This study investigated the reliability of seven tests of mathematical abilities and their interrelationships among Spanish-speaking and English-speaking pre-algebra Hispanic students. Mathematical abilities were assessed by tests of divergent thinking, general reasoning, field-dependence, mathematics achievement, reading of mathematicalprose, syllogistic reasoning, and mathematical word problem solving. The results of the study indicated that all of these tests are reliable measures for Spanish-speaking students but that only four were reliable for the English-speaking subjects. None of the intercorrelation coefficients reached significance for the English-speaking pupils, but three intercorrelation indices were significant at the .01 level for the Spanish-speaking students. The implications of these findings for educational policy and mathematics education research are discussed.
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References
1.
Anick, C. M.
, Carpenter, T. P., & Smith, C. (1981, October). Minorities and mathematics: Results from the National Assessment of Educational Progress. Mathematics Teacher, 74, 560-566.
2.
Begle, E. G. (1972, November). Learning correlates for Mexican American students. Unpublished manuscript, Stanford University, SMSG Research and Analysis Section, Working Paper No. 12, Stanford, CA.
3.
Begle, E. G., Pence, B., Tsang, S-L., & Ginther, J. (1975a). The effect of review of prerequisite skills and concepts on learning a topic in mathematics for Chicano students. Unpublished manuscript, Stanford University, Stanford Mathematics Education Study Group, Working Paper No. 9, Stanford, CA.
4.
Begle, E. G., Pence, B., Tsang, S-L., & Ginther, J. (1975b). An exploratory analysis of math content structure as it relates to cognitive structure for Chicano students. Unpublished nmanuscript, Stanford University, Stanford Mathematics Education Study Group, Working Paper No. 11, Stanford, CA.
5.
Buriel, R.
, & Cardoza, D. (1988). Sociocultural correlates of achievement among three generations of Mexican American high school seniors. American Educational Research Journal, 25(2), 177-192.
6.
Carpenter, T. P.
, Corbit, M. K., Kepner, H. S. Jr., Lindquist, M. M., & Reys, R. E. (1980, May). Results of the second NAEP mathematics assessment: Secondary school. Mathematics Teacher, 73, 329-338.
7.
Carpenter, T. P.
, Lindquist, M. M., Matthews, W., & Silver, E. (1983, December). Results of the third NAEP mathematics assessment: Secondary school. Mathematics Teacher, 76, 652-659.
8.
Cole, M.
(1975). Culture, cognition and IO testing.National ElementaryPrincipal, 54(4), 49-52.
9.
Coleman, J. S.
, Campbell, E. O., Hobson, C. J., McPartland, J., Mood, A. M., Weinfield, F. D., & York, R. L. (1966). Equality of educational opportunity. Washington, DC: U.S. Government Printing Office.
10.
Collis, K. F.
(1987, March). Levels of reasoning and assessment of mathematical performance. In Thomas A. Romberg and Deborah M. Stewart (Eds.), The monitoring of school mathematics: Background papers, Vol. 2 (pp. 203-224). Madison: Wisconsin Center for Education Research.
11.
Cronbach, L. J.
(1970). Essentials of psychological testing (3rd ed.). New York: Harper & Row.
12.
Cronbach, L. J.
(1975). Five decades of public controversy over mental testing. American Psychologist, 30(1), 1-14.
13.
Cummins, J.
(1980). Psychological assessment of immigrant children: Logic or intuition. Journal of Multilingual and Multicultural Development, 1, 97-111.
14.
Darcy, N. T.
(1953). A review of the literature on the effects of bilingualism on the measurement of intelligence. Journal of Genetic Psychology, 87, 21-57.
15.
Darcy, N. T.
(1963). Bilingualism and the measurement of intelligence: Review of a decade of research. Journal of Genetic Psychology, 103, 259-282.
16.
Davis, O. L., Jr.
, & Personke, C. R., Jr. (1968, Fall). Effects of administering the Metropolitan Readiness Test in English and Spanish to Spanish-speaking school entrants. Journal of Educational Measurement.
17.
Dawe, L.
(1984, August). A theoretical framework for the study of effects of bilingualism on mathematics teaching and learning. Paper presented at the Fifth International Congress on Mathematical Education, Adelaide, Australia.
18.
Duran, R.
(in press). Testing of linguistic minorities. In Educational Measurement (3rd ed.). New York: Macmillan.
19.
French, J. W.
, Ekstrom, R. B., & Price, L. A. (1963, June). Kit of Reference Test for Cognitive Factors. Princeton, NJ: Educational Testing Service.
20.
Ginther, J. R.
(1978). Pretraining Chicano students before administration of a mathematics predictor test. Journalfor Research in Mathematics Education, 9(2), 118-125.
21.
Hakuta, K.
(1986). Mirror of language: The debate on bilingualism. New York: Basic Books.
22.
Hanson, E. J. (1931). A study of intelligence test results for Mexican children based on English and Mexican test forms. Unpublished master's thesis, University of Southern California, Los Angeles, CA.
23.
Jarvis, R. K. (1972, July). Predicting mathematics achievement on the basis of ability in reading mathematical material: Missing words tests. Pilot studies. Unpublished manuscript, Stanford University, School Mathematics Study Group, Research and Analysis Section, Working Paper No. 11, Stanford, CA.
24.
Keston, M. J.
, & Jimenez, C. (1954). A study of the performance on English and Spanish editions of the Stanford-Binet intelligence test by Spanish-American children. The Journal of Genetic Psychology, 85, 263-269.
25.
Kilpatrick, J.
, & Wagner, S. (1983). Bibliography on mathematical abilities. Athens: The University of Georgia, Mathematical Abilities Project.
26.
Llabre, M. M.
, & Cuevas, G. (1983). The effects of test language and mathematical skills assessed on the scores of bilingual Hispanic students. Journal for Research in Mathematics Education, 14(4), 318-324.
27.
Mahakian, C.
(1939, June). Measuring intelligence and reading capacity of Spanish-speaking children. The Elementary School Journal, 39, 760-768.
28.
Manuel, H. T.
(1935). A comparison of Spanish-speaking and English-speaking children in reading and arithmetic. Journal ofApplied Psychology, 19, 189-202.
29.
Manuel, H. T.
(1952). Bilingualism: The measurement of ability in two languages. Texas Journal of Science, 4(4), 490-493.
30.
Maspons, M. M.
, & Llabre, M. M. (1985). The influence of training Hispanics in test taking on the psychometric properties of a test. Journalfor Research in Mathematics Education16(3), 177-183.
31.
Massaroti, M. C. (1971). Effects of the Spanish language as auditory stimulation during test administration on the measured achievement of fifth grade Spanish-surnamed pupils (Doctoral dissertation, University of Denver, 1971). Dissertation Abstracts International, 32, 3865A-3866A.
32.
Matthews, W.
(1984, March). Influences on the learning and participation of minorities in mathematics. Journal for Research in Mathematics Education, 15, 84-95.
33.
Matthews, W.
, Carpenter, T. P., Lindquist, M. M., & Silver, E. (1984, March). The third national assessment: Minorities and mathematics. Journal for Research in Mathematics Education, 15, 165-171.
34.
Mestre, J. P.
, & Gerace, W. J. (1986). A study of the algebra acquisition of Hispanic and Anglo ninth graders: Research findings relevant to teacher training and classroom practice. NABE Journal, 10(2), 137-167.
35.
Moore, E. G. J.
, & Smith, A. W. (1987). Sex and ethnic group differences in mathematics achievement: Results from the National Longitudinal Study. Journal for Research in Mathematics Education, 18(1), 25-36.
36.
Padilla, A. M.
(1979). Critical factors in the testing of Hispanic Americans: A review and some suggestions for the future. In R. W. Tyler and S. H. White (Eds.), Testing, teaching and learning (pp. 219-243). Washington, DC: The National Institute of Education.
37.
Palmer, M.
, & Gaffney, P. (1972). Effects of administration of the WISC in Spanish and English and relationship of social class to performance. Psychology in the Schools, 9, 61-64.
38.
Roca, P.
(1955). Problems of adapting intelligence scales from one culture to another. High School Journal, 38, 124-131.
39.
Romberg, T. A.
(1987, March). Measures of mathematical achievement. In Thomas A. Romberg and Deborah M. Stewart (Eds.), The monitoring of school mathematics: Background papers, Vol. 2 (pp. 131-151). Madison: Wisconsin Center for Educational Research.
40.
Romberg, T. A.
, & Zarinnia, A.(1987, March). Consequences of the new world view to assessment of student's knowledge of mathematics. In Thomas A. Romberg and Deborah M. Stewart (Eds.), The monitoring of school mathematics: Backgroundpapers, Vol. 2 (pp. 153-202). Madison: Wisconsin Center for Educational Research.
41.
Sanchez, G. I.
(1932, October). Group differences and Spanish-speaking children: A critical review. Journal of Applied Psychology, 16, 549-558.
42.
Sanchez, G. 1.
(1934). Bilingualism and mental measurement. Journal of Applied Psychology, 8(6), 765-772.
43.
Sheldon, W. H.
(1924, February). The intelligence of Mexican school children. School and Society, 19, 139-142.
44.
Swanson, F.
, & Deblassie, R. R. (1971, October). Interpreter effects on the WISC performance of first grade Mexican-American children. Measurement and Evaluation in Guidance, 4(3), 172-175.
45.
Thomas, S. (c. 1970). Low achiever study. Unpublished manuscript, Stanford University, SMSG Research and Analysis Section, Working Paper No. 5, Stanford, CA.
46.
Tsang, S-L. (1976). The effects of the language factor and the cultural content factor of mathematics achievement tests on Chinese and Chicano students (Doctoral dissertation, Stanford University, 1976). Dissertation Abstracts International, 37, 714A.
47.
Webb, N. L.
(1987, March). Another look at assessment: Areaction to Chapters 17-20. In Thomas A. Romberg and Deborah M. Stewart (Eds.), The monitoring of school mathematics: Background papers, Vol. 2 (pp. 242-260). Madison: Wisconsin Center for Educational Research.
48.
Wilson, J. W.
, Cahen, L. S., & Begle, E. G. (Eds.). (1968a). Y-Population test batteries (NLSMA Reports, No. 2, Part A). Stanford, CA: Stanford University.
49.
Wilson, J. W.
, Cahen, L. S., & Begle, E. G. (Eds.). (1968b). Z-Population test batteries (NLS MA Reports, No. 3). Stanford, CA: Stanford University.
50.
Wilson, J. W.
, Cahen, L. S., & Begle, E. G. (Eds.). (1968c). Description and statisticalproperties of Y-population scales (NLSMA Reports, No. 5). Stanford, CA: Stanford University.
51.
Wilson, J. W.
, Cahen L. S., & Begle E. G. (Eds.). (1968d). Description and statisticalproperties of Z-population scales (NLSMA Reports, No. 6). Stanford, CA: Stanford University.
52.
Wilson, J. W.
, Cahen, L. S., & Begle, E. G. (Eds.). (1969). The development of tests (NLSMA Reports, No. 7) Stanford, CA: Stanford University.
53.
Yoder, D.
(1928). Present status of the question of racial differences. Journal of Educational Psychology, 19, 463-470.
