architectural inefficiencies and educational outcomes in stem dan sturtevant massachusetts institute...
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Architectural Inefficiencies and Educational Outcomes in STEM
Dan SturtevantMassachusetts Institute of Technology
Engineering Systems [email protected]
Question
• Christensen, Horn, & Johnson assert that a technology enabled transformation will occur in education in the next ten years.
• Such a transformation could change the very character of how the educational function is performed.
• One potential benefit could be the elimination of the “common pace requirement” within classrooms.
What are the potential benefits of removing the common pacing requirement on societal production of scientists,
technologists, mathematicians, and engineers?
Simulate one cohort of students under different education architectures
Movement through the pipeline• Give each between 0 and 1 ‘unit’ of knowledge• Every year (repeat until graduation):
– Move students up one grade.– Assign students to the appropriate schools based on geographic
district.– Assign students to a classroom within that school.– Administrators set expectations and teachers adapt to skills of
students they have in the class.– Teaching and learning for one year. Goal is to gain 1 unit of
knowledge per year.
After 16 years, one may hope that each studentwill contain 16 additional units of knowledge.
Schools and Classrooms
Test impact of:
Pace setting policiesVariation in student and teacher abilityStudent tracking policies
Rules for setting class Start Point (SP):
Fixed Common Standards
Floating Teacher chooses the mean student as the point at which instruction begins.
HalfFixedFloat Teacher feels pressure to account for both factors.
Rules for setting variation in student ability and teacher quality:
NoIndividualVariationTQ = teacher quality.SA = student ability.
TQ = 1 for all teachers.SA = 1 for all students.
TeacherQualityVariation TQ is a random Normal variable with mean 1 and standard deviation 0.1.SA = 1 for all students.
StudentAbilityVariation TQ = 1 for all teachers.SA is a random Normal variable with mean 1 and standard deviation 0.1.
TeacherAndStudentVariation Both TQ and SA are random Normal variables with mean 1 and standard deviation 0.1.
Rules for assigning students to classrooms:
RandomAssignment Every year, students within a school at the same grade level are randomly assigned to classrooms within that school.
TrackingAssignment Every year, students are sorted by their total knowledge to that point (TK) and then assigned to classrooms with other similar students. Note that this assignment is not based on student ability (SA). This assignment scheme serves to reduce variability within each classroom.
Rules for imposing learning penalty to student based on pacing requirement:
PacingPenaltyOnCSP = class start point.TK = student’s total knowledge at the beginning of the year.
PacingPenaltyModifier =
This function peaks at 1 when the student is at the start point and decays exponentially as the distance increases. The function also has the property that SSP + PacingPenaltyModifier is monotonically increasing. This function was chosen because of some of its useful properties.
PacingPenaltyOff PacingPenaltyModifier = 1.
StudentYearlyProgress =
TecherQuality * StudentAbility * PacingPenaltyModifier
Six Simulation Tests
SP = Floating NoIndividualVariation RandomAssignment PacingPenaltyOn
SP = Floating TeacherAndStudentVariation RandomAssignment PacingPenaltyOn
SP = Fixed TeacherAndStudentVariation RandomAssignment PacingPenaltyOn
SP = HalfFixedFloat TeacherAndStudentVariation TrackedAssignment PacingPenaltyOn
SP = Float TeacherAndStudentVariation TrackedAssignment PacingPenaltyOn
TeacherAndStudentVariation RandomAssignment PacingPenaltyOff
Results
Simulation 1
SP = Floating NoIndividualVariation RandomAssignment PacingPenaltyOn
Simulation 1
SP = Floating NoIndividualVariation RandomAssignment PacingPenaltyOn
Simulation 1
SP = Floating NoIndividualVariation RandomAssignment PacingPenaltyOn
Simulation 2
SP = Floating TeacherAndStudentVariation RandomAssignment PacingPenaltyOn
Simulation 2SP = Floating TeacherAndStudentVariation RandomAssignment PacingPenaltyOn
Simulation 2SP = Floating TeacherAndStudentVariation RandomAssignment PacingPenaltyOn
Simulation 3
SP = Fixed TeacherAndStudentVariation RandomAssignment PacingPenaltyOn
Simulation 3
SP = Fixed TeacherAndStudentVariation RandomAssignment PacingPenaltyOn
Simulation 4
SP = HalfFixedFloat TeacherAndStudentVariation TrackedAssignment PacingPenaltyOn
Simulation 5
SP = Float TeacherAndStudentVariation TrackedAssignment PacingPenaltyOn
Simulation 5
SP = Float TeacherAndStudentVariation TrackedAssignment PacingPenaltyOn
Simulation 6
TeacherAndStudentVariation RandomAssignment PacingPenaltyOff
NAEP Scores 2005Mathematics4th 200 220 239 258 2738th 231 255 280 304 324
Reading4th 171 196 221 244 2638th 216 240 265 286 30512th 235 262 288 313 333
Percentiles 10th 25th 50th 75th 90th
NAEP Scores 2005Mathematics4th 200 220 239 258 2738th 231 255 280 304 324
Reading4th 171 196 221 244 2638th 216 240 265 286 30512th 235 262 288 313 333
Percentiles 10th 25th 50th 75th 90th
Final Thoughts• Lots of attention in education research is placed on relating
individual attributes (student ability, teacher quality, socioeconomic status) to social outcomes.
• Increased focus on system architecture and the way structure leads to behavior might provide insights of significant value.
• Technology enabled education represents a fundamental change (from cellular to network centric)in the very nature of the education system.
• Simulation modeling can be used to explore potential benefits and costs of alternative architectures in a risk free environment.