864 SCHOOL SCIENCE AND MATHEMATICS

BRIDGING THE GAP BETWEEN THEORY AND PRACTICE INNINTH GRADE MATHEMATICS.

BY WM. HERBERT EDWARDS,

Northeastern High School^Detroit, Mich,

You have but to compare educational theory with the educa-tional practice found in any high school class familiar to you torealize that a distinct gap exists between theory and practice inthe teaching of mathematics. Teachers are not applying in theirclasses any appreciable amount of the tested educational psy-chology available.We are not concerned in this paper with causes. Our purpose

is to show how this gap between theory and practice may bebridged in the mathematics class room by any teacher willingto make the effort. Two examples from ninth grade mathema-tics will suffice to illustrate how theory may be adapted to actualteaching situations.

EXAMPLE I. PROBLEM MATERIAL.One of the theories of education supported by objective evi-

dence is that the problem material in a mathematics text bookshould be within the social experience of the learner. How canthe mathematics teacher apply this theory in his teaching?The first thing the teacher has to do is to determine the social

situations involved in the problem material in the text book he isusing. This determination can be made by analyzing the prob-lem material. For example, the writer analyzed the problemmaterial in the text used by his first semester ninth grade mathe-matics pupils and found fifty-nine words or phrases having socialconnotation. Social connotation is involved in a phrase such as^500 acres^ appearing in a problem. The text infers that stu-dents know the meaning of these words from previous experiencein arithmetic perhaps.The next step is to determine the extent to which the social

experiences involved in the problem material are social exper-iences of the pupils in the class. This can be accomplishedby testing the pupils on the words or phrases discovered by theanalysis of the problem material.The writer submitted to his beginning ninth grade pupils the

fifty nine words and phrases representing social situations foundin the problem material of the text book used in his mathema-tics classes. The results are summarized in Table I in evidence

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that it cannot be taken for granted that the problem materialin a text book is within the social experience of the pupils in agiven class. For example, there were twenty words and phrases,almost 40% of the entire list, that from 51 to 60% of the classdid not know.

TABLE I.�GROUPED PERCENTAGE OP FIFTY-NINE WORDS OR PHRASESHAVING SOCIAL CONNOTATION NOT KNOWN BY 69 PUPILS

IN NINTH GRADE.Words or Phrases

Grouping not Known91�100% of pupils--.-.-----.---------.- 181� 90% of pupils������������ 271� 80% of pupils-���������--- 4:61� 70% of pupils������������� 551� 60% of pupils-�����������- 841� 50% of pupils�������������� 831� 40% of pupils-������������� 521� 30% of pupils������������� 511� 20% of pupils�������������141� 10% of pupils��������������� 7

The final step in attempting to use in the class room thetheory that the problem material should be within the socialexperience of the learner is to provide for the class the socialexperiences that the class has not had and which are involved inthe problem material in the text book. The results of the testjust discussed will reveal the social experiences that need to beprovided. In the event that any given social experience cannotbe provided, then the teacher should not assign the problem orproblems involving this particular experience.

EXAMPLE II. AIMS OF MATHEMATICS INSTRUCTION.

Another of the theories of education backed by ample in-vestigation is that pupils should have "immediate and undis-puted use of the fundamental processes/7 to use the words of theReorganization Committee in listing the aims of mathematicsinstruction.

Obviously the first step in utilizing this ideal in ninth grademathematics is that of determining the command of the funda-mental processes existing in a given group of students. Forexample, the writer used the Monroe Diagnostic Tests in Arith-metic in his ninth grade classes. The results (summarizedin Table II) show that the teacher cannot assume that his pupilsin ninth grade have a reliable or a uniform command of theessentials of arithmetic.||The results of fhe diagnostic test are used to design a set ofremedial self-testing drills. These drills would be changed from

866 SCHOOL SCIENCE AND MATHEMATICS

TABLE II.��RESULTS OF MONROE DIAGNOSTIC TEST IN ARITHMETICGIVEN TO SEVENTY-FOUR PUPILS IN NINTH GRADE.

Ability’

Percent Rights1. Adding single columns--.-.�., -.-.-.-��.-��..� .�.-.....................82.42. Adding four columns�����.-.-.��-���.-.�..........................70.53. Adding fractions��-.-�.-����.�����.�.�........................55.24. Substracting whole numbers� .-.�����.-.�.�.-..�-........... ..92.65. Substracting fractions.�..-..-�.....-..-.� �.-�.--.-.--.-...................53.76. Multiplying by a unit number� �.�������������� 89.57. Multiplying by higher than unit number�.�..������73.48. Multiplying fractions��.������������.�.��.�.�...67.39. Pointing off decimal point in multiplication�.����.���. 94.0

10. Simple division�.�.����..������ ���-.--� ....�82.011. Long division.-..-.� -�-������.���������� ��56.712. Division of fractions��������� �.��

������� .35.713. Pointing off decimal point in division..-� -.�����... ���.-42.9

time to time as improvement in one or more of the arithmeticabilities was evidenced.Thus we see that the theory of facility with the fundamental

operations may be made to operate in ninth grade mathematics.

SUMMARY.1. The two examples cited here suggest how the existing

gap between theory and practice in ninth grade mathematicsmay be significantly narrowed by the teacher willing to makethe effort.

2. We cannot assume that text books bridge the gap betweentheory and practice for us.

3. We cannot assume that the previous teachers of our pupilshave been successful in applying any of the theories or aims ofeducation.

SOVIET HEALTH PROBLEM.The government ban on vice in Soviet Eussia has turned the age-old

problem of disease into new channels. In a book on the venereal diseasesituation in Russia recently published in Paris, Dr. L. Fridland, a workerin the public hospitals of Moscow, indirectly shifts the blame for theSoviet’s mounting disease rate among married couples on the easy divorceconditions prevalent since the Revolution.

In 1917 only two per cent. of the cases of venereal disease seen in Mos-cow hospitals occurred among married people. In 1924 this rate hadrisen to ten per cent., Dr. Fridland declares. Out of 100 diseased indi-viduals, only seven infected members of their own families before thewar in all Russia, he stated, while in 1918 the figure mounted to 33,and in 1924 had risen to the appalling proportion of 69.Incomplete cures and the casual marriages that have ensued since

divorce laws have become less stringent are believed to be importantfactors in the situation, which the government is endeavoring to combatby the establishment of ^prophylactorium^ stations for the disinfectionof people at the earliest possible stages of the disease.�Science News-Letter. ^