Prospective Middle School Mathematics Teachers Research Articles

Prospective middle school mathematics teachers’ conceptualizations of slope

In this study, the conceptualizations used by prospective middle school mathematics teachers when defining, representing, and exemplifying the slope concept and relating it with other mathematical situations were examined. Participants’ conceptualizations were identified by Nagle, C., Moore-Russo, D., Viglietti, J., & Martin, K. [(2013). Calculus students’ and instructors’ conceptualizations of slope: A comparison across academic levels. International Journal of Science and Mathematics Education, 11(6), 1491–1515. https://doi.org/10.1007/s10763-013-9411-2] framework. The findings showed the prospective teachers mostly used trigonometric and parametric conceptions. Real-world situation, calculus conception, geometric ratio, and determining property were other common conceptualizations used by the participants. On the other hand, algebraic ratio, behaviour indicator, physical property, and functional property conceptualizations were seldom used and linear constant conceptualization was never used by them. The implications for mathematics teacher educators and mathematics education researchers on how to remedy prospective teachers’ possible difficulties and errors about slope are discussed.

Types of Global Argumentation Structures in Conjecture-Generation Activities Regarding Geometry

Toulmin’s argumentation model is an effective tool in the description of one step of an argument. However, there is a need to consider more than this model to portray a comprehensive argumentation process. The purpose of the study is to investigate types of global argumentation structures that emerged while prospective middle school mathematics teachers were working on conjecture-generation activities related to geometry. The participants were junior prospective middle school mathematics teachers at a state university in Ankara, Turkey. The eight global argumentation structures that emerged via conjecture-generation activities of two groups were classified as mono structures and hybrid structures. According to the findings, three types of mono structures, which are the reservoir-structure, the funneling-structure, and the branching-structure, were seen among four possible cases. Three types of hybrid structures were observed among eleven possible combinations of the mono structures, namely, the reservoir-funneling-structure, the line-branching-structure, and the line-reservoir-branching-structure.

Öğretmen Adaylarının İki Niceliğin Eş Zamanlı Değişimini İçeren Dinamik Fonksiyonel Durumlar İçin Oluşturdukları Grafik Temsilleri

This study aims to reveal how prospective teachers express the relationships between variables through graphical representations when interpreting dynamic functional situations involving two simultaneously changing quantities. 100 prospective middle school mathematics teachers participated to this case study. The data consisted of prospective teachers’ written responses to the task involving filling bottles with water and the graphs of volume as a function of height and clinical interviews were used to examine their covariational reasoning and graphing abilities. The findings showed that only six prospective teachers' graphical representations were correct for both dynamic functional situations. The most significant and common problems in the graphical representations were found such as (i) inability to coordinate slopes for linear relationships between variables, (ii) representing nonlinear relations of variables as linear relations, (iii) reversing the roles of dependent and independent variables, (iv) representing the relationship between variables as decreasing rather than increasing and (v) representing the relationships between variables to include more or less partitions to the graph than required by the given dynamic functional situation.

The relationship between prospective middle school mathematics teachers’ critical thinking skills and reflective thinking skills

The aim of this study was to analyze the relationship between critical thinking skills and reflective thinking skills of prospective middle school mathematics teachers. In addition, it was aimed to examine critical thinking skills and reflective thinking skills of prospective middle school mathematics teachers with regard to some variables (gender, grade level, academic achievement level). This study adopts one of the general survey models: relational survey model. 201 prospective middle school mathematics teachers studying in Elementary Mathematics Teacher Education Program at a state university participated in this study. Reflective Thinking Scale and Critical Thinking Standards Scale were used. For the data analysis, descriptive statistics, independent sample t-test, one-way analysis of variance, correlation analysis, and simple linear regression analysis were used. The findings of this study showed that the prospective teachers' critical thinking skill level is high (agree), reflective thinking skill level is at moderate level (neutral). Critical thinking skills of the prospective teachers were significantly different in terms of gender and academic achievement. On the other hand, reflective thinking skills of the prospective teachers were significantly different in terms of grade level. Besides, there was a positive, significant and moderate relationship between critical thinking skills and reflective thinking skills of the prospective teachers. The prospective teachers’ critical thinking skills were the significant predictors of their reflective thinking skills. It was found that critical thinking skills explained 24% of the variance related to reflective thinking skills.

Matematik öğretmeni adaylarının bilimsel araştırma hakkındaki eleştirel düşünme süreçleri: Gazete haberi örneği

This study aimed to explore how prospective middle school mathematics teachers think critically about a newspaper article that reported the findings of a statistical research. Participants of the study were four fourth-year students enrolled at the mathematics teacher education program of a public university. To investigate the research question of the study, case study method was employed. In-depth semi-structured interviews were done to examine participants’ critical thinking processes. The findings of the study indicated that prospective mathematics teachers made use of a variety of critical thinking processes (comprehending, making connections, inferring ideas, critiquing, and self-reflecting) and provided clues about the interrelated nature of these processes. This study would shed light on the characterization of critical thinking in the context of statistical literacy by suggesting a blended framework. It also suggests the design of the tasks including media articles to promote both statistical literacy and critical thinking in statistics education courses for prospective mathematics teachers.

Prospective Middle School Mathematics Teachers’ Problem Posing Abilities in Context of Van Hiele Levels of Geometric Thinking*

Prospective Middle School Mathematics Teachers’ Problem Posing Abilities in Context of Van Hiele Levels of Geometric Thinking*

Prospective Middle School Mathematics Teachers’ Awareness of Students’ Errors regarding the Use of Letters in Algebra and Algebraic Operations

Bu calismanin amaci ortaokul matematik ogretmeni adaylarinin cebirde harflerin kullanimi ve cebirsel islemler konusunda ogrenci hatalarina yonelik farkindaliklarini, ogretmen adaylarinin ogrenci hatalarina yonelik tahminleri ve ogrenci dusunme sekilleri bilgilerine yonelik oz degerlendirmeleri acisindan incelemektir. Calisma bir devlet universitesinin Ilkogretim Matematik Ogretmenligi programinda sunulan, Ozel Ogretim Yontemleri-1 dersi kapsaminda gerceklestirilmistir. Bu calismanin katilimcilarini, derse katilan 44 ucuncu sinif matematik ogretmeni adayi arasindan secilen dort ogretmen adayi olusturmaktadir. Arastirma surecinde, ogretmen adaylari verilen cebirsel sorulara yonelik ogrencilerin hatali cevaplarini tahmin etme ve gercek ogrenci cozumleri araciligiyla hatali ogrenci cozumlerini inceleme sureclerinden gecmislerdir. Bu calismanin veri kaynaklarini, dort ogretmen adayinin ogrenci hatalarini tahminleri uzerine yapilan birebir gorusmeleri ve oz-degerlendirmeleri ile ilgili on ve son gorusmeleri olusturmaktadir. Bulgular, dort ogretmen adayinin bazi temel ogrenci hatalarinin farkinda oldugunu gosterirken, ogrencilerden gelebilecek farkli tur hatalara yonelik farkindalik duzeylerinin dusuk oldugunu gostermistir. Bu calisma matematik egitimcilerine ogretmen adaylarinin ogrenci hatalarina yonelik farkindaliklarini gelistirmek amaciyla ogrenme ortami tasarlamalarini onermektedir.

A Different Look at the Reasoning Process of Prospective Middle School Mathematics Teachers: Global Argumentation Structures

Argumentation is an important part of education in different disciplines such as science teaching and psychology. Numerous research studies have revealed that the use of argumentation practices in courses have a positive impact on students' both cognitive (critical thinking, reasoning, etc.) and affective abilities. Recently, the number of studies on argumentation in the field of mathematics education has increased. It is expected that prospective teachers today are key elements of the argumentation process as they can encourage students to produce strong mathematical arguments; hence, they themselves are also expected to develop their own argumentation skills. In the literature, there is a need for studies on the reasoning processes and argumentation structures of prospective teachers. Thus, the present study aimed to investigate the global argumentation structures used by prospective middle school mathematics teachers while they were solving geometry tasks. In line with this purpose, a qualitative case study was conducted with 8 prospective teachers who were enrolled in the elementary mathematics education department of a state university located in Ankara. Two argumentation applications were conducted with the participants. In the first application, two problems on triangles and in the second one two problems on circles were solved by the participants. Then, the global argumentation structures of the participants were examined. The results showed that mathematical reasoning of prospective middle school mathematics teachers was weak and, therefore, they mostly used simple global argumentation structures. On the other hand, it was found that the researcher's directions lead participants to use more complex global argumentation structures. Therefore, it was concluded that the teachers who orchestrate the argumentation process should have sufficient knowledge and experience regarding argumentation. This result revealed the importance of focusing on the development of mathematical reasoning skills of prospective teachers. Based on this, it is recommended that necessary adjustments be made in teacher training programs to include argumentation so that prospective teachers can be equipped with the ability to orchestrate argumentation in their lessons.

Prospective Middle School Mathematics Teachers’ Global Argumentation Structures

The aim of the present study was to investigate the nature of global argumentation structures of prospective middle school mathematics teachers in a technology enhanced environment. A qualitative case study was conducted with 8 participants from an Elementary Mathematics Education undergraduate program of one of the public universities in Ankara. Two implementations, 1 of which included 2 geometry tasks on triangles and another which included 2 geometry tasks based on circles, were conducted. Subsequently, global argumentation structures were revealed via data analysis. The findings indicated that the prospective middle school mathematics teachers resort frequently to simple global argumentation structures since their mathematical reasoning was insufficient. On the other hand, technology had a positive impact on argument construction and global argumentation structures of prospective middle school mathematics teachers. However, it was deduced that prospective middle school mathematics teachers need to be challenged on argumentation and about how to facilitate argumentation effectively in their future classroom experiences.

Prospective Middle-School Mathematics Teachers’ Quantitative Reasoning and Their Support for Students’ Quantitative Reasoning

The aim of this research is to examine prospective mathematics teachers’ quantitative reasoning, their support for students’ quantitative reasoning and the relationship between them, if any. The teaching experiment was used as the research method in this qualitatively designed study. The data of the study were collected through a series of exploratory teaching interviews and debriefing interviews with nine focus group participants, and clinical interviews that the participants conducted with middle-school students. The results indicated that the participants with strong quantitative reasoning use problem-solving approaches that focused on the quantity, whereas the participants with poor quantitative reasoning use problem-solving approaches that focused on performing calculations, using formulas and procedures devoid of quantitative meaning in solving of the problem. During the questioning process, the participants with strong quantitative reasoning led their students to identify and interpret the quantities, determine relationships among the quantities, represent all the quantities and their interrelationships, whereas the participants with poor quantitative reasoning led their students to perform calculations, make algebraic manipulations and focus on numbers by ignoring the quantities in the problem. These results suggest that prospective mathematics teachers’ quantitative reasoning is strongly associated with their support for students’ quantitative reasoning in the problem-solving process.

Prospective Teachers’ Knowledge on Middle School Students’ Possible Descriptions of Integers

This study aims to reveal prospective middle school mathematics teachers' knowledge regarding the possible misconceptions and/or errors of middle school students in describing integers. In addition to this, it aims to reveal the possible reasons underlying these from the perspective of prospective teachers. Data was qualitatively collected from 38 Turkish prospective teachers by an open-ended questionnaire. The results show that although prospective teachers are familiar with possible misconceptions and/or errors of middle school students in describing integers, each prospective teacher does not have a rich repertoire regarding students’ thinking process even though it seems that there is a rich repertoire in total. They did not give sufficient details about the content and pedagogical aspects of the misconceptions and/or errors. They proposed quite general ideas about the misconceptions and/or errors and the reasons for them.

Explanations of prospective middle school mathematics teachers for potential misconceptions on the concept of symmetry

This study is an explanatory study, which follows a qualitative methodology and aims to reveal the explanations of prospective mathematics teachers for the potential misconceptions of secondary school students in relation to the concept of symmetry and the correction of such misconceptions. The study group consisted of a total of 26 prospective middle school mathematics teachers, who were senior students. The data of the study were obtained from the open-ended test prepared by the researchers. Following the data analysis, it was found out that the majority of the participants failed to identify the mistakes of students and suggested the ways to “letter the corners of the shape and measure the distance based on the axis of symmetry” in order to correct these mistakes. Moreover, the study notably observed that the participants adopted practical solutions such as the use of a mirror, paper folding, and the use of unit squares more in teaching the concept of symmetry. It may be stated that the prospective teachers, in this way, overlooked the development of conceptual knowledge in students.

Turkish Prospective Middle School Mathematics Teachers’ Beliefs and Perceived Self-Efficacy Beliefs Regarding the Use of Origami in Mathematics Education

Background:The purpose of this study was to investigate beliefs and perceived self-efficacy beliefs of Turkish prospective elementary mathematics teachers in using origami in mathematics education and gender differences in their beliefs and perceived self-efficacy beliefs.Materials and methods:Data for the current study was collected via Origami in Mathematics Education Belief Scale (OMEBS) and Origami in Mathematics Education Self-Efficacy Scale (OMESS).Results:Descriptive analysis results indicated that prospective mathematics teachers strongly believe that origami is beneficial and effective to be used in mathematics education. However, their perceived self-efficacy beliefs are at little higher than moderate level. Lastly, independent sample t-test results revealed that female teacher candidates have significantly higher beliefs and perceived self-efficacy beliefs in using origami in mathematics education when compared with male teacher candidates.Conclusions:Prospective mathematics teachers' positive beliefs regarding the use of origami in mathematics education were not supported with their perceived self-efficacy belief levels. Therefore, it is possible to claim that prospective mathematics teachers need further support to successfully implement origami-based mathematics lessons.

Prescriptions Guiding Prospective Teachers in Teaching Mathematics

(ProQuest: ... denotes formulae omitted.)Relevant LiteratureProspective teachers go through teacher training programs and take many courses that partially or mostly address teacher knowledge categories (as detailed later in the article) at different universities in the world. Thus, they gain experience in contentspecific and generic knowledge types and in pedagogical reasoning that will shape their future teaching. prospective teachers bring to those courses or to their programs is as important as what they are taught in those courses (Ball, 1988; Goulding, Rowland, & Barber, 2002) and the experiences they gain from their programs. they bring to courses is crucial because of the two following reasons: (1) They are likely to operate from that knowledge in their future classrooms, which may not be parallel to the type of teaching that is expected of them when they graduate from those programs and enter the teaching practice. (2) This factor is also important to inform the field about the needs of teachers and teacher education programs. Such information may help us to revise and enhance teacher education programs and the teaching of those future teachers.As Ball (1988, p. 46) mentioned,How can teacher educators productively challenge, change, and extend what teacher education students bring? Knowing more about what teachers bring and what they learn from different components of and approaches to professional preparation is one more critical piece to the puzzle of improving the impact of mathematics teacher education on what goes on in elementary mathematics classrooms.Related information on this matter can be obtained through analyses of teachers' knowledge levels as they go through the programs using certain measurement instruments (e.g., Hill, Schilling, & Ball, 2004; Toluk Ucar, 2011; Turnuklu, 2005) or through analyses of teachers' actual teaching approach (e.g., Rowland, Turner, Thwaites, & Huckstep, 2009; Haciomeroglu, 2012). Our study falls into the latter category because we also believe that an investigation of teacher knowledge as they teach is informative in identifying teachers'needs and the nature of teaching knowledge. Such information can be obtained through investigations of in-service or prospective teachers. The current study strictly focuses on actual teaching of prospective teachers and deliberates the methods/ways of teaching, which we call prescriptions that guide these teachers' mathematics teaching. We pursued the following research question: teaching methods (prescriptions) guide prospective middle school mathematics teachers in their teaching of mathematics? The relevant literature that oriented us in pursuing this question and the rationale for the study is detailed below.The relevant literature suggests that mathematics teachers draw on various resources in teaching mathematics. One of these resources is mathematics teacher knowledge (Ball & Forzani, 2009), which has a special feature specific to mathematics teaching (Ball, Thames, & Phelps, 2008). Identification of the core of (mathematics) teacher knowledge is pursued extensively in mathematics education literature (e.g., Hill et al., 2004; Rowland, Huckstep, & Thwaites, 2005; Shulman, 1986). Revealing how and in what ways teacher knowledge guides, limits, or shapes teachers' teaching approach is as important as understanding the nature of teacher knowledge. An articulation of the factors that affect the teaching of mathematics teachers may inform decisions as to what should be focused on in teacher education programs and policy development. The current study aims to contribute to such knowledge base through investigating prospective teachers' teaching.Our search in the relevant literature also reveals the following questions that many researchers have struggled with for the last few decades: What kind of knowledge do teachers need to teach effectively? is the nature of the knowledge that is specific to teaching? …

Prospective Middle School Mathematics Teachers’ (PMTs) Content Knowledge about Concepts ‘Fraction’ and ‘Rational Number’

The present study aims to examine the content knowledge of prospective middle school mathematics teachers (PMTs) on the concepts ‘fraction’ and ‘rational number’ and relationship between them. This study, in which mixed type (quantitative+qualitative) research approach is used, was carried out with 164 PMTs in total, who study in the department of middle school mathematics teaching of the Faculties of Education in three different state universities in Turkey. “Fraction-Rational Number Test (FRNT)” consisting of six questions was used as data collection tool. Descriptive statistics were used in the analysis of the data, and each question was separately assessed. Results showed that approximately 37% of the PMTs answered the questions in FRNT as completely true, and approximately 23% of them answered as wrong category. It was also found out that some of PMTs confused the concepts of fraction and rational number and used them interchangeably. From these results, it can be said that the content knowledge of PMTs on ‘fraction’ and ‘rational number’ concepts and relationship between them is not at sufficient level.

Prospective Middle School Mathematics Teachers’ Covariational Reasoning for Interpreting Dynamic Events During Peer Interactions

This study investigated the covariational reasoning abilities of prospective middle school mathematics teachers in a task about dynamic functional events involving two simultaneously changing quantities in an individual process and also in a peer interaction process. The focus was the ways in which prospective teachers’ covariational reasoning abilities re-emerge in the peer interaction process in excess of their covariational reasoning. The data sources were taken from the individual written responses of prospective teachers, transcripts of individual comments, and transcripts of conversations in pairs. The data were analyzed for prospective teachers in terms of the cognitive and interactive aspects of individual behavior and also interaction. The findings revealed that prospective teachers at different levels working in pairs benefited from the process in terms of developing an awareness of their own individual and also a pair’s understanding of covarying quantities. Furthermore, the prospective teachers had opportunities to develop their knowledge on the connection between variables, rate of change, and slope. The prospective teachers’ work in pairs provided salient explanations for their reasoning about the task superior to their individual responses.

Examining Prospective Middle School Mathematics Teachers’ Modelling Skills of Multiplication and Division in Fractions / Ispitivanje vještina modeliranja budućih nastavnika matematike u višim razredima osnovnih škola na zadatcima množenja i dijeljenja raz

Modelling can be considered as an effective way of ensuring permanent learning in the ‘Fractions’ topic, as well as the other topics of mathematics. When the effect of teacher’s knowledge on students’ learning is considered, it is important to investigate modelling skills of tomorrow’s teachers regarding fractions. Within this context in the present study, prospective middle school mathematics teachers’ modelling skills of multiplication and division in fractions were examined. The study was carried out with a total of 104 prospective middle school mathematics teachers who study at the Faculties of Education at two different universities in Turkey. The Modelling Fractions Test (MFT) with six items, three of which were on multiplication and three of which were on division in fractions, was used as a data collection tool. In analyzing the data, descriptive statistics was used and items were evaluated one by one. The findings indicated that the participants showed better performance on modelling with operations in multiplication than with the ones in division, created better models regarding operations requiring multiplication and division of a whole number and unit fraction, and also half of the participants answered questions in MFT as completely correct.Key words: fractions; mathematics teaching; modelling multiplication and division in fractions; prospective middle school mathematics teachers.Modeliranjem se učinkovito osigurava trajno učenje matematičkoga sadržaja razlomaka i ostalih matematičkih sadržaja. Kako bi se utvrdilo znanje koje nastavnici imaju o učeničkom učenju, važno je ispitati vještine modeliranja budućih nastavnika u rješavanju računskih operacija s razlomcima. U ovome se radu u navedenome kontekstu istražuju vještine modeliranja koje posjeduju budući nastavnici matematike u višim razredima osnovnih škola u rješavanju računskih operacija množenja i dijeljenja razlomaka. Istraživanje je provedeno na uzorku od 104 buduća nastavnika matematike u višim razredima osnovnih škola koji studiraju na učiteljskim fakultetima na dva različita turska sveučilišta. Za prikupljanje podataka upotrijebljen je Test modeliranja računskih operacija s razlomcima (engl. Modeling Fractions Test – MFT) koji se sastoji od tri pitanja o množenju razlomaka i tri o dijeljenju razlomaka. U analizi podataka upotrijebljena je deskriptivna statistika te je svako pitanje analizirano zasebno. Ispitanici su pokazali bolje vještine modeliranja u svojim odgovorima na pitanja s računskim operacijama množenja, nego dijeljenja, izradili su bolje modele u slučaju operacija množenja i dijeljenja cijelih brojeva i jediničnih razlomaka te je polovica ispitanika potpuno točno odgovorila na pitanja u TMR-u.Ključne riječi: budući nastavnici viših razreda osnovnih škola; modeliranje računskih operacija množenja i dijeljenja razlomaka; podučavanje matematike; razlomci

A Technology-Based Exploratory Course in Geometry for Middle School Teachers

A course for prospective middle school mathematics teachers was developed to integrate instructional technologies into the course design. The course used dynamic geometry explorations software (Geometer’s Sketchpad), and electronic communication (the World Wide Web and file-server technology) to improve the teaching of geometry for preservice middle school teachers. Technology was integrated into the course first as a tool for exploring and understanding mathematical concepts and second as a means of sharing information. Students accessed daily lessons electronically. Student perceptions of the use of technology indicated that it was a valuable and integral part of the course.