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ERIC Number: ED017465
Record Type: RIE
Publication Date: 1967
Pages: 101
Abstractor: N/A
Reference Count: 0
ISBN: N/A
ISSN: N/A
TEACHING COLLEGE STUDENTS HOW TO LEARN MATHEMATICS. WHAT IS LEARNED IN MATHEMATICAL DISCOVERY.
SCANDURA, JOSEPH M.
THIS STUDY RELATED TO DISCOVERY METHODS OF TEACHING AND LEARNING WAS CONCERNED WITH TWO MAJOR QUESTIONS. FIRST, CAN "WHAT IS LEARNED" THROUGH MATHEMATICAL DISCOVERY BE IDENTIFIED AND TAUGHT BY EXPOSITION WITH EQUIVALENT RESULTS. SECOND, HOW DOES "WHAT IS LEARNED" DEPEND ON PRIOR LEARNING AND ON THE NATURE OF THE DISCOVERY TREATMENT ITSELF. IN A PREVIOUS STUDY, GAGNE AND BROWN FOUND THAT DISCOVERY GROUPS WERE BETTER ABLE TO DERIVE NEW FORMULAS THAN WERE RULE-GIVEN GROUPS. IN THE PRESENT STUDY IT WAS HYPOTHESIZED THAT (1) WHAT WAS LEARNED BY GUIDED DISCOVERY IN THE GAGNE AND BROWN STUDY CAN BE PRESENTED BY EXPOSITION WITH EQUIVALENT RESULTS, (2) PRESENTATION ORDER IS CRITICAL WHEN THE HINTS PROVIDED DURING DISCOVERY ARE SPECIFIC TO THE RESPECTIVE FORMULAS SOUGHT RATHER THAN RELEVANT TO A GENERAL STRATEGY, AND (3) PRESENTATION ORDER IS NOT CRITICAL WHEN THE PROGRAM EFFECTIVELY FORCES THE STUDENT TO LEARN THE GENERAL STRATEGY IRRESPECTIVE OF THE EXPOSITION OR DISCOVERY LEARNING METHOD. ONE OR TWO OF FOUR PROGRAMS--RULE GIVEN (R), DISCOVERY (D), GUIDED DISCOVERY (G), AND HIGHER-ORDER EXPOSITION (E)--WERE ADMINISTERED TO SEVEN GROUPS--R, RD, DR, RG, GR, RE, AND ER. ALL STUDENTS WERE REQUIRED TO DERIVE NEW RULES WITHIN THE SCOPE OF THE IDENTIFIED HIGHER-ORDER RULE. AS HYPOTHESIZED, GROUPS R AND RD PERFORMED AT ONE LEVEL WHICH WAS RELIABLY BELOW THE COMMON LEVEL OF THE OTHER FIVE GROUPS. TWO POINTS OF EMPHASIS IN THE CONCLUSION AND IMPLICATIONS WERE (1) "WHAT IS LEARNED" DURING GUIDED DISCOVERY CAN AT LEAST BE IDENTIFIED AND TAUGHT BY EXPOSITION WITH EQUIVALENT RESULTS, AND (2) IF A PERSON ALREADY KNOWS THE DESIRED RESPONSES, HE IS NOT LIKELY TO DISCOVER A HIGHER ORDER RULE BY WHICH SUCH RESPONSES MAY BE DERIVED. (RP)
Publication Type: N/A
Education Level: N/A
Audience: N/A
Language: N/A
Sponsor: N/A
Authoring Institution: Pennsylvania Univ., Philadelphia.
Identifiers: UNIVERSITY OF PENNSYLVANIA