Architectural Inefficiencies and Educational Outcomes in STEM

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Architectural Inefficiencies and Educational
Outcomes in STEM

• Dan Sturtevant
• Massachusetts Institute of Technology
• Engineering Systems Division
• dan.sturtevant_at_sloan.mit.edu

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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?
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Simulate one cohort of students under different
education architectures
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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 student
• will contain 16 additional units of knowledge.

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Schools and Classrooms
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Test impact ofPace setting policiesVariation
in student and teacher abilityStudent tracking
policies
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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.
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Rules for setting variation in student ability
and teacher quality
NoIndividualVariation TQ 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.
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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.
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Rules for imposing learning penalty to student
based on pacing requirement
PacingPenaltyOn CSP class start point. TK students 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.
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StudentYearlyProgress TecherQuality StudentAbility PacingPenaltyModifier
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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
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Results
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Simulation 1
SP Floating NoIndividualVariation
RandomAssignment PacingPenaltyOn
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Simulation 1
SP Floating NoIndividualVariation
RandomAssignment PacingPenaltyOn
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Simulation 1
SP Floating NoIndividualVariation
RandomAssignment PacingPenaltyOn
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Simulation 2
SP Floating TeacherAndStudentVariation
RandomAssignment PacingPenaltyOn
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Simulation 2
SP Floating TeacherAndStudentVariation
RandomAssignment PacingPenaltyOn
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Simulation 2
SP Floating TeacherAndStudentVariation
RandomAssignment PacingPenaltyOn
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Simulation 3
SP Fixed TeacherAndStudentVariation
RandomAssignment PacingPenaltyOn
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Simulation 3
SP Fixed TeacherAndStudentVariation
RandomAssignment PacingPenaltyOn
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Simulation 4
SP HalfFixedFloat TeacherAndStudentVariation
TrackedAssignment PacingPenaltyOn
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Simulation 5
SP Float TeacherAndStudentVariation
TrackedAssignment PacingPenaltyOn
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Simulation 5
SP Float TeacherAndStudentVariation
TrackedAssignment PacingPenaltyOn
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Simulation 6
TeacherAndStudentVariation RandomAssignment
PacingPenaltyOff
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NAEP Scores 2005 Mathematics 4th 200 220
239 258 273 8th 231 255 280 304 324 Rea
ding 4th 171 196 221 244 263 8th 216 240
265 286 305 12th 235 262 288 313 333 Per
centiles 10th 25th 50th 75th 90th
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NAEP Scores 2005 Mathematics 4th 200 220
239 258 273 8th 231 255 280 304 324 Rea
ding 4th 171 196 221 244 263 8th 216 240
265 286 305 12th 235 262 288 313 333 Per
centiles 10th 25th 50th 75th 90th
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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.