Pre-service Elementary Mathematics Teachers Research Articles

Problem Posing and Quantitative Reasoning Opportunities Provided by Mathematics Textbooks for Pre-service Elementary Teachers: A Qualitative Document Analysis

ABSTRACT This qualitative document analysis study reports on opportunities to learn provided by textbooks for mathematics content courses for pre-service elementary teachers. Specifically, the study examined opportunities to engage in problem posing and quantitative reasoning, in the context of fractions, provided by six textbooks commonly used in the teaching of content knowledge courses for pre-service elementary mathematics teachers in the United States. Among other things, this examination revealed two key findings. First, all the textbooks provide numerous opportunities that could potentially trigger students’ quantitative reasoning. This is commendable, and a positive response to growing calls to increase such opportunities in mathematics education. Second, there is a paucity of opportunities to engage in problem posing in all the textbooks. Given the numerous benefits of using problem posing in the teaching and learning of mathematics, we recommend that authors of textbooks for mathematics content courses for pre-service elementary teachers provide more opportunities to engage in problem posing in their textbooks. We argue that the act of problem posing requires significant quantitative reasoning, and thus problem posing provides the opportunity for students to develop such reasoning. Implications for instruction and directions for future research are discussed.

Subject, functionality and level of proofs preferred by pre-service elementary mathematics teachers

This study examined the subject(s) that elementary mathematics teacher candidates find most suitable for proving in analysis courses, the functional structure of proof they remember most, the level of proof, and the reasons for preferring this proof. For this reason, this research aims to reveal the pre-service teachers' preferences for proof in analysis courses, the proof they keep in mind the most and its functional structure, their level of proof, and their views on proof relationally and holistically. In this study, which was conducted with a qualitative research approach, a form consisting of open-ended questions was applied to teacher candidates. In this form, teacher candidates were asked various questions about the mathematical proofs they made. With descriptive analysis, the answers of the pre-service teachers who participated in the research were systematically defined, and data were tried to be defined through content analysis. Accordingly, while the subject that the pre-service teachers found the most appropriate application of the proof approach to be the subject of trigonometry, it was determined that the proof that remained in their minds the most was also related to the subject of trigonometry. By examining the functional structure of these proofs written by pre-service teachers, it has been seen that they have the function of explanation and systematization. In addition, the reasons for preferring the proof they made were asked of the pre-service teachers, and the answers were gathered on the fact that proof provides the most permanence and causal learning. It was emphasized that theorems that require formula memorization generally become more understandable with the proof method. According to the results of the research, it is stated that the common opinion of the prospective teachers is that teaching how to obtain the proof method of formulas in trigonometry, instead of memorizing them, is beneficial in ensuring both meaningful and permanent learning. In light of the findings of these studies, more sensible suggestions can be made to improve pre-service teachers' knowledge systems and classroom teaching on proof. By determining which topics and theorems students have difficulty in proving in addition to trigonometry, additional learning on these subjects can be recommended.

Pre-service Elementary Mathematics Teachers’ Planning Processes of Mathematical Modeling Practices

Bu çalışmada, ortaokul matematik öğretmen adaylarının ders imecesi boyunca matematiksel modelleme öğretiminde öğretmen yeterliklerinden biri olan öğretme boyutunda yer alan matematiksel modelleme problemleriyle uygulamayı planlama süreçlerindeki değişimin incelenmesi amaçlanmıştır. Nitel bir durum çalışması olan araştırma, teorik eğitim ve uygulama olmak üzere iki boyutta gerçekleştirilmiştir. Matematiksel modelleme ile ilgili teorik eğitim alan öğretmen adayları iki farklı matematiksel modelleme problemi için uygulama planı hazırlamış ve bu planlarını sınıf ortamında hayata geçirmişlerdir. Planlama süreçlerinden elde edilen veriler nitel veri analiz yöntemleri kullanılarak analiz edilmiştir. Elde edilen bulgular, ders imecesi modelinin, öğretmen adaylarının matematiksel modelleme problemleriyle uygulama planlama süreçlerine önemli katkılarının olduğunu göstermiştir. Öğretmen adaylarının ayrıntılı planlama süreçlerinden geçtikleri ve planlarında benzerliklerin yanı sıra önemli farklılıkların olduğu görülmüştür.

Pre-Service Elementary Mathematics Teachers’ Evaluations of Meetings with Expert and Peer Participation Based on van Hiele Geometric Thinking Levels

In this study, it was aimed to present the pre-service elementary mathematics teachers’ (PEMT) evaluations of meetings with expert and peer participation based on van Hiele geometric thinking levels (vHGTL). The case study method was used and the study group of the research consists of three PEMT who are studying in the third year of a state university. Data were collected with meeting records, reflection reports of the PEMTs, researcher’s field notes and interviews and were analyzed simultaneously by two researchers to ensure coding reliability with content analysis method. As a result of the research, it was seen that there was a positive change in PEMTs’ criteria for determining vHGTL. It was determined that they had difficulties in clearly distinguishing the differences between the levels at the beginning, and that in the last meetings, they insisted on the criteria related to the levels they determined and made more accurate determinations about the levels. As a matter of fact, the teacher candidates also stated that meetings enabled them to determine the achievements’, solved and unsolved problems’ vHGTL better. In addition, they stated that allowing them to freely express their ideas in meetings contributed to their professional development in geometry teaching knowledge. Suggestions regarding experts and peers participatory meetings were presented.

The Opinions of Pre-Service Elementary Mathematics Teachers on the Courses in the Undergraduate Programs Before 2018 and 2018 According to the Framework of General Competencies for Teaching Profession

Bu araştırmada öğretmenlik mesleği genel yeterlikleri çerçevesinde ilköğretim matematik öğretmeni adaylarının 2018 öncesi ve 2018 lisans programlarındaki derslere yönelik görüşlerinin incelenmesi amaçlanmıştır. Bir fenomenoloji çalışması olarak desenlenen bu araştırma, 10 ilköğretim matematik öğretmeni adayı ile yürütülmüştür. Veri toplama aracı, Milli Eğitim Bakanlığı’nın (2017) yayınladığı öğretmenlik mesleği genel yeterlikleri doğrultusunda hazırlanmıştır. Katılımcılardan öğretmenlik mesleği genel yeterlikleri çerçevesinde belirtilen 65 farklı göstergenin kazanılması için 2018 lisans programında yer alan hangi derslerin katkı sağladığını belirtmesi ve nedenini açıklamaları istenmiştir. Buna ek olarak göstergelerin kazanılmasında 2018 öncesi uygulanan lisans programındaki dersleri de inceleyip, eksik gördükleri dersleri belirtmeleri ve neden eklenmesi gerektiğini açıklamaları istenmiştir. Toplanan veriler betimsel olarak analiz edilmiştir. Araştırma sonuçları genel olarak değerlendirildiğinde 2018 lisans programında yer alan genel kültür ve meslek bilgisi derslerinin öğretmenlik mesleği yeterliğini karşılamada yeterli olduğu ancak alan eğitimi ile ilgili derslerin eksikleri olduğu sonucuna ulaşılmıştır. Yine öğretmen adaylarının görüşleri doğrultusunda özellikle alan bilgisi bağlamında, 2018 öncesi uygulanan programın da dikkate alınması gerektiği önerilmektedir.

Opinions of Pre-service Elementary School Mathematics Teachers on Misconceptions

The aim of this study is to determine the opinions of pre-service elementary school mathematics teachers about misconceptions. For this purpose, case study, which is one of the qualitative research methods, was used. The study was conducted with 54 pre-service elementary school mathematics teachers. The data collection tool of the research consists of written response papers that they give to open-ended questions asked to participants. The views of pre-service elementary school mathematics teachers to open-ended questions were analyzed by content analysis. In order to prevent misconceptions that may arise during the lesson, pre-service elementary school mathematics teachers stated that they would; investigate the misconceptions, prepare for the lesson, study the subject, concretize the subject, visualize, determine the pre-learning, give daily life examples, etc. In order to determine whether their students have misconceptions, they stated that they would ask questions, evaluate the answers, solve the test, examine the mistakes and questions, observe the reactions, etc. It is recommended for further research to examine how pre-service elementary school mathematics teachers take precautions to avoid misconceptions by preparing a lesson plan, and to examine the situations of determining and correcting mistakes in students by observing the lessons of the teachers.

The Effect of Error-Based Activities on the Reflective Thinking Skills of Pre-service Elementary Education Mathematics Teachers

"The purpose of the current study is to investigate the effect of error-based activities on the reflective thinking processes of pre-service elementary education mathematics teachers. To this end, qualitative research method was employed. The current study was carried out with the participation of six pre-service elementary education mathematics teachers attending a university in Turkey in the spring term of the 2017-2018 academic year. In order to collect the data in the study, the participating pre-service teachers were asked to write diaries and face-to-face interviews were conducted with them. The collected data were analyzed by coding them on the basis of the pre-service teachers’ responses to the questions asked to them in line with the pre-determined conceptual framework. The obtained data have revealed that the error-based activities had positive effects on the pre-service teachers’ thinking processes. In addition to this, the pre-service teachers’ reflective thinking processes positively changed over the week"

Examination of the Estimation Skills and Strategies of Pre-Service Elementary Mathematics Teachers

The present study aimed to determine the estimation skills of elementary education pre-service mathematics teachers and the strategies they adopt in estimation. The case study methodology was employed in the study, and the participants included 37 volunteering students attending the fourth grade in the Primary Education Mathematics Instruction Department at a university located in the Central Anatolia Region in Turkey. The study data were collected with an 8-item Estimation Strategy Test developed by the authors. The test included numerosity, computational, and measurement estimation questions. In addition to making estimations, the students were asked to write the reasons behind their estimations. The descriptive analysis technique was employed to analyze the study data, and the data were coded based on the estimation strategies adopted by the pre-service teachers and similarity of their estimations with the actual values. The data are presented as MAXQDA maps, and excerpts from student responses are also presented. The study findings demonstrated that the responses of most pre-service teachers were similar to the actual value in computational estimations; however, numerosity or measurement estimations were not similar. Furthermore, certain pre-service teachers inclined to conduct the actual operation instead of estimating the results during computational estimation, and directly counted the results in numerosity estimation. Also, it was determined that a significant number of pre-service teachers made computational errors in numerosity and computational estimation.

We train, but how well? Assessing mathematical knowledge for teaching of future Turkish teachers

This study aims to assess and compare–at the national and regional sizes–mathematical knowledge for teaching of pre-service elementary mathematics teachers (PEMTs). Participants of the study were composed of 1,367 pre-service teachers selected among 21 universities in 12 regions of Turkey. Mathematical knowledge for teaching (MKT) test, which were developed by TEDS-M project were used to collect the data. The instruments were adapted into Turkish by the researchers. According to results, while there wasn’t much differentiation among the regions in terms of the MKT, pre-service teachers in the West Marmara, Mediterranean, and Northeast Anatolia regions are more successful than the other regions. PEMTs’ mathematics pedagogical content knowledge (MPCK) performance was close but somewhat better than their mathematics content knowledge (MCK) performance, in terms of both regions and universities. In the case of the MPCK test, the regions exhibited a more homogeneous picture, while in the case of MCK, the universities did so. Algebra content domain is where the PEMTs’ performance is lowest. When we compared the results obtained from this study with published international averages from TEDS-M study, Turkish PEMTs had appreciably higher performance on both MCK and MPCK components.

Examination of Mathematical Errors and Mistakes in Calculus Course

This study was conducted to identify mathematical errors and mistakes made by preservice elementary mathematics teachers in the calculus course. To that end, the document analysis method of qualitative research models was used in the research. The sample of the research included a total of 75 preservice teachers who were attending the Department of Elementary Mathematics Education in the Faculty of Education at a public university and taking the calculus I course during the fall term of 2016-2017 academic year. Accordingly, written documents including the participant preservice teachers’ papers of interim exams, practice exams, and general exams constituted the data source. The exam papers were scanned with a scanner and transformed into the electronic environment. A content analysis was performed with the data by using MAXQDA 12 qualitative data analysis program, and “data coding” of data analysis techniques was utilized. It was concluded that the preservice teachers made procedural and conceptual errors and mistakes, mathematical errors and mistakes such as recalling generalizations incompletely or incorrectly. Some recommendations were made in light of these results.

Preservice Science and Mathematics Teachers’ Mathematics Anxiety and Beliefs about the Nature of Mathematics:

This study aims to examine preservice science and mathematics teachers’ mathematics anxiety and beliefs about the nature of mathematics, as well as to reveal whether they differ according to the department. Moreover, this study investigates whether there is a relationship between beliefs about the nature of mathematics and mathematics anxiety. The participants of the study were 213 junior and senior preservice elementary science and mathematics teachers. Data collection tools were Philosophical Thoughts about the Nature of Mathematics Scale (PTNM) and Mathematics Anxiety Scale (MAS). Both descriptive and inferential statistics were used to analyze mathematics anxiety and beliefs scores of preservice elementary teachers. The study revealed that most of the preservice teachers’ scores on beliefs about the nature of mathematics high and their mathematics anxiety scores were low. The results indicated that there were significant differences in both belief scores and mathematics anxiety scores in favor of preservice mathematics teachers. In addition, there was a high negative correlation between pre-service teachers’ PTNM and MAS scores.

Preservice elementary mathematics teachers’ use of patterns and pattern problems when planning and implementing lessons

This study examines how preservice elementary mathematics teachers create patterns, write pattern problems, and prepare and apply lesson plans on this topic. In this context, five preservice elementary mathematics teachers who were in the final semester of their undergraduate education volunteered to participate in this research. The study was carried out within the scope of an elective course which lasted eleven weeks and in which patterns were discussed. Data were collected through interview, observation and document analysis. The results show that besides the complexity and originality criteria of written problems, preservice teachers have difficulty in writing quadratic growing pattern problems. In addition, some preservice teachers adopt a teacher-centered approach in planning and implementing their lesson plans. Most of the preservice teachers did not make connections between patterns and daily life and most of them did not use concrete materials in their lesson plans or lessons.

Entrepreneurship and Entrepreneurial Skills in Middle School Mathematics Lesson Curriculum and Teaching Profession Through the Eyes of Pre-service Elementary Mathematics Teachers

These days, when the age of industrial society has passed to the age of information and technology, the profile of people with intelligent, logical, and practical intelligence stands out instead of the labor force. In this sense, education is the most important element in the education of entrepreneurial individuals who can keep up with the rapid changes of the age. Entrepreneurship trainings are also important for individuals to gain entrepreneurship and entrepreneurial skills. These trainings are usually given at the university level. At this point, the main goal in entrepreneurship education is to introduce entrepreneurship, and to educate entrepreneurial individuals. The aim of this research was to examine the thoughts and knowledge of pre-service elementary mathematics teachers about the concepts of entrepreneurship and entrepreneurial skills from the point of view of the middle school mathematics course curriculum, as well as from the point of view of the teaching profession. Qualitative research was used in the research. A total of 40 pre-service elementary mathematics teachers, including 10 pre-service teachers (5 females and 5 males) from each year of study, who were studying at a Faculty of Education. The data was collected using a semi-structured interview form. The interview form consisted of 5 questions. The content analysis technique was used in the data analysis. The findings of the middle school mathematics curriculum in entrepreneurship and entrepreneurial skills of entrepreneurship and entrepreneurial skills in the place and on the importance of the teaching profession and the faculty were examined under 2 titles. All of the first-year pre-service teachers stated that they had never studied the curriculum in terms of entrepreneurship and entrepreneurial skills. Pre-service teachers have skills that can be associated with entrepreneurial skills, creativity, problem solving, communication, critical thinking, and forecasting skills. Mathematics lessons are taught the most by pre-service teachers to help them gain entrepreneurship skills. The importance of having entrepreneurship and entrepreneurship skills for the teaching profession, in terms of the teacher-student and teacher-teaching processes. All of the pre-service teachers stated that they had not taken courses on entrepreneurship. The concepts of entrepreneurship and entrepreneurship skills, whose place and importance are increasing day by day, should be included more in curricula and their importance in terms of teaching should be taught. Keywords: Entrepreneurship, Entrepreneurial Skills, Entrepreneurship Education, Pre-service Elementary Mathematics Teachers DOI: 10.7176/JEP/12-5-06 Publication date: February 28 th 2021

KNOWLEDGE AND IMAGES OF PRE-SERVICE ELEMENTARY MATHEMATICS TEACHERS ABOUT ENTREPRENEURSHIP AND ENTREPRENEURSHIP SKILLS

Entrepreneurship is related to awareness, ideas, imagination, and effort. Entrepreneurship training is now being carried out in order to increase the extent of entrepreneurial activities. In this regard, when entrepreneurship education practices are examined in many countries, it is seen that students are introduced to entrepreneurship and entrepreneurship education before they reach high school. In Turkey, entrepreneurship skills are among the basic skills in all curriculum programs since 2005. By establishing relations through images, people build stronger and understandable connections when they encounter a new concept or new knowledge. In this respect, the aim of this study is to reveal pre-service elementary mathematics teachers’ perceptions of entrepreneurship and the skills of the concept from freshmen to seniors in terms of what they know from their previous and current educational experiences and their perceptions about the importance of the concept of entrepreneurship. Twelve pre-service elementary mathematics teachers (6 women and 6 men) from each grade level for a total of 48 pre-service teachers (24 women and 24 men) studying at Bolu Abant Izzet Baysal University participated in the study. During the selection process of the participants, only voluntary participants were considered. As a data collection tool, the interview protocol, which included 6 questions and was based on the literature, was prepared by the researcher. Data were collected through interviews, and interviews took approximately 40 minutes for each participant. The content analysis technique was used in the analysis of the collected data. The data were analyzed under headings of the prior knowledge and perceptions of entrepreneurship and entrepreneurship skills, the importance of entrepreneurship and entrepreneurship skills, the place of entrepreneurship in daily life, and findings about images of entrepreneurship skills. According to the findings of the research, it is concluded that the concepts of entrepreneurship and entrepreneurship skills are not sufficiently heard of or recognized among pre-service elementary mathematics teachers. As the image categories of entrepreneurship and entrepreneurship skills, 4 image categories and related subcategories were determined for entrepreneurship. For “entrepreneurship skills,” 3 image categories and related subcategories were determined. Entrepreneurship training can be given in entrepreneurship courses or teaching courses in faculties of education. In these courses, not only theoretical knowledge about entrepreneurship skills, which are among the skills that should be acquired by individuals within the scope of lifelong learning, but also studies involving applications can be applied for pre-service teachers. There is no previous study in the literature that reveals the knowledge and images of pre-service elementary mathematics teachers regarding the concepts of entrepreneurship and entrepreneurship skills. Therefore, other studies that support the results of this study should be pursued. Article visualizations:

A STUDY ON THE PRE-SERVICE ELEMENTARY MATHEMATICS TEACHERS' KNOWLEDGE ON THE CONVERGENCE AND DIVERGENCE OF SERIES IN THE CONTEXT OF THEORETICAL AND APPLICATION

The focus of this research is the examination of theoretical and practical knowledge about the convergence and divergence of the series. In line with the research focus, the pre-service mathematics teachers on the convergence and divergence of the series with the help of the real-life problem in the context of theory and application using the concept of harmonic series. The research was guided by a qualitative method, case study. The research data consisted of two written questions and a problem and four interview questions that were formed by the researchers and their validity and reliability were ensured. The study concluded that pre-service mathematics teachers have theoretical knowledge about the convergence of series and harmonic series, their perception of series, harmonic series, the concepts of convergence and divergence changed in the application process and adopted different approaches to problem solving.

Strategies Applied by Pre-service Elementary School Mathematics Teachers for Coping with Tasks that Require a Mental Rotation

Despite the plethora of research in the field of mental rotation, researchers are still divided over a range of related issues, particularly the processes involved in coping with mental rotation tasks. This field of research, for the most part, is descriptive rather than interpretative, leading to the absence of a theoretical framework to enable the development of a coherent dedicated training program. Against this background, the present study is underpinned by the assumption that identifying relations between strategies that potentially lead to a successful coping with mental rotation tasks and those that do not lead to success might help us in designing a dedicated training program for pre-service teachers. The study involved 122 pre-service elementary school mathematics teachers. They responded to a questionnaire that included, among others, two tasks that required performing mental rotation. In line with other studies, the results of the present study indicate that there is an advantage to implementing a holistic strategy over an analytic one. However, the mere implementation of a certain strategy does not guarantee that one would draw a correct conclusion, as the same strategy might lead to either correct or incorrect conclusion. Based on these results, we inferred that there is a mechanism that mediates between the strategy employed and the conclusion reached. Apparently, in the context of mental rotation, the study of strategies does not allow understanding the essence of this mechanism, and in order to construct an interpretative theory, an alternative course of inquiry is needed.

Investigation of pre-service elementary mathematics teachers’ problem posing situations in dynamic geometry environment

This study examined problem posing situations of pre-service elementary mathematics teachers in dynamic geometry environment by using problem posing strategies. The qualitative method of multiple case study was applied and geometric concepts that participants used for each type of problem posing are examined. Eight participants from 3rd grade pre-service mathematics teachers voluntarily participated in the study in 2015-2016 fall semester had previously received Computer Aided Mathematics course in the 2014-2015 spring semester. During six weeks’ data collection period, participants tried to pose new problems via dynamic geometry software by using given problem posing situations and their studies were recorded by screen saving program. The relationship between the problems that given to them and the concepts in the new problems were examined through screen recordings. Findings show new problems are established in parallel with the shape or problem statement in the problem posing situations given to them. Compared with other types of problem posing situations, it is seen the concepts are more diversified in the free problem posing. Participants develop their problem posing skills during the process so it is suggested these topics should be included in mathematics education undergraduate program in order for future students to gain these skills.

Pre-Service Elementary Mathematics Teachers' Specialized Content Knowledge: The Case of Integer Addition and Subtraction

Pre-service mathematics teachers’ content knowledge is an important issue. Therefore, detailed studies are needed to be conducted on mathematical topics. The study examines preservice elementary mathematics teachers’ (PEMTs) special content knowledge (SCK) of integer addition and subtraction in the context of using multiple representations, explaining mathematical reasons lying behind the concepts and justifying them. The findings obtained from the written responses of 42 PEMTs reveal that preservice teachers do not have sufficient and balanced special content knowledge. This is especially more so in the case of addition and subtraction of numbers with opposite signs. The preservice teachers were observed to have more difficulty in using the number line model compared to the use of other representations. The findings offer some indicators about how PEMTs understand integer addition and subtraction through multiple representations and why more emphasis on the SCK components

Effects of the Instruction with Mathematical Modeling on Pre-service Mathematics Teachers’ Mathematical Modeling Performance

The purpose of the study was to investigate the effects of the instruction with mathematical modeling on pre-service mathematics teachers’ mathematical modeling performance. The participants were 24 pre-service elementary mathematics teachers. A mixed method approach was used to conduct the research. Each week, the participants were given two mathematical modeling problems and solved them as a group. After that, each group shared their solutions with the class so that there was an opportunity to focus on different solution methods. The data was collected via a pre and a post mathematical modeling test. SPSS package program was utilized in order to determine the significance level of the difference between the test results. One of the participants’ solutions in the pre-test and in the post-test was also analyzed to enhance the results. The result showed that the instruction based on mathematical modeling improved pre-service teachers’ mathematical modeling performance.

Uncovering the Relation between CK and PCK: An Investigation of Preservice Elementary Mathematics Teachers’ Algebra Teaching Knowledge

This article discuss the algebra teaching knowledge of preservice elementary mathematics teachers in the context of CK and PCK as well as the relationship between them. The study was conducted with 101 preservice teachers sampled from a state university in Turkey. Rasch analysis was used to interpret the data. The results revealed that preservice teachers performed at mid-level for both CK and PCK tests. It was also found that there was significant correlation between the CK and PCK test scores. Weaknesses of the preservice teachers in terms of knowledge of the learner component of PCK, in comparison with presentation of content, were identified.