Prospective Elementary Mathematics Research Articles

The Roles of Argumentation Structures for The Conviction of Proof Types

"This phenomenology research aims to examine prospective elementary mathematics teachers’ proving and proof evaluation and their thoughts on convincing according to proof type and argument type. The participants were eight prospective teachers. The data collection tools were semi-structured group interviews, interviews video recordings and the participants' written proof documents. The participants were expected to prove different mathematical statements presented to them with different proof types, to convince each other, and to identify the convincing arguments in the interviews. The results revealed that prospective mathematics teachers had absolute conviction about empirical arguments, while their level of convincing about deductive arguments increased as a result of discussions on convincing regardless of the proof type. In addition, the unconvincing for induction and visual proof types’ arguments have emerged and this category has changed to convincing over time. Accordingly, suggestions about increasing the convincing of deductive and visual arguments have been presented"

Creative Problem Posing: Analysis of the Problems Posed Towards Different Strategies by Prospective Mathematics Teachers

The purpose of this study is to analyze problems posed by prospective elementary mathematics teachers of towards different strategies in scope of creativity. Participants of the study are 36 prospective teachers, who take the course of “Problem Solving Strategies”. In this course they study problem-solving strategies. At the end of the course, they were asked to pose three problems suitable for the strategies. Each participant posed a total of 27 problems with three problems for each 9 problem-solving strategies. Problems posed by participants were analyzed in terms of the indicators of fluency, flexibility and originality and chi-square independence test was applied so as to determine whether the creativity of problem posing depends on the strategies. It was seen that fluency had the highest average among all strategies excluding the conscious guessing and control strategy. It was seen that the drawing strategy had the highest average among the strategies in scope of flexibility and the conscious guess and control strategy had the highest average among the strategies in scope of originality. Also it as seen that participants’ creativity levels for various strategies are usually high, and in some cases in the higher echelons of the medium category. This small variation is found to be statistically significant.

An investigation of prospective elementary mathematics teachers understanding of the formal definition of the limit of a sequence

The purpose of this study was to investigate the understanding of prospective elementary mathematics teachers of the formal definition of the limit of a sequence. The participants were 32 prospective mathematics teachers (8 male and 24 female) who were in their third year of study in a four-year mathematics teacher preparation programme Istanbul University-Cerrahpasa in Türkiye. The data were collected via a test that was developed by the authors. The findings of the study demonstrate that the prospective elementary mathematics teachers had difficulty in defining the concept of limit of a sequence and in determining the graphical representations of the variables and the inequalities in the formal definition. Moreover, they also had difficulty comprehending the relationship between the variables of 𝜀 and 𝑛0 , and hence, when a numerical value was assigned to one of these variables, they were not able to find an appropriate value for the other. It was concluded that the prospective mathematics teachers generally tended to memorize the formal definition of the limit of sequences but lacked conceptual understanding of its meaning. Therefore, they were not able to reason about the variables it contained.

Examining graphic drawing skills for a socioscientific problem situation

The aim of the study is to examine the graphing skills of prospective elementary mathematics teachers for a socioscientific problem situation related to Covid-19. The research is a qualitative research and was carried out with the case study method.The participants consisted of 43 prospective elementary mathematics teachers studying in the third year of a state university in Turkey. Typical case sampling, one of the purposive sampling methods, was used to determine the participants. In the research, an open-ended question that requires drawing three graphs with vital aspects based on a socio-scientific situation-based scenario was used as a data collection tool. Data analysis consists of two stages. First, the graphs drawn by the prospective elementary mathematics teachers were scored with the descriptive analysis method.Then, the errors in the graphics drawn using the content analysis method were grouped and determined. When the data were analyzed, it was observed that a significant portion of prospective elementary mathematics teachers had deficiencies in their ability to draw graphs about the problem situation in the context of Covid-19. For this reason, when teaching graphics, drawing activities that require more context-based qualitative understanding or technology-assisted teaching applications can be used.

The Analysis of Problem Posing Skills about Integers of Prospective Primary School Mathematics Teachers Who Have Experienced in Problem Posing

This study aims to analyze the problem-posing skills of primary school mathematics teacher candidates with problem-posing experience and their views on problem posing. The case study, one of the qualitative studies, was used in the study. The study group is ten prospective elementary mathematics teachers who were selected using the purposive sampling method and are in their third year in the academic years 2020-2021 Teaching Mathematics in Primary Schools Major at a private university in Istanbul.The data collection process consists of two stages: 9 problem-posing drafts in total for performance evaluation prepared by examining the literature and obtaining an expert opinion and semi-structured interview forms with three questions. The participants were asked to pose problems on the subject of integers. The problems were evaluated and analyzed by the researchers and two mathematics teachers according to the problem-posing evaluation criteria developed by the researchers. As a result of the findings obtained in the performance determination phase of the study, it was determined that the participants posed more successful problems in the case of structured problem posing. It was determined that some of the problems were not problematic; they were prepared without paying attention to grammar rules, the sentences were not in a clear and logical framework that the middle school students could understand. The numbers were not used according to a certain logic pattern to make the problem solvable. Some problem situations were left unanswered. In the second stage of the study, the data obtained through semi-structured interviews with the primary school mathematics prospective teachers were analyzed using content analysis. In examining the research findings, the main issues are what the participants pay attention to in problem setting, whether they emphasize problem setting in the instructional process, whether problem setting is necessary for each student, and whether anxiety occurs in problem setting.

How the questions of prospective teachers evolve when linking research to practice

This research-to-practice study examines the dynamic characteristics of question formation when teachers begin to research problems of teaching or learning in the classroom. Prospective elementary mathematics teachers (n = 27) documented their questioning process using research logs and recorded 41 changes to their initial research-guiding questions: 22% of changes reflected a shift in language use, and 78% reflected an evolution in the topic itself. Based on study data, the 5C Stages of Questioning framework names the specific stages and changes seen in the evolution of research questions as prospective teachers find literature to address problems of practice in the classroom.

Pre-service primary school mathematics teachers’ beliefs on mathematics assessment

Assessment is an important component in learning mathematics. The practice of mathematics assessment is influenced by teachers' beliefs about the assessment. This study aims to explore the beliefs of primary school mathematics teachers regarding mathematics assessment. The research used quantitative research methods using survey methods to 71 prospective elementary school mathematics teachers. Confidence data regarding mathematics assessment was collected using closed and open questionnaires based on a framework of productive beliefs and unproductive beliefs. Data from closed questionnaires were analyzed using descriptive statistics. Meanwhile, open questionnaire data were analyzed using deductive coding method based on productive and unproductive beliefs. The results showed that prospective elementary school mathematics teachers held mixed beliefs in mathematics assessment. On the one hand, it can be said that the beliefs of prospective elementary school mathematics teachers regarding mathematics assessment tend to be contradictory. These results imply the importance of an attempt to intervene in the beliefs of prospective elementary school mathematics teachers regarding mathematics assessment. Thus, assessment practice can lead to productive assessment, which is to encourage meaningful mathematics learning.

The Effect of an Elective Algebra Teaching Course on Prospective Mathematics Teachers’ Pedagogical Content Knowledge

Effective teachers have knowledge not only of the subject they are teaching, but also of how to teach it appropriately. To develop these aspects of knowledge, faculties of education include a number of courses that address the related skills. From the perspective of mathematics teacher education, courses related to mathematics teaching have come to the forefront in recent years. The current study, in particular, attempted to test whether prospective elementary mathematics teachers’ (PEMTs) pedagogical content knowledge (PCK) in the domain of algebra improved through attendance in a structured elective course. The study was conducted according to a comparison group research design with 155 prospective teachers. The data collection tool consisted of a 20-question algebra pedagogical content knowledge (APCK) test developed by the researchers in consideration of the knowledge for algebra teaching framework of Ferrini-Mundy and colleagues (2005). The results indicated that the PEMTs who took the algebra teaching course performed better than their peers, with statistically significant differences in the various components of algebra teaching knowledge. Given the findings, some implications for mathematics teacher educators are discussed.

The Investigation of Prospective Elementary Mathematics Teachers’ Problem Posing Self-Efficacy Beliefs

Problem-solving and posing are skills at the center of mathematics education and mathematical thinking. However, little is still known about the affective aspects of problem-posing. This study aimed to determine the level of prospective elementary mathematics teachers’ problem-posing self-efficacy beliefs and to compare their beliefs according to the variables of gender, grade, and academic achievement levels. This study was carried out by survey method. Descriptive and causal-comparative survey research design was used in this study. The study group consisted of 130 prospective teachers studying at the Elementary Mathematics Education department in a state university, located in the Eastern Anatolia Region of Turkey. Problem-Posing Self-Efficacy Beliefs Scale was used as a data collection tool. In data analysis, descriptive statistics, the independent samples t-test, and one-way analysis of variance were used. Findings of the study indicated that levels of the prospective teachers’ PP self-efficacy beliefs were high. It was found in the present study that the problem-posing self-efficacy beliefs of the prospective teachers did not differ significantly with regard to gender. Furthermore, a statistically significant difference was found between the prospective teachers’ problem-posing self-efficacy beliefs in terms of their grade and academic achievement. In the light of the research results, suggestions were presented.

Elementary prospective teachers’ visions of moving beyond mathematics anxiety

Previous studies of prospective elementary mathematics teachers’ mathematics anxiety have documented that many prospective teachers often worry about managing their repeated experiences of anxiety while developing their pedagogical and content knowledge to teach mathematics. The literature further indicates the importance of developing learning opportunities for prospective teachers to confront their past experiences while they (re)learn and learn to teach mathematics during methods courses. This study is situated within one such learning opportunity and seeks to analyze potential mathematics anxiety coping strategies generated by forty-eight prospective elementary teachers enrolled in a mathematical methods course. Written responses generated by the prospective teachers were subjected to qualitative thematic analysis to identify patterns of key ideas related to lesson planning for content they felt anxious and/or not confident about teaching and patterns focused on episodes of mathematics anxiety they might experience in the moment of teaching mathematics. Findings indicate that prospective teachers envision using between two and seven strategies grouped across eight coping strategy themes when given the opportunity to reflect on how they might deal with future instances of anxiety when they are tasked with teaching mathematics to their students. We highlight how some of the coping strategies that the prospective teachers envisioned as a means to cope with mathematics anxiety may have more potential to be helpful than others and present implications of our research for mathematics teacher educators.

Analyzing Conceptual and Procedural Knowledge of Geometry Among Prospective Teachers: Indonesian Perspective

It is well established that to scaffold students’ learning of mathematics, teachers themselves need a substantial body of content knowledge of mathematics (Ma, 1989) to drive their lessons and design of learning experiences. In this paper, we address the above issue among prospective elementary mathematics teachers in Indonesia. Evidence suggests that elementary school Indonesian teachers tend to acquire surface-level knowledge of geometry, which does not support deep learning. This paper aims to bring a higher degree of insight into the above problem by analyzing prospective teachers’ geometry knowledge along two knowledge strands: conceptual and procedural. Examples of these knowledge components are provided with suggestions for future research.

An analysis of preservice elementary teachers’ professional noticing skills in a mathematics education setting

Prospective elementary mathematics teachers (PTs) were asked to analyze 28 videos of cognitive interviews. The purpose of this study was to determine if experiences analyzing videos would lead to improvements in PTs’ professional noticing skills. Using a coding schema that reflected three levels of understanding (periphery, transitional, and accomplished), a frequency table was constructed that allowed PTs’ use and understanding of a noticing framework to be analyzed. Findings indicate that experiences analyzing videos leads to improvements in PTs’ professional noticing skills.

Investigation Relationship Between Mathematics Teacher Candidates’ Mathematics Anxiety and Mathematics Teaching Anxiety

The aim of this study is to examine whether the mathematics anxiety of prospective elementary mathematics teachers predict their anxiety about mathematics teaching. In addition, it is aimed to examine the anxiety levels of prospective elementary mathematics teachers towards mathematics and mathematics teaching whether these concerns differ according to grade level. For this purpose, the research model is chosen as the general survey model. The research was carried out with a total of 307 prospective teachers studying in the department of mathematics education in the fall semester of the 2018-2019 academic year. In the research, “Mathematics Anxiety Scale for Teachers and Prospective Teachers” developed by Uldas (2005) and “Anxiety Scale for Teaching Mathematics” developed by Peker (2006) were used. At the end of the research, it is determined that both mathematics anxiety and mathematics teaching anxiety levels of prospective mathematics teachers are low. On the other hand, there is no significant difference as regards grade levels in mathematics anxiety and mathematics teaching anxiety levels of prospective mathematics teachers. It is concluded that there is a moderately positive significant relationship between mathematics anxiety and mathematics teaching anxiety of prospective mathematics teachers. Finally, it is determined that mathematics anxiety of prospective mathematics teachers predicts their mathematics teaching anxiety.

Prospective elementary mathematics teachers’ noticing of childrens’ mathematics: a focus on extending moves

Professional noticing of children’s mathematical thinking (Jacobs et al. in J Res Math Educ 41(2):169–202, 2010) is a construct that is used frequently to understand the ways in which teachers attend to, interpret, and respond to children’s mathematical thinking. In this paper, we present our analysis of prospective elementary mathematics teachers’ (PTs’) responses to a pedagogical activity designed to engage them in an approximation (Grossman et al. in Teach Coll Rec 111(9): 2055–2100, 2009) of professional noticing of children’s mathematical thinking in the moment of teaching, with a focus on developing responses which extend the student’s thinking. PTs were provided two different examples of student work and a series of questions designed to elicit information about their ability to professionally notice student work. We present data and analysis of 73 PTs’ abilities to engage in the individual skills associated with noticing as well as their abilities to use the skills cohesively in concert. Our results demonstrate the type of representation used determined PTs’ success in all three facets of noticing, with a particular effect on interpreting. Further, our focus on a specific type of response move, along with the introduction of a scaffold for that response move, made a difference in PTs’ ability to successfully respond to student work when compared to a prior study with the same PTs (Tyminski et al. 2014). We unpack these results along with suggestions for pedagogical practice as well as directions for future research.

Prospective Early Childhood and Elementary School Mathematics Teachers’ Concept Images and Concept Definitions of Triangles

This study presents a characterization of prospective early childhood teachers’ (ECEPTs) and prospective elementary school mathematics teachers’ (EMEPTs) concept images and concept definitions of triangles through a defining task and an example generation task. Data consisted of 62 EMEPTs’ and 72 ECEPTs’ written statements for the definition of a triangle, drawings for examples and non-examples of triangles, and written reasons for drawings. The results showed that most of the prospective teachers wrote inappropriate statements for the definitions of a triangle by using necessary but not sufficient conditions or using neither necessary nor sufficient conditions with frequent inaccurate terminology usage. The appropriate statements for the definition of a triangle included necessary and sufficient conditions, but were mostly considerably not minimal and/or included inappropriate mathematical terminology. A very large portion of the examples drawn by the prospective teachers consisted of acute triangles with typical positions rather than right and obtuse triangles, which can be evaluated as the indication of prototypical concept images. Drawings of non-triangles also revealed that the prospective teachers mostly drew non-triangular non-examples that can be immediately accepted as non-triangles with the lack of a relatively long list of missing critical attributes, but they provided a small number of triangular non-examples that bear significant similarity to valid examples of a triangle. This result indicates that the prospective teachers’ concept images regarding non-triangles also formed by intuitive non-examples which can be considered as prototypes for non-triangles.

Prospective mathematics teachers’ ways of reasoning on differentiability and corner points in a real-life context

This study investigates prospective elementary and secondary school mathematics teachers’ ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled in the ‘Calculus-1’ course (Case-1) and 20 prospective secondary school mathematics teachers enrolled in the ‘Mathematics Teaching Methods’ course (Case-2). We adapted a task from the well-known filling bottle problem and implemented it as a regular part of each course. Written group solutions, individual reflection papers and task-based group interviews were the data sources. Constant comparative analysis method was employed in analysing the data. The results from both cases indicated that prospective mathematics teachers frequently relied on roughly drawn graphs while deciding differentiability. They had difficulties in writing an algebraic model and comprehending the meaning of a corner point in the filling water context. Prospective mathematics teachers got confused when they got different results for differentiability at a critical point through the roughly sketched graph and algebraic model. The data also showed that thinking about these concepts while working on such dynamic situations fostered prospective mathematics teachers in developing more productive ways of thinking.

Prospective Elementary Mathematics Specialists’ developing instructional practices: support and mentorship during an authentic residency

This case study explored Prospective Elementary Mathematics Specialists’ (PEMSs) pedagogical practices during a K-5 Mathematics Endorsement (K-5 ME) program, specifically focusing on the authentic residency with mentor sessions. Participants included nine PEMSs, with qualitative and quantitative data collected via individual interviews, professional portfolios, and observations of classroom practices. Upon completion of the K-5 ME program, all participants were implementing instructional practices learned about in the program in substantial ways. Participants were honing their skills for orchestrating effective discourse, and the application of those skills became more meaningful as they saw the impact it was having on student learning. This implementation and documentation program coursework was rigorous as PEMSs worked to develop themselves as mathematics teachers and teacher leaders. The collaborative support during the authentic residency and mentor sessions seem to have been significant for PEMSs in supporting implementation of newly learned instructional practices. Ultimately, PEMSs completed the program feeling more prepared as elementary mathematics teachers and teacher leaders.

Covariational Reasoning of Prospective Mathematics Teachers: How Do Dynamic Animations Affect?

Covariational reasoning is about the ability of coordinating the variation in two simultaneously and dynamically changing quantities and being able to see these quantities at the same time by forming a multiplicative unit. Covariational reasoning ability has been considered as necessary and foundational to the understanding of many mathematical concepts ranging from elementary to tertiary levels. In this study, covariational reasoning abilities of prospective elementary school mathematics teachers and the effects of dynamic animations created in computer-based environments on these abilities have been investigated. Case study was used as a research design one of which is a qualitative research methodology. The participants of the study were 19 prospective elementary school mathematics teachers attending to an elective Computer-Assisted Mathematics Education course and four of them were selected for semi-structured interviews. The results showed the weakness in prospective elementary school mathematics teachers’ covariational reasoning abilities and the potential of dynamic animations in supporting covariational reasoning. The animations in dynamic computer environments seem to have minimal effect on paper and pencil solutions in general. However, these animations, if they were used with their data collection and graph drawing properties, affected prospective teachers ways of reasoning in two ways: (i) forcing them to revise and rethink about the current ways of reasoning used during paper and pencil solutions, and (ii) lowering the cognitive load or removing the necessity of deep thinking on the situation. For the first case, the activities supported with the dynamic animations play a supportive role in developing covariational reasoning. For the second case, the dynamic animations did not contribute to prospective teachers’ covariational reasoning, rather they just played a mediating tool role that helps them to find a result.

초등 예비교사들이 수학 과제 변형에서 겪는 어려움에 대한 사례 연구: 분수 과제를 중심으로

This study aims to analyze prospective elementary mathematics teachers’ textbook task modification and identify their difficulties. We identified prospective teachers’ difficulties in modifying visual models, questions, contexts of fraction tasks, systems of fraction tasks, and various meanings of fractions. We conducted semi-structured interviews amongst the prospective teachers to identify their difficulties. As a result, we found prospective teachers’ several difficulties with regard to task modification and identified their difficulties in the process of discerning differences between the mathematical processes and objects as well as clarifying differences in meanings among similar representations.

Developing the Pedagogical Capabilities of Elementary Mathematics Specialists during a K-5 Mathematics Endorsement Program

This mixed-methods study explored the pedagogical practices of Prospective Elementary Mathematics Specialists (PEMSs) as they completed a university K-5 Mathematics Endorsement program. Participants were 13 elementary teachers at an urban, high-needs charter school. Data were collected via individual interviews, written reflections on enacted teaching practices, two observations of classroom teaching practices, and a 36-item Cognitively Guided Instruction Teacher Knowledge Assessment. The findings show the PEMSs were connecting their learning during program courses with instructional practices in their classrooms, as 85% were implementing standards-based learning environments (SBLEs) at a high level, with the classroom event of providing their students opportunities to make conjectures about mathematical ideas as a relative struggle. The PEMSs described pedagogical shifts across the program, providing insights into these changes, along with how particular program components contributed, with the emergent themes of skepticism, trying it on, shifters, and need more support.