Textbooks, Testing, Training: How We Discourage Thinking

64 Pages·2014·0.89 MB·English

by  Stephen S. Willoughby

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Textbooks, Testing, Training
How We Discourage Thinking
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(cid:13)c 2014by
TheMathematicalAssociationofAmerica(Incorporated)
LibraryofCongressCatalogCardNumber2014935311
PrintversionISBN978-0-88385-914-8
ElectronicversionISBN978-1-61444-803-7
PrintedintheUnitedStatesofAmerica
CurrentPrinting(lastdigit):
10987654321
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Textbooks, Testing, Training
How We Discourage Thinking
Stephen S. Willoughby
PublishedandDistributedby
TheMathematicalAssociationofAmerica
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Acknowledgments
ThankstomymanycolleaguesandstudentsfromwhomIhavelearnedmuch
andwhosewisdomandinsightsIamtryingtopassoninthisshortbooklet.
Ialso wish toexpress my special thanksto StephenKennedy forhis in-
sightfulcomments andfor shepherdingthe manuscriptthroughtothe final
document,andtoCarolBaxterandBeverlyRuediwhohavedoneanexcel-
lentjobeditingthefinalmanuscript.
Mywife(Sali)andchildren(WendyandTodd)haveshowngreatpatience
and love over thepast 60years, puttingupwithand withoutme, as I have
taughtandoccasionallywrittenaboutmathematicseducation.
Thankyouall.
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Contents
Acknowledgments v
Introduction 1
1 Textbooks 3
1.1 WordProblems . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 PuzzlesandGames . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 ChoosingTextbooks . . . . . . . . . . . . . . . . . . . . . 9
1.5 TextbookPublishers . . . . . . . . . . . . . . . . . . . . . 9
1.6 SRA/McGraw-Hill . . . . . . . . . . . . . . . . . . . . . . 11
1.7 CommentsonChapterOne . . . . . . . . . . . . . . . . . 13
2 Tests 17
2.1 CEEBReview . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 WisconsinMathematicalAssociationofAmericaTest . . . 20
2.3 SomeDangersofMultiple-ChoiceTests . . . . . . . . . . . 22
2.4 PossibleGoodinStandardizedTests . . . . . . . . . . . . . 25
2.5 TheRealFailureofAmericanEducation . . . . . . . . . . 26
2.6 InternationalStudies . . . . . . . . . . . . . . . . . . . . . 28
2.7 CommentsonChapterTwo . . . . . . . . . . . . . . . . . 29
3 Teachers 31
3.1 AcademicDisapproval . . . . . . . . . . . . . . . . . . . . 31
3.2 TeacherQuality . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 TeacherEducators . . . . . . . . . . . . . . . . . . . . . . 36
3.5 TeacherCompetence . . . . . . . . . . . . . . . . . . . . . 38
3.6 Tenure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.7 EvaluatingTeachers andStudents . . . . . . . . . . . . . . 41
3.8 Gender . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.9 CommentsonChapterThree . . . . . . . . . . . . . . . . . 46
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viii Contents
4 Conclusion 47
4.1 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Index 53
AbouttheAuthor 55
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Introduction
Themindisnotavesseltobefilledbutafiretobekindled.
—Plutarch
The abilitytoreadanddoarithmeticare certainlyimportantbothtothein-
dividualand tothesociety inwhichthe person lives. However, Imaintain,
andhavealwaysbelieved,thattheabilityanddesiretothinkareeven more
importantbothtoindividualsandtosociety.Thinkingisabasicskill.What
gooddoesitdoustobeabletoreadifwedon’tthinkaboutwhatweread?
Whatgooddoesitdoustobeabletodoarithmeticifwecan’tdecidewhen
arithmeticisdesirableordecidewhattheresultsofthearithmeticmean?The
traditionalbasicskillsmustbelearnedbuttheyshouldnotbelearnedtothe
exclusionofthinking;rathertheyshouldbelearnedinawaythatencourages
thinkingandtheintelligentuseofotherbasicskills.
Evenwhentheyadvocatethinking,manypeople,especiallythosewitha
strongpoliticaloreconomicinterest,seemtomean“think,butthinktheway
I do and reach the same conclusions.” Whenever twopeople thinkexactly
thesamethingabouteverysubject,atleastoneofthemisnotthinking.
Statistical studies regarding what is wrong or right about American ed-
ucation abound and are widely used to advocate various policies that the
advocates believe are needed toimproveeducation. Mostpeopleseem dis-
inclinedtostudythe statisticscarefully, partiallybecause they donothave
the time or the necessary backgroundto understandthe statistics, and par-
tiallybecause theydon’tbelievestatisticalstudies.Perhaps, insome cases,
thepeoplehavealreadymadeuptheirmindsanddon’twanttobeconfused
bymerefacts.
This short book recounts many specific true stories from my fifty-nine
yearsofteachingthatIbelievecastsomelightonwhatiswrongwithAmer-
icaneducationandperhapssomecluesastowhatmightimproveit.Mainly
I taught mathematics but I also taught other subjects (science, English for
thegifted,American history,basketball,volleyball,soccer, and allthe sub-
jectsinelementaryschool)andIbelievetheconclusionsIdrawarevalidfor
educationgenerally,andcertainlyformathematicseducation.
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