Solving Equations with Parameters

ABSTRACT

This study examines how high school pupils and student teachers tackle equations that are presented in various ways. Some presentations are non-standard, for example having to express “a” (usually perceived as a parameter) in terms of “x” (usually perceived as a variable). We investigate how subjects solve those equations as well as the differences between pupils and student teachers.Our findings suggest that equations containing parameters are more difficult to solve than equations without parameters. The difficulties are associated with the letters that should be expressed and in the arrangement of the equation. The results of this study may expand the knowledge of teachers on the subject of equations with parameters and on the specific difficulties encountered by students during the solution process.

This study examines how high school pupils and student teachers tackle equations that are presented in various ways. Some presentations are non-standard, for example having to express “a” (usually perceived as a parameter) in terms of “x” (usually perceived as a variable). We investigate how subjects solve those equations as well as the differences between pupils and student teachers.Our findings suggest that equations containing parameters are more difficult to solve than equations without parameters. The difficulties are associated with the letters that should be expressed and in the arrangement of the equation. The results of this study may expand the knowledge of teachers on the subject of equations with parameters and on the specific difficulties encountered by students during the solution process.

KEYWORDS

Equations, Parameters, High School Pupils, Student Teachers, Mathematics Education, Mathematics Knowledge, Cognition and Mathematics

Equations, Parameters, High School Pupils, Student Teachers, Mathematics Education, Mathematics Knowledge, Cognition and Mathematics

Cite this paper

Ilany, B. and Hassidov, D. (2014) Solving Equations with Parameters.*Creative Education*, **5**, 963-968. doi: 10.4236/ce.2014.511110.

Ilany, B. and Hassidov, D. (2014) Solving Equations with Parameters.

References

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[1] Almog, N., & Ilany, B.-S. (2012). Absolute Value Inequalities: High School Students’ Solutions and Misconceptions.

http://dx.doi.org/10.1007/s10649-012-9404-z

[2] Davis, R. B., & Henkin, L. (1978).

[3] Fischbein, E., & Muzicant, B. (2002). Richard Skemp and His Conception of Relational and Instrumental Understanding: Open Sentences and Open Phrases. In D. Tall, & M. Thomas (Eds.),

[4] Ilany, B. (1998). The Elusive Parameter. In

[5] Ilany, B. (1997).

[6] Kieran, C. (1992). The Learning and Teaching of School Algebra. In D. A. Grouws (Ed.),

[7] Kieran, C. (2014).

[8] Sedivy, J. (1976). A Note on the Role of Parameters in Mathematics Teaching.

http://dx.doi.org/10.1007/BF00144365

[9] Skemp, R. (1987).