This document provides an overview of differentiated instruction using problem-based learning. It describes problem-based learning as an instructional model that allows students to solve real-world problems through self-directed learning. The document then presents two examples of problem-based learning challenges that involve students solving heating and cooling system issues for homes. It outlines the process used, including introducing the problem, providing discussion resources, monitoring student problem-solving, and having students present their solutions. Finally, the document discusses assessing problem-based learning activities for both students and teachers.

1. Differentiated
Instruction Using
Problem Based Learning
Anthony Kadnar
University of New England

2. Introduction
 In the following slides, you will be introduced to Problem Based Learning and
how this teaching model can differentiate your classroom.
 Problem Based Learning allows the student to solve real world problems using
differentiation.
 During the problem based activities, students develop spatial understanding,
and are able to work in small groups or individually.
 In this model, teachers monitor progress and can give suggestions, but do not
guide the student to the answer.

3. Project-Based Model
 “ A project-based Model provides a framework for the goals and objectives,
the topic choices, the outline for the task, progress checks and assessment
tools, the timeline, and the presentation format. Projects engage students in
an expanded independent, partner, or student-choice contract” (Chapman, C.
& King R., 2012)
 “ PBL (project based learning) organizes learning around projects defined as
complex tasks, based on challenging problems and involving students in
problem-solving, decision making, collaboration, design and
development.” (O'Sullivan, D. & Krewer, F., 2015)
 “Problem based learning is a teaching and learning strategy that uses a
problematic stimulus as a means of motivating and directing students to
develop and acquire knowledge.” (Rogal, S. M. M., & Snider, P. D., 2008).

4. Student Centered
 In Problem Based Learning, students have the ability to choose their path to
solving the problem, instead of a predetermined pathway to the answer.
 Students can find their way through a problem in their own way. If they get
stuck, teachers can provide hints. Teachers must not guide, but hint a
possible direction.

5. How It Works?
 In the following slides, I will show two examples of Problem Based Learning
challenges that I have introduced into my classroom.

6. How It Works: Introduction
 Students are brought through the introduction first.
 Once introduced, students have time to take notes and start collecting data.
 The teacher is not allowed to answer any questions at this point.

7. How It Works: The Problem
 Next, students are given the problem they have to solve.
 In this section, students are allowed to take notes, but once again, the
teacher cannot answer questions.

8. How It Works: Discussion Resources
 In this section, students are introduced to resources that will help them get
started solving the problem presented.
 Once introduced to the resources, students are released to start solving the
problem.

9. How It Works: Teacher Monitoring
 During the problem solving phase, teachers can monitor student progress, but
are not allowed to give assistance unless the student is completely stumped.
 At this point, the teacher is only allowed to give limited direction to steer
students back to a productive path.

10. How It Works: Solution
 Once students solve the problem, they are asked to present their findings to
the class.
 In this presentation, they tell the class how they arrived at their solution.
 Going step-by-step on how they came up with the solution allows the class to
see the many differentiated ways the class can solve a problem.

11. How It Works: Teacher/Industry Solution
 Once students have presented their findings, the teacher, then, presents their
solution to the class and how they came up with their answer.
 After the presentations are concluded, there is a class dialogue where
students are able to ask questions and defend their findings, if different from
the teacher’s solution.
 In this model, always remember there is a possibility to have a different
approach to solving the problem.
 Also, make sure your students know that there is more than one way to solve
a problem and there is not just one answer.

12. Problem Based Learning
Challenge 1

13. Introduction
 With energy costs increasing on a yearly basis, the cost associated with
keeping our homes climate controlled are becoming very expensive.

14. Introduction
 With new products on the market today, such as geothermal, air source heat
pumps, biomass, and condensing boilers and furnaces, these costs can be
dramatically reduced.

15. System Examples
Biomass System Geothermal System

16. System Examples
Air Source Heat Pump Condensing Furnace

17. Introduction
 With some of these technologies coupled to PV solar, we can make a home net
zero. This means, after installation, there is no energy bill for that structure.
 Is this an expensive option?

18. Introduction
 Yes, these projects can be quite costly up front, but have major overall cost
reductions over the life of the system.
 Are there any incentives to switch to a system like this?

19. Introduction
 Yes, there are many federal tax incentives as well as state programs that can
dramatically reduce the cost of a project like this.

20. Introduction

21. Organization Overview
 KDNR Heating is located in Belgrade, and has been in the installation and
service business for 27 years.

22. Problem
 Jim and Jane are planning to build a house and have hired KDNR Heating to
install the new heating and cooling system for them.

23. Problem
 While talking with the customers, Jim states that he will be doing the building
himself and provides KDNR with a set of plans outlining the dimensions of the
structure.

24. Heat Loss/Gain Data
Walls sqft Notes:
1st Floor - Old Side 1038.3 2x4 framed
1st Floor Addition 785 New Construction: 2x6 framed
2nd Floor - Old side end wall 297.5 2x4 framed
2nd Floor - Old side knee wall 188 2x4 framed
2nd Floor - Middle section knee wall 143.5 2x4 framed
2nd Floor - Old side back end wall 160 2x4 framed
2nd Floor - Addition knee wall 170 New Construction: 2x6 framed
2nd Floor - Addition end wall 180 New Construction: 2x6 framed
2nd Floor - Dormers 120 : 2x4 framed
Ceiling sqft Notes:
Old side Front section 594 Blown in - estimated 9"
Old side Middle section 535.5 Blown in - estimated 9"
New Addition lower Roofs 458.25 9" fiberglass - 2x10 framed
New Addition Upper Roofs 385.25 12" Fiberglass - 2x12 framed
Floor sqft Notes:
Old Section Basement 1301 26x25
New Section - Basement 544 20x28
Windows sqft Notes:
South Facing 171.35 Double pane windows
East Facing 45 Double pane windows
West Facing 66 Double pane windows
North Facing 57.8 Double pane windows
Doors sqft Notes:
Front Door 33.3 south facing
Side Door 20 East facing
Side Door 20 West facing
Sliding Glass door 40 West facing

25. Discussion
 Keith from KDNR Heating asks Jim where the house will be constructed; Jim
replies “The house will be built in Waterville, ME in the spring.”

26. Discussion
 Jim- “Keith, with all the options out on the market today, from furnaces to
geothermal, what is the best bang for my buck?” Keith replies “There are
many great options out on the market today to suit your needs and save you
money.” Keith goes on to ask “What is your budget for the heating and cooling
system?”
 Jim replies “We are open on budget as long as we are saving over the long
term.”

27. Discussion
 Jim states they would like a quote for a geothermal heat pump system, an air
source heat pump system, and a conventional natural gas furnace/air
conditioning system.
 With these quotes, Jim requests a 10 year energy cost. With this data, he can
estimate a return on investment for the project.

28. Discussion Resources
 Efficiency Maine:
 http://www.efficiencymaine.com/
 Federal tax incentives:
 https://www.energystar.gov/about/federal_tax_credits
 Build it solar:
 http://www.builditsolar.com/References/Calculators/HeatLoss/HeatLoss.htm
 Heat loss/ heat gain worksheet:
 http://www.ci.brainerd.mn.us/building/docs/heat_loss_calculation.pdf

29. Solution
 With $5,000.00 incentives from Efficiency Maine and a tax credit for 30%
through the federal government, a geothermal system gives Jim and Jane the
best return on investment. This system also gives them the opportunity to add
PV solar to their home at a later date to make their home Net Zero, thus
eliminating their monthly energy bill.

30. Problem Based Learning
Challenge 2

31. Introduction
 When homeowners buy a house, they like to maximize their home’s space.
 The best place to do this is to refinish a basement.
 When doing this, the mechanical room always seems to be the smallest room.

32. Introduction
 All heating systems must have a specific amount of combustion air in order to
have perfect to ideal combustion.
 Most new appliances are designed to be direct vented to the outside and do
not require a vertical chimney.
 They also bring their combustion air in from the outside as well.
 This eliminates the need to draw air for combustion from inside the space.
 With older conventional type 1 systems, air for combustion comes from inside
the room.

33. Organizational Overview
 MRM Mechanical is an HVAC contractor in Sterling Heights, MI.
 They have been in the installation and service business for 23 years.

34. Problem
 Mike from MRM Mechanical gets a service call to one of their long time
customers, Donna and Frank.
 They are complaining their old type 1 gas furnace and hot water heater are
on the fritz.
 Mike heads downstairs to see if he can find a problem and get the two
appliances back online.

35. Problem
 Mike enters the basement and notices there is a change from the last time he
was there.
 Frank and Donna remodeled their basement last summer.
 Mike makes his way down the new hallway and opens the door to the new
mechanical room.
 When he opens the door half-way, it hits the front of the furnace.
 Shimmying his way into the very small room, that he can barely fit in, he
notices some black soot on the front of the furnace.

36. Problem
 As these systems get walled off, they tend to lose their ability to function as
they would in an open basement.
 Sometimes, this can go unnoticed until the middle of the winter.

37. Discussion Resources: System Data
 The original basement was 30’x 50’ and was open.
 The new mechanical room is 8’x 12’.
 The furnace is a type 1 natural draft furnace with an input of 145,000 BTUs
with an efficiency of 88%.
 All the air for combustion comes from within the structure.
 The 41 gallon hot water is also a type 1 natural draft appliance. This system
has an input rating of 35,000 BTUs.
 All of its combustion air comes from within the structure.

38. Dialogue
 Mike- “Frank I really like what you and Donna have done with your
basement.”
 Frank replies “Thank you.”
 Donna asks “Mike, what do you think the problem might be?”
 Mike replies “I think the furnace and hot water heater is being starved of air
and not able to fire correctly.”
 Frank- “We did our remodel at the beginning of the summer and it has been
working fine until now.” (it is now December)

39. Dialogue
 Mike- “That could very well be because the furnace was not running during
the summer, only the hot water heater.”
 Mike- “The problem did not show until the furnace and hot water heater both
started to operate at the same time.”
 Frank- “What do we do now?”
 Mike- “I will do some calculations and see if we can come up with a solution.”

40. Solution
 Mike uses the alternative method to find out the maximum BTUs that can be
used in that room.
 L x W x H= Room Volume
 8 x 12 x 8= 1,152 ft³
 1,152 x 20= 23,040 BTUs maximum
 Appliance BTUs:
 Furnace 135,000 BTUs / Hot water heater 35,000 BTUs
 Total = 170,000 BTUs

41. Solution
 The maximum BTUs that can be fired in this new mechanical room is 23,040 BTUs.
 The total BTUs for the furnace and hot water heater are 170,000 BTUs.
 This is a differential of 146,960 BTUs.

42. Solution
 Mike must next come up with a way to get the rest of the combustion air into
the room, so both appliances can operate with enough combustion air.

43. Solution
 Mike decides to put a louvered door on the mechanical room door.
 He uses the 146,960 BTUs to size the louvers for the door.
 Code states there needs to be 4000 BTUs per inch of free air opening.
 146,960/4000= 36.74 in²
 Mike will use metal louvers and with 75% of the free air opening.
 This would require a 49 in² louver to get the required additional combustion
air.

45. Assessing the Problem Based Learning
Activity
 Once the Challenge is completed, students are given a self assessment sheet
to prompt reflectively:
 Was this learning experience worth the time I spent on it? Why or why not?
 I learned…
 Where did I need more direction?
 I am proud of the following tasks…
 Which tasks needed more time to complete?
 My deepest thinking was used when…
 I want to know more about…
 If I could select another project, it would be… (Chapman, C. & King R., 2012)

46. Assessing the Problem Based
Learning Activity
 For the teacher, we can assess the students’ progress through the Challenge
by asking:
 Is the problem worth the time?
 Do the assignment and activities enhance the content and standards required at
this grade level?
 Is it age appropriate?
 Will the results be observable for the learner?
 How will individual roles and tasks be assigned?
 What checkpoints and self-assessment tools will be used?
 Do the learners understand the assessment process? (Chapman, C. & King R., 2012)

47. Differentiated Learning Using Problem
Based Learning
 In conclusion, students and teachers alike can experience Problem Based
Learning as an alternative to the current teaching methods we are practicing
today.
 Allowing the teacher to become the “facilitators rather than disseminators”
(Wilkerson and Gijselaers 1996). This is the way to a true differentiated
classroom, where the traditional lecture approach is taken away and students
take control of their own learning.
 In my experience, students take a little while to adapt, but once they have,
the learning process is like no other. Students transform their learning and are
engaged, and learning is fun!
 Please give Problem Based Learning a try in your classroom and see what a
true differentiated classroom looks like!

48. Link To Problem Based Learning Site With
Passwords to Access the Challenges:
 http://www.pblprojects.org/stem-pbl-challenges/
Challenge Discussion Solution Teacher
Resources
FloDesign Students need to design a
new way to extract electrical energy
from a wind turbine
PD1095 PS0109 trfenna
RLS Fiber Systems is designing a new,
energy efficient lighting system for
submarines. Can this lighting system
be ergonomic as well?
PD6108 PS0610 trfenna
Cape Cod Cranberry Growers
Association Can a cranberry bog use
technology to become energy
efficient?
PD2330 PS0233 trfenna
Tookany/Takony-Frankford Watershed
Partnership needs to protect a
watershed that is invisible to the
neighborhood.
PD9138 PS1913 trfenna
SPG Solar/City of Tucson The city of
Tucson, AZ wants SPG Solar to put a
solar array on a large building but the
roof is not strong enough to support a
traditional panel array.
PD4949 PS9494 trfenna
Johnson & Johnson enlists a team of
scientists to develop a treatment for
eczema based on plant-derived active
ingredients.
PD8993 PS0899 trfenna

49. Link To Problem Based Learning Site With
Passwords to Access the Challenges:
 http://www.pblprojects.org/photon-pbl-challenges/
Challenge Discussion Solution Teacher
Resources
Blinded by the Light – What dangers does
a pilot face in an aircraft targeted by a
laser pointer?
PD2819 PS3281 Trfenna
Stripping with Light, Fantastic! –
Photomachining, Inc. needs to develop a
process for stripping the coating from 50
micron wire
PD3076 PS0307 Trfenna
DNA Microarray Fabrication – Boston
University graduate students need to
determine the best starting exposure
time for a DNA microarray fabricator
PD2215 PS0221 Trfenna
High Power Laser Burn-In Test – IPG
Photonics needs a way to run 100 hour
unattended burn-in tests on a 2 kwatt
laser.
PD1540 PS0154 Trfenna
Shining Light on Infant Jaundice – Can
technology provide a safe and effective
portable home treatment for newborn
jaundice?
PD5081 PS7508 Trfenna
Watt’s My Light? – The package says a 26
watt fluorescent has the same light
output as a 100 watt incandescent. How
can this statement be verified?
PD1768 PS9176 Trfenna
Of Mice and Penn – Can optics provide a
non-contact measurement method as
part of a research project to study the
healing of tendons?
PD9104 PS1910 Trfenna
Hiking 911– Two boys are lost in deep
woods in rough terrain. What is the best
technology to locate them?
PD6229 PS1622 Trfenna

50. Link To Problem Based Learning Site With
Passwords to Access the Challenges:
Challenge Discussion Solution Teacher
Resources
IBM has a problem with a thin film
etching process causing an area at the
edge of the wafer to be under-etched.
How can IBM locate and repair the
problem?
PD5452 PS0545 trfenna
Sound Manufacturing needs to
manufacture a sheet metal panel with
many connector cutouts spaced closely
together. Can metal be cut and bent
beyond existing metal and machine
standards without increasing the failure
rate?
PD6475 PS0647 trfenna
Cirtec Medical Systems needs to ramp
up production of power packs for an
implantable medical device from 300
per year to 5000 per year. How do you
go from a one-person operation to full-
fledged production?
PD1028 PS0102 trfenna
FastCAP Systems’s carbon nanotubes
need a uniform thin film layer for even
growth, but the sputtered coating is
bunching into clusters. How can they
make the thin, even metal films they
need?
PD2210 PS0221 trfenna
Hypertherm is experiencing too many
defects in its wave solder process. How
can Hypertherm minimize the number
of solder defects?
PD3755 PS0375 trfenna
http://www.AMPBL.org

51. References:
 Chapman, C. & King, R. (2012). Differentiated assessment strategies. Thousand Oaks, CA.
 New England Board of Education: Problem Based Learning Projects (2015).
http://www.pblprojects.org/
 O'Sullivan, D., & Krewer, F. (2015). Structured approach to project based learning using a new
type of learning management system. Paper presented at the 460-XVII. Retrieved from
https://une.idm.oclc.org/login?url=http://search.proquest.com.une.idm.oclc.org/docview/1
728004308?accountid=12756
 Rogal, S. M. M., & Snider, P. D. (2008). Rethinking the lecture: The application of problem
based learning methods to atypical contexts. Nurse Education in Practice, 8(3), 213-9.
doi:http://dx.doi.org.une.idm.oclc.org/10.1016/j.nepr.2007.09.001
 Tomlinson, C.A, (2004). How to differentiate instruction in mixed ability classrooms. (2nd
edition) Alexandria, VA: Association for Supervision and Curriculum Development.
 Wilkerson, L., & Gijselaers, W. H. (1996). “Concluding comments.” In L. Wilkerson & W. H.
Gijselaers (Eds.), Bringing problem-based learning to higher education: Theory and practice
(pp. 101-104). San Francisco: Jossey-Bass.