This study investigated the relationship between prospective secondary mathematics teachers' pers... more This study investigated the relationship between prospective secondary mathematics teachers' perspectives and their mathematical knowledge for teaching in action. Data from two prospective teachers' practice-teachings, one in geometry and one in algebra, their lesson plans and self-reflections were analyzed with Teacher Perspectives and Knowledge Quartet frameworks. Results showed that prospective teachers who thought of mathematics and mathematics learning as dependent on the knower, corresponding with a progressive incorporation perspective, had demonstrated all the codes in Knowledge Quartet Framework. These results suggest that, once prospective teachers are given opportunities to develop a progressive incorporation perspective on mathematics, mathematics learning, and mathematics teaching during methods and practice teaching courses, this might conrtibute to the developments in their mathematical knowledge for teaching in action, independent of the particular concept they teach. Suggestions for developing a progressive incorporation perspective during methods and practice teaching courses are given.
We discuss an emerging program of research on a particular aspect of mathematics learning, studen... more We discuss an emerging program of research on a particular aspect of mathematics learning, students' learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning trajectories of students by specifying a series of conceptual steps through which students pass in the context of particular instructional approaches or learning environments. Generally missing from the literature is research that examines the process by which students progress from one of these conceptual steps to a subsequent one. We provide a conceptualization of a program of research designed to elucidate students' learning processes and describe an emerging methodology for this work. We present data and analysis from an initial teaching experiment that illustrates the methodology and demonstrates the learning that can be fostered using the approach, the data that can be generated, and the analyses that can be done. The approach involves the use of a carefully designed sequence of mathematical tasks intended to promote particular activity that is expected to result in a new concept. Through analysis of students' activity in the context of the task sequence, accounts of students' learning processes are developed. Ultimately a large set of such accounts would allow for a cross-account analysis aimed at articulating mechanisms of learning.
We discuss an emerging program of research on a particular aspect of mathematics learning, studen... more We discuss an emerging program of research on a particular aspect of mathematics learning, students' learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning ...
We discuss an emerging program of research on a particular aspect of mathematics learning, studen... more We discuss an emerging program of research on a particular aspect of mathematics learning, students' learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning ...
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
This study investigated the relationship between prospective secondary mathematics teachers' pers... more This study investigated the relationship between prospective secondary mathematics teachers' perspectives and their mathematical knowledge for teaching in action. Data from two prospective teachers' practice-teachings, one in geometry and one in algebra, their lesson plans and self-reflections were analyzed with Teacher Perspectives and Knowledge Quartet frameworks. Results showed that prospective teachers who thought of mathematics and mathematics learning as dependent on the knower, corresponding with a progressive incorporation perspective, had demonstrated all the codes in Knowledge Quartet Framework. These results suggest that, once prospective teachers are given opportunities to develop a progressive incorporation perspective on mathematics, mathematics learning, and mathematics teaching during methods and practice teaching courses, this might conrtibute to the developments in their mathematical knowledge for teaching in action, independent of the particular concept they teach. Suggestions for developing a progressive incorporation perspective during methods and practice teaching courses are given.
We discuss an emerging program of research on a particular aspect of mathematics learning, studen... more We discuss an emerging program of research on a particular aspect of mathematics learning, students' learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning trajectories of students by specifying a series of conceptual steps through which students pass in the context of particular instructional approaches or learning environments. Generally missing from the literature is research that examines the process by which students progress from one of these conceptual steps to a subsequent one. We provide a conceptualization of a program of research designed to elucidate students' learning processes and describe an emerging methodology for this work. We present data and analysis from an initial teaching experiment that illustrates the methodology and demonstrates the learning that can be fostered using the approach, the data that can be generated, and the analyses that can be done. The approach involves the use of a carefully designed sequence of mathematical tasks intended to promote particular activity that is expected to result in a new concept. Through analysis of students' activity in the context of the task sequence, accounts of students' learning processes are developed. Ultimately a large set of such accounts would allow for a cross-account analysis aimed at articulating mechanisms of learning.
We discuss an emerging program of research on a particular aspect of mathematics learning, studen... more We discuss an emerging program of research on a particular aspect of mathematics learning, students' learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning ...
We discuss an emerging program of research on a particular aspect of mathematics learning, studen... more We discuss an emerging program of research on a particular aspect of mathematics learning, students' learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning ...
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
Uploads
Papers by Gulseren Akar
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
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