Individualization: Too Much, Too Soon

Patrick J. SocciLawrence High School

Cedar Hurst, New York 11516

The educational system, as the world around us, is always in a state ofchange. Conflict and crisis seem to be the two greatest stimuli. As educa-tors we are under fire from two fronts. "Return to basics and the threeR’s," they say but "Our children are unique and each must be handleddifferently." Our solution was formed in the turbulent 60’s and we calledit "Individualized Education." Perhaps the crisis of the times forced theinstitution of education to move too rapidly too soon! Now the late 70’sseems a good time, an objective time, to dissect the new trend.The premise of developing students to their specific capacities is above

reproach. No one has ever disputed that point. This induces an analysisof the materials we use and the organization of the classroom. What aresome of the shortcomings of the present materials? How can we writemore effective materials? What administrative details need revision for asuccessful program? These are the three questions we shall try to re-search.

Before I proceed, allow me to summarize a brilliant outline of thethought process presented by Dr. James Lewis, Professor of Education,Medger Evers College of the City University of New York. He divides thethought process into seven levels:

THOUGHTLEVEL SYNONYMS1) Memory Define, List, State2) Translation Rewrite, Rephrase, Restate3) Interpretation Classify, Differentiate, Compare4) Application Discover, Relate, Manipulate, Demonstrate5) Analysis Separate, Illustrate, Generalize6) Synthesis Organize, Devise, Build, Create7) Evaluation Criticize, Describe, Summarize, Support

These are listed from lowest to highest forms. There is nothing reallyunusual about this classification. Whether we all agree on the listing ornot, the point is that there are many levels of thinking and some formsrequire greater insight. When we teach on the memory level and test onthe analysis level, problems will result. When students say, "The test wastoo hard." they could possibly be telling us that the instruction was notadequate for the desired expectation. They are prepared to tell us whatthe definition of a monomial is but cannot distinguish one from a poly-nomial. The level of instruction must be equal to or higher than the de-sired level of expectation. If it is not, thoughts unrelated to the behav-ioral objectives will result.

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234School Science and Mathematics

PRESENT MATERIALS AND IMPROVEMENT

Considering some of the popular individualized materials on themarket today, I find the publishers guilty of the aforementioned inade-quacy. Allow me to cite a few examples.

MODEL I: MULTIPLICATION AND DIVISION OF FRACTIONSLearning Unit A: Multiplying Two Proper Fractions

�>Ta}

^

1

12

_415

_218

Learning Unit B: Multiplying Two Mixed Numbers

1) 2- x 2- =^ 5x8

2)2^ ’316

3

2x3

11 x 16

4x3

40

6

176

72

4

14}Learning Unit C: Finding a Missing Factor

1)nx^-=l2) 8 x n = 4

Answer: 4.

_1_Answer: ~~

3) n x - = -

32 6

4) ~ofwhat number is 21?

Answer:

Answer:

3

28

Remarks: Learning Units A and B are sufficiently narrow in scope so as to concentrate on aspecific "wrinkle" in multiplying fractions. Learning Unit C engulfs the studentsin the concept of a variable within the context of an equation and word problem.None of these concepts have been developed previously in the text. This is a clearlack of sequential development. The material also requires thinking on the syn-thesis level while the instruction is only on the application level.

MODEL II: PERCENTS AND FRACTIONSLearning Unit A: Converting Fractions to Percents

1?%1)

2)

or

33� %3

II1- %

3

1 .33 R.I3-y��� = ?%9

7 .77 R. 7

9

1.00

7.00

Individualization 235

Test Question: James answers six questions incorrectly on a test. What percentage ofthe questions does he answer correctly if there are twenty questionson the test?

Remarks: Here the unit is on the level of application, using model examples to onvert frac-tions to percents. The test question is on the analysis level. The student has toreason out the difference between the percent answered correctly and the percentanswered incorrectly. This problem involves an extra twist for which no previoustraining has been given. The arithmetic is also questionable. How does .33 R. 1become 33’/aW

MODEL III: DIVISION OF WHOLE NUMBERSLearning Unit A: Dividing by Three-Digit Numbers

1) 34245 - 451

451 34245 7031570

2675 52255

420Answer: 75 Rem. 420

Test Question: A car odometer reads 2314 on Monday and 2742 on Tuesday. If thecar gets 14 miles per gallon, approximately how much gas must thedriver use?

Remarks: Division has not been used in word problems yet. The concept of approximationhas not been explained. I also think the definition of an odometer and the con-cept of gas consumption should be developed prior to use as a test question. If astudent does poorly on this test, does it indicate an ineptness in division by three-digit numbers? Incidentally, the test question has a two-digit divisor.

MODEL IV:Learning Unit A: ConstructionProblem: The Bedford City Youth Association has decided to enclose the two sides of

its hockey rink from goal line to goal line with side boards and panels. Theside boarding is to be five feet high. The panels which snap together are tobe placed side by side on top of the boards, which are also to be placed sideby side. The frame to which the panels and glass are to be attached was do-nated and has been constructed. Using the scale drawing of the rink, and thegiven figures, determine the amount of material needed for the construc-tion. Assume that from goal line to goal line is a straight line. (It may benecessary to read about scale models as a review.)

Remarks: Wow!!The grade level of reading material is determined by many methods. Averagingthe number of syllables per sentence is the most common. The above passage isat least eleventh grade reading material while the text is designed for ninth gradegeneral math. Hard to believe, isn’t it? The problem, as posed, brings to mindpictures of a hockey rink which may not be familiar to the reader. In fact, thesport may dissuade the student’s interest. If the child cannot complete this as-signment, it certainly is through no fault of his mathematics. Do you wonderwhy the student may be a little restless now? This is a clear cut case of confusedbehavioral objectives in the cognitive domain. Mathematics is not being taughtbut rather the physical considerations of a hockey rink, at an unrealistic readinglevel.

These are four of the more notorious types of errors in the individual-ized materials of today’s market. Apathy, bad conduct and complaintsare the child’s naive way of relating the dissatisfaction and confusion heor she is unable to articulate, that is, that the instruction was inadequate.

236 School Science and Mathematics

Clearly, most, if not all, materials must be rewritten with greater caretaken to insure that the finer points of pedagogy are followed. The levelof development must be equal to or higher than the desired level of com-petency. A wide variety of problems must be in each learning unit to pro-vide greater flexibility in instruction and to give the student more op-tions. There must be enrichment for students of different levels. Childrenwho learn mathematics by rote must be given sufficient repetition whilethe prodigy must also be stimulated on a different level. Students in themiddle of the spectrum must also be given material at their level as well.We must go one step further to insure that the reading level of the text

is compatible with that of the student. Otherwise, problems unrelated tothe subject matter at hand will arise to complicate the situation. Cleardistinction must be made between mathematical and verbal skills. Whileequal in the former, children can be very different in the latter skill. Iwould be remiss if no mention were made of the lack of developmentalstructure in many of today’s books. Surprising a reader with equationsolving in order to multiply fractions (MODEL I) is simply unacceptableon elementary levels. Consequently, a writer must be scrupulous in hisefforts to organize and prepare materials for classroom texts.

GORILLAS: GENTLE VEGETARIANS OF THE RAIN FOREST

Ambling peaceably through mountain rain forests, munching on wild celery,thistles and nettles, mountain gorillas lead a precarious existence in a world thatno longer seems to have room for them. These gentle vegetarians are threatenedby burgeoning human populations encroaching on their habitat, which is nowlimited to two adjacent federal parks in Rwanda and Zaire in east central Africa.

In 1959, the number of gorillas in this area was estimated to be 400 to 500. Re-cent census data, however, indicate that there are now only about 250 individu-als.Amy Vedder, a graduate student in zoology at the University of Wisconsin-

Madison, and her husband, A. William Weber, a graduate student in the Insti-tute of Environmental Studies, have spent 18 months at the Karisoke ResearchCenter in Rwanda conducting research they hope will promote conservation ofthese remarkable primates, which are one of man’s closest living relatives.Weber has established public education programs that not only inform the

Rwandan people of the value of the park and its inhabitants, but also promoteenvironmentally compatible agricultural practices. He is also working closelywith government officials and conservation groups to encourage better enforce-ment of anti-poaching laws�adult gorillas are sometimes killed so that infantscan be captured and sold.

"But conservation of gorillas is not just Rwanda’s responsibility," says Ved-der. "It’s really an international problem."Weber, together with Rwandan government officials and a few conservation

organizations, is petitioning the United Nations Educational, Scientific, andCultural Organization to grant the park biosphere status, which would give thepark international recognition as a preserve.