# Multiple solution methods and multiple outcomes—is it a task for kindergarten children?

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## Abstract

Engaging students with multiple solution problems is considered good practice. Solutions to problems consist of the outcomes of the problem as well as the methods employed to reach these outcomes. In this study we analyze the results obtained from two groups of kindergarten children who engaged in one task, the Create an Equal Number Task. This task had five possible outcomes and five different methods which may be employed in reaching these outcomes. Children, whose teachers had attended the program Starting Right: Mathematics in Kindergartens, found more outcomes and employed more methods than children whose teachers did not attend this program. Results suggest that the habit of mind of searching for more than one outcome and employing more than one method may be promoted in kindergarten.

## Keywords

Multiple solution methods Multiple solution outcomes Mathematics in kindergarten## References

- Ainsworth, S., Wood, D., & O'malley, C. (1998). There is more than one way to solve a problem: Evaluating a learning environment that supports the development of children's multiplication skills.
*Learning and Instruction, 8*(2), 141–157.CrossRefGoogle Scholar - Carpenter, T., Ansell, E., Franke, M., Fennema, E., & Weisbeck, L. (1993). Models of problem solving: A study of kindergarten children’s problem solving processes.
*Journal for Research in Mathematics Education, 24*(5), 427–440.CrossRefGoogle Scholar - Clements, H. D., & Sarama, J. (2007). Early childhood mathematics learning. In F. K. Lester Jr. (Ed.),
*Second Handbook of Research on Mathematics Teaching and Learning*(pp. 461–556). Charlotte, NC: Information Age Publishing.Google Scholar - Department for Education and Employment (DfEE) (2000).
*Investing in our future curriculum guidance for the foundation stage.*Google Scholar - Israeli National Mathematics Curriculum (2008).
*Mathematics curriculum for Pre-Elementary School.*Google Scholar - Gullen, G. E. (1978). Set comparison tactics and strategies of children in kindergarten, first grade, and second grade.
*Journal for Research in Mathematics Education, 9*(5), 349–360.CrossRefGoogle Scholar - Krutetskii, V. A. (1976).
*The psychology of mathematical abilities in schoolchildren*. In J. Teller (Trans), J. Kilpatrick & I. Wirszup (Eds.). Chicago: The University of Chicago Press.Google Scholar - Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks.
*Paper presented in the Working Group on Advanced Mathematical Thinking—CERME-5*, Cyprus.Google Scholar - Leikin, R., & Levav-Waynberg, A. (2008). Solution spaces of multiple-solution connecting tasks as a mirror of the development of mathematics teachers’ knowledge.
*Canadian Journal of Science, Mathematics, and Technology Education, 8*(3), 233–251.CrossRefGoogle Scholar - Linchevsky, L., & Vinner, S. (1998). The naïve concept of sets in elementary teachers.
*Proceedings of the 12th International Conference Psychology of Mathematics Education, Vol. 1*(pp. 471–478). Hungary: Vezprem.Google Scholar - Maher, C. A., & Martino, A. M. (1996). The development of the idea of proof: A five year case study.
*Journal for Research in Mathematics Education, 27*(2), 194–219.CrossRefGoogle Scholar - National Council of Teachers of Mathematics [NCTM]. (2000).
*Principles and standards for school mathematics*. Reston, VA: Author.Google Scholar - National Council of Teachers of Mathematics [NCTM] (2006).
*Curriculum focal points*. Retrieved from http://nctm.org/standards/focalpoints.aspx - Nührenbörger, M., & Steinbring, H. (2009). Forms of mathematical interaction in different social settings: Examples from students’, teachers’ and teacher-students’ communication about mathematics.
*Journal for Mathematics Teacher Education, 12*(2), 111–132.CrossRefGoogle Scholar - Piaget, J., & Inhelder, B. (1969).
*The psychology of the child*. New York: Basic Books, Inc.Google Scholar - Schoenfeld, A. H. (1985).
*Mathematical problem solving*. Orlando: Academic Press.Google Scholar - Silver, E. A. (1997). Fostering creativity through instruction rich mathematical problem solving and problem posing.
*ZDM The International Journal of Mathematics Education, 29*(3), 75–80.CrossRefGoogle Scholar - Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C., & Font Strawhun, B. T. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom.
*Journal of Mathematical Behavior, 24*, 287–301.CrossRefGoogle Scholar - Sfard, A., & Lavie, I. (2005). Why cannot children see as the same what grown-ups cannot see as different?—Early numerical thinking revisited.
*Cognition and Instruction, 23*(2), 237–309.CrossRefGoogle Scholar - Stigler, J., & Hiebert, J. (1999).
*The teaching gap*. New York: The Free Press.Google Scholar - Tabach, M., & Friedlander, A. (2008). Understanding equivalence of algebraic expressions in a spreadsheet-based environment.
*International Journal of Computers in Mathematics Education, 13*(1), 27–46.Google Scholar - Tirosh, D., Tsamir, P., Tabach, M. & Levenson, E. (technical report available from the authors) (2009).
*From kindergarten teachers' professional development to children' knowledge: The case of equivalence*.Google Scholar - Watson, A., & Mason, J. (2005).
*Mathematics as a constructive activity: Learners generating examples*. Mahwah: Lawrence Erlbaum.Google Scholar - Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics.
*Journal for Research in Mathematics Education, 27*(4), 458–477.CrossRefGoogle Scholar