An Identification of Conceptual and Procedural Understanding: Study on Preservice Secondary Mathematics Teacher

Preservice mathematics teachers (PSMTs) need to master teaching material besides pedagogical competence. This knowledge is a combination of conceptual and procedural knowledge. Teachers should possess the ability to explain a concept, the reason for the concepts used, and the relationship among several concepts clearly and effectively to identify why the concept is used. This study aimed to identify the conceptual and procedural knowledge of PSMTs in Linear Algebra courses. Data collection was carried out through tests and interviews. The interview was conducted with several participants to clarify their test answers. The participants' interview answers revealed that they had difficulty in choosing the proper concept answering modified questions. Also, the participants tried to answer the question using a procedural approach. According to the findings, it is vital to construct appropriate teaching materials appropriate for the learning objective and material map concept.

Pedagogical design capacity of lower-secondary mathematics teacher and her interaction with curriculum resources

Various curriculum resources emerged in the last decades, but the textbook still remains the most used teaching and learning resource in mathematics classrooms. In this paper, we use a case study to analyze teaching practice of one math teacher. The aim of the study is to examine how math teacher interacts with the textbook and teacher guide, especially when teacher offloads on those resources, adapts them or improvises in the classroom. The study was conducted using lessons observations and semi-structured interviews. The results showed that teacher does not favour particular type of resource mobilization. Her interaction with resources can be characterized as a dynamic interplay, where type of resource mobilization exchange between the lessons and within a lesson as well. Moreover, teacher’s mobilization of textbook and teacher guide depends on teacher’s goals and assessment of the most pedagogically beneficial instruction for students.

EXTERNAL REPRESENTATION FLEXIBILITY OF DOMAIN AND RANGE OF FUNCTION

This study attempts to analyze pre-service secondary mathematics teachers’ flexibility of external representations of domain and range of functions. To reach the purpose, a task consisted of thirty question items were designed. Participants of the study were thirty-eight Indonesian pre-service secondary mathematics teachers attending mathematics education department at one private university in Jakarta, Indonesia. Based on the analysis participants written responses, this paper revealed participants’ difficulties in providing a proper and consistent definition of the concept of domain and range of functions. We also disclosed the participants’ lack of flexibility in doing translation among representations under the concept of domain and range of function. In general, participants written responses to the task did not provide evidence of a solid understanding of domain and range. There are several implications of these findings offered for secondary mathematics teacher education’s program.

An Innovative STEM Education Framework for a Changing Educational Landscape

This article describes features of NAUTeach, a secondary mathematics teacher preparation program that is modeled onthe UTeach program at the University of Texas-Austin. NAUTeach is a research-based STEM program that developsthe next generation of mathematics and science teachers by engaging them in rigorous content and methodologycoursework specifically developed to provide a broad, cross-curricular framework of innovativeinstruction. NAUTeach has been specifically designed to serve the needs of preservice mathematics and scienceteachers as they embark on teaching a new generation of students in an ever changing world. The NAUTeachprogram focuses on the development of inquiry-based instructional methods, reflective practice, and peercollaboration through a carefully sequenced series of courses that consistently promote early and frequent field workand a learner-centered focus of teaching and learning. Though the NAUTeach program is a blended mathematics andscience teacher preparation program, this article will focus on the preparation of secondary mathematics teachers bydescribing the cross-curricular (mathematics & science) methodological sequence of courses, along with themathematics-specific pedagogical courses, that preservice mathematics teacher candidates take as part of this program.Connections between the NAUTeach program and guidelines for the content and pedagogical preparation of teacherswill be made with specific attention paid to the development of reflective, innovative, flexible, and reform-orientedmathematics teachers.

A National Effort to Integrate Field Experiences Into Secondary Mathematics Methods Courses

This chapter shares the experience and preliminary findings from a national collaboration to improve secondary mathematics teacher preparation programs in the United States. Specifically, the chapter focuses on a research group tasked with strengthening field experiences into methods courses. Two modules are shared that a group of methods instructors have developed and are implementing in their courses. Findings from the first module are explained with implications for continued module development. These findings show the impact of the module on mentor teachers as well as the benefit the module has demonstrated in relation to the preservice teacher-mentor teacher relationship. Challenges and lessons learned from this national effort are also included.