Can technology really improve teaching introductory physics?

Technologyfor Pedagogy

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Can technology really improveteaching introductory physics?

Joel A. [email protected]

Rutgers University

February 27, 2008, Physics Colloquium at Rutgers


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Structure of this TalkThe Need for ChangePedagogic Needs

LecturesTextbookHomeworkExams

Current Pedagogical Uses of TechnologyClickersCourse Management SystemExamsHomework Systems

Tutorial SystemsWhat that meansAndesSystem ComponentsWhat I want

Summary


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Problems with our intro courses

I PER claims - need for active intellectual involvementof students.

I our dissatisfaction with what they learnI one term later they remember nothingI low numbers of students take physics voluntarily


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The Large LectureRutgers’ Physics Lecture Hall


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I Here is where we expound on the fundamentals ofphysics!

I But the students aren’t thinking about what I amsaying!

I And their attention is wandering.I And they don’t even come any more!


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I And their attention is wandering.

I And they don’t even come any more!


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Getting them active

How to get students actively intellectually involved inthinking about the fundamental ideas?

The answer is wellknown:


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Getting them active

How to get students actively intellectually involved inthinking about the fundamental ideas?

The answer is wellknown:


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Human tutoring (Socratic method)

Expert human tutoring has been shown to raiseperformance by two standard deviations,i. e. 16th percentile −→ 84th percentile,

low C −→ B+.

No other added teaching component comes close.


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The textbook

Fundamental ideas aren’t easily absorbed. How do textsaddress this? Chapter 8 of Sears and Zemansky (nowYoung and Freedman)

First Edition 12th EditionMomentum,

Title Impulse and Impulse andMomentum Collisions

Size of 6′′ × 812

′′83

4

′′ × 1034

′′

page (51 in2) (94 in2)Number of pages 11 (561 in2) 27 (2538 in2)

Ratio examplesexposition 0.45 0.96

26 discussion Q’sEnd of Chapter 19 problems 112 exercises

4 challenge P’s


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Textbook changes (cont.)

I haven’t quantified theI “Learning Goals”I “test your understandings”I “problem-solving strategies”I “Activ Physics” links,I pictures of football players and other “relevant”

irrelevancieswhich, of course, occur only in the 12th edition.

Does any of this work? I doubt it!


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I too much plug-and-chug (single formula problems)I too much “just like the example” problemsI students give up on challenging problemsI too much grading for instructorsI painful keeping track of grades


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I grading written (open-ended) problems too muchwork, consistency difficult.

I computer-graded easy and objective, but:I validity: written vs. computer-graded ?I if computer graded: True/False, MC, or numerical

answer?


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How can technology help?Biggest improvements from technology:

I stick and sand (Archimedes, 287-212 BC)I Gutenburg (1455)

I blackboards (not Blackboard) (1801)


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How can technology help?Biggest improvements from technology:

I stick and sand (Archimedes, 287-212 BC)I Gutenburg (1455)

I blackboards (not Blackboard) (1801)


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Technology that can be used today

I Presentation: Web, PowerPoint, computer demos, ...I Simulations.I Computer interface in labs, demos

I am not going to talk about the above — I just don’tknow very much about them.Uses I will talk about

I ClickersI Course Management SystemsI ExamsI Homework SystemsI Tutorial Systems


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Clickers can help!

Now we talk about clickers!Uses:

I Improve attendanceI promote active participationI promote interactionI give reading quiz at beginning of lectureI real quizzes (dubious, I think)I tells teacher if he needs to discuss something further.


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Some Clicker Systems

I Littauer: Built a five-button system at Cornell 1972from discarded HEX equipment. Pushing a buttondischarged a capacitor to the appropriate chargecounter!

I SRS: A system I built at Rutgers

My keypad Computer screen after(normally in arm-rest) double session


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Commercial Clickers

PRS iclicker Turning Pointfrom GTCO CalComp Response Card

eInstruction Meridia h-itt TI-84+CPS IR and RF Calculator


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Clicker issues

I hardwired, IR or RF?I Hardwired not available commercially, takes lots of

work. But provides seat info.I IR came first, but student clicks can interfere, doesn’t

work reliably enough for grading in a large class.I RF seems completely reliable

I feedback: none, few LEDs, or screen?I Students don’t trust their answer has been received

without feedback. Some systems show student ID onprojector, but that doesn’t work well in a large class

I Even one LED is enough to show response received.But this requires transmitter to receive info.

I A multicharacter screen is enough for sophisticatedinteraction, but I don’t know anyone who makes useof this.


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Course Management Systems

I Facilitates web posting (for novices)I provides restrictive accessI provides discussion boards, chat roomsI provides a gradebook

I for your recordsI with student access to his/her own gradesI Some systems:

I BlackBoardI WebCTI SakaiI MoodleI Lon-Capa

I provides some homework grading / quiz facilities


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Exams

Most of us give computer-graded exams. In ourdepartment, we have a homemade system (grtex) which

I facilitates making up exams, with scrambling ofanswers and/or questions

I in LATEX!I I have been collecting such questions for yearsI We have the ability to give numerical answer

questions!


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A LATEXquestion

1. The figure shows the electric field lines due to two charged parallel metalplates. We conclude that:

a. the upper plate is positiveand the lower plate is neg-ative.

b. a positive charge at X wouldexperience the same force ifit were placed at Y.

y z

x

metal

plates up

c. a positive charge at X experiences a greater force than if it wereplaced at Z.

d. a positive charge at X experiences less force than if it were placedat Z.

e. a negative charge at X could have its weight balanced by the elec-trical force.

1

This question shows how flexibly figures can be included.Even when answers are permutted, the wrapping aroundthe figure will work okay.


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Answers on the Figures

23. You also might want to have thefigure on the right of the question,with the answers (a)—(e) appear-ing on the figure, as with mvaquest.This question is of that type. Notethat the placement adjusted for onetype is unlikely to work for the other.Note also that this format requiresa width as well as the file namefor the figure. This question endedwith \lmvaquest{2in}{mvapix.eps}

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24. Here are the rules for the format of the exam so that GRTEXwill be able to do what it has to. Note they still permit immenseflexibility

a) The file begins with a latex header. This should include allthe material needed to set things up, which does not needto be repeated for each version. It needs to be ended witha line that says exactly%%End of header

b) Next should follow all the material before the questions,which is to be repeated on each version of the exam. It mustnot have the command \setup in it starting in column 1or 2.

c) Then follows any number of questions, separated by blanklines, each beginning with \setup, followed by exactly eightarguments, then followed by a question formatting macro\???quest, followed by the correct number of argumentsfor that style question.

d) After all the questions follows any material which shouldfollow the questions on each version.

e) Finally, the file ends with

{ \bye for TEX

\end{document} for LATEX

25. There are other possible styles which should probably be devel-oped.

a) You could design additions to exammac.tex.b) You could find a student to do it for you.c) You could make do with the styles I’ve provided.d) You can include the picture directly in the question text.

Note that the answers can also have figures included. Thesewill move with the answer when permutted.

e) You could give a clear description of the required style anda convincing argument for why I should spend the timecreating it.

26. For a certain charge distribution, the potential as a function of ris given by

V (r) =Q(3R − r)

8πε0Rfor r < R.

(The quantities Q, R, and e) are all constants). Then the electricfield as a function of r (for r < R) is

a) [+Q/4πε0r2]r̂

b) [−Q/4πε0r2]r̂

c) [−Q(3R2 − 2r)/8πε0R3]r̂

d) [−Qr/4πε0R3]r̂

e) [+Qr/4πε0R3]r̂

27. A semi-infinite line charge of uniform density λ lies along thenegative x-axis from x = 0 to x = −∞. The magnitude of theelectric field at any point x on the positive x-axis is 1/4πε0 times

a. λ/x

b. λ/x2

c. 2λ/x

d. λ/2x

λy

xx

e. None of the other answers

Here the five choices are shown on the figure, and arepermuted in different exam versions.


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Numerical Answer Exam Questions

Need a special answer form:


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One Numerical Question

What is the chargeof an electron?

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E- 1 .6 0 1 90

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Are Computer-Graded Exams Good?

Computer-graded exams areI much less painful to grade!I objective and consistent gradingI Can they test deep understanding as well as

open-ended written exams?I Questions must be more carefully written, clear and

unambiguous, with well thought-out distractorsI Some studies show that they can grade as accurately

as written examsI But possibly they fail to encourage deep-thinking

studying. I don’t really know.


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Homework Systems

Without computers, most homework in large intro coursesgoes ungraded. Not good for feedback or for motivation.So computer systems came into existence.Non-science courses use MC or precisely specified shortanswers. Not good enough for us. For physics:

I Homework Service (Univ. of Texas at Austin)I CyberProf (Univ. of Illinois Urbana-Champaign)I WebAssign (evolved from North Carolina)I Mastering Physics (evolved from MIT)I Capa (Michigan State U)I WebWork (mostly for math)


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Commercial vs. Open-source

I Commercial advantages/disadvantagesI Excellent technical supportI Publishers support extensively with their problemsI Cost: Uncontrolled! Webassign cost $8.50/stud-sem

in fall 2002, $32.00/stud-sem now, for Wileyproblems, unless purchased with new textbook.

I Open-SourceI less well supported with publisher’s problemsI need to run your own serverI less polished CMS and ease of useI minimal tech support

Both systems allow teachers to write their own questions,but none of us at Rutgers does.


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Why what we have is not enough

Current homework and exam systems ask the students topresent a single well-defined answer, quantitative or asymbolic expression, rather than present a full“show-your-work” solution.

My students get 95% on the WebAssign homework but60% when asked simpler questions on the exam.

Old fashioned human grading of homework and examscould tutor on the ideas as well as the answer.


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What I would like

A computer-based “intelligent tutoringsystem” (ITS)

I present a complex problem to studentI understand student input including drawings, sets of

equations, numerical quantities (with units).I give feedback on

I correctness of entriesI explanation of what is wrong with entriesI hints for making further progressI possibly summary of solution

I Pipe-dream? Natural language dialog with students.


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Is this possible?

We won’t get there by adding hints for each problem (asdone in the tutorial problems in Mastering Physics)

Sporadic efforts have been made: Plato, Andes

Such a system for high school algebra is rather successful,commercialized and used in many high-schools (fromCarnegie-Learning)

I believe Andes goes a good way towards developing auseful system, but is not really all there. Can it get there?


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View of Andes

Opening problem presentation


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Progress in Andes

Andes in mid-solution


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What does such a system need

I to understand the physicsI a problem specification language that it can

understandI the ability to solve the problem, in all possible waysI the ability to match what the student inputs to

features of a solutionI a model of what the student already understands

about the problemI the ability to match wrong entries to some

remediationI the ability to provide “what’s next” help on requestI (hopefully) a model of what physics the student

knows how to use.


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Needed components:1. A user interface

I displaying text and graphics, including the problemstatement

I accepting input in the form ofI at least vectors and dots, maybe line segments, arcs,

etc.I text: for variable names, properties, student turns in

dialog.I equations (in symbolic form, with greek, exponents,

subscripts, numbers with units, etc.)I help requests.

I display typeset-quality equations, summary of what’sbeen done (variables defined, vectors drawn, etc)

I engaging in typed dialog with the student.Depending on how much natural language recognition itcan handle, student input might be largely by pulldownmenus and multiple choice.


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2. A problem solver

Current homework systems do not understand anyphysics. The author writes the problem in a form thatshould be clear to the student, and gives the answer in aform the computer can compare to the student’s answer.Maybe he gives specific wrong answers and accompanyinghints. But complex problem solving does not consist of awell defined sequence of identifyable answers. The ITSneeds

I production rules for making conclusions underappropriate conditions. These are physics principlesand techniques for applying them

I a store of known conditions for the given problemI the ability to know when all possible conclusions have

been drawn, and when the problem has been solved.Does this sound far-fetched? In fact, the strongest part ofAndes is its ability to solve problems, given only a formalpresentation of the problem.


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The help system

The help system controls the interaction with the student.The problem solver provides it with solution paths,including correct equations with their justifications, andlist of variables involved in the problem.

The help system needs to judge whether student entriesare correct or not. For equations, a correct entry need notbe among the list the problem solving component haspresented, the canonical equations. But it should bederivable from these. A student equation could be judgedcorrect

I if it is derivable from the canonical equations.I if it is correct on the set of solutions to the canonical

equations.The second is much easier to check, especially onproblems where that solution is a point with numericalcoordinates in the space of all the variables. And it isequivalent to the first.

What does a correct equation tell us about what thestudent has understood and applied?

What about wrong equations? Can the system determinewhat the student was trying to do, and what he didwrong?

I left out a term?I wrong projection for component of a vector?I wrong concept?


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The algebra system

I Solves a system of equations.I Checks the correctness of an equation.I Determines whether a given equation is independent

of a set of other equations. NeededI by the problem-solver to determine if a new

production has supplied new information.I by the help system to determine which canonical

equations a student equation entry entails.

The Andes tutor uses the solver not only to find thesolution (which is needed to check the correctness ofstudent equations) but also to provide a solving tool forthe students. USNA professors offer the students thissolving tool so they will focus on getting the basicequations, not on the algebraic manipulations on theseequations to get the final answer.


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The student model system

Ideally the tutor would have a model of all the knowledgeand abilities we want the student to learn, and keep arecord of how well each student has learned them, basedon the performance on all the problems he has worked on.Even listing all such knowledge is a long way off, andusing performance to accurately judge how well thestudent possesses this knowledge is another very longrange problem.


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What I would like to see happen

As I have mentioned, Andes is a step in the rightdirection. However

I It originally only ran on the student’s identical PC,not on the web.

I It has been partially web-ized, but needs to be donemore completely.

I Currently has built in some onerous pedagogicrequirements. In particular, every variable needs tobe explicitly and exhaustively defined by the student,which may be useful at the beginning but becomesquite painful with experience.

I The help system needs a lot of improvement in betterrecognition of wrong equations, better what’s nexthinting, etc.

I it is being used at USNA, St. Anselm College, andby Sophia Gershman in Honors Physics at WatchungHills Regional High School.


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My Group

Other than the year I spent with the Andes group,headed by Kurt VanLehn, at the Learning Research andDevelopment Center, University of Pittsburgh,My work has been done jointly with

I Donald E. Smith, Computer Science, RutgersI Chun-Wai Liew, Computer Science, Lafayette College

This is the Watchung Group.

We have concentrated at removing the requirement forthe student to define each variable. Can a tutor knowwhat the student equations refer to when the studentchooses his own variable names and doesn’t declare whatthey represent? Most of the time, yes!


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What is to be done

Progress has been disappointing. Why?I Simple systems can be created by a few people in a

short time, tempting not to embark on a veryambitious system. Look at all the simulationpackages! At the early Homework Systems!

I The Artificial Intelligence (AI) community is moreinterested in systems of general applicability, i.e. noalgebra! And they are fascinated with naturallanguage.

I Many journals insist all developments bepedagogically tested for publication. This makesdevelopment of components difficult.

I Ditto for grant agencies. If you can’t develop aworking system in three years, they are notinterested. Andes has been in development for morethan a decade!


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What can we do?

I would like to see people work on components, much theway the Open-Software community has built Linux

I Someone should build an expression/equation slot,with robust ability to accept equations both in latexstyle and in Word style, or other reasonable form, andparse them and present them back in typeset (TEX)form, with facility for editing. And with units!

I Someone should work on a graphics buffer good fordrawing free body diagrams and other diagrams ofthe kind we would like to see students draw.

I Someone should design an API for an interface,including the above components and the others Imentioned earlier, that could be united with a helpsystem like Andes’.

(cont.)


Shapiro

Intro

Needs

Lectures

Textbook

Homework

Exams

Current Tech

Clickers

CMS

Exams

HW Systems

TutorialSystems

What thatmeans

Andes

SystemComponents

What I want

Summary

I Someone should work on a more robust knowledgerepresentation than what Andes has, although Andesis pretty advanced. Should it use real vectors (withvector equations, not just components)? Does it needvariable functions (x(t))?

I My group has been working on variable recognitionwithout explicit declaration. A major problem withAndes is how long it takes to do a problem becauseof this excessively demanding scaffolding. We havebeen reasonably successful, but have no way oftesting our methods on real students.


Shapiro

Intro

Needs

Lectures

Textbook

Homework

Exams

Current Tech

Clickers

CMS

Exams

HW Systems

TutorialSystems

What thatmeans

Andes

SystemComponents

What I want

Summary

References

If you go to my Home Pagehttp://www.physics.rutgers.edu/∼shapiro/, andlook under “Technology and Physics Teaching”, you canfind this talk, including a reference page. You can alsofind links to Andes, to my homemade clicker system(SRS), and to the Watchung Group home page, to ourhomemade exam system, and a few other things.

Warning: many of these pages are very obsolete(particularly the SRS).


Shapiro

Intro

Needs

Lectures

Textbook

Homework

Exams

Current Tech

Clickers

CMS

Exams

HW Systems

TutorialSystems

What thatmeans

Andes

SystemComponents

What I want

Summary

I am not a plagiarist

I Sleeping student image courtesy ofhttp://www.DailyClipArt.net

I School of Athens, by Raphaelhttp://www.odu.edu/∼mcarhart/hist102/slides/

athens school.htm

I Gutenburg bible page fromhttp://commons.wikimedia.org/wiki/

Image:Gutenberg detail.jpg

I clicker pictures of PRS and Turning Point from theirsales literature


Shapiro

Intro

Needs

Lectures

Textbook

Homework

Exams

Current Tech

Clickers

CMS

Exams

HW Systems

TutorialSystems

What thatmeans

Andes

SystemComponents

What I want

Summary

Summary

In this talk, I haveI explained why improvements need to be made in our

teaching of introductory physicsI told you some of the technological aids you could use

nowI told you what I think an intelligent tutor might do in

the future, and how it would need to function.I encouraged you to jump in. But I am not responsible

for the results!Thank you for your attention. Perhaps one of you wouldlike to work on inventing a piece of my dream system.

Documents

Can technology really improve teaching introductory physics?