Steeple Run Steeple Run Elementary SchoolElementary School

Steeple Run Steeple Run Elementary SchoolElementary School

Curriculum OptimizationCurriculum Optimization

EnvirogroupEnvirogroupEnvirogroupEnvirogroupJennifer MorganJennifer Morgan

Amy SilderAmy Silder

Introduction• Naperville, Illinois

– 130,000 citizens

• Naperville Community School District• Steeple Run School’s mission:

– Graduate students who think critically, solve problems, make decisions, and have the skills necessary for productive citizenship and lifelong learning by providing comprehensive programs and services.

Constraints• School day: 8:15 to 2:30• Classes:

– 4 kindergarten (two AM and two PM)– 4 classes each: 1st, 2nd, and 3rd grades– 5 classes each: 4th and 5th

• 4 classrooms per grade (grades 1 – 5)

• 2 kindergarten classrooms

More Constraints• Teachers require at least 1 hour and 15

minutes of planning and lunch time per day.

• Classes may also attend:– Art– Music– Gym– Library– Computer Lab– Lunch/Recess

Objectives• Maximize the time each class

spends in:– Art– Music– Gym

• And, in turn, maximize teacher planning time.

Methods• Used standard linear programming

to formulate the problem.• Solved the problem using

Mathematica.• Variable units were based on 1

hour time blocks, with 31.25 units per week.

Variables• K1#, k2#, k3#, k4# –

kindergarten classes• a1#, b1#, c1#, d1# –

first grade classes• a2#, b2#, c2#, d2# –

second grade classes• a3#, b3#, c3#, d3# –

third grade classes• a4#, b4#, c4#, d4#, e4# –

fourth grad classes• a5#, b5#, c5#, d5#, e5# –

fifth grade classes

• a, m, g, e, c = total time in art, music, gym, lunch, and the computer lab respectively

• where # = a – artm – musicg – gyme – libraryr – recessl – lunchc –

computer labs – time in

classroom

ResultsArt Gym Music Lunch

Kindergarten 40 min

50 min 40 min 0 min

1st 50 min

50 min 50 min 4 hrs

2nd 50 min

50 min 50 min 4 hrs

3rd 50 min

50 min 50 min 4 hrs

4th 50 min

50 min 50 min 4 hrs

5th 50 min

50 min 50 min 4 hrs

Note: none of the classes require attendance at either the library or the computer lab

Discussion• All constraints can be met.• Very little flexibility in daily

scheduling.• No attendance for library or

computer lab.– Allows for more out-of-the classroom

learning experiences

Conclusion• Usefulness of linear programming.• Mathematica is an excellent tool.

– Allows curriculum planners to easily change constraints.

• “An employee that understands goal programming is a valuable asset to any organization.”

-Ms. Lenore Johnson