Pre-service Secondary Mathematics Teachers Research Articles

Mathematical Connections in Preservice Secondary Mathematics Teachers’ Solution Strategies to Algebra Problems

This study investigated the mathematical connections found in the solutions provided by 22 preservice secondary mathematics teachers to a set of algebra problems. Interest in, and research on, mathematical connections has gained prominence of the past decade. Here, we use the Extended Theory of Mathematical Connections or ETMC to explore the types of connections that this framework does and does not capture in the preservice teachers’ solutions. The ETMC surfaced four types of mathematical connections across four problems: ‘different representations’, ‘procedural’, ‘part-whole’ and ‘meaning’. The other types of connections defined in ETMC such as ‘reversibility’ or ‘feature’ were not found in our data, perhaps because of the specific problems that were used. Some mathematical connections were not highlighted when examining the solutions through the lens of ETMC (‘meaning’, ‘implication or if/then’ and modelling) addressing areas in which ETMC might be limited in its capacity to support researchers in identifying mathematical connections in different contexts.

Using different digital tools in designing and solving mathematical modelling problems

AbstractWhile existing studies acknowledge the importance of using technology in the mathematical modelling process, questions about how to integrate digital tools into mathematical modelling are not still answered. This study aims to examine pre-service mathematics teachers’ designing and solving mathematical modelling problems by using different digital tools through the collaboration of two different courses in their education program. The GeoGebra-supported modelling cycle was adopted as the conceptual framework of the study. The case study was used to design the research. The participants of the study were three volunteer pre-service secondary mathematics teachers, who were able to use and integrate digital tools in mathematics education. The pre-service teachers were asked to design a mathematical modelling problem by integrating different digital tools as the final assignment in both courses. The designed mathematical modelling problem, the video records of pre-service teachers’ explanations including the designing and solving process, and the video records of the focus group interview were the data of the study. The results showed that the pre-service teachers were able to design and solve an effective and comprehensive mathematical modelling problem using technology by combining their skills that they had learnt through different courses. In particular, they were able to use different digital tools in both designing and solving a mathematical modelling problem. Their solution also led to the extension of the adopted framework by adding new technological actions into the modelling stages.

Educational Game Design Experiences of Secondary School Preservice Mathematics Teachers

In this study, it was aimed to reveal the mathematical games designed by secondary school preservice mathematics teachers and their views on this process. The participants of the study, in which a case study, one of the qualitative research designs, was used, consisted of 45 pre-service secondary school mathematics teachers who took the Teaching Mathematics with Games course. The data obtained from the study were subjected to descriptive and content analysis. According to the results obtained from the study, while the majority of the games were designed as board/card games, the most preferred learning area was numbers and operations. In addition, according to the grade levels, the most games were designed for the 8th grade and the least for the 5th grade level. In the process of mathematical game design, pre-service teachers mostly aim to provide meaningful learning, develop procedural skills, reinforce what has been learned, and make learning mathematics fun. In addition, although the pre-service teachers experienced some difficulties during the game design process, it was determined that this process affected them positively in cognitive, affective, and pedagogical terms.

A framework to support teacher noticing of students' mathematical thinking in technology‐mediated environments

AbstractThe practice of teacher noticing students' mathematical thinking often includes three interrelated components: attending to students' strategies, interpreting students' understandings, and deciding how to respond on the basis of students' understanding. This practice gains complexity in technology‐mediated environments (i.e., using technology‐enhanced math tasks) because it requires attending to and interpreting students' engagement with technology. Current frameworks implicitly assume the practice includes noticing the ways students use tools (including technology tools) in their work, but do not explicitly highlight the role of the tool. While research has shown that using these frameworks supports preservice secondary mathematics teachers (PSTs) developing noticing practices, it has also shown that PSTs largely overlook students' technology engagement when they are working on technology‐enhanced tasks (Journal for Research in Mathematics Education, 2010; 41(2):169–202). In this article, we describe our adaptation of Jacobs et al.'s framework for teacher noticing student mathematical thinking to include a focus on making students' technology‐tool engagement explicit when noticing in technology‐mediated environments, the Noticing in Technology‐Mediated Environments (NITE) framework. We describe the theoretical foundations of the framework, provide a video case example, and then illustrate how the framework can be used by mathematics teacher educators to support PSTs' noticing when students are working in technology‐mediated environments.

What’s the Lesson?: Using Lesson Study to Develop Curriculum for Preservice Secondary Mathematics Teachers

Lesson study, a popular method of professional development in which instructors collaborate to critique and improve a lesson, can be used for curriculum development. This paper describes an implementation of lesson study that went through two iterations across different, related, contexts: an undergraduate mathematics content course for secondary preservice teachers and a professional development session with practicing middle and secondary teachers. We describe the ways in which the lesson study process helped us develop curriculum for advanced undergraduate courses for future teachers and provide our insights into the benefits and challenges of this approach.

Teacher self-efficacy sources during secondary mathematics initial teacher education

This one-year phenomenological study focuses on exploring sources of teacher self-efficacy (TSE) among pre-service secondary mathematics teachers during their initial teacher education. The findings of the study shed light on the significance of enactive, social and affective sources of TSE, and suggest the need to broaden the understanding of these sources. They also emphasize the need to explore previously unexamined aspects of TSE, in order to gain a more comprehensive understanding of this important construct in the field of education. Furthermore, the study highlights the importance of considering factors beyond just mathematics teacher knowledge when considering mathematics teacher professional learning.

Considering Proofs: Pre-Service Secondary Mathematics Teachers' Criteria for Self-Constructed and Student-Generated Arguments

In this paper, we examined 14 pre-service secondary mathematics teachers' (PSMTs) criteria used in evaluating the validity of self-constructed and student-generated arguments in the domains of algebra, geometry, and number theory. During the interviews, participants produced and analyzed their own proofs or counterexamples for the three tasks first and analyzed if six student-generated arguments could be counted as proofs next. The two criteria most frequently used by PSMTs in evaluating their own construction and a student-generated argument as a proof or not a proof were verification and clear details. Our finding showed that more PSMTs were inclined to pay attention to clear details presented in students’ work than their own productions. Our finding also showed that more PSMTs focused on the verification feature in their self-constructions than in student-generated arguments. These results suggest that the criteria–verification and clear details–do not have the same weight for PSMTs when evaluating the validity of their own work and student-generated products. This study also has implications for proof-intensive courses, as PSMTs’ conceptions of proofs are more likely affected by their instructors in those proof-intensive classes.

Developing Equity Literacy and Critical Statistical Literacy in Secondary Mathematics Preservice Teachers

There is a lack of teacher education materials that develop equity literacy in content courses for preservice secondary mathematics teachers. In response, we created teacher education curriculum materials for introductory statistics that include an integrated focus on developing equity literacy and critical statistical literacy. In this article, we provide an overview of our materials’ design along with a detailed look at one activity regarding racial demographics and tracking in high school STEM courses. We present evidence regarding the positive impact of these materials on the teacher candidates’ competency, value, and likelihood of applying their equity literacy and critical statistical literacy. Implications for mathematics teacher educators working to develop equity literacy together with content knowledge are discussed.

An Analysis of the Relationship between Pre-Service Secondary Mathematics Teachers' Epistemological Beliefs towards Learning, their Educational Beliefs, and Critical Thinking Dispositions

This study attempts to identify the pre-service secondary mathematics teachers’ epistemological beliefs towards learning, their educational beliefs, and critical thinking dispositions as well as the relationship between them. A relational survey model was employed and the study group consisted of 152 pre-service teachers. The study used Epistemological Beliefs Scale towards Learning (EBStL), The Educational Philosophy Tendencies Scale (EPTS), and Marmara Critical Thinking Dispositions Scale (MCTDS) as data collection tools. The results suggested that pre-service secondary mathematics teachers’ epistemological beliefs and critical thinking dispositions were above the average value. Moreover, they were found to have progressive and reconstructivist tendencies. The results also revealed that the pre-service secondary mathematics teachers’ epistemological beliefs towards learning did not differ across their gender, academic achievement, parents’ educational level while significantly differed in terms of their grade level. The pre-service secondary mathematics’ teachers’ educational beliefs significantly varied across their gender, grade level while that was not the case for their academic achievement and parents’ educational level. Besides, the results confirmed positive and significant relationships between the pre-service teachers’ epistemological beliefs towards learning and their critical thinking disposition levels and progressivism, further positive and significant relationships were noted between the critical thinking dispositions and progressivism, reconstructionism and perennialism. Progressivism was found to be explained by epistemological beliefs towards learning and critical thinking dispositions; reconstructionism was found to be explained by critical thinking disposition; epistemological beliefs towards learning was determined to be explained by progressivism and critical thinking disposition, and critical thinking dispositions were identified to be explained by reconstructionism and perennialism

Cognitive and Motivational Person Characteristics as Predictors of Diagnostic Performance: Combined Effects on Pre-Service Teachers\u2019 Diagnostic Task Selection and Accuracy

The acquisition of diagnostic competences is an essential goal of teacher education. Thus, evidence on how learning environments facilitate pre-service teachers’ acquisition of corresponding competences is important. In teacher education, approximations of practice (such as simulations) are discussed as being learning environments that can support learners in activating acquired knowledge in authentic situations. Simulated diagnostic interviews are recommended to foster teachers’ diagnostic competences.The conceptualization of diagnostic competences highlights the importance of cognitive and motivational characteristics. Motivational learning theories predict that the activation of acquired knowledge in learning situations may be influenced by motivational characteristics such as individual interest. Although teachers’ diagnostic competences constitute an increasing research focus, how cognitive and motivational characteristics interact when shaping the diagnostic process and accuracy in authentic learning situations remains an open question.To address this question, we report on data from 126 simulated diagnostic one-on-one interviews conducted by 63 pre-service secondary school mathematics teachers (students simulated by research assistants), studying the combined effects of interest and professional knowledge on the diagnostic process and accuracy. In addition to the main effect of content knowledge, interaction effects indicate that participants’ interest plays the role of a “door-opener” for the activation of knowledge during simulation-based learning. Thus, the results highlight the importance of both, cognitive and motivational characteristics. This implies that simulation-based learning environments should be designed to arouse participants’ interest to support their learning or to support less interested learners in activating relevant knowledge.

The Teacher and Peer Intervention for Pre-Service Mathematics Teachers on the Validity of Mathematical Models

The aim of this study is to investigate the types of teacher and peer interventions to test the validity of modelling along with the modelers’ reactions to these interventions. A teaching experiment was employed in the study. Forty-five pre-service secondary school mathematics teachers participated in the research. As a data collection tool, a worksheet was prepared by taking the monthly average temperature values of the last five years from the Meteorology Directorate of the province in which the study was conducted. At the end of the mathematical modelling process, teacher and peer interventions were carried out. The types of teacher and peer interventions were categorized. The reasons for intervening in the modelling process by both the teacher and peers were insufficient explanations and student error. In addition, the teacher intervened to advance the process. The teacher intervened for diagnosis, advice and feedback, and the peers intervened for diagnosis and feedback in this process. While teacher intervention occurred at the stage of mathematical model and results, peer intervention occurred at the stage of testing the real model and result. The participants returned to revise their real model, mathematical model and results. In the modeling process, while peer support may be sufficient to test the validity of the real model and real results, teacher support is required to test the validity of the mathematical model and its results.

Effects of Teaching in a Summer STEM Camp on the Mathematics Teaching Self-efficacy of Highly Qualified Preservice Secondary Mathematics Teachers

Educational opportunity gaps experienced by students of color living in poverty, with accompanying lower levels of mathematics achievement, remain a roadblock to their access to college-level training in STEM fields. To address this problem, secondary teachers must be confident in their ability to share mathematics content effectively with students from cultures different than their own. Bridging the opportunity gap is more likely with two elements in place: intellectually stimulating pre-college experiences and community partnerships that establish connections between underserved neighborhoods and resource-filled environments such as university campuses.
 This study explored the effects of teaching in a four-week STEM summer camp for ethnically diverse, high-needs middle school girls on the teaching self-efficacy of highly-qualified preservice secondary mathematics teachers, a group that has been less studied than preservice elementary teachers. Participants were scholarship students in a federally-funded teacher preparation scholarship program at an urban, metropolitan university. Teaching self-efficacy was measured by the Mathematics Teaching Efficacy Belief Instrument (MTEBI) and by follow-up qualitative analysis of questionnaire responses and focus groups. Participants’ gains on the MTEBI were significant for Personal Mathematics Teaching Efficacy, but not for Mathematics Teaching Outcome Expectancy. Qualitative analyses suggested that both instructional coaching and everyday interactions in a summer camp setting contributed strongly to the preservice teachers’ increased confidence about teaching mathematics to culturally diverse, high-needs learners.

Supporting Pre-Service Secondary Mathematics Teachers’ Professional Noticing of Student Thinking Professional Noticing of Student Thinking

A growing body of evidence suggests developing the attention of preservice, secondary mathematics (PSMTs) teachers towards professional noticing of student thinking should feature in teacher education programs. There were two aims for this qualitative study: first, to explore the extent to which an Interview Module (IM) supported the development of PSMTs’ ability to notice and make pedagogical decisions based on student thinking evidenced in video- and paper-based work samples. A secondary aim was to establish the viability of the IM in an Australian context. Overall, PSMTs regarded their involvement in the IM as beneficial to their development as teachers. Specifically, participants outlined that the IM helped to shift their beliefs about teaching and learning, and helped promote productive teacher dispositions. Furthermore, these shifts were enabled through opportunities to engage with authentic student work, and the access they were given to new forms of responding.

Modeling in Pre-service Secondary School Teacher Education: developing an School Scientific Model of Energy

In this document, we will present the results of an investigation carried out in initial teacher education for pre-service secondary school Physics and Mathematics teachers in Chile. A Teaching and Learning Sequence (TLS) was iteratively designed following a Design-based research approach and implemented to promote the construction of an adequate School Scientific Model (SSM) of energy. This SSM is based on the well-known work on energy related concepts in physics education, including the ideas of energy degradation, conservation and transference. The methodology followed in the TLS is based on modeling and model-based inquiry. Subsequently, we have analyzed pre-service teachers’ qualitative productions to identify which model of energy they master at both the beginning and the end of the program. This allowed us to get hints of a learning progression in this field.

Teaching mathematical proof at secondary school: an exploration of pre-service teachers’ situative beliefs

Despite the recognized importance of mathematical proof in secondary education, there is a limited but growing body of literature indicating how preservice secondary mathematics teachers (PSMTs) view proof and the teaching of proof. The purpose of this survey research was to explore PSMTs’ knowledge and beliefs about proof and proof teaching in the context of secondary mathematics teaching and learning. Six cases (PSMTs’ survey responses) were purposively selected from an entire data set comprising participants from the United States and Australia. Using a situative learning perspective as the theoretical framework, the authors developed a sensible belief system [Leatham, K. R. (2006). Viewing mathematics teachers’ beliefs as sensible systems. Journal of Mathematics Teacher Education, 9(1), 91–102. https://doi.org/10.1007/s10857-006-9006-8] for sampled PSMTs and inductively conceptualized how their knowledge of and orientations toward proof acted as a function of their teaching and learning contexts. Furthermore, an analysis of data revealed that PSMTs’ knowledge and beliefs about proof are multifaceted, dynamic and evolving as they engage with proof in their various contexts.

Supporting Preservice Secondary Mathematics Teachers’ Professional Judgment Around Digital Technology Use

The pervasiveness of digital technology creates an imperative for mathematics teacher educators to prepare preservice teachers (PSTs) to select technology to support students’ mathematical development. We report on research conducted on an assignment created for and implemented in secondary mathematics methods courses requiring PSTs to select and evaluate digital mathematics tools. We found that PSTs primarily focused on pedagogical fidelity (ease of use), did not consider mathematical fidelity (accuracy), and at times superficially attended to cognitive fidelity (how well the tool reflects students’ mathematical thinking processes) operationalized as the CCSS for Mathematical Practice and Five Strands of Mathematical Proficiency. We discuss implications for implementing the assignment and suggestions for addressing PSTs’ challenges with identifying the mathematical practices and five strands.

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.

Preservice Secondary Mathematics Teachers’ Actional Beliefs about Teaching Geometric Transformations with Geometer’s Sketchpad

<p style="text-align: justify;">Preservice mathematics teachers' beliefs about actions related to the use of the technological tools in teaching mathematics may affect how they are going to use them in their classroom activities. However, there is a limited evidence of what beliefs they hold on their intended actions of using technological tools in teaching mathematics. This study presents two preservice high school mathematics teachers' actional beliefs related to their intended actions in teaching geometric transformations (GTs) using Geometer's Sketchpad (GSP). The study comprised of a series of five task-based qualitative interviews with each of two senior undergraduate preservice teachers at a medium-sized public university in the Rocky Mountain Region of the United States. This study used a radical constructivist grounded theory (RCGT) with five assumptions—symbiosis, voice, cognition, adaptation, and praxis as a theoretical framework to guide the study process. The thematic findings of the study included four in vivo categories of their beliefs associated with actions of teaching GTs with GSP – assessment of student learning, engaging students in a group activity in exploring GTs with GSP, engaging students in individual activity in exploring GTs with GSP, and exploring GTs with GSP as 'suck it up and do it.' Pedagogical implications of these categories have been discussed.</p>

Creating a Third Space for Learning to Design Technology-Based Mathematics Tasks

In this article, we examine the ways in which the creation of a third space can bridge the divide between coursework and practice for preservice secondary mathematics teachers (PSTs) taking a technology, pedagogy, and content course. A university-based instructor partnered with two high school teachers to create a space in which PSTs draw upon and use both academic and practitioner knowledge while creating technology-based tasks for high school students to use. Our results revealed increased focus on pedagogical decisions in areas such as technology-task design and questioning techniques. The data also indicate that the success of this collaboration was connected to fair distribution of work, feeling valued, and personal benefit and challenges centered on maintaining rejection of hierarchy.

Design Principles for Examining Student Practices in a Technology-Mediated Environment

In this article, we present a set of design principles to guide the development of instructional materials aimed to support preservice secondary mathematics teachers (PSMTs) examining student practices in technology-mediated environments. To develop design principles, we drew on the literature related to technological pedagogical content knowledge (TPACK; Niess, 2005), video cases as learning objects (Sherin & van Es, 2005), and professional noticing (Jacobs, et al., 2010). After presenting the design principles, we share a task created using these design principles. Finally, we share PSMTs’ reflections about changes in their own understanding after examining students’ practices. Their responses provide insights into the usefulness of the design principles for deepening PSMTs’ mathematical knowledge and knowledge of students’ understanding, thinking, and learning with technology.