Three mathematical reasoning tasks (proportions, reasoning with an unknown, and a spatial reasoning task), and an attitude interview were individually administered to 260 8th grade students from three predominately minority urban schools. The three schools and neighborhoods varied in educational advantages as well as in socioeconomic characteristics. An additional 60 students, from a middle class and predominately white school in which a similar study had been conducted previously, was included in some comparisons. A battery of groupadministered cognitive tasks and attitude scales was also administered to the students. The results showed a significant effect for site on all three tasks; however, the variance accounted for by site was slight for the spatial reasoning task and reasoning with unknowns (approximately 5%) while it was substantially larger for porportions (21%). Other characteristics that differed across sites were: (a) solution strategies for reasoning with unknowns and in the simple proportion problems; (b) cognitive correlates for each task; and (c) attitude regarding perceived competence and need for mathematics as well as for the perceived amount of effort expended on mathematics. The results are interpreted to indicate the need for an ecological approach to research on adolescent reasoning. Multiple tasks should be examined in multiple settings, and the relationship between attitudes and cognition should be considered.
Get full access to this article
View all access options for this article.
References
1.
Adi, H.
, & Pulos, S.Individual differences in formal thought among college students. Journal for Research in Mathematics Education, 1980,11,150-155.
2.
Anyon, J.Social class and school knowledge
. Curriculum Inquiry, 1981, 11, 2-44.
3.
Bereiter, C.
, & Scardamalia, M.Pascual-Leone's M construct as a link between cognitive developmental and psychometric concepts of intelligence. Intelligence, 1979, 3, 41-64.
4.
Bronfenbrenner, U.The ecology of human development. Cambridge, MA: Harvard University Press, 1979.
5.
Boyle, R. P.The effect of the high school on students' aspirations
. American Journal of Sociology1966, 71, 628-639.
6.
Buck-Morss, S.Socioeconomic bias in Piaget's theory. In A. R. Buss (Ed.), Psychology in social context. New York: John Wiley, 1979.
7.
Carroll, J. B.Psychometric tests as cognitive tasks. In L. B. Resnick (Ed.), The nature of intelligence. Hillsdale, NJ: LEA, 1976.
8.
Case, R.Mental Strategies, mental capacity and instruction: A neo-Piagetian investigation
. Journal of Experimental Child Psychology, 1974,18, 382-397.
9.
Case, R.The underlying mechanism of intellectual development. In J. R. Kirby & J. B. Briggs (Eds.), Cognitive development and instruction. New York: Academic Press, 1980.
10.
Charlesworth, W. R.Human intelligence as adaptation. In L. B. Resnick (Ed.), The nature of intelligence. Hillsdale, NJ: LEA, 1976.
11.
CTB/McGraw-Hill
, Comprehensive Test of Basic Skills. Monterey: CTB/McGraw-Hill, 1975.
12.
DeAvila, E.
, Havassy, B., & Pascual-Leone, J.Mexican-American school children: A neo Piagetian analysis. Washington D.C.: Georgetown University Press, 1976.
13.
de Ribaupierre, A.
& Pascual-Leone, J.Formal operations and M power: A neo-Piagetian investigation. In D. Kuhn (Ed.) Intellectual development beyond childhood. San Francisco: Jossey-Bass, 1979.
14.
Douglas, J.
& Wong, A.Formal operations: Age and sex differences in Chinese and American children. Child Development, 1977, 48, 689-692.
15.
Ekstrom, R. B.
, French, J. W., Harman, H. H., & Dermen, D.Manual for kit offactorreferenced cognitive tests. Princeton, NJ; Educational Testing Services, 1976.
16.
Fennema, E.
& Sherman, J.Sex-related differences in mathematics achievement, spatial visualization and affective factors. American Education Research Journal. 1977, 14, 51-71.
17.
Green, D.Attitudes. In S. Ball (Ed.), Motivation in education. New York: Academic Press, 1977.
18.
Horn, J. L.Human ability systems. In P. B. Baltes (Ed.) Life-span development and behavior (Vol. 1). New York: Academic Press, 1978.
19.
Inhelder, B.
& Piaget, J.The growth of logical thinking from childhood to adolescence. New York: Basic Books, 1958.
20.
Karplus, R.Proportional reasoning in the People's Republic of China
. Genetic Epistemologist, 1978, 7, 5-6.
21.
Karplus, R.
, Karplus, E., Formisano, M., & Paulsen, A. C.Proportional reasoning and control of variables in seven countries. In J. Lochhead & J. Clements (Eds.), Cognitive process instruction. Philadelphia: Franklin Institute Press, 1979.
22.
Karplus, R.
, Pulos S., & Stage, E. K.Early adolescents' reasoning with unknowns. In C. Comiti (Ed.), Proceedings of the fifth international conference for the psychology of mathematics education, Grenoble, France: Laboratoire I.M.A.G., 1981.
23.
Karplus, R.
, Pulos, S., & Stage, E. K.The development of proportional reasoning in adolescence. In R. Lesh & M. Landau (Eds.) Acquisition of mathematical concepts and process. New York: Academic Press, in press.
24.
Keating, D.Adolescent thinking. In J. Adelson (Ed.), Handbook of adolescence. New York: Wiley, 1979.
25.
Kishta, M.Proportional and combinatorial reasoning in two cultures
. Journal of Research in Science Teaching, 1979,16, 439-443.
26.
Kulm, G.Research on mathematics attitudes. In R. J. Shumway (Ed.), Research in mathematics education. Reston, VA: NCTM, 1980.
27.
Linn, M. C.
, & Kyllonen, P.The field dependence-independence construct: Some, one, or none. Journal of Educational Psychology, 1981, 73, 261-273.
28.
Linn, M. C.
, & Swiney, J. F.Individual differences in formal thought: Role of expectations and aptitudes. Journal of Educational Psychology, 1981, 73, 274-286.
29.
Neimark, E.Intellectual development during adolescence. In F. Degdn (Ed.), Review of Child Development Research (Vol. 4). Chicago: University of Chicago, 1975.
30.
Neimark, E.Current status of formal operations research
. Human Development, 1979, 22, 60-67.
31.
Ogbu. J. U.The next generation: An ethnography of education in an urban neighborhood. New York: Academic Press, 1974.
32.
Pascual-Leone, J.
, & Goodman, D.Intelligence and experience: A neo-Piagetian approach. Instructional Science, 1979,8, 301-367.
33.
Piaget, J.
, & Inhelder, B.Mental imagery in the child. New York: Basic Books, 1971.
34.
Pulos, S.
, & Linn, M. C.Generality of the controlling variable in early adolescence. Journal of Early Adolescence, 1981,1, 26-37.
35.
Pulos, S.
, Stage, E. K., Karplus, E., & Karplus, R.Spatial visualization and proportional reasoning of early adolescents. In C. Comiti (Ed.), Proceedings of the fifth annual international conference for the psychology of mathematics education. Grenoble, France: Laboratoire I.M.A.G., 1981.
36.
Riegel, K. F.Foundations of dialectical psychology. New York: Academic Press, 1979.
37.
Roberts, J.Intellectual characteristics of children by demographic and socioeconomic factors. Washington, D. C.: U.S. Government Printing Office, 1972.
38.
Simon, H. A.Identifying basic abilities underlying intelligent performance of complex tasks. In L. B. Resnick (Ed.), The nature of intelligence. Hillsdale, NJ: LEA, 1976.
39.
Riegler, R. S.Developmental sequences within and between concepts. Monograph of the Society for Research in Child Development, 1981, 184-184.
40.
Stage, E. K.
, Karplus, R., & Pulos, S.Social context of early adolescents' proportional reasoning. In R. Karplus (Ed.), Proceedings of the fourth international conference for the psychology of mathematics education. Berkeley: University of California, 1980.
41.
Thurstone, T. G.Primary mental abilities for grades6-9. Chicago: Science Research Associates, 1962.
42.
Vandenberg, S.
, & Kuse, A.Spatial ability. In M. A. Wittig & A. C. Peterson (Eds.), Sex-related differences in cognitive functioning. New York: Academic Press, 1979.
43.
Vygotsky, L. S.Mind in society. Cambridge: Harvard University Press, 1978.
44.
Witkin, H. A.
, & Goodenough, D. P.Cognitive styles: Essence and origins. New York: International Universities Press, 1981.
