Pre-service Secondary Mathematics Teachers Research Articles

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.

Investigating peer-assessment strategies for mathematics pre-service teacher learning on formative assessment

Formative assessment practices for secondary mathematics have been advocated as valuable for students, but difficult for teachers to learn. There have been calls in the literature to increase the emphasis on formative assessment in mathematics teacher preparation courses. This study explored the use of peer-assessment strategies for helping pre-service secondary mathematics teachers (PSTs) cultivate formative assessment principles and practices for assessing school students. Twenty-seven PSTs participated in a peer-assessment cycle comprised of: sourcing a rich mathematics task; constructing an assessment rubric for it; and collecting and analysing a selection of secondary student responses to the task. Each PST then provided written and verbal feedback to a peer on his/her rubric and student solution assessments. We draw on theoretical conceptions of Teacher Assessment Literacy in Practice to characterize the PSTs’ perceptions of their experience of formative assessment processes for learning to assess school students, in terms of cognitive and affective dimensions of their conceptions of assessment. The cohort evidenced a wide range of levels of confidence with the various aspects of formative assessment practices but on average less confidence in assessing school student task responses themselves than in assessing peer work. In addition to highlighting specific changes to different types of assessment knowledge, the PSTs also evidenced an awareness of shifts in their attitudes, in coming to view student task responses with more appreciation and humility.

How Secondary Mathematics Preservice Teachers Grapple with Enacting Culturally Responsive Practices at Placement Sites

Many scholars call for teacher educators to provide experiences that can lead prospective teachers to adopt and implement culturally responsive pedagogy in mathematics classrooms. This qualitative investigation analyzed interviews from preservice secondary mathematics teachers using Hernandez, Shroyer, and Morales framework for culturally responsive mathematics teaching. Analysis of the data demonstrates how preservice teachers grapple with enacting a culturally responsive framework at practicum sites. Findings reveal that while some participants reported comfort implementing some aspects of culturally responsive practices at placement sites, others reported apprehension. The data suggests strategies for teacher educators interested in supporting culturally responsive teacher-learners through professional modeling.

Social media usage among pre-service secondary mathematics teachers in Zambia

Social media technologies have reshaped our lives today and Zambian teachers do a massive use of smart phones, tablets, and other portable tools. In addition, they are continually searching for forefront innovations. Frequently, the utilization of these gadgets is not in manners foreseen by innovation advocates. This study focuses on exploring the use of social media platforms and the impact of such social networking services in the teaching and learning of mathematics by pre-service teachers. To explore pre-service teachers’ use of social media in their teaching and learning experiences, the authors administered an adapted and validated research instrument via a quantitative survey system to a sample of 102 pre-service teachers from the Copperbelt University. Analysis of variance and multiple regression analysis were used to test the interplay of relationships between pre-service teachers’ attitudes towards the use of social media based on year of study and gender, social media use and classroom integration, social media use, and mathematics pedagogy. Further, a statistical test was run to show whether positive correlations existed or not. Results disclosed that respondents showed an average use of social media tools in mathematics and provide a prediction model for pre-service teachers’ future integration of social media in the teaching and learning of mathematics.

Investigating Preservice Mathematics Teachers’ Pedagogical Content Knowledge through Microteaching

The purpose of this study was to investigate how pre-service mathematics teachers’ pedagogical content knowledge was reflected in their microteaching. Twenty preservice secondary mathematics teachers participated in the study. The participants formed groups of two, three or four people of their choice, resulting in six groups in total. Each group designed and conducted a microteaching on a topic of their choice. The videotapes of the groups’ microteaching and their lesson plans constituted the data set for the study. We analyzed the data per the components of the pedagogical content knowledge framework outlined by various researchers. We found that the preservice mathematics teachers in general were knowledgeable about different instructional strategies and the curriculum about the topic of their microteaching, but their knowledge of learners was relatively poor. Implications for teacher education are discussed.

Preparation and The Real World of Education: How Prospective Teachers Grapple with Using Culturally Responsive Teaching Practices in the Age of Standardized Testing

The most highlighted provision and consequence of the reauthorization of the 1965 Elementary and Secondary Education Act (ESEA), the No Child Left Behind (NCLB) Act of 2001, is obsessive practices of assessing students across the United States (U.S.). Despite newly named policies, including Every Student Succeed Act (ESSA) of 2015, which governs current U.S. K-12 education standards, concerns over NCLB’s unprecedented fixation on high stakes testing remain acute for many school districts. This manuscript examines the struggles of four preservice secondary mathematics teachers (PMTs) who grappled with enacting culturally responsive teaching practices at schools that aimed to meet accountability standards.

Helping Preservice Secondary Mathematics Teachers Construct Pedagogical Content Knowledge

This paper intends to shed light on understanding of Mathematical Pedagogical Content Knowledge (MPCK) from an empirical angle. Examples are utilized to explicitly demonstrate how a class activity in a capstone course of preservice secondary mathematics teachers (PSMTs) could be structured for PSMTs to build MPCK.

The Three-Minute-Rehearsal Cycle of Enactment and Investigation: Preservice Secondary Mathematics Teachers Learning to Elicit and Use Evidence of Student Thinking

In the last decade, mathematics teacher educators have begun to design learning opportunities for preservice mathematics teachers using a pedagogies-of-practice perspective. In particular, learning cycles provide a structure for engaging PSTs in learning to teach through the use of representations, approximations, and decompositions of practice (Grossman et al., 2009). In this article, we provide details of one learning cycle designed to support secondary mathematics preservice teachers' learning to elicit and use evidence of student thinking and pose purposeful questions (National Council of Teachers of Mathematics, 2014). Through qualitative analyses conducted on learning reflections, we provide evidence of the impact on engagement of this cycle through the lens of the Framework for Learning to Teach (Hammerness et al., 2005).

Engaging Preservice Secondary Mathematics Teachers in Authentic Mathematical Modeling: Deriving Ampere's Law

Incorporating modeling activities into classroom instruction requires flexibility with pedagogical content knowledge and the ability to understand and interpret students' thinking, skills that teachers often develop through experience. One way to support preservice mathematics teachers' (PSMTs) proficiency with mathematical modeling is by incorporating modeling tasks into mathematics pedagogy courses, allowing PSMTs to engage with mathematical modeling as students and as future teachers. Eight PSMTs participated in a model-eliciting activity (MEA) in which they were asked to develop a model that describes the strength of the magnetic field generated by a solenoid. By engaging in mathematical modeling as students, these PSMTs became aware of their own proficiency with and understanding of mathematical modeling. By engaging in mathematical modeling as future teachers, these PSMTs were able to articulate the importance of incorporating MEAs into their own instruction.

A Thinking-Based Learning Module for Enhancing 21st Century Skills

This study aims to develop the Thinking-Based Learning (TBL) module for learning secondary school Algebra. This study uses the developmental model design and the TBL module is designed using the combination of ADDIE Model and Kemp Model. It is conducted in five phases: (1) Analysis (2) Design of TBL Module, (3) Development of TBL Module (4) Implementation, and (5) Assessment of TBL Module. The research instruments are the Content Validity Form and Module Reliability Survey. The validity of the module is validated by three experts in the field of mathematics education. Sample of the study in the evaluation phase consisted of the pre-service secondary school mathematics teachers which are selected using random sampling technique.The findings showed that the content validity and the reliability indices for the TBL module are at a satisfactory level.Significantly, the TBL module is able to provide guidance to all secondary school mathematics teachers in customary teaching practices for the inculcation of higher level thinking, thus generating knowledgeable generation and a good problem solver for the present and future challenges.

Combining Theoretical Approaches: Socio-Didactic-Mathematical Norms and Perspectives in Pre-service Secondary Mathematics Teachers’ Discourse

This study is part of wider research that seeks to investigate the existence (or not) of socio-didactic-mathematical norms in the discourse arises within a group of pre-service secondary mathematics teachers when they are solving a didactic-mathematical task. In addition, we try to analyze whether any of these norms could have relationships with teachers’ perspectives that they can adopt in their future practice. The data comes from the transcriptions of the audio recordings of the dialogues among the pre-service teachers when they are solving a didactic-mathematical task in the classroom. Based on our analysis, we have been able to identify five socio-didactic-mathematical norms. Three of them were in some way related to the mathematical content and its learning. The other two are related to teachers’ role, providing information about characteristics that the future teachers associate with said role. Furthermore, we have identified features related to teachers’ perspectives through the above-mentioned norms.

Perceptions on proof and the teaching of proof: a comparison across preservice secondary teachers in Australia, USA and Korea

Despite the recognised 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 investigate how PSMTs in Australia, the USA and Korea perceive of proof in the context of secondary mathematics teaching and learning. PSMTs were able to outline various mathematical and pedagogical aspects of proof, including purposes, characteristics, reasons for teaching and imposed constraints. In addition, PSMTs attended to differing, though overlapping, features of proof when asked to determine the extent to which proposed arguments constituted proofs or to decide which arguments they might present to students.

Graphs of Two Variable Inequalities: Alternate Approaches to the Solution Test

In this article I suggest some alternatives to the solution test for the understanding of graphs of inequalities in two variables. Based on the work done with two groups of preservice secondary mathematics teachers, and by using the idea of variation and the framework of action and process conceptions of inequalities, I explain how graphs of inequalities can be viewed as a collection of rays or curves. I also explain the potential benefits of these alternative explanations in the solving of optimization problems and in the instruction of functions as a medium of one variable and two variable functions.

Preservice Secondary Mathematics Teachers’ Statistical Knowledge: A Snapshot of Strengths and Weaknesses

ABSTRACTAmid the implementation of new curriculum standard regarding statistics and new recommendations for preservice secondary mathematics teachers (PSMTs) to teach statistics, there is a need to examine the current state of PSMTs’ knowledge of the statistical content they will be expected to teach. This study reports on the statistical knowledge of 217 PSMTs from a purposeful sample of 18 universities across the United States. The results show that PSMTs may not have strong Common Statistical Knowledge that is needed to teach statistics to high school students. PSMTs’ strengths include identifying appropriate measures of center, while weaknesses involve issues with variability, sampling distributions, p-values, and confidence intervals.

Technological, Pedagogical, and Content Knowledge (TPACK) and Beliefs of Preservice Secondary Mathematics Teachers: Examining the Relationships

The purpose of this paper is to examine the relationships between preservice secondary mathematics teachers’ beliefs and knowledge regarding teaching mathematics with technology. By conducting three semi-structured interviews, I investigated four preservice secondary mathematics teachers’ technological, pedagogical, and content knowledge (TPACK) and their beliefs about the nature of mathematics, learning and teaching mathematics, and technology use in the mathematics classroom. The findings of this study suggest that preservice teachers with constructivist-oriented or student-centered beliefs about the nature of mathematics, learning mathematics, and technology use displayed higher levels of mathematical knowledge, pedagogical content knowledge, and technological content knowledge, respectively, than preservice teachers with traditional or teacher-centered beliefs about mathematics, learning, and technology use.