Elementary Mathematics Teachers Research Articles

The Perspectives of Elementary School and Mathematics Teachers Towards Realistic Mathematics Education

The Perspectives of Elementary School and Mathematics Teachers Towards Realistic Mathematics Education

Understanding children’s reasoning in multiplication problem-solving

ABSTRACTThis article investigates two children’s intuitive thinking in solving multiplication problems from different educational backgrounds. One of the children is in a southern elementary school in the US. He was given the same problems both in first and second grades. The other child was a first grader in a southwest region of China, and she was given the same problems. The findings reveal a variety of intuitive thinking in solving the multiplication problems through addition beyond direct modeling and counting strategies. The authors also discussed how different educational backgrounds in early elementary mathematics education may affect children’s intuitive ideas and reasoning in solving multiplication problems. The study implies the importance of understanding children’s intuitive ideas of multiplication and highlights potential opportunities for developing children’s understanding of multiplicative thinking and algebraic thinking in earlier stages of arithmetic learning.

Examination of decision-making skill in the context of critical situations

A teacher, who has a major role in the formation of class culture, needs to have proficiencies to design effective learning environments. The reflection of these proficiencies on classroom practices takes place via the decisions taken under critical situations. This study aims to find out the components underlying teachers’ decision-making. Participants of the study which was designed as a case study were elementary school mathematics teachers. The study was carried out through the individual interviews with participants about the decision making under critical situations after analysing participant teachers’ course observations which were video-recorded by the researchers. Data obtained from the interviews were analysed through content-analysis method. Based on the findings, it was found that teachers’ professional proficiencies could be presented in the same frame with the variables reflected on decision making.

Knowledge of Prospective Elementary Mathematics Teacher Related to Pattern Generalization and Justification

The aim of this study is to investigate the generalizations created by pre-service elementary mathematic teachers, to explore the justifications predicted for their generalizations, and to determine any relationships between generalization and justification. We used phenomenology design from qualitative research methods in the study. The study was conducted by the 4th grade students/pre-service teachers who are studying in a department of Elementary Mathematics Teaching at a university located in the Eastern Black Sea region. Data collection tools are linear and quadratic pattern problems which are prepared with the support of literature and teaching staff and in which different solution strategies and justification types can be produced. Interviews were analyzed using the descriptive analysis technique within the conceptual framework of the research. The results show that the most common type of strategy used by pre-service teachers was functional strategy, contextual, recursive, guess-check and mixed strategies. While many of the pre-service teachers have justified their verification by numerical control, pre-service teachers who have justified through explanation and external knowledge sources have also been identified.

AN EXAMINATION OF THE NUMBER SENSE PERFORMANCES OF PRESERVICE ELEMENTARY SCHOOL MATHEMATICS TEACHERS

The aim of this study is to examine the number sense skills of preservice elementary school mathematics teachers. This study was conducted by using the survey model among descriptive research methods. A total of 111 preservice teachers studying at second and third grades in the elementary school mathematics teaching program at a state university participated in the study. The data of the study were collected by using the number sense test consisting of 17 questions and developed by Kayhan-Altay (2010). The findings of the study indicated that the number sense performances of preservice elementary mathematics teachers were lower than expected and there was a significant difference in favour of third-grade students. It is considered that the “Special Training Methods I and II” courses and the “Mathematics Curriculum” course, which are taught in third grades and in which subjects such as estimation and making mental calculations, etc. superficially related to number sense are mentioned, may cause this difference. Thus, it was suggested that it was necessary to include courses consisting of number sense and how it can be developed in the curriculum. Article visualizations:

School District Educational Infrastructure and Change at Scale: Teacher Peer Interactions and Their Beliefs About Mathematics Instruction

While current reform efforts press for ambitious changes to teachers’ instructional practice, teachers’ instructional beliefs are also consequential in such efforts as beliefs shape teachers’ instructional practice and their responses to instructional reforms. This article examines the relationship between teachers’ instructional ties and their beliefs about mathematics instruction in one school district working to transform its approach to elementary mathematics education. Quantitative results show that while teachers’ beliefs did not predict with whom they interacted about mathematics instruction, teachers’ interactions with peers about mathematics instruction were associated with changes in their beliefs over time. Qualitative analysis confirms and extends these findings, revealing how system-level changes in the district’s educational infrastructure facilitated change in teachers’ beliefs about mathematics instruction at scale.

Knowledge, Monitoring, and Beliefs: A Comparative Analysis among Preservice Teachers from Three Different STEM-focused Programs

In the current study, we investigated how preservice teachers (N = 242) from three different teacher-training programs with a STEM focus, namely the Elementary Education (ELM), Science Education, and Mathematics Education, compare with respect to science content knowledge, metacognitive monitoring, and their belief system. Findings revealed that the ELM preservice teachers reported higher levels of science reformed beliefs (e.g., constructivist instruction), but low science content knowledge and teaching efficacy beliefs. Alternatively, Science Education students exhibited the highest levels of content knowledge, accurate monitoring, and higher teaching efficacy beliefs. Implications for teacher education programs with a STEM training focus are discussed.

Contextualizing the Identity Development of Preservice Elementary Mathematics Teachers in Methods Courses and Mentor Teacher Support

Drawing on a situative perspective, this study explores how preservice elementary teachers develop themselves as teachers of mathematics and critical experiences in their identity development, in particular, from teacher education coursework through their student teaching experiences. Through two cases, this study reveals that mentor relationships were critical in shaping preservice teachers’ identities as mathematics teachers and in building their initial mathematics teaching practices. Findings suggest that successful mentoring is necessary, and this generally requires sharing common goals, receiving feedback, and having opportunities to practice knowledge, skills, and identities on the part of beginning teachers. This study adds to the field of teacher education research by focusing on prospective teachers’ identity constructions in relation to their communities of practice, and also by emphasizing the role of mentors in preservice teachers’ identity development.

On the Teaching and Learning of Fractions through a Conceptual Generalization Approach

This paper deals with precursory (propaedeutic) learning of the concept of number in the elementary mathematical education. The authors’ objective is to suggest a method allowing for the increase of the effectiveness of interactive expansion of the concept of number by using a grade-appropriate learning framework for elementary mathematical education content. A theoretical background for the creation of this method is based on the description of various characteristics of precursory learning and interactive teaching of mathematics as well and the flexible differentiation approach. The paper especially emphasizes the possibilities of propaedeutic understanding of the concept of fraction and examine the effects of such approach in terms of student achievement in elementary mathematics education, on the basis of a methodological approach. Results obtained during the experimental research suggest that under the influence of the methodological approach of introducing fractions through propaedeutic learning, students achieve significantly better results in learning compared to students who have not used this method.

Practices that cross disciplines?: Revisiting explicit instruction in elementary mathematics and English language arts

Practices that cross disciplines?: Revisiting explicit instruction in elementary mathematics and English language arts

Pedagojik Alan Bilgisi Bağlamında Öğretmen Adaylarının Kesirlerdeki Kavram Yanılgılarını Giderme Yeterliklerinin Farklı Değişkenlere Göre İncelenmesi

The aim of this study is to determine the pre-service teachers' competencies to eliminate possible misconceptions about fractions and to examine these competencies according to different variables. The teaching methods preferred by the prospective teachers have also been investigated. The study has been conducted on the mixed method. The study group is composed of 52 teacher candidates who are senior students of a state university elementary mathematics education program. Eliminating Misconceptions Form was used as data collection tool in the study. The analysis of the data was carried out in four stages. Scoring Scale was used in this process. As a result of the research, it was seen that the teacher candidates mostly preferred the method of using a model in order to eliminate the misconceptions. They generally propose valid methods but they are found to be inadequate to use these methods. Furthermore, there were no significant relationships/differences between the competencies according to variables of taking (or not) elective course of Misconceptions in Mathematics Education , school type and general academic average.

The importance of structure, clarity, representation, and language in elementary mathematics instruction

ABSTRACTThis article presents a study that investigated potential misconceptions presented in third grade mathematics classrooms and the association of these potential misconceptions with Mathematical Knowledge for Teaching (MKT) and standards-based teaching practices (as measured by the Mathematics Scan). A sequential explanatory mixed methods model was used to analyze the frequency of potential misconceptions presented via instances of lack in teacher clarity or misuse of representations as well as the association to MKT and M-Scan scores. A qualitative multiple case study design was then used to identify patterns in lessons where potential misconceptions were often present as opposed to lessons where no potential misconceptions were presented. The results document the prevalence of potential misconceptions related to representations and language use. These potential misconceptions were most frequently conveyed through a lack of clarity or overgeneralization. Teachers who had higher frequencies of potential misconceptions were found to relate to lower MKT and M-Scan composites. This supports professional development and policy initiatives in mathematics education of the importance of teachers’ content knowledge for mathematics teaching.

The Effects of Learning-Style Based Activities on Students’ Reading Comprehension Skills and Self-Efficacy Perceptions in English Foreign Language Classes

This study investigated the effects of learning-style based activities on students’ reading comprehension skills and self-efficacy perceptions in English foreign language classes. A quasi-experimental, matching-only pretest-posttest control group design was utilized. The study was conducted with freshmen university students majoring in Elementary Mathematics Education at Necmettin Erbakan University in the fall semester of academic year 2012-2013. English was one of their compulsory courses and their self-reported language level was A1/A2 in terms of the self-assessment grid included in the Language Passport which is one of the three components of the European Language Portfolio. A total of 39 students in the experimental group and 39 in the control group participated in the study. The learning-style based activities were implemented in the experimental group, while the control group continued with routine classroom instruction without any attention to their learning styles. Both groups received three one-hour sessions weekly, for a total of eight weeks. Both the Reading Comprehension post-test scores and the Self-Efficacy Scale for English post-test scores were significantly different in favor of the experimental group. Also, a significant moderate positive correlation was found between English reading comprehension achievement and English self-efficacy. It can be concluded that learning-style based activities enhanced reading comprehension skills and English self-efficacy perceptions during this study.

The Effect of Cooperative Learning Methods on Pre Service Elementary Mathematics Teachers' Academic Achievement and Retention in the Subject of Analytical Examination of the Circle

The aim of this study is to determine the effects of Student Teams Achievement Divisions (STAD) and Learning Together (LT) methods of cooperative learning model and the conventional methods on academic achievement and retention of the knowledge leraned in the subject of Analytic Examination of the Circle of candidates of primary school mathematics teaching. Quantitative research methods are used in and this study is designed according quasi-experimental to pre-test, post-test design with control group. The sampling of the study is formed by the 76 students in normal and evening education groups of 3rd grade in primary school mathematics teaching department at a state university. The achievement test formed by the researcher, module tests are used as data collection tools in the study. The study is held with 2 experimental and 1 control groups in tottally three classes. STAD method is used in the first group, LT is used in the second group, and the conevtional methods are used in the third group. Descripitve statistics, one way variance analyses (ANOVA) and LSD multiple comparison tests are used in the analyses of quantitative data. Consequently, it is seen that STAD and LT methods are more effective on academic achievement of the students and the retention of the knowledge. It is also seen that STAD is more effective on academic achievement and LT is more effective on retention.

Understanding Students’ Mathematical Thinking for Effective Teaching: A Comparison between Expert and Nonexpert Chinese Elementary Mathematics Teachers

It is widely believed that teachers’ knowledge of students’ thinking has a significant impact on teachers’ teaching and students’ learning. However, there is far less research on how teachers acquire their knowledge of students’ thinking before, during, and after lessons. This study is designed to compare the differences between expert and nonexpert mathematics teachers on their behaviors and perceptions related to understanding students’ mathematical thinking. Based on 554 Chinese elementary mathematics teachers’ responses to a survey, the study found that teachers took actions to understand students’ thinking more often when students were learning new topics or encountering difficulties, and they were more likely to do so before lessons than during or after lessons. The comparison revealed that significantly more expert elementary mathematics teachers attempted to understand students’ thinking from a variety of perspectives before making the necessary adjustments to their predetermined teaching plans than did nonexpert teachers. Significantly more expert teachers also relied on their own teaching experiences to understand students’ thinking. In contrast, significantly more nonexpert teachers claimed that they did not rely on prior teaching experiences because they “did not know how to.”

By Way of Introduction: Extend an invitation

Share news about happenings in the field of elementary school mathematics education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles.

Using the concrete representational abstract (CRA) instructional framework for mathematics with students with emotional and behavioral disorders

ABSTRACTMr. Buxton is a perplexed elementary mathematics teacher. He co-teaches a second-grade classroom, with Ms. Snyder. In their classroom they have 25 students; five are identified as academically at risk, and three receive special education services. In the past Mr. Buxton successfully used an instructional approach consisting of (a) modeling, (b) guided practice, (c) independent practice, and (d) formative assessment. Currently, students are struggling to subtract two- and three-digit numbers requiring regrouping. The co-teacher, Ms. Snyder, suggests that the students need more visuals and concrete examples during instruction.Mrs. Zampelli teaches third grade in a general education classroom. She has support from the special education teacher and a paraeducator who provide consultation and instructional coaching. Of the 18 students in her class, nine have Individual Education Programs. The special education teacher, Mr. Ortiz, provides great suggestions to make learning “hands-on.” However, the concept of fractions and specifically comparing fractions with like numerators or denominators causes problems every year. Both teachers emphasize multiple representations (e.g., fraction cubes, fraction circles, fraction bars, number lines) of the concepts. Students are able to solve problems when working with manipulatives but struggle to solve problems in the abstract. Leading teammates suggest a more structured framework for incorporating manipulatives and representations.

Inquiry-Oriented Instruction: A Conceptualization of the Instructional Principles

Research has highlighted that inquiry-based learning (IBL) instruction leads to many positive student outcomes in undergraduate mathematics. Although this research points to the value of IBL instruction, the practices of IBL instructors are not well-understood. Here, we offer a characterization of a particular form of IBL instruction: inquiry-oriented instruction. This characterization draws on K-16 research literature in order to explicate the instructional principles central to inquiry-oriented instruction. As a result, this conceptualization of inquiry-oriented instruction makes connections across research communities and provides a characterization that is not limited to undergraduate, secondary, or elementary mathematics education.

Relationships between Observations of Elementary Mathematics Instruction and Student Achievement: Exploring Variability across Districts

AbstractMuch debate surrounding teacher quality has focused on students’ standardized test scores, but recent federal and state initiatives have emphasized the use of multiple measures to evaluate teacher quality, including classroom observations. In this study, we explore differences across school districts in the relationship between student achievement outcomes and the observed quality of teachers’ instruction. Using data from 298 elementary mathematics teachers in five urban US districts, we examine relationships between teachers’ performance on the Mathematical Quality of Instruction observation instrument and their students’ scores on both state standardized and researcher-developed tests. We find that these relationships differ across school districts. We explore the extent to which differences in skills and expectations for students across tests may explain this variability. An improved understanding of the relationship between classroom observations and student tests may help districts to better ...

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching

The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which was conducted in accordance with relational survey model, consists of 380 university students, who studied at the department of Elementary Mathematics Education at two state universities. In order to collect data for the present research, “Self-efficacy Beliefs towards Mathematics Scale”, “Self-efficacy Beliefs toward Mathematics Teaching Scale”, “Mathematics Anxiety Scale” and “Mathematics Teaching Anxiety Scale” were utilized. Researchers developed a model in accordance with the related literature, and tested the direct and indirect relations between self-efficacy belief toward mathematics, mathematics anxiety and self-efficacy belief for mathematics teaching, mathematics teaching anxiety variables. Data were analysed with structural equation model on AMOS 19.0 program. The model shows that the most important independent variable affecting mathematics teaching anxiety is mathematics anxiety; the most important independent variable affecting self-efficacy belief toward mathematics teaching is mathematics anxiety; the most important variable affecting mathematics anxiety is self-efficacy belief toward mathematics; and the most important variable affecting mathematics teaching anxiety is self-efficacy belief toward mathematics teaching.