Prospective Elementary Mathematics Teachers Research Articles

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.

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 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.

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.

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.

Head of Departments' Evaluation of Learning Opportunities Provided for Prospective Elementary Mathematics Teachers

Bu calismanin amaci; ilkogretim matematik ogretmeni adaylarina sunulan ogrenme firsatlari ile ilgili anabilim dali baskani ogretim elemanlarinin degerlendirmelerini tespit etmektir. Bu amacla yurutulen calisma betimsel nitelik tasimaktadir. Arastirmada yontem olarak nitel arastirma yontemlerinden durum calismasi kullanilmistir. Bu calisma, konuyla ilgili yurutulen proje kapsaminda yer alan 21 universitenin ilkogretim matematik ogretmenligi programlarinda okuyan ogretmen adaylarina sunulan ogrenme firsatlari arasinda farklilik oldugu belirlenen 6 devlet universitesini kapsamaktadir. Orneklemini, bu 6 devlet universitesinin ilkogretim matematik ogretmenligi anabilim dali baskanlari olusturmaktadir. Veri toplamak icin yari yapilandirilmis mulakat kullanilmis, elde edilen veriler nitel veri analiz teknigi olan icerik analizine tabi tutulmustur. Anabilim dali baskani ogretim elemanlarinin ogretmen adaylarina sunulan firsatlar dogrultusundaki gorusleri, programlarindaki dersler, icerigi ve yeri, derslerin yurutulmesi, derslere giren ogretim elemanlarinin uzmanlik alanlari, derslerin niteligi ve niceligi boyutlarinda farkliliklarin oldugunu ortaya koymustur. Anabilim dali baskanlari tarafindan, ogretmen adaylarinin meslege yonelik deneyim kazanmalarina iliskin olarak programdaki uygulama derslerinin saatlerinin arttirilmasi ve daha cok doneme yayilmasi gerektigi belirtilmistir.

Prospective Elementary Mathematics and Prospective Classoom Teachers’ Beliefs Towards Mathematics

Prospective Elementary Mathematics and Prospective Classoom Teachers’ Beliefs Towards Mathematics

Elementary School Students' and Prospective Teachers' Proportional Reasoning Skills

The purpose of this study is to investigate prospective elementary school mathematics teachers and elementary school students' ability to distinguish proportional situations from non-proportional situations. Participants of the study were 319 prospective elementary teachers and 320 elementary school students. Four problems consisting of two proportional and two non-proportional situations were used as a data collection tool. Participants' strategies were coded as multiplicative, additive, and other. Findings indicated that while elementary school students were dominantly additive reasoners, prospective teachers were multiplicative reasoners. While prospective teachers tended to display multiplicative errors, elementary school students inclined to make additive errors in choice of strategy. It was striking that less than half of the prospective elementary mathematics teachers and only one-third of the prospective primary teachers was able to apply appropriate strategies.

Prospective Elementary Mathematics Teachers’ Problem Designing Situations about Pattern

Araştırmanın amacı öğretmen adaylarının örüntüler konusunu diziler ve seriler ile ilişkilendirmelerinde Analiz III dersinin etkisini incelemektir. Nitel paradigma takip edilerek tasarlanan araştırma bir içsel durum çalışmasıdır. Araştırmanın katılımcılarını 39 matematik öğretmen adayı oluşturmaktadır. 12 hafta boyunca devam eden Analiz III dersi kapsamında diziler ve serilerin örüntüler ile bağlantısının kurulmasına yönelik problem tasarlamaya ilişkin bir eğitim verilmiştir. Öğretmen adaylarından Analiz III dersi öncesinde ve sonrasında bu doğrultuda bir problem tasarlamaları istenmiştir. Öğretmen adaylarının yedinci sınıf kapsamında ele alınan örüntüler konusuna ilişkin tasarladıkları problem durumlarında eğitim öncesi ilişkilendirmekte zorlandıkları ancak eğitim sonrasında ilişkilendirebildikleri ortaya çıkmıştır. Eğitim sonrasında genel kural yazmada ciddi bir başarı elde etmişlerdir. Öğretmen adaylarının problem tasarlama eksenli ilerleyen bir öğretimin Analiz III dersinde teorik ve soyut kalan noktaların aydınlanmasında yardımcı olduğunu belirttikleri görülmüştür.

The PISA Tasks: Unveiling Prospective Elementary Mathematics Teachers’ Difficulties with Contextual, Conceptual, and Procedural Knowledge

ABSTRACTThe aim of this mixed methods study was to investigate the difficulties prospective elementary mathematics teachers have in solving the Programme for International Student Assessment (PISA) 2012 released items. A mathematics test consisting of 26 PISA items was administered, followed by interviews. Multiple data were utilized to provide rich insights into the types of mathematical knowledge that a particular item requires and prospective teachers’ difficulties in using these knowledge types. A sample of 52 prospective teachers worked the mathematics test, and 12 of them were interviewed afterwards. The data-sets were complementary: the quantitative data showed that PISA items could be categorized under contextual, conceptual, and procedural knowledge and indicated the most frequent difficulties in the combined contextual, conceptual, and procedural knowledge items. The qualitative data revealed that few prospective teachers could give mathematical explanations for conceptual knowledge items, and that their contextual knowledge was fragmented. Educational implications were discussed.

Problems Posed by Prospective Elementary Mathematics Teachers in the Concept of Functions: An Analysis Based on SOLO Taxonomy

Abstract: The aim of this study is to carry out an analysis according to SOLO-taxonomy about problem posing knowledge of prospective elementary mathematics teachers on mathematical functions. The methodology adopted in the current study was a case study. The participants of the study consisted of 67 prospective elementary mathematics teachers. According to the findings of the study, the knowledge of the prospective elementary mathematics teachers on functions in mathematics is open to development through proper teaching methods. Moreover, the majority of their knowledge levels have been grouped as pre-structural level, multi-structural level and relational level while only a few of their knowledge levels were at extended abstract level. Based on the results, it might be beneficiary to train prospective mathematics teachers who can creatively use problem posing activities in their classrooms and who will become a model for their students with their problem-posing performances to overcome their conceptual deficiencies concerned with functions. Keywords: Mathematical knowledge, problem posing, prospective mathematics teachers, SOLO taxonomy

JUSTIFICATION FOR THE SUBJECT OF CONGRUENCE AND SIMILARITY IN THE CONTEXT OF DAILY LIFE AND CONCEPTUAL KNOWLEDGE

This study aims to examine prospective elementary mathematics teachers' conceptual knowledge level for congruence and similarity in triangles subject and to examine their ability to represent the knowledge, to associate the knowledge with daily life, and to justify and solve the geometry problems about this subject. The study is designed in a characteristic pattern. Total of 46 prospective elementary mathematics teachers were selected using purposive sampling method. The instruments used to collect data in this study are: GJP (Geometry Justification Problems), GCKQ (Geometry Conceptual Knowledge Questions) and GQDLE (Geometry Questions of Daily Life Examples). The data were analyzed using descriptive statistics method. The results of the study show that 1) the prospective teachers are successful in geometry conceptual knowledge questions but had difficulty in the justification problems; 2) there is a relationship between the theoretical knowledge levels and the argument standards of the prospective teachers; 3) the prospective teachers had difficulty in the daily life examples of congruence and similarity in triangles subject. Keywords : Congruence and Similarity, Justification, Conceptual Knowledge, Daily Life Association

JUSTIFICATION FOR THE SUBJECT OF CONGRUENCE AND SIMILARITY IN THE CONTEXT OF DAILY LIFE AND CONCEPTUAL KNOWLEDGE

This study aims to examine prospective elementary mathematics teachers' conceptual knowledge level for congruence and similarity in triangles subject and to examine their ability to represent the knowledge, to associate the knowledge with daily life, and to justify and solve the geometry problems about this subject. The study is designed in a characteristic pattern. Total of 46 prospective elementary mathematics teachers were selected using purposive sampling method. The instruments used to collect data in this study are: GJP (Geometry Justification Problems), GCKQ (Geometry Conceptual Knowledge Questions) and GQDLE (Geometry Questions of Daily Life Examples). The data were analyzed using descriptive statistics method. The results of the study show that 1) the prospective teachers are successful in geometry conceptual knowledge questions but had difficulty in the justification problems; 2) there is a relationship between the theoretical knowledge levels and the argument standards of the prospective teachers; 3) the prospective teachers had difficulty in the daily life examples of congruence and similarity in triangles subject. Keywords : Congruence and Similarity, Justification, Conceptual Knowledge, Daily Life Association

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.

Difficulties of Prospective Elementary Mathematics Teachers' Regarding to Reflection Symmetry

Bu calisma ile ilkogretim matematik ogretmeni adaylarinin simetri kavramina iliskin kavram yanilgilarinin ortaya konulmasi amaclanmistir. Arastirmanin katilimcilari, 2012-2013 ogretim yili guz doneminde Kocaeli Universitesi Egitim Fakultesi Ilkogretim Matematik Ogretmenligi programinin dorduncu sinifinda ogrenim gormekte olan 28 ogretmen adayindan olusmaktadir. Betimsel bir arastirma niteligindeki bu calismanin verileri, arastirmacilar tarafindan hazirlanan acik uclu bir test ile elde edilmistir. Verilerin analizi sonucunda, ogretmen adaylarinin buyuk bir cogunlugunun yansima kavramini tanimlayamadigi gorulmustur. Bununla birlikte ogretmen adaylarinin genellikle yansimanin alinmasi sonucu elde edilen goruntunun ters oldugunu ihmal ettikleri gozlenmistir. Simetri eksenine yonelik kendilerine yoneltilen soruya verdikleri cevaplarin da dogru tanimdan uzak oldugu soylenebilir. Genelde simetri ekseni icin “Bir cismi iki es parcaya bolen dogrudur” ifadesini kullandiklari gorulmustur. Ogretmen adaylarinin buyuk bir cogunlugu paralelkenarin simetrik bir sekil oldugunu ve dort tane simetri ekseni oldugunu belirterek yanlis cevap vermislerdir. Ayrica ilgili cokgenlerin simetrik olup olmama durumlarini aciklamalari istenilen kisimda ise memnun edici cevaplar veremedikleri gorulmustur. Anahtar Kelimeler: Simetri kavrami, kavram yanilgilari, ilkogretim matematik ogretmeni adaylari

English

One of the general discussion in the studies about learning style is what degree of students whose learning style is determined, have other learning styles. In this context, the aim of this study is to determine the learning styles of prospective elementary mathematics teachers and to explore the relationships between these styles by using data mining techniques. Data mining can be defined as applications of different algorithms to identify patterns and relationships in a data set. For this purpose, Grasha-Reichmann Learning Styles Inventory was applied to 400 prospective elementary mathematics teachers at Dokuz Eylul University. Cronbach's alpha reliability coefficient of the scale was found as 0.83.Results show that more than 50% of female students have independent’’ learning style. At the same time students who have competitive learning style had the least number of students. The male students who have collaborative and dependent learning styles were the majority.. From Class 1 to Class 4, it was observed that the number of students who have individual learning styles was decreasing and the number of students who have cooperative learning styles was increasing. In network graph, it was found that one of the strongest relationships was between the students who have cooperative and independent learning style with high level. On the other hand the relationship between the students who have passive and independent learning style with low level was not seen in graph. The decision tree indicates that the most effective attribute is independent learning style to identify which level of the learning style students have. Besides in the Data mining, learning styles, Mathematics Education association rules model several rules are constructed with %75 confidence.