Equation
Properties
Units
Top-Level Model:
Disengaged_Student_Behaviors(t)
Disengaged_Student_Behaviors(t - dt) + (Increase_in_Disengaged_Behaviors - Decrease_in_Disengaged_Behaviors) * dt
INIT Disengaged_Student_Behaviors = Initial_Student_Disengagement
Behaviors
Experienced_Teacher_Effectiveness(t)
Experienced_Teacher_Effectiveness(t - dt) + (Increase_in_Experienced_Teacher_Effectiveness_from_Hiring + Increase_in_Experienced_Teacher_Effectiveness + Increase_in_Effectiveness_from_New_to_Experienced_Teachers - Decrease_in_Experienced_Teacher_Effectiveness_from_Retiring_and_Leaving - Decrease_in_Experienced_Teacher_Effectiveness_From_EE) * dt
INIT Experienced_Teacher_Effectiveness = Initial_Exp_Teachers * Initial_Experienced_Teacher_Effectiveness
Teacher Effectiveness Units
Experienced_Teachers(t)
Experienced_Teachers(t - dt) + (Experienced_Teacher_Hiring + New_Teachers_Becoming_Experienced - Experienced_Teacher_Leaving - Experienced_Teacher_Retiring) * dt
INIT Experienced_Teachers = Initial_Exp_Teachers
Teachers
New_Teacher_Effectiveness(t)
New_Teacher_Effectiveness(t - dt) + (Increase_in_New_Teacher_Effectiveness_from_Hiring + Increase_in_Effectiveness - Decrease_in_New_Teacher_Effectiveness_From_Leaving - Increase_in_Effectiveness_from_New_to_Experienced_Teachers - Decrease_in_New_Teacher_Effectiveness_from_EE) * dt
INIT New_Teacher_Effectiveness = Initial_New_Teachers * Initial_New_Teacher_Effectiveness
Teacher Effectiveness Units
New_Teachers(t)
New_Teachers(t - dt) + (New_Teacher_Hiring - New_Teacher_Leaving - New_Teachers_Becoming_Experienced) * dt
INIT New_Teachers = Initial_New_Teachers
Teachers
Student_Performance(t)
Student_Performance(t - dt) + (Student_Performance_Increase - Student_Performance_Decrease) * dt
INIT Student_Performance = Initial_Student_Performance
Student Performance Units
Students_Enrolled(t)
Students_Enrolled(t - dt) + (Student_Enrollment - Students_Leaving) * dt
INIT Students_Enrolled = Initial_Students_Enrolled
Students
Teacher_Emotional_Exhaustion(t)
Teacher_Emotional_Exhaustion(t - dt) + (EE_Accumulation - Teacher_Recovery) * dt
INIT Teacher_Emotional_Exhaustion = Initial_Teacher_EE
EE Units
Teacher_Stress(t)
Teacher_Stress(t - dt) + (Increase_in_Teacher_Stress - Decrease_in_Teacher_Stress) * dt
INIT Teacher_Stress = Initial_Teacher_Stress
Stress Units
Decrease_in_Disengaged_Behaviors
Disengaged_Student_Behaviors *Effect_of_EE_on_reducing_disengaged_behaviors * Disengaged_Behavior_Recovery_Rate_from_Effective_Reengagement_Actions
Behaviors/Months
Decrease_in_Experienced_Teacher_Effectiveness_From_EE
Experienced_Teacher_Effectiveness * Normal_Experienced_Teacher_Effectiveness_Decline_Rate * Effect_of_EE_on_Experienced_Teacher_Effectiveness
Teacher Effectiveness Units/Months
Decrease_in_Experienced_Teacher_Effectiveness_from_Retiring_and_Leaving
(Experienced_Teacher_Leaving + Experienced_Teacher_Retiring) * Avg_Experienced_Teacher_Effectiveness
Teacher Effectiveness Units/Months
Decrease_in_New_Teacher_Effectiveness_from_EE
New_Teacher_Effectiveness * Normal_New_Teacher_Effectiveness_Decline_Rate * Effect_of_EE_on_New_Teacher_Effectiveness
Teacher Effectiveness Units/Months
Decrease_in_New_Teacher_Effectiveness_From_Leaving
New_Teacher_Leaving * Avg_New_Teacher_Effectiveness
Teacher Effectiveness Units/Months
Decrease_in_Teacher_Stress
Teacher_Stress * Effect_of_EE_on_stress_coping_strategies / Teacher_Stress_Recovery_Time
Stress Units/Months
EE_Accumulation
Effect_of_Stress_on_EE * Teacher_Emotional_Exhaustion * Normal_EE_Accumulation_Rate
EE Units/Months
Experienced_Teacher_Hiring
Teacher_Staffing_Gap *Effect_of_school_reputation_on_ability_to_hire / Time_to_Hire_Experienced_Teachers
Teachers/Months
Experienced_Teacher_Leaving
Experienced_Teachers * Normal_Experienced_Teacher_Leaving_Rate * Effect_of_EE_on_Experienced_Teacher_Leave_Rate * Effect_of_Pay_on_Teachers_Leaving
Teachers/Months
Experienced_Teacher_Retiring
Experienced_Teachers / Experienced_Teachers_Retirement_Time
Teachers/Months
Increase_in_Disengaged_Behaviors
Disengaged_Student_Behaviors * Normal_Disengagement_Rate *Effect_of_Student_Performance_on_disengaged_behaviors
Behaviors/Months
Increase_in_Effectiveness
New_Teacher_Effectiveness * Normal_Effectiveness_Growth_Rate_from_Experience * (1+ Fraction_of_New_Teachers_Being_Mentored * Effect_of_Time_Spent_Mentoring_on_teacher_effectiveness + Effect_of_Admin_Support_on_teacher_effectiveness)
Teacher Effectiveness Units/Months
Increase_in_Effectiveness_from_New_to_Experienced_Teachers
New_Teachers_Becoming_Experienced * Avg_New_Teacher_Effectiveness
Teacher Effectiveness Units/Months
Increase_in_Experienced_Teacher_Effectiveness
Experienced_Teacher_Effectiveness*Normal_Effectiveness_Growth_Rate_from_Experience*(1+Effect_of_Admin_Support_on_teacher_effectiveness)
Teacher Effectiveness Units/Months
Increase_in_Experienced_Teacher_Effectiveness_from_Hiring
(Experienced_Teacher_Hiring)*Effectiveness_of_Experienced_Teacher_Hires
Teacher Effectiveness Units/Months
Increase_in_New_Teacher_Effectiveness_from_Hiring
New_Teacher_Hiring * Effectiveness_of_New_Teacher_Hires
Teacher Effectiveness Units/Months
Increase_in_Teacher_Stress
Teacher_Stress * Normal_Stress_Increase_Rate * Effect_of_Disengaged_Behaviors_on_Teacher_Stress * Effect_of_Teacher_Workload_on_Stress
Stress Units/Months
New_Teacher_Hiring
Teacher_Staffing_Gap *Effect_of_school_reputation_on_ability_to_hire / Time_to_Hire_New_Teachers
Teachers/Months
New_Teacher_Leaving
New_Teachers * Normal_New_Teacher_Leaving_Rate *Effect_of_EE_on_New_Teacher_Leave_Rate * Effect_of_Pay_on_Teachers_Leaving
Teachers/Months
New_Teachers_Becoming_Experienced
New_Teachers / Time_for_New_Teachers_to_Become_Experienced
Teachers/Months
Student_Enrollment
Normal_Student_Enrollment_Rate*Effect_of_School_Reputation_on_Enrollment
Students/Months
Student_Performance_Decrease
Student_Performance * Normal_Student_Performance_Decrease_Rate
Student Performance Units/Months
Student_Performance_Increase
Effect_of_Student_Teacher_Ratio_on_Student_Performance * Effect_of_Teacher_Effectiveness_on_Student_Performance * Student_Performance_Gap / Avg_Time_to_Close_Performance_Gap
Student Performance Units/Months
Students_Leaving
Students_Enrolled/Normal_Student_Graduation_Time + Students_Enrolled*Student_Unenrollment_Rate
Students/Months
Teacher_Recovery
Teacher_Emotional_Exhaustion / Teacher_EE_Recovery_Time
EE Units/Months
"Policy_Lever:_Fraction_Available_Funds_Directed_to_Pay_Raise_vs._Supports"
.5
Dimensionless
Average_salary_and_benefits_per_teacher
70000
Dollars/Teachers
Avg_Experienced_Teacher_Effectiveness
Experienced_Teacher_Effectiveness / Experienced_Teachers
Teacher Effectiveness Units / Teachers
Avg_New_Teacher_Effectiveness
New_Teacher_Effectiveness / New_Teachers
Teacher Effectiveness Units / Teachers
Avg_Teacher_Availability_After_Mentoring
(Fraction_of_New_Teacher_Time_Available_After_Mentoring*New_Teachers + Fraction_of_Experienced_Teacher_Time_Available_After_Mentoring*Experienced_Teachers)/ (New_Teachers+Experienced_Teachers)
Dimensionless
Avg_Teacher_Effectiveness
(Experienced_Teacher_Effectiveness + New_Teacher_Effectiveness) / Total_Teachers
Teacher Effectiveness Units / Teachers
Avg_Time_to_Close_Performance_Gap
6
Months
Budget
Students_Enrolled*Per_pupil_expenditure_reimbursement+Other_Revenue
Dollars
Budget_Remaining_for_Compensation_and_Supports_Per_Teacher
(Budget-Other_Expenditures)/Total_Teachers
Dollars/Teachers
Budget_Remaining_for_Pay_Raise_and_Additional_Admin_Supports_Per_Teacher
Budget_Remaining_for_Compensation_and_Supports_Per_Teacher - Average_salary_and_benefits_per_teacher
Dollars/Teachers
Desired_Teacher_Staffing_Level
Students_Enrolled / Target_Student_to_Teacher_Ratio
Teachers
Disengaged_Behavior_Recovery_Rate_from_Effective_Reengagement_Actions
.05
Per Month
EE_perception_delay
3
Months
Effect_of_additional_support_funding_on_admin_support
GRAPH(Policy_Additional_Supports_Per_Teacher) Points: (0, 0.000), (1000, 0.06121), (2000, 0.1289), (3000, 0.2036), (4000, 0.2862), (5000, 0.3775), (6000, 0.4785), (7000, 0.590), (8000, 0.7132), (9000, 0.8495), (10000, 1.000)
Dimensionless
Effect_of_admin_support_on_reducing_workload
GRAPH(Effect_of_Perceived_EE_on_Admin_Support *Effect_of_additional_support_funding_on_admin_support) Points: (0.000, 1.0000), (0.200, 0.9548), (0.400, 0.9140), (0.600, 0.8770), (0.800, 0.8435), (1.000, 0.8133), (1.200, 0.7859), (1.400, 0.7611), (1.600, 0.7387), (1.800, 0.7184), (2.000, 0.7000)
Dimensionless
Effect_of_Admin_Support_on_teacher_effectiveness
GRAPH(Effect_of_additional_support_funding_on_admin_support*Effect_of_Perceived_EE_on_Admin_Support) Points: (0.000, 0.000), (0.200, 0.1505), (0.400, 0.2868), (0.600, 0.410), (0.800, 0.5215), (1.000, 0.6225), (1.200, 0.7138), (1.400, 0.7964), (1.600, 0.8711), (1.800, 0.9388), (2.000, 1.000)
Dimensionless
Effect_of_Disengaged_Behaviors_on_Teacher_Stress
GRAPH(Disengaged_Student_Behaviors / Normal_Student_Behaviors) Points: (0.000, 0.000), (0.200, 0.02526), (0.400, 0.08682), (0.600, 0.2331), (0.800, 0.5352), (1.000, 1.000), (1.200, 1.465), (1.400, 1.767), (1.600, 1.913), (1.800, 1.975), (2.000, 2.000)
Dimensionless
Effect_of_EE_on_Experienced_Teacher_Effectiveness
GRAPH(Teacher_Emotional_Exhaustion / Normal_Teacher_EE) Points: (0.000, 0.000), (0.200, 0.02526), (0.400, 0.08682), (0.600, 0.2331), (0.800, 0.5352), (1.000, 1.000), (1.200, 2.054), (1.400, 2.636), (1.600, 2.911), (1.800, 3.000), (2.000, 3.000)
Dimensionless
Effect_of_EE_on_Experienced_Teacher_Leave_Rate
GRAPH(Teacher_Emotional_Exhaustion / Normal_Teacher_EE) Points: (0.000, 0.500), (0.200, 0.5126), (0.400, 0.5434), (0.600, 0.6165), (0.800, 0.7676), (1.000, 1.000), (1.200, 1.232), (1.400, 1.383), (1.600, 1.457), (1.800, 1.487), (2.000, 1.500)
Dimensionless
Effect_of_EE_on_New_Teacher_Effectiveness
GRAPH(Teacher_Emotional_Exhaustion / Normal_Teacher_EE) Points: (0.000, 0.000), (0.200, 0.0379), (0.400, 0.1302), (0.600, 0.259), (0.800, 0.534), (1.000, 1.000), (1.200, 2.938), (1.400, 4.461), (1.600, 4.852), (1.800, 4.973), (2.000, 5.000)
Dimensionless
Effect_of_EE_on_New_Teacher_Leave_Rate
GRAPH(Teacher_Emotional_Exhaustion / Normal_Teacher_EE) Points: (0.000, 0.500), (0.200, 0.5316), (0.400, 0.567), (0.600, 0.668), (0.800, 0.776), (1.000, 1.000), (1.200, 1.895), (1.400, 2.623), (1.600, 2.891), (1.800, 2.968), (2.000, 3.000)
Dimensionless
Effect_of_EE_on_reducing_disengaged_behaviors
GRAPH(Teacher_Emotional_Exhaustion / Normal_Teacher_EE) Points: (0.000, 2.000), (0.200, 1.981), (0.400, 1.935), (0.600, 1.825), (0.800, 1.599), (1.000, 1.000), (1.200, 0.787), (1.400, 0.6748), (1.600, 0.5651), (1.800, 0.5189), (2.000, 0.500)
Dimensionless
Effect_of_EE_on_stress_coping_strategies
GRAPH(Teacher_Emotional_Exhaustion / Normal_Teacher_EE) Points: (0.000, 2.000), (0.200, 1.981), (0.400, 1.935), (0.600, 1.825), (0.800, 1.599), (1.000, 1.250), (1.200, 0.9014), (1.400, 0.6748), (1.600, 0.5651), (1.800, 0.5189), (2.000, 0.500)
Dimensionless
Effect_of_Pay_on_Teachers_Leaving
GRAPH(Policy_Pay_Raise_Fraction) Points: (0.500, 4.985), (0.600, 3.423), (0.700, 2.439), (0.800, 1.775), (0.900, 1.317), (1.000, 1.000), (1.100, 0.620), (1.200, 0.404), (1.300, 0.323), (1.400, 0.283), (1.500, 0.296)
Dimensionless
Effect_of_Perceived_EE_on_Admin_Support
GRAPH(Perceived_Teacher_EE / Normal_Teacher_EE) Points: (0.000, 0.500), (0.200, 0.5276), (0.400, 0.5868), (0.600, 0.650), (0.800, 0.755), (1.000, 1.000), (1.200, 1.610), (1.400, 1.831), (1.600, 1.913), (1.800, 1.972), (2.000, 2.000)
Dimensionless
Effect_of_Pressure_to_improve_student_outcomes_on_Teacher_Workload
GRAPH(Measured_student_performance_vs_standard) Points: (0.000, 2.000), (0.100, 1.757), (0.200, 1.569), (0.300, 1.422), (0.400, 1.308), (0.500, 1.220), (0.600, 1.152), (0.700, 1.098), (0.800, 1.057), (0.900, 1.025), (1.000, 1.000)
Dimensionless
Effect_of_school_reputation_on_ability_to_hire
GRAPH(Measured_student_performance_vs_standard) Points: (0.000, 0.500), (0.200, 0.5126), (0.400, 0.5434), (0.600, 0.6165), (0.800, 0.7676), (1.000, 1.000), (1.200, 1.232), (1.400, 1.383), (1.600, 1.457), (1.800, 1.487), (2.000, 1.500)
Dimensionless
Effect_of_School_Reputation_on_Enrollment
GRAPH(Measured_student_performance_vs_standard) Points: (0.000, 0.500), (0.200, 0.5126), (0.400, 0.5434), (0.600, 0.6165), (0.800, 0.7676), (1.000, 1.000), (1.200, 1.232), (1.400, 1.383), (1.600, 1.457), (1.800, 1.487), (2.000, 1.500)
Dimensionless
Effect_of_Stress_on_EE
GRAPH(Teacher_Stress / Tolerable_Stress) Points: (0.000, 0.000), (0.200, 0.02526), (0.400, 0.08682), (0.600, 0.2331), (0.800, 0.5352), (1.000, 1.000), (1.200, 1.465), (1.400, 1.767), (1.600, 1.913), (1.800, 1.975), (2.000, 2.000)
Dimensionless
Effect_of_Student_Performance_on_disengaged_behaviors
GRAPH(Student_Performance_vs_Standard) Points: (0.000, 5.000), (0.100, 4.949), (0.200, 4.826), (0.300, 4.534), (0.400, 3.930), (0.500, 3.000), (0.600, 2.070), (0.700, 1.466), (0.800, 1.174), (0.900, 1.051), (1.000, 1.000)
Dimensionless
Effect_of_Student_Teacher_Ratio_on_Student_Performance
GRAPH(Student_to_Teacher_Ratio / Target_Student_to_Teacher_Ratio) Points: (0.000, 2.000), (0.200, 2.000), (0.400, 1.999), (0.600, 1.985), (0.800, 1.841), (1.000, 1.000), (1.200, 0.1589), (1.400, 0.01478), (1.600, 0.001279), (1.800, 0.0001032), (2.000, 0.000)
Dimensionless
Effect_of_Teacher_Effectiveness_on_Student_Performance
GRAPH(Avg_Teacher_Effectiveness / Normal_Teacher_Effectiveness) Points: (0.000, 0.000), (0.200, 0.02526), (0.400, 0.08682), (0.600, 0.2331), (0.800, 0.5352), (1.000, 1.000), (1.200, 1.465), (1.400, 1.767), (1.600, 1.913), (1.800, 1.975), (2.000, 2.000)
Dimensionless
Effect_of_Teacher_Workload_on_Stress
GRAPH(Teacher_Workload) Points: (0.000, 0.000), (0.200, 0.02526), (0.400, 0.08682), (0.600, 0.2331), (0.800, 0.5352), (1.000, 1.000), (1.200, 1.465), (1.400, 1.767), (1.600, 1.913), (1.800, 1.975), (2.000, 2.000)
Dimensionless
Effect_of_Time_Spent_Mentoring_on_teacher_effectiveness
GRAPH(Fraction_of_Time_Spent_Mentoring) Points: (0.000, 0.000), (0.100, 0.1505), (0.200, 0.2868), (0.300, 0.410), (0.400, 0.5215), (0.500, 0.6225), (0.600, 0.7138), (0.700, 0.7964), (0.800, 0.8711), (0.900, 0.9388), (1.000, 1.000)
Dimensionless
Effectiveness_of_Experienced_Teacher_Hires
.8
Teacher Effectiveness Units/ Teachers
Effectiveness_of_New_Teacher_Hires
.5
Teacher Effectiveness Units/Teachers
Experienced_Teachers_Retirement_Time
312
Months
Fraction_of_Experienced_Teacher_Time_Available_After_Mentoring
Fraction_of_Experienced_Teachers_Mentoring * (1-Fraction_of_Time_Spent_Mentoring) + (1-Fraction_of_Experienced_Teachers_Mentoring)
Dimensionless
Fraction_of_Experienced_Teachers_Mentoring
MIN(New_Teachers, Experienced_Teachers)/Experienced_Teachers
Dimensionless
Fraction_of_New_Teacher_Time_Available_After_Mentoring
Fraction_of_New_Teachers_Being_Mentored*(1-Fraction_of_Time_Spent_Mentoring) + (1-Fraction_of_New_Teachers_Being_Mentored)
Dimensionless
Fraction_of_New_Teachers_Being_Mentored
MIN(New_Teachers, Experienced_Teachers) / New_Teachers
Dimensionless
Fraction_of_Time_Spent_Mentoring
.05
Dimensionless
Impact_of_Mentoring_Burden_on_Workload
GRAPH(Avg_Teacher_Availability_After_Mentoring) Points: (0.000, 10.000), (0.100, 7.471), (0.200, 5.621), (0.300, 4.269), (0.400, 3.280), (0.500, 2.556), (0.600, 2.028), (0.700, 1.641), (0.800, 1.358), (0.900, 1.151), (1.000, 1.000)
Dimensionless
Initial_Exp_Teachers
72
Teachers
Initial_Experienced_Teacher_Effectiveness
.8
Teacher Effectiveness Units / Teachers
Initial_New_Teacher_Effectiveness
.5
Teacher Effectiveness Units / Teachers
Initial_New_Teachers
8
Teachers
Initial_Student_Disengagement
10
Behaviors
Initial_Student_Performance
.75
Student Performance Units
Initial_Students_Enrolled
2400
Students
Initial_Teacher_EE
10
EE Units
Initial_Teacher_Stress
1
Stress Units
Measured_student_performance_vs_standard
SMTH1(Student_Performance_vs_Standard,Student_Performance_Measurement_Delay)
Dimensionless
Normal_Disengagement_Rate
.05
Per Month
Normal_EE_Accumulation_Rate
1/12
Per Month
Normal_Effectiveness_Growth_Rate_from_Experience
.03
Per Month
Normal_Experienced_Teacher_Effectiveness_Decline_Rate
.03
Per Month
Normal_Experienced_Teacher_Leaving_Rate
.01
Per Month
Normal_New_Teacher_Effectiveness_Decline_Rate
.03
Per Month
Normal_New_Teacher_Leaving_Rate
.01
Per Month
Normal_Stress_Increase_Rate
1/12
Per Month
Normal_Student_Behaviors
10
Behaviors
Normal_Student_Enrollment_Rate
62
Students/Months
Normal_Student_Graduation_Time
48
Months
Normal_Student_Performance_Decrease_Rate
.3
Per Month
Normal_Teacher_EE
10
EE Units
Normal_Teacher_Effectiveness
.8
Teacher Effectiveness Units / Teachers
Other_Expenditures
24000000
Dollars
Other_Revenue
13200000
Dollars
Per_pupil_expenditure_reimbursement
7000
Dollars/Students
Perceived_Teacher_EE
SMTH1(Teacher_Emotional_Exhaustion, EE_perception_delay)
EE Units
Policy_Additional_Salary_Per_Teacher
Budget_Remaining_for_Pay_Raise_and_Additional_Admin_Supports_Per_Teacher*"Policy_Lever:_Fraction_Available_Funds_Directed_to_Pay_Raise_vs._Supports"
Dollars/Teachers
Policy_Additional_Supports_Per_Teacher
Budget_Remaining_for_Pay_Raise_and_Additional_Admin_Supports_Per_Teacher * (1-"Policy_Lever:_Fraction_Available_Funds_Directed_to_Pay_Raise_vs._Supports")
Dollars/Teachers
Policy_Pay_Raise_Fraction
(Average_salary_and_benefits_per_teacher+Policy_Additional_Salary_Per_Teacher)/Average_salary_and_benefits_per_teacher
Dimensionless
Student_Performance_Gap
Student_Performance_Standard-Student_Performance
Student Performance Units
Student_Performance_Measurement_Delay
12
Months
Student_Performance_Standard
1
Student Performance Units
Student_Performance_vs_Standard
Student_Performance/Student_Performance_Standard
Dimensionless
Student_to_Teacher_Ratio
Students_Enrolled / Total_Teachers
Students/Teachers
Student_Unenrollment_Rate
.005
Per Month
Target_Student_to_Teacher_Ratio
30
Students/Teachers
Teacher_EE_Recovery_Time
12
Months
Teacher_Gap
Student_to_Teacher_Ratio / Target_Student_to_Teacher_Ratio
Dimensionless
Teacher_Staffing_Gap
MAX(Desired_Teacher_Staffing_Level - Total_Teachers, 0)
Teachers
Teacher_Stress_Recovery_Time
12
Months
Teacher_Workload
Teacher_Gap * Normal_Teacher_Effectiveness * Impact_of_Mentoring_Burden_on_Workload * Effect_of_admin_support_on_reducing_workload * Effect_of_Pressure_to_improve_student_outcomes_on_Teacher_Workload/ Avg_Teacher_Effectiveness
Dimensionless
Time_for_New_Teachers_to_Become_Experienced
48
Months
Time_to_Hire_Experienced_Teachers
6
Months
Time_to_Hire_New_Teachers
4
Months
Tolerable_Stress
1
Stress Units
Total_Teachers
Experienced_Teachers + New_Teachers
Teachers