort Optional 0 cohort outperformed all of Optional 0 cohort outperformed all of
the Required cohortsthe Required cohorts Optional 1-5 cohort outperformed the Optional 1-5 cohort outperformed the
Required 0 and Required 1-5 cohortsRequired 0 and Required 1-5 cohorts Optional 6-10 and Optional 11-13 Optional 6-10 and Optional 11-13
cohorts outperformed the Required 0, cohorts outperformed the Required 0, Required 1-5, and Required 11-13 Required 1-5, and Required 11-13 cohortscohorts
Required 6-10 cohort significantly Required 6-10 cohort significantly outperformed the Required 0 cohort. No outperformed the Required 0 cohort. No other comparisons were significant. other comparisons were significant.
Exam Average by CohortExam Average by CohortCohort N Mean Exam Avg SD
Optional 0 34 73.11 22.63
Optional 1-5 37 64.48 16.62
Optional 6-10 17 76.45 9.45
Optional 11-13 12 74.41 13.48
Required 0 62 40.46 27.64
Required 1-5 61 49.58 25.89
Required 6-10 42 56.56 20.68
Required 11-13 37 49.70 18.91
Lab Average by CohortLab Average by Cohort
All Optional cohorts outperformed All Optional cohorts outperformed the Required 0 cohortthe Required 0 cohort
Required 6-10 and Required 11-13 Required 6-10 and Required 11-13 cohorts outperformed the Required 0 cohorts outperformed the Required 0 cohortcohort
No other comparisons were No other comparisons were significant significant
Lab Average by CohortLab Average by CohortCohort N Mean Lab Avg SD
Optional 0 34 77.97 26.18
Optional 1-5 39 78.48 27.77
Optional 6-10 18 87.73 22.62
Optional 11-13 12 86.02 12.08
Required 0 67 51.30 39.26
Required 1-5 63 65.50 32.33
Required 6-10 46 71.75 30.18
Required 11-13 37 78.46 26.03
Exam by ExamExam by Exam In these analyses the cohorts are In these analyses the cohorts are
determined by the most previous determined by the most previous test performancetest performance Exam 1 (2 SI sessions) Optional 0 cohort Exam 1 (2 SI sessions) Optional 0 cohort
outperformed all Required cohorts outperformed all Required cohorts Exam 2 (4 SI sessions) all Optional Exam 2 (4 SI sessions) all Optional
cohorts outperformed the Required 1 cohorts outperformed the Required 1 and 2 cohorts. The Optional 0, 1, and 3 and 2 cohorts. The Optional 0, 1, and 3 outperformed the Required 3 and 4 outperformed the Required 3 and 4 cohorts. Only the Optional 0 cohort cohorts. Only the Optional 0 cohort significantly outperformed the Required significantly outperformed the Required 0 cohort. Required 0 cohort 0 cohort. Required 0 cohort outperformed the Required 2 cohortoutperformed the Required 2 cohort
Exam by ExamExam by Exam In these analyses the cohorts are In these analyses the cohorts are
determined by the most previous test determined by the most previous test performanceperformance Exam 3 (4 SI sessions) Optional 0, 1, 2, Exam 3 (4 SI sessions) Optional 0, 1, 2,
and 3 cohorts outperformed all Required and 3 cohorts outperformed all Required cohorts on Exam 3. Optional 4 cohort cohorts on Exam 3. Optional 4 cohort significantly outperformed Required 0 and significantly outperformed Required 0 and 1 cohorts 1 cohorts
Final Exam (3 SI sessions) Optional 0 and 3 Final Exam (3 SI sessions) Optional 0 and 3 cohorts outperformed all Required cohorts. cohorts outperformed all Required cohorts. Optional 1 and 2 cohorts outperformed Optional 1 and 2 cohorts outperformed Required 0, 1, and 3 cohorts. Required 0, 1, and 3 cohorts.
Exam by ExamExam by Exam Overall the examination of SI exam Overall the examination of SI exam
by exam reveals that Optional SI by exam reveals that Optional SI students continue to outperform their students continue to outperform their Required SI counterpoints. Required SI counterpoints. Surprisingly, Required SI students Surprisingly, Required SI students who attend all of the required who attend all of the required sessions did not score significantly sessions did not score significantly better on the following exam, better on the following exam, although the trend was that exam although the trend was that exam scores did increase as attendance scores did increase as attendance increased.increased.
Attitude SubscalesAttitude Subscales A paired-samples t-test was conducted on A paired-samples t-test was conducted on
the average responses for the Attitude the average responses for the Attitude SurveySurvey
No significant difference between the two No significant difference between the two administrations of the Attitude Surveyadministrations of the Attitude Survey
No significant correlation between students’ No significant correlation between students’ final grades and their responses on the final grades and their responses on the Attitude Surveys Attitude Surveys
There were some general effects on the There were some general effects on the Utility, Locus of Control, and Belief Utility, Locus of Control, and Belief subscales, where the pretest scores were subscales, where the pretest scores were more positive than the posttest scoresmore positive than the posttest scores
There were no significant differences There were no significant differences between the Application SI and Algorithm SI between the Application SI and Algorithm SI sectionssections
Attitude SubscalesAttitude SubscalesAttitude Survey 1 Attitude Survey 2
Subscale Number of Questions
Mean SD Mean SD
*Utility 7 24.73 4.694 23.19 5.389
Concept vs. Skill
10 29.83 4.95 29.62 4.94
*Locus of Control
6 19.50 4.507 18.25 4.704
*Belief about Math
3 6.12 2.611 5.78 2.681
Technology 4 15.03 2.866 15.06 3.581
DiscussionDiscussion
