11th Grade Students’ Conceptions Of Logarithm
Author(s):
Duygu Oren Vural (presenting / submitting)
Conference:
ECER 2012
Format:
Paper

Session Information

24 SES 08, Student Learning of Mathematics

Parallel Paper Session

Time:
2012-09-20
09:00-10:30
Room:
ESI 3 - Aula 2
Chair:
Martha Daniela Concepción García Moreno

Contribution

The concept of logarithms is considered as one of the great moments in mathematics (Eves, 1980) and regarded as an important mathematical concept that are useful for modeling and understanding population growth, radioactive decay, and compound interest (Smith & Confrey, 1994). It is also one of the core concepts for many mathematical courses such as calculus, differential equations, complex analysis. Despite its’ importance, students have many difficulties in learning the concept of logarithm. For example, Weber (2002) noted that students often forget many properties of logarithms shortly after they learn them and can seldom explain why these properties are true. Brezovski & Zazkis (2006) denoted that students often perform operations in logarithmic expression successfully when the meaning is overlooked. Moreover, Kastberg (2002) found that students characterize the logarithmic function as a symbol or a notation and understand logarithms as “problem to do”, and they have great difficulty to recognize non-standard problems based on logarithms without mentioning logarithmic function. Several researchers argued that approaches for teaching logarithm have a great role in students’ limited understanding of logarithm (Confrey, 1991; Confrey & Smith, 1995).  While students are encountering such difficulties, the instructional methods and strategies that we used to teach logarithms to students are considered important.
The secondary school mathematics curriculum of Turkey has been changed dramatically in recent years. In old curriculum, logarithm concept was taught mainly using procedural approaches and with routine problems.  Exponential and logarithmic functions were typically presented as formulas and students were assumed to associate the rules for exponents and logarithms with routine algorithms as a formal algebraic way. On the contrary, in the new curriculum, approaches such as mathematical modelling, problem solving, and reasoning have become primary components of mathematics teaching. The logarithm concept in the new curriculum is based on these approaches. Including several real life situation, new curriculums creates several opportunities for students to explore logarithm concept while connecting between numerical and algebraic experiences. On the other hand, we don’t know yet whether implementation of reformed mathematics curricula has a positive influence on students’ conceptions of logarithm. Therefore the purpose of this study is to investigate 11.th grade secondary school students’ conceptions of logarithm concept.

Method

The participants of this study will be 11th grade secondary school students. Sample selection method will be purposive sampling. 11th grade classes of teachers who are implementing the new mathematics curriculum will be selected among in the schools located in Ankara, the capital city of Turkey. An open-ended logarithm test including standard (algorithmic manipulations) and non-standard questions (real life problems including mathematical modelling) will be prepared. After pilot testing, the test will be administered on actual sample of students. After administration of the test, 6 students will be selected for further investigations of quality their understanding (strategies, approaches and reasoning used while solving problems). Data gathered from administration of the test and interviews will be analyzed qualitatively.

Expected Outcomes

The curriculum reform process can be seen as an opportunity to develop not only the content of the mathematics but also to improve students learning. As a result of this study, it is expected to find out that implementation of reformed mathematics curriculum will have a substantial contribution on students’ conceptions of the logarithm concept. Moreover, the quality of students understanding will shed light on pros and cons of curriculum reform and implementation of it.

References

Confrey, J. & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for research in mathematics education, 26(1), 66-8 Eves, H. (1980). Great moments in mathematics (before 1650),The Mathematical Association of America (MAA). Berezovski, T & Zazkis, R. (2006). Logarithms: Snapshot from two tasks. Proceedings on 30th International Conference for Psychology of Mathematics Education. Praque, CZ. Kastberg, S.E. (2002). Understanding mathematical concepts: The case of logarithmic function. Unpublished Doctoral Dissertation, University of Georgia.

Author Information

Duygu Oren Vural (presenting / submitting)
Middle East Technical University
Secondary Science and Mathematics Education
ANKARA

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