# Quantitative Reasoning in the Planning Curriculum

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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 DavidsonQuantitative Reasoning in the Planning Curriculum Published by: http://www.sagepublications.comOn 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 http://jpe.sagepub.com/http://jpe.sagepub.com/content/6/1/30http://www.sagepublications.comhttp://www.acsp.org/http://jpe.sagepub.com/cgi/alertshttp://jpe.sagepub.com/subscriptionshttp://www.sagepub.com/journalsReprints.navhttp://www.sagepub.com/journalsPermissions.navhttp://jpe.sagepub.com/content/6/1/30.full.pdfhttp://online.sagepub.com/site/sphelp/vorhelp.xhtmlhttp://jpe.sagepub.com/http://jpe.sagepub.com/30Quantitative Reasoning in the PlanningCurriculumJ Mark Davidson SchusterMassachussets Institute of Technology~ AbstractFour goals and five course principles arearticulated for a process of turning statisticscourses into quantitative reasoningcourses.IntrodutionI have recently finished reading GarretHardins 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 Hardins 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 thecontroversy 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 Hardinsprescription is significant m that heconcludes we need new ways to thinkabout problems rather than new technicalskills not yet inventedI have thought a lot about Hardins 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 Hardinsprinciples The current core planningcurriculum at M I T is fundamentally aconceptual core focussed on presentingand reflecting on ways of knowing inplanning practiceFollowing Hardins lead, the core can beseen as being organized around five filters~ A Historical Filter What about planningpractice do we understand better whenwe view it in the context of its historicalevolution?~ An Institutional Filter What aboutplanning practice do we understandbetter when we view it in the context ofthe institutional arrangements in which itis embedded?~ A Political/ Economic Filter What aboutplanning 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 Hardins&dquo;ecolate&dquo; filter, other parts of the third andfourth would correspond to the numeratefilter, and the fifth is identicalIncorporating 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 andmeaning 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 ourteaching must encourage the application ofmultiple perspectives not only in theaggregate across the curriculum, but asmuch as possible within individual coursesThe MCP core curriculum at MIT includesfive elements These are~ A course on Institutional Processes andPlanning~ A course on Political Economy forPlanning~ A course in Quantitative Reasoning andStatistical Methods for Planners. A Core Practicum~ A wnting diagnostic and supportprogram that operates in parallel, and inclose coordination, with the courseworkThough 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 anintegrated 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 http://jpe.sagepub.com/31GoalsWhen 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 toopoorly 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 shouldnt be doing, with littleguidance as to what we should be doingGradually, 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 coreGoal #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 definedWhile I have been unable to find any textsor other primary materials that directlyaddress the question of teaching numberssense and have found that somewhatfrustrating,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 cant 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 examsGoal #2 Develop the students ability toformulate and substantiate well-thought-out quantitatme argumentsThe focus should be on quantitativetechniques m use. It is not enough to teachthe correct calculation of statistical results,thats 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 theirthought processes in ways that are newand that may be uncomfortable to themUsing statistical hypothesis testing toestablish whether or not discriminationexists, for example, requires the temporaryacceptance 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 ofdeveloping 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 ones positionGoal #3 Develop an ability to use a range ofquantitative/statistical techniquesI 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 thedog, 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 endBut I want to argue that that sense ofcompleteness is illusory If the connectionsto planning practice havent 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 http://jpe.sagepub.com/32Goal #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 aparticular 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 4A critical literature is developing, and thereare a number of sources that can beparticularly useful in planning courses,5though there is still a huge need for inquiryin this areaPrinciples for Course DesignThough 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 andpossible.Principle #1 Make the genenc activities inwhich planners engage with quantitativeinformation as visible as possible m boththe structure and content of the courseWhen I actually sat down to redesign ourcore course, the first exercise I wentthrough was to take a look at the statisticstexts we had used in earlier versions of thecourses and ask the question What are thegeneric 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~ ExplanationWhen 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 movethroughout the material. The intent of thevarious segments of the course and theirinterrelationships become very clearI 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 beenclearly 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 isprobably 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 syllagusIn 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 orguess) answers to these questions Forexample 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 http://jpe.sagepub.com/33area, 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 locatedBecause of the time that is necessary toestablish the underpinnings of statisticalestimation - probability, simple randomsampling, central limit theorem, standarderrors, confidence intervals - it becomesvery 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 thesequestions 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 beenkidnappedlabducted, 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 estimationPrinciple #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 incorrectcalculations, these are often the leastinteresting parts of the answer to astatistical problem Once you havecalculated the number correctly, what areits implications? Often, reasonableindividuals differFor example, rarely in our practice will wefind ourselves in the enviable situation ofhaving 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 aproblemA major related issue for me is how to teachstudents to talk candidly and humbly abouttheir results and conclusions We oftenplace 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 thepassive voice as though we had no role toplay in the outcome &dquo;this study concludedthat....&dquo; sequence in a Ph D. programPrinciple #4 Resist the &dquo;Back-of-the-BookSyndrome &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, wegive the impression that we value what is atthe 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 researchsequence in a Ph. D program where it wasvery clear that the general view was &dquo;whenin doubt use factor analysis.&dquo; Advisors gavethis advice assuming that the mostsophisticated 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 verysmallPrinciple#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 dont prepare students fordealing with messy problemsActual problems are particularly helpful inbreaking the students 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 quantitativemethodsA 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 http://jpe.sagepub.com/34preparation 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 otherapproaches 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 inpreparing 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, its aquestion of designing a better course Itmay 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 planningpracticeI now turn to a brief discussion of twoancillary implementation issues posed bythe transformation of Statistics intoQuantitative ReasoningThe Role of Calculators and ComputersOn 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 setsI 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 thesemester, we would enable thosefunctions, 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 introductorycourseFor the moment, I have settled on anunsatisfactory compromise. A number ofthe exercises we pose on homework setsthroughout 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 handThe 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 askourselves if our answer makes sense Inthis 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 ofsensitivity 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 decisionThe Role of WritingThe transformation of a course from&dquo;Statistics&dquo; into &dquo;Quantitative Reasoning&dquo;makes writing a cntical skill It is notenough 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 writingOver the years, I have gradually incorpo-rated more and more writing into thehomework sets We give the students agraph, 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 http://jpe.sagepub.com/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 areaThe students find this exercise bothextremely 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,perspectivesThe Emperors New ClothesSome 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 havent 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 andbetter, 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 graduationNotes1Hardin G 1885 Filters Against Folly Howto Survive Despite Economists, Ecologists,and the Merely Eloquent New York Viking2In 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 OxfordUniversity 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 Kaufmann3There are a number of articles, chaptersand entire books that deal with logic andthe analysis of policy arguments The threeI have used in my teaching areHorwitz L and Ferleger L 1980 Statisticsfor Social Change Boston South EndPress Chapter 1 integrates the discussionof logic directly into a statistics text with acritical perspectiveDunn, W 1981 Public Policy Analysis Anlntroduction Englewood Cliffs, NewJersey Prentice-Hall Chapter 4Hambrick, R 1974 A Guide for theAnalysis of Policy Arguments PolicySciences 5There are a number of excellent textsfocussed on writing and reasoning thatinclude many useful examplesKahane, H 1980 Logic and ContemporaryRhetoric The Use of Reason in EverydayLife Belmont, California WadsworthLemn, G 1982 Writing and Logic NewYork Harcourt Brace JovanovichToulmin, S , Rieke, R , and Janik, A 1984An Introduction to Reasoning New YorkMacmillan at UNIV NEBRASKA LIBRARIES on November 6, 2014jpe.sagepub.comDownloaded from http://jpe.sagepub.com/364The 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 PlannersCambridge, Massachusetts MIT PressChapter 3.5To develop a critical perspective onquantitative methods in planning andpolicy, we use two booksHorwitz, L and Ferleger, L Statistics forSocial Change.Irvine, J , Miles, I , and Evans, J , eds1979. Demystifying Social StatisticsLondon Pluto Press, 1979And several articlesdeNeufville, J 1984 Functions of Statisticsin Planning Paper presented at the AnnualConference of the Association of CollegiateSchools of Planning, New YorkGerard, K 1984 Why Cant EconomistsSay, "I Dont Know?" In AmericanSurvivors: Cities and Other Scenes. SanDiego: 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 pastincludeWeiss, R 1968 Statistics in SocialResearch: An Introduction New York. JohnWiley & SonsWinkler, R and Hays, W 1975 StatisticsProbability, Inference, and Decision NewYork: Holt, Rinehart and WinstonBlalock Jr., H 1972 Social Statistics NewYork. McGraw-HillWillemain, T. 1980 Statistical Methods forPlanners Cambridge MIT PressMueller, J , Schuessler, K , and Costner, H1977 Statistical Reasoning in SociologyBoston Houghton MifflinFreedman, D , Pisani, R , and Purves, R1978 Statistics New York: W W. NortonSince we have reformulated the course intoone on quantitative reasoning, we haveused two pairs of books, both pairs withexcellent resultsMatlack, W. 1980. Statistics for PublicPolicy and Management North Scituate,Massachusetts Duxbury PressHorwitz, L. and Ferleger, L 1980 Statisticsfor Social Change Boston South EndPressorSmith, G 1985 Statistical ReasoningBoston. Allyn & BaconMoore, D. 1979. Statistics Concepts andControversies. San Francisco. W.WFreemanUnfortunately, 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 printing7To introduce the notion of back-of-the-envelope estimation and intelligentguessing we use four articlesSinger, M 1971. The Vitality of MythicalNumbers Public lnterest No 23Reuter, P. 1984 The (Continued) Vitality ofMythical Numbers Public Interest No 75Mosteller, F. 1977. Assessing UnknownNumbers: Order of Magnitude EstimationIn Statistics and Public Policy, eds , W.Fairley and F. Mosteller. Reading,Massachusetts. Addison-WesleyTversky, 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 wonderfulexamples8For a discussion of this particularestimation problem see Keely, C 1982,Illegal Migration, Scientific American, No.39See, 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 http://jpe.sagepub.com/

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