On a Clear Day…

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684On a Clear Day . .Doris GlassOn the Feast of Stephen do we see thesnow so crisp and even? Do we trod inour masters steps? No doubt we do.Isnt that what education is all about?There are those who make footprints,and those who step in the footprintsothers have made. What purpose isthere in either without the other?Sir John TennielArtistThe time has come.f the Walrus said,To talk of many things:Ofshoesand shipsand sealing waxOfcabbagesand kingsThrough the Looking Glassby Lewis CarrollAre schools, like the earths crust,subject to cyclical changerelievingstress of faults by shock, potentiallycatastrophic in magnitude? Or is theeducational establishment, proudlypluralistic, more like a glacier?an un-fortunate simile, since glaciers move downhill, irresistibly, to inevitable dissolu-tion at sea level.A case can always be made for cycles, as Jean Baptiste Joseph Fourier so wellexplained. Note the dates: Sputnik Zemli 1957, GI Bill 1944, nationwide IQ test-ing 1917.2 But perhaps change as discrete or continuous, linear or logarithmic, issecondary to eternal verity. Perhaps plus ca change, plus cest la meme chose3Guess the date, and try these: 41. This arthmetic is designed to give students an intelligent knowledge of thesubject and a moderate power of independent thought. Whether arithme-tic is studied for mental discipline or for practical mastery over everydayproblems of common life, mechanical processes and routine methods areof no value.2. It is intended to have the first fourteen pages of this text read in class, withsuch running comment and discussion as may be useful to help beginnerscatch the spirit of the subject matter, and not leave them to the mere letterof dry definitions.School Science and MathematicsVolume 85 (8) December 1985On a Clear Day 6853. Much of the emphasis now generally placed on formal exercises should beshifted to concrete or verbal problems.4. The selection of problem material is of the highest importance. The de-mand for practical problems should be fully met in so far as the maturityand previous experience of the pupil will permit. Above all, problems mustbe real to the pupil, must connect with ordinary thought, and must bewithin the world of experience and interest.5. Examinations as a whole should, as far as practicable, reflect the principlethat algebraic technique is a means to an end, and not an end in itself.6. Emphasis has been placed on the function concept or, better, the idea ofrelationship between variable quantities. This is peculiary open to misun-derstanding on the part of teachers. A prime danger is that teachers maythink that notation and definition are to be emphasized; indeed, it seemsthat the-word/unction had best not be used at all in the first course.7. We are constantly being asked to add new subjects to the curriculum (safe-ty instruction, health instruction, thrift instruction, and like), but no oneever suggests that we eliminate anything. I defy you to show me how wecan cut out anything.8. It seems to me that we waste such time in schools wrestling with stuff thatought to be omitted or postponed until students have a real need of study-ing it. ... The whole subject of arithmetic could be postponed until theseventh year of school, and it could be mastered in two years study by anynormal child.9.1 was distressed at the inability of the average student to use the Englishlanguage. If students had original ideas, they were very poor in translatingthem into understandable English.10. If some of the students do not grasp the problems easily and quickly, theteacher simply moves on, knowing that the power to reason will probablydevelop in them a year or two subsequently. The one thing to be avoided isthat children get the idea that a fixed method or formula can be used as asubstitute for thinking.11. Before starting on a problem in any of the four fundamental processes, thestudents are asked to estimate or guess about what the answer will be andthen check their final result by this preliminary figure. The teacher is care-ful not to let the teaching of arithmetic degenerate into mechanical ma-nipulation without thought. The teacher keeps in mind that the objectivesto be gained are first of all reasoning and estimating, rather than mere easein manipulation of numbers.12.1 am appalled at the changes which are taking place; the great number ofnew activities which have developed, each good in itself, but neverthelesscluttering up the time of the children.School Science and MathematicsVolume 85 (8) December 1985686 On a Clear Day13. A motion was made that we throw out the new course of study in mathe-matics and go back to the old. It was defeated by a vote of nine to four,but a committee of three was appointed to study the problem carefully.14. This may seem a very unsuitable time for proposing innovations in educa-tion. Barring a fundamental change in the economy, we can anticipate in-adequate financing of education for the foreseeable future. This meanslarge classes, with shortages of books and materials. We may get by withineffective methods in normal times; in times of difficulty, it can be disas-trous if we do not find the most efficient means.15. A problem is any question concerning which the preliminary inquiry is todecide which process or processes are involved. Problems should be taughtfrom the earliest stages. As the reading difficulty is profound and the ex-perience of the child is limited, questions should in all cases be simple; lan-guage should be clear and precise, and the situations considered should beworthwhile and within the orbit of experience.16. Science is news; mathematics is not. In part this is the fault of school (anduniversity) teaching of mathematics. The result is that no one expects any-thing new to happen in mathematics. When children learn mathematicsthey do not have the incentive of seeing an attainable goal before them asthey have when learning science.17. An analysis of the errors of pupils take time. A very large number of er-rors can be classed within a very small number of types. We believe that er-ror analysis, supported by instrumental theory, is time-saving in the longrun, quite apart from its obvious educational advantages.18. If teachers are persuaded that error is not "any old answer, and that thereis a good reason for every wrong answer given, their own experience willsuggest methods of treatment. The important point is that wrong answersmake sense once we understand how the pupil has been thinking.19. In an ideal world, teaching would be under continual review. The argu-ments for necessary changes would be carefully examined and there wouldbe a slow but steady evolution of content and teaching method. In reality itseldom works like that.20. Another difficulty stems from the hostility of local egalitarians towardelitism. This contravening view does not carry much weight with teachers.To put highly gifted students in a regular classroom would be to punishthem and hold them back. Some people think democracy means being ab-solutely equal and having the same curriculum for each student. But in areal democracy, we owe to all individuals the opportunity to develop tal-ents to the utmost.School Science and MathematicsVolume 85 (8) December 1985On a Clear Day 687Thats why my friend said, as we reached the top of the steps from the beachto the top of the cliff (ability to speak, not the quality of the thought, proof thatwe were not overdoing), "If I were King, Id immediately issue the followingedict. All schools from P-K to P-Gpre-kindergarten to post-graduateshallconsist of three departments. One, the Department of Communication. Two, theDepartment of Perception. And three, the Department of Action. Every studentshall take exactly three subjects, one in each department, and thus have exactlythree teachers each year.""And what subjects would your subjects be taking, good King?""The Department of Communication would have what we call Language Artsand Social StudiesEnglish, History, Social Studies, and all that. The Depart-ment of Perception is Mathematics and Science, to include the quantitative partsof social studies. The Department of Action is simply Athletics, Music, Voca-tional, and extra-curricular.""It shall be done, Sire! And what method? Shall it be Socratic?""Absolutely not! Thats a ridiculous way to teach! Old Socrates got to ask allthe questions, and his student was supposed to just keep saying things like "So itseems*, tions, and for the teacherto have the answer, of course!""And a generous sprinkling of questions by the learner that the teacher cantanswer adds spice to life?"GOOD KING WENCESLASGood King Wenceslas looked outOn the feast of StephenWhen the snow lay round aboutDeep and crisp and even.Brightly shone the moon that night,Though the frost was cruel,When a poor man came in sight,Gathring winter fuel.* * *School Science and MathematicsVolume 85 (8) December 1985688 On a Clear DayIn his masters steps he trod,Where the snow lay dinted;Heat was in the very sodWhich the Saint had printed.Therefore, all good men, be sure,Wealth or rank possessing,Ye who now will bless the poor,Shall yourselves find blessing.John Mason NealeWhat do you think?Doris Glassc/o Editor, School Science and MathematicsReferences: Editors Notes1. Stephen was the first of the first seven deacons (Acts 6:5), and the first Christian martyr(d c. A.D. 36). Saint Stephens Festival is celebrated December 26not to be confusedwith Saint Stephen I, Pope 254-57 A.D., whose feast is celebrated August 2, or with Ste-phen I, Apostolic King of Bohemia (1001) and patron saint (1083) of Hungary. Therehave been ten popes and six kings named Stephen. The traditional carol refers to KingWenceslas I (1361-1419)there were four. The patron saint of Bohemia is Saint Wen-ceslas(d929).2. Sputnik Zemli was the Russian earth-orbiting satellite that initiated emphasis on scienceand mathematics in our schools. The GI bill (GIGeneral /ssue, a Quartermaster Corpsterm), was the Servicemens Readjustment Act 1944, amended 1952, and replaced by theServicemens Readjustment Benefits Act 1966. An mtelligence quotient was determinedfor all men entering the army by means of the Army General Classification Test,AGCT, 1917.3. Plus qa change, plus cesf la meme chosethe more it changes, the more its the same.4. The 20 statements are listed chronologically from 1885 to 1985.School Science and MathematicsVolume 85 (8) December 1985