TY - JOUR

T1 - Mathematical-educational implications of some statistical distribution problems

AU - Yeshurun, Shraga

AU - Merzbach, Ely

PY - 1983

Y1 - 1983

N2 - HHC (hand-held calculators) and computers have spread more and more in schools generally, and in secondary schools especially. Their use can be seen as a new item in learning and teaching methods. As with any new item in learning and teaching methods, the use of HHC and computers influences both the way of solving problems and the kind of problems to solve. One of the new kinds of problems to solve is: how often has a given problem different kinds of solutions? Some of these problems and their emanations into mathematical education are dealt with in this paper, assuming the data (e.g., coefficients of an equation or lengths of segments) are chosen from a uniformly distributed continuous population. The main results are: Theoretical probability of solutions Problem Restrictions Complex Double Two real One real Quadratic equation -03728 0.0000 0.6272 -Quadratic equation Positive coefficients 0.7456 0.0000 0.2544 -SSA triangle problem -0.4092 0.0000 00908 0.5000 Linear goniometric equation -0.2618 0.0000 0.7382 -Linear goniometric equation Positive coefficients 0.2618 0.0000 0.7382 -From the psychological, pedagogical point of view, this kind of problem furnishes further, till now not very common, examples of the relative frequency (von Mises [1, 2]) interpretations of probability.

AB - HHC (hand-held calculators) and computers have spread more and more in schools generally, and in secondary schools especially. Their use can be seen as a new item in learning and teaching methods. As with any new item in learning and teaching methods, the use of HHC and computers influences both the way of solving problems and the kind of problems to solve. One of the new kinds of problems to solve is: how often has a given problem different kinds of solutions? Some of these problems and their emanations into mathematical education are dealt with in this paper, assuming the data (e.g., coefficients of an equation or lengths of segments) are chosen from a uniformly distributed continuous population. The main results are: Theoretical probability of solutions Problem Restrictions Complex Double Two real One real Quadratic equation -03728 0.0000 0.6272 -Quadratic equation Positive coefficients 0.7456 0.0000 0.2544 -SSA triangle problem -0.4092 0.0000 00908 0.5000 Linear goniometric equation -0.2618 0.0000 0.7382 -Linear goniometric equation Positive coefficients 0.2618 0.0000 0.7382 -From the psychological, pedagogical point of view, this kind of problem furnishes further, till now not very common, examples of the relative frequency (von Mises [1, 2]) interpretations of probability.

UR - http://www.scopus.com/inward/record.url?scp=84946364147&partnerID=8YFLogxK

U2 - 10.1080/0020739830140208

DO - 10.1080/0020739830140208

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

SN - 0020-739X

VL - 14

SP - 189

EP - 200

JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

IS - 2

ER -