http://jpe.sagepub.com/Journal of Planning Education and Research

http://jpe.sagepub.com/content/6/1/30The online version of this article can be found at:

 DOI: 10.1177/0739456X8600600106

1986 6: 30Journal of Planning Education and ResearchJ. Mark Davidson

Quantitative Reasoning in the Planning Curriculum  

Published by:

http://www.sagepublications.com

On behalf of: 

  Association of Collegiate Schools of Planning

can be found at:Journal of Planning Education and ResearchAdditional services and information for    

  http://jpe.sagepub.com/cgi/alertsEmail Alerts:

 

http://jpe.sagepub.com/subscriptionsSubscriptions:  

http://www.sagepub.com/journalsReprints.navReprints:  

http://www.sagepub.com/journalsPermissions.navPermissions:  

What is This? 

- Oct 1, 1986Version of Record >>

at UNIV NEBRASKA LIBRARIES on November 6, 2014jpe.sagepub.comDownloaded from at UNIV NEBRASKA LIBRARIES on November 6, 2014jpe.sagepub.comDownloaded from

30

Quantitative Reasoning in the PlanningCurriculum

J Mark Davidson SchusterMassachussets Institute of Technology

~ Abstract

Four goals and five course principles arearticulated for a process of turning statisticscourses into quantitative reasoningcourses.

Introdution

I have recently finished reading GarretHardin’s new book Ftlters Agamst FollyHow to Survlve Despite Ecologlsts, and theMerely Eloquent, in which he makes hisplea for an improved education for policymakers and analysts That educationwould be constructed around three filtershe identities as being critical to an informedunderstanding of policy and planningproblems the literate filter, the numeratefilter, and the &dquo;ecolate&dquo; filter The first twodeal, respectively, with an ability toformulate and understand events in writtenterms and in quantitative terms and thethird with an understanding of theinterrelationships among events inecological terms Hardin’s analysis of anumber of recent public policy controversiesleads him to the conclusion that much ofthe needless debate surrounding theseissues has come from an inability of theactors in each controversy to filter therelevant information inherent in the

controversy through all the filters, a self-imposed myopia that comes from onlyapplying one or at most two of the filtersand failing to apply all three Hardin’s

prescription is significant m that heconcludes we need new ways to thinkabout problems rather than new technicalskills not yet invented

I have thought a lot about Hardin’s model asI have reviewed our experience with corecurriculum reform m the Department ofUrban Studies and Planning at M IT, and Ihave come to the conclusion that, to asurprising degree, the core curriculumwhich has evolved at M I T in the last fouror five years is m harmony with Hardin’sprinciples The current core planningcurriculum at M I T is fundamentally aconceptual core focussed on presentingand reflecting on ways of knowing inplanning practice

Following Hardin’s lead, the core can beseen as being organized around five filters~ A Historical Filter What about planning

practice do we understand better whenwe view it in the context of its historicalevolution?

~ An Institutional Filter What about

planning practice do we understandbetter when we view it in the context ofthe institutional arrangements in which itis embedded?

~ A Political/ Economic Filter What about

planning practice do we understandbetter when we view it in the context ofthe politicalleconomic system m which itoperates?

~ A Quantitative Argument Filter Whatabout planning practice do weunderstand better when we view it interms of how it incorporates research,marshalls evidence, and makes policyprescriptions?

~ A Literate Filter What about planningpractice do we understand better whenwe reflect on it through oral and writtencommunication?

The first two and parts of the third andfourth would correspond to Hardin’s&dquo;ecolate&dquo; filter, other parts of the third andfourth would correspond to the numeratefilter, and the fifth is identical

Incorporating these ways of knowing, theseknowledge filters, into a set of courses isfull of pitfalls While it is tempting to createa one-to-one correspondence betweencourses and filters, we have found that theartificial separation of these issues has aserious cost in lost coherence and

meaning Students are extremelyconscious of an artificial separation and areskeptical about the implicit message thatthe choice of knowledge filter is like thechoice of which clothes to wear today, inthat you wear only one outfit at a time Wehave come to the conclusion that our

teaching must encourage the application ofmultiple perspectives not only in theaggregate across the curriculum, but asmuch as possible within individual courses

The MCP core curriculum at MIT includesfive elements These are~ A course on Institutional Processes and

Planning~ A course on Political Economy for

Planning~ A course in Quantitative Reasoning and

Statistical Methods for Planners. A Core Practicum~ A wnting diagnostic and support

program that operates in parallel, and inclose coordination, with the coursework

Though it is my intent to focus onQuantitative Reasomng (&dquo;QR&dquo;) in thispaper, this particular course cannot be fullyunderstood or appreciated independentlyfrom the context I have suggested above Itis a course that is offered within an

integrated core curriculum and that isinformed by, and in turn informs, the otheractmties m that curriculum through bothconscious design and serendipity

at UNIV NEBRASKA LIBRARIES on November 6, 2014jpe.sagepub.comDownloaded from

31

Goals

When we set out to redesign the coreofferings four or five years ago, there wasno shortage of student (or faculty) critiquesof earlier attempts, particularly with thevarious versions of statistics/quantitativemethods we had attempted The coursewas too fast, the course was too slow Thecourse included too much, the courseincluded too little The course was tooabstract The course was too a-contextual(urns with red balls and blue balls) Thecourse was too hard The course was too

poorly taught The course had too little tooffer to urban designers, or to transportationplanners, or to (fill in the blank)We had collected a lot of information aboutwhat we shouldn’t be doing, with littleguidance as to what we should be doing

Gradually, as a group of faculty membersformed around the task of redefining theentire MCP core, four goals emerged forthe design of the &dquo;quantitative&dquo; portion ofthe core

Goal #1 Develop the students’ &dquo;numberssense

&dquo;

When we began the task of redesigning thecore curriculum, we asked facultymembers and students what they thoughtthe content of the &dquo;quantitative&dquo; courseshould emphasize The phrase &dquo;numberssense&dquo; kept popping up in discussions, andit soon became the touchstone for judgingeach proposed element of the course Wecame to believe the most important goal ofthe new course should be to give thestudents a sense of ease and facility withquantitative data and of the use of thosedata in making persuasive, coherentarguments We would emphasizequestions such as: Is a particular piece ofquantitative information large or small?Unusual or typical? Suspicious? Is itmasked or confused by something else thatis going on simultaneously? How much is itdetermined by the definitions andassumptions embedded in the analysis? Isit relevant to the problem at hand?

This goal was extremely important mshaping the structure of the coursebecause it moved us quickly away fromtraditional statistics, narrowly defined

While I have been unable to find any textsor other primary materials that directlyaddress the question of teaching numberssense and have found that somewhat

frustrating,2 another part of me rejoices thatthat is true, because it means that everyday I have to be on my toes in my teachingto make sure I remember the importance ofthis goal I can’t rely on the subsidiarymaterials to do it for me, I have to do itmyself in lecture, in discussion, and in thedesign of homework exercises and exams

Goal #2 Develop the students’ ability toformulate and substantiate well-thought-out quantitatme arguments

The focus should be on quantitativetechniques m use. It is not enough to teachthe correct calculation of statistical results,that’s a fairly uninteresting endeavor, to thestudents as well as to the faculty. Theemphasis must be on developing positionson issues, on struggling with the questionson what one does with quantitative results,a question about which most statisticstexts (and most quantitative methods texts)have nothing to say.

There are a number of very useful materialsfor teaching and studying the developmentof policy arguments.3 We are notconstrained by their absence We areconstrained by our reluctance to letanything distract us from what has beendrummed into us as the central mission ofsuch a course teaching technique.

We also, of course, have to pay attention toteaching the particular type of quantitativeargument at the heart of statisticalhypothesis testing This is one of the mostproblematic areas in statistics for students,because we ask them to structure their

thought processes in ways that are newand that may be uncomfortable to them

Using statistical hypothesis testing toestablish whether or not discriminationexists, for example, requires the temporary

acceptance of a null hypothesis of nodiscrimination. To many of our studentswho take the issue of discrimination veryseriously and who are convinced thatdiscrimination is ever-present, evenadmitting the possibility that nodiscrimination exists for the sake of

developing a statistical argument isobjectionable. A statistical test fordiscrimination, particularly one that startswith the assumption of no discrimination(and which you may end up not rejectingincorrectly), is unnecessary when you arequite sure from the outset there isdiscrimination. At the very least, ourteaching has to set this type of statisticalargument in the context of ways ofpresenting and arguing one’s position

Goal #3 Develop an ability to use a range ofquantitative/statistical techniques

I have chosen to list this goal third becauseit is all too tempting to let it float to the topof this list and become the tail that wags the

dog, as it has been in our teaching for somany years It is seductive, to both thestudent and the professor, to focus solelyon quantitative techniques. There are well-developed pedagogical models for teachingthe material There are clear criteria tojudge how well you have done (Is theanswer right or wrong?) And you leave withthe feeling that you have learned somethingof substance. At the end of the semester astime becomes short, we all have beentempted to get the last five formulas on theboard so that we can say we have &dquo;coveredthe matenal,&dquo; we have survived to the end

But I want to argue that that sense of

completeness is illusory If the connectionsto planning practice haven’t been made andif the student has not been forced toconfront the question of once you have theanswer calculated correctly, what do youdo as a result, then we have taught thestudent something about technique but notmuch about planning

at UNIV NEBRASKA LIBRARIES on November 6, 2014jpe.sagepub.comDownloaded from

32

Goal #4. Develop a critical perspective onquantitative technique.

A corollary to the first three goals, but onewhich deserves to be emphasizedseparately, is the development of a criticalperspective among our students is a

particular approach appropriate orinnappropriate to a given problem? Indeveloping a method to address a particulartype of problem, decisions are made as towhat should be accounted for in themethod and what can be left out. In manycases this may make a previouslyintractable problem &dquo;soluble,&dquo; but doesthat happen at the risk of transforming itinto a different problem? The match oftechnique to problem should be particularlyclearly spelled out in considering thequantitative activities of counting, ordering,and measuring, each of which haveimposed their own restrictions ontechnique An understanding of thedistinction between nominal, ordinal, andmetric data is critical m planning where sofew of our problems lend themselves tomeasurement and to manipulation by themore commonly taught and morequantitative (&dquo;higher level&dquo;) statisticaltechniques 4

A critical literature is developing, and thereare a number of sources that can be

particularly useful in planning courses,5though there is still a huge need for inquiryin this area

Principles for Course Design

Though all of us might find these goalsunobjectionable, when we have to makedecisions concerning the allocation of timewithin the context of a course, we begin toweigh them against one another searchingfor an acceptable compromise. Perhapsone cannot do them all, at least with equaljustice. So the problem becomes how toavoid letting micro-compromises lead to asituation in which the third goal reemergesas the only goal. To help me deal with thistemptation, I have formulated a series ofcourse design principles that I use to helpremind me of what is desirable and

possible.

Principle #1 Make the genenc activities inwhich planners engage with quantitativeinformation as visible as possible m boththe structure and content of the course

When I actually sat down to redesign ourcore course, the first exercise I went

through was to take a look at the statisticstexts we had used in earlier versions of thecourses and ask the question What are the

generic activities in which planners engagethat are represented here? The answerswere not terribly surprising, but yet theywere very suggestive of what we ought tobe doing.

The matenal in these texts encompassedfour generic activities~ Description~ Estimation~ Comparison~ Explanation

When the content of a statistics text isviewed in this way, it highlights rather thanobscures the links to planning practiceMoreover, seeing this list in this way makesit absolutely clear that statistical techniquesare distinct subsets of each of theseactivities (a point to which I return below)We have turned the traditional statistics textinside out, exposed its spine, and madethat the central organizing principle of thecourse. It is very useful to have each ofthese themes clearly established becausecollectively, they offer a roadmap to whichwe can constantly refer as we move

throughout the material. The intent of thevarious segments of the course and theirinterrelationships become very clear

I do not pretend that this list is exhaustiveIn a two semester sequence, for example,you would want to expand it to includePREDICTION and MODELLING as genericactivities in planning.

Principle #2. Expand the coverage in eachof these topic areas to go beyond thetraditional statistical topics that fall underthe rubric fo each one (or, resist falling intothe trap of teaching statistics)

Once these generic activities have been

clearly established as the structure of thecourse, you are forced to recognize thatstatistics helps you with only a small subsetof tasks within each of these genericactivities And this, in turn, forces you toask the question In which ways is thisactivity manifested in planning practice? Inour teaching we need to set &dquo;statistics&dquo; inthe context of &dquo;ways of doing withnumbers.&dquo;

Consider estimation In my course this is

probably the most fully developed exampleof this broader, contextual approach. Theclassic statistical estimation problem is theestimation of a population parameter froma sample statistic While this procedure iscertainly useful in planning and deserves tobe taught, it is clearly not the only type ofestimation planners do, nor perhaps is itthe most common type of estimationPlanners need to be able to guessintelligently, often using small back-of-the-envelope models We need to estimate formissing data; we need to calculate orders-of-magnitude to see if what we are doingmakes sense.These are critical skills that areignored in the standard statistics syllagus

In my course, when I turn our attentionfrom description to estimation, I begin myfirst estimation lecture with a short in-classexercise. I put four or five questions on theboard and give the students 10 or 15minutes to come up with (to estimate or

guess) answers to these questions For

example How many people were killed inhighway traffic accidents in Massachusettsin 1984? Given 1970 and 1980 census dataon the number of Hispanics in a particular

at UNIV NEBRASKA LIBRARIES on November 6, 2014jpe.sagepub.comDownloaded from

33

area, what would you predict thepopulation will be in 1990? How much tax-exempt land does M I T. own inCambridge? You can choose a variety ofquestions to capture the variety ofestimation problems faced by planners Iask the students to do two things come upwith a number and, more importantly,consciously record the steps they wentthrough in arriving at the number. We thenlook at each question, establishing therange of student answers and looking at themodels they used to arrive at a result Weask which models are likely to produce thelargest errors and why And all the while,we are establishing the rich context ofestimation in which statistical estimationwill eventually be located

Because of the time that is necessary toestablish the underpinnings of statisticalestimation - probability, simple randomsampling, central limit theorem, standarderrors, confidence intervals - it becomes

very tempting to jettison all the soft, non-statistical stuff about estimation, but if youremphasis is on the ways planners thinkwith numbers you will find yourself muchless willing to skip that material There areseveral very good articles that can helpstructure the consideration of these

questions’ and there is a wealth ofexamples in planning practice I think ofrecent controversies concerning thenumber of homeless in various Americancities, the number of illegal aliens m theUnited States,’ the number of children mthe United States who have been

kidnappedlabducted, the number ofunserved mentally retarded individuals inMassachusetts (the subject of a recentmasters thesis at M.I.T 1. all importantplanning problems, all estimationproblems, but all problems that cannot beaddressed solely through traditionalstatistical estimation

Principle #3. Resist the &dquo;Right AnswerSyndrome

&dquo;

Because courses in quantitative methods,are, m part, mathematical, it is easy forstudents to assume that any problem mustlead to a right answer While there arecorrect calculations and incorrect

calculations, these are often the least

interesting parts of the answer to a

statistical problem Once you havecalculated the number correctly, what areits implications? Often, reasonableindividuals differ

For example, rarely in our practice will wefind ourselves in the enviable situation of

having a simple random sample survey inwhich all of the respondents have answeredevery question My students are oftenmuch to quick to dismiss any deviationfrom this ideal The real question iscontextual. What can we conclude fromthe survey we actually ended up with in thisinstance?, Do the deviations from&dquo;acceptable practice&dquo; jeopardize our abilityto draw conclusions or not?

We have to push our students intograppling with these questions Posequestions with no clear right answer, butreward better answers. Develop anenvironment in which questioning isencouraged What are the assumptionsunderlying a particular technique? Are theysatisfied in this situation ? If not, is that aninsurmountable impediment to analysis?From this perspective research is the art ofmaking intelligent compromises to study aproblem

A major related issue for me is how to teachstudents to talk candidly and humbly abouttheir results and conclusions We often

place a misplaced premium on definitive-ness, even though the analysis cannotreally support such certainty The way inwhich we write about these problems givesus away. We &dquo;collect&dquo; data, when it mightbe more helpful and more honest to think ofthe procedure as &dquo;producing&dquo; data Wespeak about our reserach results as&dquo;findings&dquo; rather than &dquo;creations.&dquo;’ Andwe write about our conclusions in the

passive voice as though we had no role toplay in the outcome &dquo;this study concludedthat....&dquo; sequence in a Ph D. program

Principle #4 Resist the &dquo;Back-of-the-Book

Syndrome &dquo;

Another trap m teaching quantitativemethods, particularly statistics, is the rushto the back of the book Because we are insuch a hurry to cover a given amount ofmaterial in a limited amount of time, we

give the impression that we value what is at

the back of the book more than what is atthe front We imply that means, medians,modes, frequency distributions, andwhatever else we cover up front are onlyimportant as building blocks to what comeslater, when, in fact, these early elementsare powerful tools in and of themselves ’° Insome cases we may even explicitly give themessage that using a technique nearer theback of the book is better. I have taught m afour semester statistics and social research

sequence in a Ph. D program where it was

very clear that the general view was &dquo;whenin doubt use factor analysis.&dquo; Advisors gavethis advice assuming that the most

sophisticated was the best, even thoughtby the time you get this far toward the backof the book you have accumulated so manyassumptions, caveats, and constraints thatthe likelihood the technique will beapplicable to your particular problem is verysmall

Principle#5 Recognize the true complexityof planning problems.

Grapple as much as possible with realplanning problems Though sanitizedproblems may be useful for short-termpedagogical purposes, they ultimately failbecause they don’t prepare students fordealing with messy problems

Actual problems are particularly helpful inbreaking the student’s overreliance onpattern recogmton as a learning device&dquo;Oh, this problem is posed in the sameformat as all the binomial problems we havehad this semester Therefore, it must be abinomial problem, too

&dquo;

A recongition of the true complexity ofplanning problems also helps to illustratewhat part of the problem is extra-statistical,a realization that should be an importantpart of learning about quantitativemethods

A helpful pedagogical device is toperiodically incorporate planning reportsand journal articles which use the particulartechniques under consideration to addressparticular planning problems We also usethis device as the synthetic part of our finalexam The students are given a journalarticle a week or so before the final exam,and they are told to study it and criticize it in

at UNIV NEBRASKA LIBRARIES on November 6, 2014jpe.sagepub.comDownloaded from

34

preparation for the final Half of the final Iexam is then devoted to questions aboutthe article How well did the author do whathe or she set out to do? What other

approaches might have been used? Whatdid the author mean when he or she said? In this way, part of the final examcan actually be focussed on the use ofquantitative methods in planning (and, atthe same time, we can minimize some ofthe inappropriate anxiety students feel in

preparing for a completely unknown finalexam)

Taken together, these four goals and fiveprinciples of course design can dramaticallytransform a course in quantitative methodsfor planning And it is not a question ofmaking the course more palatable, it’s aquestion of designing a better course It

may be impossible to remain faithful to allnine points throughout the semester - Iconstantly struggle with the teachingcompromises I have to make - but thedecision to adopt these goals andpnnciples and to make them part of mythinking about my teaching has graduallymoved me toward a course better-

grounded in the context of quantitativereasoning and in the context of planningpractice

I now turn to a brief discussion of two

ancillary implementation issues posed bythe transformation of Statistics intoQuantitative Reasoning

The Role of Calculators and Computers

On the issue of the appropriate use ofcalculators and computers m this course, Iam something of a Luddite While I firmlybelieve one of the goals of our curriculumshould be to enable our students tobecome &dquo;computer literate,&dquo; because ofcompeting demands on my students’ firstsemester time, I have not been able to insiston the use of computers in homework sets

I have gradually come to the conclusionthat not only is this okay, it is probablydesirable The student who immediatelyturns to the statistical functions of a handcalculator or to the computer to solve aproblem misses the critical step of havingto grapple with the formula, and theopportunity for developing a fuller, intuitiveunderstanding of that formula is lost (i e ,what comparison is at the heart of astandard deviation?) At the onset, I wouldprefer to have the students comfortableenough with the computer to use aspreadsheet program with ease, but aspreadsheet program whose statisticalfunctions have been disabled Later in the

semester, we would enable those

functions, but only after the student hasbeen forced to lay out the calculations stepby step in the rectangular spreadsheetformat. For the same reasons, I haveargued against the use of statisticalcomputer packages in the introductorycourse

For the moment, I have settled on anunsatisfactory compromise. A number ofthe exercises we pose on homework sets

throughout the semester are available onthe microcomputers so that they can besolved using a spreadsheet program if thestudent chooses, but we will also acceptsolutions done with a calculator or by hand

The move toward calculators andcomputers has also had another importantconsequence for our ability to reasonquantitatively. How many of us now receivehomework set solutions in which thestudents have calculated answers to four orsix or even eight decimal places? In thepresence of such seductive precision, weincreasingly run the risk of forgetting to ask

ourselves if our answer makes sense In

this regard, the era of the slide rule, whosepassing few of us regret, had something torecommend it. In solving each problem youhad to make an accompanying back-of-the-

envelope calculation to set the decimalpoint in the correct place and, at the sametime, you were forced to ask whether or notthe answer you got was reasonable.

Another &dquo;reasonableness test&dquo; must alsoreceive increased attention If we teachstudents to use spreadsheet programs toplay with problems - to ask &dquo;What if ?&dquo; -then we will be able, for the first time m ourteaching, to address the question ofsensitivity analysis time-effectively But weneed to be clear that there are two types of

sensitivity analysis that can inform ourplanning practice the sensitivity ofestimates to the parameters used in ourmodel and the sensitivity of policies to ourestimates The latter is easy to neglect in acomputerized world, even though it can bea key element m a planning decision

The Role of Writing

The transformation of a course from&dquo;Statistics&dquo; into &dquo;Quantitative Reasoning&dquo;makes writing a cntical skill It is not

enough to calculate the right number Theimplications of that number and of all theattendant data have to be exploredStudents must be asked to write aboutresults and their implications Four of fivewords or a phrase is not sufficient, weshould ask them to write paragraphs withcomplete thoughts and well-developedarguments And the students deservefeedback from us on their writing

Over the years, I have gradually incorpo-rated more and more writing into thehomework sets We give the students a

graph, a dataset, or a set of age-sexpyramids and ask them to write aparagraph or two on what they see Wealso try to push the more traditionalstatistics problem by asking the studentsabout what the policy implications of itsresults might be And we have scrapped thefirst midterm exam, which had traditionallybeen scheduled at the end of the

at UNIV NEBRASKA LIBRARIES on November 6, 2014jpe.sagepub.comDownloaded from

35

&dquo;Descnption&dquo; section of the course, andhave substituted a &dquo;descriptive StatisticsExercise&dquo; in which the students use theCensus of Population and Housing todocument changes in a particular censustract over time, perhaps also in relation toanother tract or a larger geographical area

The students find this exercise both

extremely frustrating and extremelyrewarding They do not know how to writeclearly, never mind elegantly, withnumbers They find it hard to decide whatis relevant and what is not Trying to makesense out of such a mess of data is anexercise that we too rarely ask them to doinside the academy I give each paper twogrades one for the correct use andmanipulation of quantitative informationand one for the quality of the overallconception of the paper and the quality ofthe writing If I believe In teachingquantitative reasoning, I must value both.

We have even crossed traditionallyinviolable course boundaries with thisexercise We use it in three ways as aQuantitative Reasoning exercise, as anexercise m Planning and InstitutionalProcesses, and as the writing diagnosticEach student receives three complete setsof comments and three different gradesfrom three faculty members who wereviewing the final product from very differentperspectives. Within our compartmental-ized teaching it is rare that the students getthe luxury of feedback from multipleaudiences, but that is not at all rare inpractice, where the many different peoplewho react to your work react to it from verydifferent, and often contradictory,perspectives

The Emperor’s New Clothes

Some mornings when I wake up and thinkabout what I have done with this course, Iwonder if I have anything new here orwhether I have just tailored a new set ofclothes for the emperor In one sense,much of what I have said is obvious But Iask myself, if it is obvious, why haven’t wedone a better job at making the necessarychanges m our teaching?

I am happy to report that most morningswhen I now wake up I am convinced thatwhat we have is new and different and

better, and it is paying dividends inincreased student engagement m a subjectthat they once found to be an irrelevantburden and that they saw only as a hurdleto graduation

Notes

1Hardin G 1885 Filters Against Folly Howto Survive Despite Economists, Ecologists,and the Merely Eloquent New York Viking

2In my experience, the book that perhapscomes closest to discussing the idea of"numbers sense" is Hastings, W M 1979How to Think About Social Problems APrimer for Citizens New York Oxford

University Press Another might be Zeisel,H 1968 Say if With Figures New YorkHarper & Row Many statistics books havesmall sections that deal with numberssense See, for example, Chapter 1 ofKimble, G R 1978 How to Use (andMisuse) Statistics (Englewood Cliffs, NewJersey Prentice-Hall A wonderful newbook that addresses numbers sense in thearea of environmental planning is Harte, J1985 Consider a Spherical Cow A Coursein Environmental Problem Solving LosAltos, California William Kaufmann

3There are a number of articles, chaptersand entire books that deal with logic andthe analysis of policy arguments The threeI have used in my teaching are

Horwitz L and Ferleger L 1980 Statisticsfor Social Change Boston South EndPress Chapter 1 integrates the discussionof logic directly into a statistics text with acritical perspective

Dunn, W 1981 Public Policy Analysis Anlntroduction Englewood Cliffs, NewJersey Prentice-Hall Chapter 4

Hambrick, R 1974 A Guide for the

Analysis of Policy Arguments PolicySciences 5

There are a number of excellent textsfocussed on writing and reasoning thatinclude many useful examples

Kahane, H 1980 Logic and ContemporaryRhetoric The Use of Reason in EverydayLife Belmont, California Wadsworth

Lemn, G 1982 Writing and Logic NewYork Harcourt Brace Jovanovich

Toulmin, S , Rieke, R , and Janik, A 1984An Introduction to Reasoning New YorkMacmillan

at UNIV NEBRASKA LIBRARIES on November 6, 2014jpe.sagepub.comDownloaded from

36

4The best article on the planningimplications of this topic is Hodge, G1963 The Use and Mis-use of Measure-ment Scales in City Planning. Journal of theAmerican Institute of Planners A usefuldiscussion can also be found in Willemain,T R . 1980 Statistical Methods for Planners

Cambridge, Massachusetts MIT PressChapter 3.

5To develop a critical perspective onquantitative methods in planning andpolicy, we use two books

Horwitz, L and Ferleger, L Statistics forSocial Change.

Irvine, J , Miles, I , and Evans, J , eds1979. Demystifying Social StatisticsLondon Pluto Press, 1979

And several articles

deNeufville, J 1984 Functions of Statisticsin Planning Paper presented at the AnnualConference of the Association of CollegiateSchools of Planning, New York

Gerard, K 1984 Why Can’t EconomistsSay, "I Don’t Know?" In AmericanSurvivors: Cities and Other Scenes. San

Diego: Harcout Brace Jovanovich, 1984.

Johnston, D. 1983. Census Concepts asKnowledge Filters for Public PolicyAdvisors. Knowledge, Creation, Diffusion,Utilization. No 5.

6Textbooks we have used in the pastinclude

Weiss, R 1968 Statistics in SocialResearch: An Introduction New York. John

Wiley & Sons

Winkler, R and Hays, W 1975 Statistics

Probability, Inference, and Decision NewYork: Holt, Rinehart and Winston

Blalock Jr., H 1972 Social Statistics NewYork. McGraw-Hill

Willemain, T. 1980 Statistical Methods forPlanners Cambridge MIT Press

Mueller, J , Schuessler, K , and Costner, H1977 Statistical Reasoning in SociologyBoston Houghton Mifflin

Freedman, D , Pisani, R , and Purves, R1978 Statistics New York: W W. Norton

Since we have reformulated the course intoone on quantitative reasoning, we haveused two pairs of books, both pairs withexcellent results

Matlack, W. 1980. Statistics for PublicPolicy and Management North Scituate,Massachusetts Duxbury Press

Horwitz, L. and Ferleger, L 1980 Statisticsfor Social Change Boston South EndPress

or

Smith, G 1985 Statistical ReasoningBoston. Allyn & Bacon

Moore, D. 1979. Statistics Concepts andControversies. San Francisco. W.WFreeman

Unfortunately, both Matlack and Horwitzand Ferleger are plagued with a higher thanusual density of typographical errorsSeveral faculty members in planningdepartments have compiled errata sheetsfor Matlack, but these corrections have notfound their way into a corrected secondedition. Most, though not all, of the errorsin Horwitz and Ferleger were corrected inthe second printing

7To introduce the notion of back-of-the-envelope estimation and intelligentguessing we use four articles

Singer, M 1971. The Vitality of MythicalNumbers Public lnterest No 23

Reuter, P. 1984 The (Continued) Vitality ofMythical Numbers Public Interest No 75

Mosteller, F. 1977. Assessing UnknownNumbers: Order of Magnitude EstimationIn Statistics and Public Policy, eds , W.Fairley and F. Mosteller. Reading,Massachusetts. Addison-Wesley

Tversky, A and Kahneman, D. JudgementUnder Uncertainty Heuristics and BiasesIn Statistics and Public Policy, eds. W.Fairley and F Mosteller Reading,Massachusetts: Addison-Wesley.

The first chapter of Consider a SphericalCow begins with several wonderfulexamples

8For a discussion of this particularestimation problem see Keely, C 1982,Illegal Migration, Scientific American, No.3

9See, for example, the introduction toIrvine, Miles and Evans (eds.), DemystifyingSocial Statistics.

10Early in the course we use Savas, E S.1973 The Political Properties of CrystallingH2O. Planning for Snow Emergencies inNew York, Management Science, No. 2This article shows how a seeminglycomplex problem involving equitableprovision of snow removal throughout NewYork City was addressed through theapplication of simple summary statisticsand the comparison of several frequencydistributions

at UNIV NEBRASKA LIBRARIES on November 6, 2014jpe.sagepub.comDownloaded from