Abstract
In an attempt to address shortcomings revealed in international assessments and lamented in legislation, many schools are reducing or eliminating elective courses, applying the rationale that replacing “non-essential” subjects with core subjects, such as mathematics and language arts, will better position students in the global market. However, there is evidence that systematically pairing a core subject with another, complementary subject, may lead to greater overall learning in both subjects. In this paper, we analyze two subject area pairs—first and second language, and computer programming and mathematics—to demonstrate in what ways two subjects might complement each other. We then analyze the relationships between these pairs to better understand the principles and conditions that encourage what we call convergent cognition, the synergistic effect that occurs when a learner studies two complementary subjects.
Similar content being viewed by others
References
Agalianos, A., Noss, R., & Whitty, G. (2001). Logo in mainstream schools: The struggle over the soul of an educational innovation. British Journal of Sociology of Education, 22(4), 479–500.
American Council of Teachers of Foreign Languages. (2009). What does research show about the benefits of language learning? Retrieved December 12, 2009 from http://www.actfl.org/i4a/pages/index.cfm?pageid=4724.
Andrade, C. (1989). Two languages for all children: Expanding to low achievers and the handicapped. In E. Muller (Ed.), Languages in the elementary schools (pp. 177–203). New York: The American Forum.
Austin, H. S. (1987). Predictors of Pascal programming achievement for community college students. In Proceedings of the Eighteenth SIGCSE Technical Symposium on Computer Science Education (pp. 161–164). Dordrecht: Kluwer Academic Publishers.
Bae, J. (2007). Development of English skills need not suffer as a result of immersion: Grades 1 and 2 writing assessment in a Korean/English two-way immersion program. Language Learning, 57(2), 299–332.
Barber, G. E. (1985). Latin as a practical study. The Classical Journal, 81(2), 158–160.
Barnett, S. M., & Ceci, S. J. (2002). When and where do we apply what we learn?: A taxonomy for far transfer. Psychological Bulletin, 128(4), 612–637.
Bassok, M., & Holyoak, K. J. (1989). Interdomain transfer between isomorphic topics in algebra and physics. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15(1), 153–166.
Bassok, M., & Holyoak, K. J. (1993). Pragmatic knowledge and conceptual structure: Determinants of transfer between quantitative domains. Ablex Publishing.
Bastian, T. R. (1980). An investigation into the effects of second language learning on achievement in English. Dissertation Abstracts International. 40(12-A, Pt. 1), 6176–6177.
Bergin, S., & Reilly, R. (2006). Predicting introductory programming performance: A multi-institutional multivariate study. Computer Science Education, 16(4), 303–323.
Bloch, S. (2007). Teach scheme!: A functional-first approach to beginning programming. Journal of Computing Sciences in Colleges, 22(3), 161–163.
Byrne, P., & Lyons, G. (2001). The effect of student attributes on success in programming. ACM SIGCSE Bulletin, 33(3), 49–52.
California dept. of Education. (2010). Student access to core courses. Retrieved October 1, 2010 from http://www.cde.ca.gov/ta/lp/vl/hsepc2.asp.
Campione, J. C., & Brown, A. L. (1981). Inducing flexible thinking: The problem of access. In M. P. Friedman, J. P. Das, & N. O’Connor (Eds.), Intelligence and learning. New York: Plenum Press.
Campione, J. C., & Brown, A. L. (1984). Learning ability and transfer propensity as sources of individual differences in intelligence. In Learning and Cognition in the Mentally Retarded (pp. 265–293). Hillsdale: Lawrence Earlbaum Associates.
Carraher, D., & Schliemann, A. (2002). The transfer dilemma. Journal of the Learning Sciences, 11(1), 1–24.
Chen, X., Xu, F., Nguyen, T. K., Hong, G., & Wang, Y. (2010). Effects of cross-language transfer on first-language phonological awareness and literacy skills in Chinese children receiving English instruction. Journal of Educational Psychology, 102(3), 712–728. doi:10.1037/a0018802.
Cisero, C. A., & Royer, J. M. (1995). The development and cross-language transfer of phonological awareness. Contemporary Educational Psychology, 20(3), 275–303. doi:10.1006/ceps.1995.1018.
Clements, D. H., Battista, M. T., & Sarama, J. (2001). Logo and geometry [Monograph]. Journal for Research in Mathematics Education, 42(2), 127–166.
Collier, V. P., & Thomas, W. P. (2002). The astounding effectiveness of dual language education for all. NABE Journal of Research and Practice, 2(1), 1–20.
Cook, V. (1992). Evidence of multicompetence. Language Learning, 42, 557–591.
Corte, E. D., Verschaffel, L., & Schrooten, H. (1992). Computer-based learning environments and problem solving (pp. 207–228). New York: Springer.
Cummins, J. (1978). The cognitive development of children in immersion programs. Canadian Modern Language Review, 34(5), 855–883.
Cunningham, T. H., & Graham, C. R. (2000). Increasing native English vocabulary recognition through Spanish immersion: Cognate transfer from foreign to first language. Journal of Educational Psychology, 92(1), 37–49.
de Corte, E., & Verschaffel, L. (1986). Effects of computer experience on children’s thinking skills. Journal of Structural Learning, 9, 161–174.
de Corte, E., & Verschaffel, L. (1989). Logo, a vehicle for thinking. In B. Greer & G. Mulhern (Eds.), New directions in mathematics education (pp. 63–81). London: Routledge.
Deary, I., Strand, S., Smith, P., & Fernandes, C. (2007). Intelligence and educational achievement. Intelligence, 35(1), 13–21.
Demie, F., & Strand, S. (2006). English language acquisition and educational attainment at the end of secondary school. Educational Studies, 32(2), 215–231.
Doye, P. (1977). Untersuchungen zum englischunterricht in der grundschule: Bericht uber D. Westermann: Braunschweiger forschungsprojekt FEU.
Eddy, P. A. (1981). The effect of foreign language study in high school on verbal ability as measured by the scholastic aptitude test-verbal. Final report. Washington, D.C.: Center for applied linguistics. (ERIC Document Reproduction Services No. ED 196 312).
Feurzeig, W., Papert, S., Bloom, M., Grant, R., & Solomon, C. (1970). Programming-languages as a conceptual framework for teaching mathematics. SIGCUE Outlook, 4(2), 13–17.
Friel, B. (2003). Don’t know much about history. National Journal, 35(31), 2550–2551.
Gagné, R. M. (1974). Essentials of learning for instruction. Hinsdale: The Dryden Press.
Gale, K., McClay, D., Christie, M., & Harris, S. (1981). Academic achievement in the Milingimbi bilingual education program. TESOL Quarterly, 15(3), 297–314.
Gorman, H., & Bourne, L. E. (1983). Learning to think by learning logo: Rule learning in third-grade computer programmers. Bulletin of Psychonomic Society, 21, 165–167.
Gruber, H. E., & Gruber, V. (1962). The eye of reason: Darwin’s development during the beagle voyage. Isis, 53, 186–200.
Haskell, R. E. (2001). Transfer of learning: Cognition, instruction, and reasoning (illustrated ed.). San Diego: Academic Press.
Honour-Werth, L. (1986). Predicting student performance in a beginning computer science class. In Proceedings of the Seventeenth SIGCSE Technical Symposium on Computer Science Education (pp. 138–143). Cincinnati: SIGCSE.
Hostetler, T. R. (1983). Predicting student success in an introductory programming course. ACM SIGCSE Bulletin, 15(3), 40–43.
Howard, E. R., Sugarman, J., & Christian, D. (2003). Trends in two-way immersion education: A review of the research (report no. 63). Baltimore: Center for Research on the Education of Students Placed at Risk. Retrieved from April 19, 2007.
Hoyles, C., & Noss, R. (1987). Synthesizing mathematical conceptions and their formalization through the construction of a logo-based school mathematics curriculum. International Journal of Mathematical Education in Science and Technology, 18(4), 581–595.
Hoyles, C., & Noss, R. (1992). Learning mathematics and logo. Cambridge: MIT Press.
Jarvis, S., & Pavlenko, A. (2008). Crosslinguistic influence in language and cognition (illustrated ed.). New York: Routledge.
Johnson, D. C. (2000). Algorithmics and programming in the school mathematics curriculum: Support is waning—is there still a case to be made? Education and Information Technologies, 5, 201–215.
Kesckes, I., & Papp, T. (2000). Foreign language and mother tongue. Hillsdale: Lawrence Earlbaum.
Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A., & Stephens, A. C. (2005). Middle school students’ understanding of core algebraic concepts: Equivalence & variable 1. ZDM, 37(1), 68–76.
Kotovsky, K., Hayes, J. R., & Simon, H. A. (1985). Why are some problems hard? Evidence from the tower of Hanoi. Cognitive Psychology, 17, 248–294.
Krashen, S. D. (1987). English language teaching series: Principles and practices in second language acquisition. London: Prentice-Hall: International (UK) Ltd.
Leatham, K. R. (2006). Viewing mathematics teachers’ beliefs as sensible systems. Journal of Mathematics Teacher Education, 9(1), 91–102. doi:10.1007/s10857-006-9006-8.
Leeper, R. R., & Silver, J. L. (1982). Predicting success in a first programming course. In Proceedings of the Thirteenth SIGCSE Technical Symposium on Computer Science Education, (pp. 147–150). Dallas: SIGCSE.
Leinhart, G., Zalavsky, O., & Stein, M. K. (1990). Functions graphs, and graphing. Tasks, Learning, and Teaching, 60(1), 1–64.
Linn, M. C., & Dalbey, J. (1985). Cognitive consequences of programming instruction, access, and ability. Educational Psychologist, 20, 191–206.
Lopato, E. (1963). FLES and academic achievement. The French Review, 36(5), 499–507.
Manis, F. R., Lindsey, K. A., & Bailey, C. E. (2004). Development of reading in grades K-2 in Spanish-speaking English-language learners. Learning Disabilities Research & Practice, 19(4), 214–224.
Masciantonio, R. (1977). Tangible benefits of the study of Latin: A review of research. Foreign Language Annals, 10(4), 375–382.
McCoy, L. P. (1988). General variable skill, computer programming and mathematics. In Paper presented at the annual meeting of the International Association for Computing in Education. New Orlean: IACE.
McCoy, L. (1996). Computer-Based mathematics learning. Journal of Research on Computing in Education, 28, 438–460.
Miller, R., Kelly, G., & Kelly, J. (1988). Effects of logo computer programming experiences on problem solving and spatial relations ability. Contemporary Educational Psychology, 13, 348–357.
Milner, S. (1973). The effects of computer programming on performance in mathematics. In Proceedings from the annual meeting of the american educational research association. New Orlean, LA.
Moreno, R., Ozogul, G., & Reisslein, M. (2011). Teaching with concrete and abstract visual representations: Effects on students’ problem solving, problem representations, and learning perceptions. Journal of Educational Psychology, 103(1), 32. doi:10.1037/a0021995.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: Author.
North, K. (2007). Integrated algebra/computer science. Retrieved December 12, 2009 from http://teachertech.rice.edu/Participants/knorth/algebra/index.htm.
Noss, R. (1986). Constructing a conceptual framework for elementary algebra through logo programming. Educational Studies in Mathematics, 17(4), 335–357.
OECD. (2007). PISA 2006: Science competencies for tomorrow’s world. Exectuve summary. Paris: OECD.
Offenberg, R. M. (1971). Evaluation of the elementary school (FLES) Latin program 1970–1971. Philadelphia: Philadelphia School District Office. (ERIC Document Reproduction Service NO. ED 056 612).
Oprea, J. M. (1988). Computer programming and mathematical thinking. Journal of Mathematical Behavior, 7(2), 175–190.
Palumbo, D. B. (1990). Programming language/problem-solving research: A review of relevant issues. Review of Educational Research, 60(1), 65–89.
Paris, S. G., & McEvoy, A. P. (2000). Harmful and enduring effects of high-stakes testing. Issues in Education, 6(1/2), 145–160.
Pavlenko, A. (2003). ‘I feel clumsy speaking Russian’: L2 influence on L1 in narratives of Russian L2 users of English. In Second language acquisition: Effects of the second language on the first (pp. 32–61). Clevedon: Multilingual Matters.
Paz, T., & Leron, U. (2009). The slippery road from actions on objects to functions and variables. Journal for Research in Mathematics Education, 40, 18–39.
Pea, R. D., & Kurland, D. M. (1984). On the cognitive effects of learning computer programming. New Ideas in Psychology, 2(2), 137–168.
Piaget, J. (1954). The construction of reality in the child. New York: Norton.
Powell, A. G., Farrar, E., & Cohen, D. K. (1985). The shopping mall high school: Winners and losers in the educational marketplace. Boston: Houghton Mifflin.
Rosenthal, B. (2004). No subject left behind? Think again. NEA Today, 23(2), 26–27.
Säljö, R. (2003). Epilogue: From transfer to boundary crossing new perspectives on transfer and boundary-crossing between school and work (p. 311). New York: Pergamon.
Salomon, G., & Perkins, D. (1989). Rocky roads to transfer: Rethinking mechanisms of a neglected phenomenon. Educational Psychologist, 24, 113–142.
Schwarz, B. B., & Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 30, 362–389.
Sheridan, R. (1976). Augmenting reading skills through language learning transfer. FLES latin program evaluation reports, 1973–74, 1974–75, 1975–76 [microform]/rita Sheridan.
Sinclair, N. (2008). The history of the geometry curriculum in the United States. Charlotte: Information Age Publishing, Inc.
Soloway, E., Lochhead, J., & Clement, J. (1982). Does computer programming enhance problem-solving ability? In R. E. Seidel, R. E. Anderson, & B. Hunter (Eds.), Computer literacy (pp. 171–185). New York: Academic Press.
Stanovich, K. E. (1986). Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy. Reading Research Quarterly, 21(4), 360–407.
Stewart, J. H. (2005). Foreign language study in elementary schools: Benefits and implications for achievement in reading and math. Early Childhood Education Journal, 33(1), 11–16.
Subhi, T. (1999). The impact of LOGO on gifted children’s achievement and creativity. Journal of Computer Assisted Learning, 15(2), 98–108.
Thompson, P. W. (1994). Students, functions, and the undergraduate curriculum. In E. Dubinsky, A. H. Schoenfeld, & J. J. Kaput (Eds.), Research in collegiate mathematics education (pp. 21–44). Providence: American Mathematical Society.
Thorndike, E. L., & Woodworth, R. S. (1901). The influence of improvement in one mental function upon the efficiency of other functions. Psychological Review, 8, 247–261.
Turnbull, M., Lapkin, S., & Hart, D. (2001). Grade 3 immersion students’ performance in literacy and mathematics: Province-wide results from Ontario (1998–1999). Canadian Modern Language Review, 58(1), 9–26.
U.S. Department of Education. (2008). Foundations for succes. The final report of the national mathematics advisory panel. Washington, DC: U.S. Department of Education.
Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In The ideas of algebra. Virginia: The National Council of Teachers of Mathematics, Inc.
Weatherford, H. J. (1986). Personal benefits of foreign language study. Eric digest # 276 305. Washington, D.C.: Office of Educational Research and Improvement.
Wertheimer, M. (1959). Productive thinking. New York: Harper & Row.
Wilson, B. C., & Shrock, S. (2001). Contributing to success in an introductory computer science course: A study of twelve factors. ACM SIGCSE Bulletin, 33(1), 184–188.
Zheng, R. (2009). Cognitive effects of multimedia learning (illustrated ed.). Hershey: Idea Group Inc (IGI).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rich, P.J., Leatham, K.R. & Wright, G.A. Convergent cognition. Instr Sci 41, 431–453 (2013). https://doi.org/10.1007/s11251-012-9240-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11251-012-9240-7