Papers by Beyhan Şener Öztürk
Abstract
The purpose of this article is twofold: We first try do reveal the points of view displ... more Abstract
The purpose of this article is twofold: We first try do reveal the points of view displayed in the programs of education of mathematics used in our country concerning the mathematical objects as stated in scope of the philosophy of mathematics. We then hope to offer a solution to some of the troubles encountered in the education of mathematics. With this purpose in mind we critically evaluate the approaches to knowledge of the behaviorist education method which has been used in our country for many years and the constructivist education method which has been in operation in our country since 2005. Then we assess the points of view of these aforementioned methods to mathematical objects keeping various conceptions concerning mathematical objects in contemporary philosophy of mathematics in mind. We reach the conclusion that, in the determination of proper educational methods, the standpoint of merely pedagogical approaches is far from adequate and the philosophical grounds of them must be taken into consideration.
This study investigated the students’ development of the relationship between the Cartesian Produ... more This study investigated the students’ development of the relationship between the Cartesian Product, relation and the
function concepts. Six 9th grade students in a private school participated in mathematics lessons, 4 hours per week for
four consecutive weeks. Students were asked to engage in GeoGebra and non-GeoGebra Tasks through focused
questioning. Data from the transcripts of the audiotapes of the classroom discussions and the teacher’s reflections
together with the written artifacts from the students were analyzed. Results revealed that students came to the
understanding of the Cartesian Product between two sets as the matching of all elements in the sets. Results also
indicated that students were able to detect why the elements of a Cartesian Product needs to be in ordered pairs. In
addition, students were able to determine the graph of a function and a relation given a graph of a Cartesian Product
and explain how they are related to each other. Data further pointed to some student difficulties in graphing a
Cartesian Product defined on two finite and infinite sets and in considering equal sign as showing the output in terms
of the input values. In this paper, we intend to contribute to the field by showing the kinds of students’ reasoning on
their development of the relationship between these concepts. Also, we propose a set of GeoGebra and non-GeoGebra
tasks and problems developing and assessing such relationships
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Papers by Beyhan Şener Öztürk
The purpose of this article is twofold: We first try do reveal the points of view displayed in the programs of education of mathematics used in our country concerning the mathematical objects as stated in scope of the philosophy of mathematics. We then hope to offer a solution to some of the troubles encountered in the education of mathematics. With this purpose in mind we critically evaluate the approaches to knowledge of the behaviorist education method which has been used in our country for many years and the constructivist education method which has been in operation in our country since 2005. Then we assess the points of view of these aforementioned methods to mathematical objects keeping various conceptions concerning mathematical objects in contemporary philosophy of mathematics in mind. We reach the conclusion that, in the determination of proper educational methods, the standpoint of merely pedagogical approaches is far from adequate and the philosophical grounds of them must be taken into consideration.
function concepts. Six 9th grade students in a private school participated in mathematics lessons, 4 hours per week for
four consecutive weeks. Students were asked to engage in GeoGebra and non-GeoGebra Tasks through focused
questioning. Data from the transcripts of the audiotapes of the classroom discussions and the teacher’s reflections
together with the written artifacts from the students were analyzed. Results revealed that students came to the
understanding of the Cartesian Product between two sets as the matching of all elements in the sets. Results also
indicated that students were able to detect why the elements of a Cartesian Product needs to be in ordered pairs. In
addition, students were able to determine the graph of a function and a relation given a graph of a Cartesian Product
and explain how they are related to each other. Data further pointed to some student difficulties in graphing a
Cartesian Product defined on two finite and infinite sets and in considering equal sign as showing the output in terms
of the input values. In this paper, we intend to contribute to the field by showing the kinds of students’ reasoning on
their development of the relationship between these concepts. Also, we propose a set of GeoGebra and non-GeoGebra
tasks and problems developing and assessing such relationships
The purpose of this article is twofold: We first try do reveal the points of view displayed in the programs of education of mathematics used in our country concerning the mathematical objects as stated in scope of the philosophy of mathematics. We then hope to offer a solution to some of the troubles encountered in the education of mathematics. With this purpose in mind we critically evaluate the approaches to knowledge of the behaviorist education method which has been used in our country for many years and the constructivist education method which has been in operation in our country since 2005. Then we assess the points of view of these aforementioned methods to mathematical objects keeping various conceptions concerning mathematical objects in contemporary philosophy of mathematics in mind. We reach the conclusion that, in the determination of proper educational methods, the standpoint of merely pedagogical approaches is far from adequate and the philosophical grounds of them must be taken into consideration.
function concepts. Six 9th grade students in a private school participated in mathematics lessons, 4 hours per week for
four consecutive weeks. Students were asked to engage in GeoGebra and non-GeoGebra Tasks through focused
questioning. Data from the transcripts of the audiotapes of the classroom discussions and the teacher’s reflections
together with the written artifacts from the students were analyzed. Results revealed that students came to the
understanding of the Cartesian Product between two sets as the matching of all elements in the sets. Results also
indicated that students were able to detect why the elements of a Cartesian Product needs to be in ordered pairs. In
addition, students were able to determine the graph of a function and a relation given a graph of a Cartesian Product
and explain how they are related to each other. Data further pointed to some student difficulties in graphing a
Cartesian Product defined on two finite and infinite sets and in considering equal sign as showing the output in terms
of the input values. In this paper, we intend to contribute to the field by showing the kinds of students’ reasoning on
their development of the relationship between these concepts. Also, we propose a set of GeoGebra and non-GeoGebra
tasks and problems developing and assessing such relationships