SpecialSession:NextGenera2on ProblemSolving 2010!ASEE!Annual!Conference! Louisville,KY June22,2010...

Special Session: Next Genera2on Problem-‐Solving

2010 ASEE Annual Conference Louisville, KY

June 22, 2010

Modeling: Elicita?on, Development, Integra?on and Assessment

Cal Poly SLO, Mines, Minnesota, Pepperdine, PiG, Purdue, USAFA

Model Elici?ng Ac?vi?es (MEAs)

•  Developed by math educators (Lesh) •  Client-‐driven, open-‐ended problems designed to be model elici?ng and thought revealing

•  Require students to mathema&ze informa?on and structure in context – e.g., quan?fy, organize, dimensionalize

•  Adapted to engineering (Diefes-‐Dux)

Brief History of MEAs •  Mathema?cs educa?on researchers created to observe student problem-‐solving competencies and growth of mathema?cal cogni?on.

•  Documented as a methodology that helped students become beGer problem solvers.

•  Became a tool that helped both instructors and researchers become more observant and sensi?ve to the design of situa?ons that engaged learners in produc?ve mathema?cal thinking.

•  Introduced to college freshmen at Purdue •  Being extended by seven university consor?um

Applica?on to Engineering •  Purdue research -‐ MEAs can be effec?ve team learning exercises

•  MEAs provide innova?ve assessment opportuni?es (combined with rubrics)

•  Reflec?on tools (RTs) help students record strategies used and group func?oning

•  MEAs hold the poten?al to measure in-‐process learning.

Typical MEA •  Elicits from a team a mathema?cal or conceptual system as part of its procedural requirements

•  Students need to make new connec?ons, combina?ons, manipula?ons or predic?ons

•  Emphasis on tes?ng, revising, refining and formally documen?ng solu?ons

A well designed MEA: •  A realis?c problem with an iden?fiable client. •  Requires the development of a problem solving procedure

involving unspecified mathema?cal, scien?fic, and engineering concepts.

•  Mo?vates students to integrate exis?ng knowledge to develop a generalizable mathema?cal model.

•  Leads to heightened conceptual understandings. •  Creates an environment where communica?on,

verbaliza?on, and collabora?on must be combined with mathema?cal and engineering thought.

•  Requires students to acquire new knowledge on a just-‐in-‐?me basis while reinforcing previously obtained knowledge.

Extending the MEA Construct

•  NSF CCLI Type 3 project •  Cal Poly SLO, Colorado School of Mines, Minnesota, Purdue, Pepperdine, PiG, USAFA,

•  Extensions – junior – senior level, ethical situa?ons, misconcep?ons, laboratory experiments, integra?on of concepts, global and societal se`ngs.

MEAs In Engineering: A Focus On Model Building

focus on model-‐building

•  interpre?ve systems that help make sense of situa?ons

•  representa?ons of ideas, connec?ons between them

•  ascendant in recent years in nsf-‐funding and in learning sciences

models vary

•  unclear to …. •  patchy or hazy to …. •  intui?ve to … •  fact-‐deficient to …. •  disconnected or uncoordinated to ….. •  weak to …. •  specialized to ….

models evolve

•  along these and other spectra •  worthy lens for engineering curriculum is to progress along the spectra

models and modeling perspec?ve

•  or mmp, focuses on nurturing growth along these dimensions

•  mmp interpreta?on of the learning science axiom to build on prior knowledge understand the models that students possess

mmp

•  beGer problem solvers don’t just do things differently, they see things differently

•  good solu?ons to complex problems rarely rely exclusively on topics that can be extracted from a single topical area of a textbook. solu?ons invoke intui?on, ethics, mul?ple disciplines

•  small groups working on realis?c problems provide far more produc?ve problem-‐solving venues than individuals in isola?on

understanding models

•  comes by seeing them •  not trivial to see models consistently

•  research tools to see or disclose models were called thought-‐revealing ac?vi?es or model-‐elici?ng ac?vi?es

interes?ng scien?fic observa?on

•  early mea research focused on how school and college age students expressed, tested and revised their models to solve realis?c problems given in small group se`ngs

•  the research se`ng changed the thing being studied – not hawthorne, but ar?fact of expression and tes2ng

•  meas became promising tools for curriculum

the word “curriculum”

•  two historical lineages – wheelbarrows – currere

research tool repurposed for curriculum

•  complex undertaking •  step one ~ generate and use elici?ve ac?vi?es •  series of design principles evolved •  general paGern in engineering courses:

– ofen client-‐driven assignments – open-‐ended but towards concrete recommenda?ons

– small groups of 2-‐4, in single class-‐periods

six design principles

1.   reality principle (the “personally meaningful” principle): could this happen in “real life”?

2.   model construc2on: does the task create the need for a model to be constructed (or modified, or extended, or refined?

3.   model documenta2on: will the response require students to explicitly reveal how they are thinking about the situa?on

six design principles

4.   self evalua2on: does the statement of the problem strongly suggest the criteria that are appropriate for assessing the usefulness of alterna?ve responses? will students be able to judge for themselves when their responses are good enough?

5.   model generaliza2on: is the model not only powerful (for the specific situa?on and client at hand) but also sharable (with others) and re-‐useable (in other situa?ons)?”

6.   simple prototype: is the situa?on as simple as possible, while s?ll crea?ng the need for a significant model? will the solu?on provide a useful prototype (or metaphor) for interpre?ng other structurally similar situa?ons?

what changes?

•  models •  students •  professors

research futures

•  cogni?ve science of model evolu?on •  curriculum theory

•  personalized learning communi?es

•  study of flow and immersive engagement –  loss of fear of failure –  loss of ?me consciousness – group flow – knowing what to do next

Interac?ve Exercise

John Christ Brian Self

Tamara Moore

Model-‐Elici?ng Ac?vi?es: An interac?ve experience

Engineering solu&ons for contaminant spill response

Learning Objec&ves: 1. Apply conserva&on of mass principles 2. Employ chemical kine&cs to predict contaminant degrada&on 3. Employ technical knowledge in decision model 4. Incorporate regulatory policy and ethical concerns in proposed solu&on evalua&on

Current Topic

Pre-‐MEA: In-‐Class Example

Creek: Q = 10 cfs

Lake: 20 acres Avg depth = 14 f

Toxic Spill: 23,500 gal

Recommenda?on: Don’t divert Stream

In-‐class example v. MEA

Step 1 – Problem introduc?on and Process ID (Reality principle, Model construc?on & documenta?on)

Individually: 1.   Read the memo and answer the following ques2ons:

1.  What informa2on will be required to enable the assessment of a wide range of spill scenarios and the development of a recommenda2on on courses of ac2on?

2.  Where might you locate this informa2on? What are valuable sources and why would you rely on these sources over other poten2al sources?

Step 1 – Problem introduc?on and Process ID (Reality principle, Model construc?on & documenta?on)

Teams: 3. Discuss your answers. Develop a list of required informa2on to include recommended sources.

4. Teams – Develop a single-‐page process diagram outlining the engineering response. The process diagram should make clear decision points and the alterna2ve engineering solu2ons considered by your decision model. The aWached memo from the recent regional directors mee2ng outlines currently available rapid engineering capabili2es that should be considered when developing your response.

Example Process diagrams (student work)

Step 2 – Model development (Documenta?on, Self Assessment & model generaliza?on)

Teams: Implement the process flow diagram in an on-‐site tool (e.g., spreadsheet) •  Evaluate alterna2ves •  Incorporate constraints •  Generalize model for different cleanup scenarios

Example – Model Implementa?on

Step 3 – Model Implementa?on (Effec?ve prototype) –  Student teams apply their model and methodology to an assigned realis?c spill scenario

–  Ask ques?ons about the human dimension

Creek: Q = 10 cfs

Lake: 20 acres Avg depth = 14 f

Toxic Spill: 23,500 gal

Transi?oning Classroom Experience

•  MEAs –  Transi?on in-‐class example problems to team-‐based learning exercises founded in real prac?ce

–  USAFA focus on civil and environmental engineering •  excellent framework to solve problems with “big picture” implica?ons (e.g., human responsibility, interna?onal rela?ons)

•  Integrates many disciplines …can tailor problems to aid students in seeing common links throughout engineering and science

•  Reinforce topics learned during founda?onal courses •  Develop hands-‐on based modeling ac?vi?es at the lab or field scale

Instructor Perspec?ves

Model-‐Elici2ng Ac2vi2es: Instructor Perspec2ves

Ronald Miller, Colorado School of Mines Tamara Moore, University of Minnesota

Brian Self, California Polytechnic State University Andrew Kean, California Polytechnic State University

Gillian Roehrig, University of Minnesota Jack Patzer, University of PiWsburgh

•UNIVERSITYOFPITTSBURGH•UNIVERSITYOFMINNESOTA•PURDUEUNIVERSITY•UNITEDSTATESAIRFORCEACADEMY• •COLORADOSCHOOLOFMINES•CALPOLY-‐SANLUISOBISPO•PEPPERDINEUNIVERSITY•

Instructor Perspec2ves •  Andrew Kean – Mechanical Engin.

– Used to follow instructor-‐based approach – Now willing to take class 2me to use MEAs

•  Deeper learning

•  Ron Miller – Chemical Engin. – Coach groups through decisions and assump2ons

– Physical versus analy2c models

Crea2ng MEAs: Reality, Model Construc2on Principles

•  Much more difficult •  Laboratory experiments or demonstra2ons

•  Computer simula2ons

•  Answers to similar cases

Crea2ng MEAs: Self Assessment Principle

Instructor Perspec2ves •  Mechanical Engineering

–  Introductory classes – Dynamics and thermodynamics

•  Common final examina2on – MEAs take 2me in and out of class

•  Student wri2ng and documenta2on

•  Instructor effort developing the MEAs and providing feedback

Grading Issues •  Cal Poly: non-‐PhD gran2ng university •  Incorporate pre-‐MEA ac2vi2es into typical homework assignments – Undergraduate TA can grade

Approach •  Break MEA solu2ons into smaller parts •  Have students apply their model to specific cases/problems

•  Accident Reconstruc2on MEA

Instructor Grades Memo

Benefits •  Provide real engineering context •  Model documenta2on

– Wri2ng to a specific audience

•  Thought revealing ac2vi2es – Greater understanding into how you students are thinking

•  Collabora2ve learning

Karen Bursic University of PiGsburgh

Engineering Economy Engineering Sta?s?cs

Instructor’s Perspec2ve: Engineering Economy

•  Use of a E-‐MEAs requires substan?al effort on the part of the instructor.

•  Students must see the connec?on between the MEAs and the concepts they must know to do well in the course.

•  The instructor must provide feedback and engage the students in a useful discussion afer the MEAs are completed.

•  MEAs can be very effec?ve in reinforcing and integra?ng course concepts.

ABET outcomes

•  MEAs are ideally suited to improve ABET outcomes.

•  We saw significant improvement for several ABET outcomes in Engineering Economy, including f and h.

•  We also saw significant improvement for mul?ple ABET outcomes in Probability and Sta?s?cs, including d and e.

Changes in Faculty Perspec?ves

Tamara Moore

Changes in Faculty Perspec?ves

•  Research on 5 faculty at three ins?tu?ons involved in the MEDIA project over 2.5 years

•  Modified Teacher’s Beliefs Interview •  asks questions about the instructor’s

beliefs regarding Learning, Teaching, and Assessment

– Pre-‐survey – Year 1 interview – Year 2 interview

Interviews

•  Pre-‐survey was online •  Interview 1 was performed by an experienced interviewer in all five cases

•  Interview 2 was performed by the same interviewer for Instructors 1, 3, and 4, but was performed by a graduate student interviewer for Instructors 2 and 5.

Analysis

•  Interviews were transcribed and coded statements made by the instructors in one of five categories: –  tradi?onal, instruc?ve, transi?onal, emerging, and reform-‐based

(Luf, Roehrig, Brooks, & Aus?n, 2003)

Frequency of codes

Instructor profiles

•  Instructor 1’s Case: – Believes that MEAs have the poten?al to change the way that engineering students learn to be engineers.

– posi?ve change his beliefs in all three categories: Learning, Teaching, and Assessment.

– has shifed his beliefs toward a student-‐centered perspec?ve.

Instructor Profiles

•  Instructor 2’s Case: – believes that MEAs are just open-‐ended problems, so he thinks that they are not any more beneficial to the students than any other problem.

– These views of MEAs did not allow any change in his beliefs of Teaching, Learning, and Assessment.

– showed no net shif in his beliefs.

Instructor Profiles

•  Instructor 3’s Case: – believes that MEAs are very beneficial for all Learning, Teaching, and Assessment in engineering educa?on

–  interested in the poten?al of MEAs for detec?ng and repairing student misconcep?ons.

– his beliefs have changed from transi?onal to reform-‐based.

– has shifed his beliefs toward a student-‐centered perspec?ve.

Instructor Profiles

•  Instructor 4’s Case: –  believes MEAs are useful for Learning and Teaching, especially valuable as teaching tools.

–  has realized the importance of quality of instruc?on and educa?onal ac?vi?es.

–  realiza?on of the poten?al of MEAs to be powerful teaching tools seems to make a steep posi?ve change in his belief of Teaching that maximizes student learning.

–  his belief is changed from tradi?onal to emerging. –  has shifed his beliefs toward a student-‐centered perspec?ve.

Instructor Profiles

•  Instructor 5’s Case: – believes that MEAs are valuable for Learning, especially the development of collabora?on and wri?ng skills.

– Despite his posi?ve feelings for MEAs and their usefulness, his interviews reported nega?ve changes in all three categories.

– has shifed his beliefs toward a teacher-‐centered perspec?ve.

Conclusions

•  Overall, instructors have shifed their beliefs toward a student-‐centered perspec?ve.

•  Instructor 2 and Instructor 5 (both associate professors) are two cases in which the instructors did not move toward a student-‐centered view. –  Different interviewers for interview 1 and interview 2. –  Instructor 2 was par?cipa?ng because it had been asked of him. This

feeling of being coerced may be a contributor to his lack of change in beliefs.

–  Instructor 5’s interviews focused on very different aspects of teaching and learning. Interview 1 focused on teaching beliefs, interview 2 focused on requirements of his department. Different focus may have played a factor.

Conclusions

•  Instructors 1, 3, and 4 moved toward Student-‐Centered view –  Instructor 4 made the most significant change. He is an assistant professor and his interviews show that working with MEAs has helped him understand that students bring knowledge to the classroom and that he is hoping to capitalize on that prior knowledge in his teaching.

–  Instructors 1 and 3 are each full professors whose commitment to student-‐centered learning was evident even in the first interview, but both aGributed their posi?ve change in beliefs to the use of MEAs in their classrooms.

Understanding Student Perspec?ves

Model-‐Elici2ng Ac2vi2es: A Construct For BeWer

Understanding Student Knowledge and Skills

Tamara Moore, Brian Self, Ron Miller, Margret Hjalmarson, Judi Zawojewski, Barbara Olds, Heidi Diefes-‐Dux, Richard

Lesh

Purpose and Method

•  Paper presents four cases of research on student learning in the case of MEAs

•  Mul?-‐case evalua?ve case study method

•  Accident Reconstruc?on & Wet Suit MEAs –  focus on using pre-‐ post analysis par?cularly using concept inventories.

•  NanoRoughness & NASA Advanced Life Support MEAs –  focus on looking at student responses in depth.

Accident Reconstruc?on

•  This MEA targets the principles of par?cle work-‐energy, impulse momentum, and impact in a sophomore-‐level dynamics class.

•  A major concept that the MEA addresses is that mechanical energy is lost during an impact.

•  The new Traffic Division in Sri Lanka has asked the student teams to develop a set of guidelines and procedures to use at an accident site. –  Provided two different accident cases to guide the students into

crea?ng their ini?al guidelines, then two addi?onal scenarios so that the students can test and refine their procedures.

–  Addi?onally, they are required to make a recommenda?on if the driver should be prosecuted.

Student Survey

Summative results from student responses to a survey

Open-‐Ended Ques?ons

•  What did you like about the Project and why? – Prac?cal applica?on, real world (54), – Group ac?vity (22), – Helped me learn the concepts (16), – Had to make assump?ons (6), – Applied mul?ple concepts (3), – Allowed us to be crea?ve (1), – Focused on process not answers (1).

Open-‐Ended Ques?ons

•  What didn’t you like about the Project and why? – Vagueness of assignment / scenarios (25) – Group difficul?es (including mee?ng ?mes outside of class) (15)

– Wri?ng a memo (8) – Simplifying the procedure to laymen’s terms (6)

– No example answers provided (3)

Dynamics Concept Inventory

•  Par2cipants: 5 sec?ons that u?lized two different MEAs (149 students) & 3 sec?ons that did not (80 students) – sec?ons were taught by different instructors

•  Normalized gain: – MEA = 29.6 / non-‐MEA = 21.1

•  Only impact DCI ques2ons – MEA = 41.1% / non-‐MEA = 14.8%

NanoRoughness MEA

•  Context -‐ Liguore Laboratories – Develops nanostructured materials that improve performance and extend the life of coated orthopedic and biomedical implants

– Currently manufactures gold to coat artery stents

– Wants to develop diamond coa?ngs for hip joints

– Needs a method to measure roughness on the nanoscale

NanoRoughness MEA

AFM images provide information about surface topology at nanoscale

NanoRoughness MEA

Propose a procedure to measure roughness using ONLY the hardcopy of the images

Demonstrate on 3 AFM images

List informa?on needed to improve procedure

Team Activity:

Research Ques?ons

•  What were students’ ways of thinking about measuring and quan?fying variability?

•  What sta?s?cal measures did students use as part of their procedures?

Par?cipants & Context

•  1478 first-‐year engineering students enrolled in an introductory engineering tools course (e.g., MatLab, Excel)

•  Students worked in teams of 3

•  35 teams were selected for the study from mul?ple sec?ons of the course

Typical Student Solu?ons

•  Sampling procedure (e.g., random points or lines)

•  Iden?fied a measure of central tendency (e.g., mean or median)

•  Iden?fied method for quan?fying variability (e.g., standard devia?on, range, average heights and depths of peaks and valleys)

Sampling from an Image

•  Since the data (the image) was a con?nuous surface, it was not clear what the popula?on was from which to sample (e.g., the whole image or just the peaks)

•  Students needed to define a process for sampling that would be random and representa?ve of the objects they considered relevant for measuring roughness

Sampling

•  Students understood need for random sample •  No ra?onale for number of data points

•  Random lines and points from those lines common method for engineers

•  Some came close to “real” solu?ons

Descrip?ve Sta?s?cs

•  Mean (22) and Standard Devia?on (23) most common

•  Some used median, mode, range, min, max, ?e breakers common

•  Complexity of task is not in calcula?ng the sta?s?c, but in deciding what to calculate and how to interpret findings in context – Does a rougher surface have more peaks, many peaks of similar height, or greater varia?on in a few peaks?

Lessons Learned

•  Instructors should use MEAs as up front inves?ga?ve tools to pull out prior knowledge and areas of struggle

•  Thought-‐revealing means we can use them as forma?ve assessments. –  Interpret evidence of student understanding – Use informa?on to provide feedback – Promotes shared understanding and ownership

Results to date

modelsandmodeling.net

Cal Poly Physical -‐ MEAs

Transducer Design MEA

-‐ Sizing program

-‐ Build the transducer

-‐ 400 level class

Sizing the Transducer •  Spreadsheet created to size the transducer based on the force applied

•  Dimensions are varied at each force level un?l the strain is large enough for reliable measurement (1000-‐1500µε)

Known Input Dimensions Stress Strain

Force [lbf] E [psi] Radius [in] Thickness [in] Width [in] Outside [psi] Inside [psi] Outside [micro] Inside [micro]

5 1.00E+07 2.00 0.0625 0.75 -‐3667.7 3774.3 -‐366.8 377.4

15 1.00E+07 2.00 0.0625 0.75 -‐11003.0 11323.0 -‐1100.3 1132.3

25 1.00E+07 2.00 0.0625 0.75 -‐18338.4 18871.7 -‐1833.8 1887.2

35 1.00E+07 2.00 0.0625 0.75 -‐25673.8 26420.4 -‐2567.4 2642.0

45 1.00E+07 2.00 0.0625 0.75 -‐33009.1 33969.1 -‐3300.9 3396.9

55 1.00E+07 2.00 0.0625 0.75 -‐40344.5 41517.8 -‐4034.4 4151.8

65 1.00E+07 2.00 0.0625 0.75 -‐47679.8 49066.5 -‐4768.0 4906.7

75 1.00E+07 2.00 0.0625 0.75 -‐55015.2 56615.2 -‐5501.5 5661.5

85 1.00E+07 2.00 0.0625 0.75 -‐62350.6 64163.9 -‐6235.1 6416.4

95 1.00E+07 2.00 0.0625 0.75 -‐69685.9 71712.6 -‐6968.6 7171.3

105 1.00E+07 2.00 0.0625 0.75 -‐77021.3 79261.3 -‐7702.1 7926.1

Our Transducer and Wiring •  Four gages across middle sec?on of ring

•  Outside/inside gages wired in opposite sides of bridge

•  Axial strains cancel, bending strains mul?ply by 4 to give high sensi?vity

1 2 4 3

F

F

Some Different Designs

Catapult MEA •  Historical reenactment

– Peterborough Museum in England

– Compe22on for 6th form students

•  Instruc2ons for students to predict how far their catapults will fire

•  Self assessment – launch raw eggs using scaled down catapults

Catapult Measurement Day

Catapult Launch Day

Electricity Rebate MEA •  Develop financial incen2ves to make homes more efficient

•  Use electricity meter, your bill, and the Kill A WaW meter

•  Develop rebate program

Traffic Controller MEA

•  Electrical and Computer Engineering •  Context: Team works for rural county’s traffic opera?ons

•  Develop general procedure to design an effec?ve traffic signal system for an intersec?on of a 4-‐lane hwy & 2-‐lane county road

Traffic Controller MEA

Model includes: •  pre-‐?med vs. semi-‐actuated controllers •  where and in what situa?ons do they place sensors

•  how to develop the logic circuit for each situa?on

Concepts Targeted: •  logic design skills with digital circuits; state diagrams

Student Created State Diagram

Thank You!

Modelsandmodeling.net Ques?ons

?

E-‐MEAs

The SUV Roll-‐over E-‐MEA:

A major insurance carrier has no?ced a rela?vely large number of claims involving SUVs that have rolled over following ?re tread separa?on. The carrier contacts an engineering firm to design a series of poten?ally destruc?ve tests on combina?ons of vehicles and ?res to iden?fy poten?al problems with either vehicle or ?re models under various environmental condi?ons. Students are given costs for conduc?ng the experiment, a budget, and asked to provide an experimental design; i.e., the vehicle –?re combina?on to test. A simulator is used to provide each team with a set of test results for its design so that a sta?s?cal analysis can be performed.

Se`ng the ethical dilemma:

•  On a more personal level, because of the sensi?vity of this informa?on, I am also concerned about our obliga?ons given certain findings, even though CWI has requested that we give the results only to them. Consequently, please provide me in a separate memorandum your professional opinion concerning what we should do with this informa?on if the results do point to par?cular companies.

Example Response: Team B:

We understand that this is a very serious issue for you because CWI has requested that the results be given only to them and that for obvious reasons they have interests in keeping this informa&on concealed from the public. You have a duty to CWI because they paid you to conduct this study, but you also have a duty to the public based on fundamental ethical principles. Before giving the results to CWI, make a copy of them to save in your files. Ask CWI if they would be able to have a mee&ng in which the informa&on is exchanged, and tell them your concerns regarding the danger of Stonehead Tires. If they do not volunteer to take any direct ac&on with the findings of that have been presented to them, or if they suggest ac&ng unethically and keeping the informa&on private, then we feel it is your professional responsibility to bring the ma;er to the a;en<on of an authorita<ve motor vehicle establishment (such as the American Associa&on of Motor Vehicle Administrators

SpecialSession:NextGenera2on ProblemSolving 2010!ASEE!Annual!Conference! Louisville,KY June22,2010...

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