Middle School Mathematics Teachers Research Articles

Skill-based mathematics questions: What do middle school mathematics teachers think and how do they implement?

Bu çalışmanın amacı ortaokul matematik öğretmenlerinin “yeni nesil” diye bilinen, PISA tarzı beceri temelli sorulara ilişkin düşüncelerini, sınıf içerisinde nasıl uyguladıklarını ve mesleki gelişim ihtiyaçlarını ortaya koymaktır. Karma yöntem metodunun kullanıldığı araştırmada ilk olarak 10 ortaokul matematik öğretmeni ile yarı-yapılandırılmış görüşmeler yoluyla nitel veriler elde edilmiştir. Daha sonra, nitel bulgular temel alınarak oluşturulan anket, tarama yöntemiyle İstanbul genelinde 217 ortaokul matematik öğretmenine uygulanarak nicel veriler elde edilmiştir. Nitel ve nicel bulgularda öğretmenlerin beceri temelli soruların doğasına ilişkin olumlu görüşler belirttikleri görülmüştür. Öğretmenlerin sınıf içi uygulamalarında bu sorulara yer verme oranı 8. sınıf düzeyinde artmakta ve genellikle haftada bir uygulandığı görülmektedir. Bu soruların sınıflarda uygulama şekli genellikle ödev verip kontrol etme, sınıf tartışması yaptırma ve öğrencilerden gelen soruları bireysel çözme şeklinde olup çalışılan okul türüne göre farklılıklar gösterse de, bu farklılık istatistiksel olarak manidar değildir. Öğretmenlerin büyük çoğunluğunun kaynak olarak Milli Eğitim Bakanlığı tarafından yayınlanan beceri temelli soruları kullandıkları ve bu soruları nitelik olarak olumlu buldukları görülmektedir. Milli Eğitim Bakanlığı ders kitaplarında bu tür soruların nicelik olarak yetersizliğine ve özel yayınevleri tarafından yayımlanan kitaplardaki soruların ise niteliğine yönelik bazı eleştiriler ortaya çıkmaktadır. Öğretmenlerin çoğunluğunun beceri temelli sorulara ilişkin soru yazımı, problem çözme becerisini geliştirme gibi çeşitli konularda hizmet içi eğitim faaliyetine ihtiyaç duyduğu görülmektedir. Beceri temelli soruların LGS gibi merkezi sınavlarda kullanılıyor olması, öğretmenlerin sınıf içi uygulamalarını etkilemekte fakat bu etkinin olumlu yönde olduğunu söylemek henüz mümkün görünmemektedir.

Middle School Mathematics Classrooms Practice Based on 5E Instructional Model

The 5E instructional model is known for increasing student engagement and participation in the learning process. While viewing the video recorded lessons of middle school mathematics teachers, the researchers noticed teachers had a difficult time implementing the 5E model with fidelity. This case study explored the extent to which mathematics teachers used the 5E instructional model in their classrooms through analyzing video recorded lessons. The findings illustrate that the challenges of the teacher varied. They had difficulty finding activities related to the phases and moving away from a teacher-centered approach to a student-centered approach were identified as challenges of the teachers. The findings of this study inform educators about the difficulty’s teachers have in implementing the 5E model with fidelity. Also, the researchers elaborate on what phases need to be addressed specifically when teachers are provided professional development regarding lesson instruction.

A Middle School Mathematics Teacher’s Noticing Observed in the Mathematical Modelling Lesson

A Middle School Mathematics Teacher’s Noticing Observed in the Mathematical Modelling Lesson

VIEWS OF TEACHERS AND 7TH GRADERS ON AN ENRICHED LEARNING ENVIRONMENT DESIGNED FOR IMPROVING MATHEMATICAL REASONING

The purpose of the present study is to reveal the views of middle school mathematics teachers and students regarding a learning environment designed around different methods for improving Mathematical Reasoning (MR). The study was conducted with 27 seventh grade students studying at a randomly selected state school in a city center in Turkey, the teacher who instructs these students’ mathematics courses, and another mathematics teacher employed at the school. For eight weeks (32 class hours in total), the students were instructed on the subjects of fractions and integers through educational games, concrete materials, cartoons, computer-assisted applications, association with daily life, and collaborative group argumentation. Data for the study were collected through interviews conducted with participants, observations of the teachers, and diaries kept by the students throughout the implementation process. The data were analyzed using a content analysis technique. Evidence was found that this environment improved the MR of students, provided effective and permanent learning, and increased attendance at lessons, but the teachers and the students also agreed that it had different effects in terms of classroom management such as noise, control over the classroom, lack of exam marks, not taking notes, time problems, and effects on students’ success in their central exams. It is also possible to say that, with the help of open-ended high-level problems, students tried to provide solutions instead of focusing on choices for answers, and thus they used more MR skill. Article visualizations:

Middle School Mathematics Teachers' Reasoning about Students' Nonstandard Strategies: Division of Fractions

Although students' nonstandard strategies have great importance in understanding students' thinking and creating effective mathematics classrooms, much remains unexplored in the literature. This study investigated 22 middle school teachers' reasoning about a student's nonstandard strategy for the division of fractions. The data were collected through semi-structured interviews and a task consisting of a student's nonstandard strategy within a classroom excerpt which simulates how mathematical work emerges in the context of teaching. Six categories of layers were formed based on their reasoning about the validity, generalizability, and efficiency of the nonstandard strategy. These layers were categorized as a surface, intermediate, and deep level of reasoning. It was found that while half of the teachers had a surface level of reasoning, only one-third of teachers are at a deep layer of reasoning. On the other hand, teachers' reasoning approaches of how and when the nonstandard strategy works for all problems were determined as equating the answer, equating the process, being multiples of each other, and equating the denominators. The results and implications are discussed, and recommendations are presented in accordance with the findings of the study.

Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalizatio

Examining the knowledge of teachers in practice may shed light on understanding how students learn and finding out why they have difficulty in learning. This paper focused on teachers' knowledge of pattern generalization in instruction with the consideration of students' generalization strategies in planning. The multiple-case study design was used for this study to compare and contrast two middle school mathematics teachers’ lesson planning and instruction. Lesson plans, pre-observation interviews, observations and post-observation interviews were used as the data collection tools. The data were analyzed by using the Mathematical Knowledge for Teaching (MKT) model. The findings showed that the two teachers used numerical reasoning in all representations, but they had difficulties in using figural reasoning. They generally used the tabular representation effectively to underlie the relationship of generalization. While one of the teachers defined the pattern concept correctly and always emphasized analyzing the relationship between the position number and the term, the other teacher defined the pattern concept partially correctly, and her inadequate explanations of functional thinking caused some misunderstandings of students about generalization. It was also observed that the students’ lack of knowledge about algebraic expressions prevented them from obtaining a general rule. Through the cases of these two teachers, it was noted that teachers need to have a good conceptual mathematical understanding and also knowledge of students’ thinking to design effective lessons.

Mentorship: Reflections from Middle School Mathematics Teachers

The aim of this phenomenology research is to define the perceptions of middle school mathematics teachers about internship trainers (mentor teachers and university supervisors). The perceptions of participant teachers about internship trainers are examined under three main themes: (i) the importance and contributions of internship trainers in their professional development, (ii) internship trainers' approach to internships and prospective mathematics teachers, (iii) characteristics that internship trainers must have. The results indicate that middle school mathematics teachers have very negative experiences and perceptions about internship trainers.

중학교 수학 교사의 기하 단원 교육과정 자료 사용 연구

This study aims to analyze how middle school mathematics teachers of teacher community use geometrical unit curriculum materials. Specifically, the focus was on analyzing what elements of the curriculum materials teachers interpret and how they attempt to supplement them. In this study, we classified categories and type of curriculum material use. The categories of curriculum material use was classified into offloading, adaptation, and improvisation. And the types of curriculum material use was classified into inclusion, modification, omission and creation. In the cases of modification, we identified how the question, example, tool, context and system of the task were modified. We found that teachers made various transformations to supplement the textbook, and the frequency of modification, omission and creation was different by system of textbook. Teachers supplemented them mainly by adding questions, modifying expressions and the role or sequence of tasks. In addition, teachers analyzed original tasks and transformed them into new forms based on the results of considering the geometric essence of major concepts. Although all the interpretations and uses of curriculum materials were not appropriate, it was significant in that it provided an opportunity to deepen the understanding of the curriculum and to seek alternative approaches.

The extent of the commitment of mathematics teachers by the quality of achievement tests from the perspective of educational supervisors in Madina: مدى التزام معلمي الرياضيات بجودة صناعة الاختبارات التحصيلية من وجهة نظر المشرفين التربويين بالمدينة المنورة

The presented study is aimed at identifying the extent of commitment of mathematics teachers at the middle and high school levels using the quality of the achievement tests. This is performed by taking samples of the evaluation forms provided by mathematics supervisors in the education offices. It is geographically distributed in the teaching area of ​​Madinah for evaluating the questions of mathematics teachers for the academic year of 1438 /1439. 235 evaluation forms were randomly chosen from a total of 591 and all data was analyzed using SPSS program. The results of the middle school mathematics teachers showed a modest quality of the achievement tests after the analysis of the questionnaire achieving(2.03). The general framework of the test for middle school teachers was of interest to them because they obtained high arithmetic average (2.81). Moreover, high averages were obtained in specific aspects as per the following order: multiple choice questions, questions of right and wrong and essay question formats ranging from(1.18 -2.65). In contrast, other aspects showing poorer results included: pairing and filling format questions. However, the results of the high school mathematics teachers showed an average trend (2.16) in the quality of the achievement tests after analyzing the questionnaires. The general framework of the test for high school teachers was of interest to them because they also obtained a high arithmetic average (2.86). High averages obtained as per the following order: multiple choice questions, questions of right and wrong and essay question formats. Conversely, the other aspect of questions showed less significant results mainly in pairing and filling format questions (ranging 1.22-2.83).) Overall, the results indicated that there were no statistically significant differences between teachers of the two stages in the industry (significance value (α=0.05). This study included some recommendations that may improve the quality of the achievement testing specifically to mathematics teachers.

Examination of Secondary School Mathematics Teachers' Feedbacks Used in Lesson Processes According to Grade Levels

In this study, it was aimed to determine the types of feedback used by middle school mathematics teachers in classroom lesson processes and to determine how feedbacks differ according to grade level. For this purpose, the special case method, one of the qualitative research methods, was used in the research. The participants of the research are three mathematics teachers working in the same public school in Kaynarca district of Sakarya province. The data collection tools are the observation form prepared based on the feedback classification of Tunstall and Gipps (1996) translated into Turkish by Köğce (2012) and video recordings in which the lessons observed are recorded. Within the scope of the research, a total of 32 lesson hours, 8 lessons per classroom level, were recorded with a camera in the classes where three mathematics teachers taught. Descriptive analysis method was used to analyze the data. In the study, it was found that the most used type of feedback from the evaluative feedbacks was approval, and the punishment feedbacks were almost never used. It was seen that the most frequently used feedbacks from descriptive feedback form were the development path and the indication of the improvement. As a result of the research, it was observed that the preferences of mathematics teachers to use evaluative feedback in 5th and 6th grades tended towards to use descriptive feedback in 7th and 8th grades.

Literacy-Based Instructional Techniques for the Middle School Mathematics Teacher

Disciplinary literacy strategies in mathematics lessons are essential and may be embedded in three necessary parts of the lesson: before reading, during reading, and after reading. In this article, we highlight disciplinary literacy strategies that middle school mathematics teachers might implement to guide students to increased mathematical understanding and performance.

How middle school mathematics teachers do measurement and assessment? A Case Study

Bu araştırmanın amacı, ortaokul matematik öğretmenlerinin yapılandırmacı yaklaşım çerçevesinde ölçme ve değerlendirme sürecini nasıl yaşadıklarını ve kullandıkları alternatif değerlendirme yöntemlerine olan farkındalıklarını incelemektir. Yapılandırmacı yaklaşım geleneksel ölçme-değerlendirmenin yerine alternatif ölçme-değerlendirme yaklaşımına vurgu yapmaktadır. Geleneksel ölçme-değerlendirme sürecinde öğrenci performansları anlık olarak değerlendirilir ve üst düzey hedef davranışları ölçmede yetersizdir (Şaşmaz Ören, Ormancı ve Evrekli, 2011). Öğrencilerin yeteneklerini ve bireysel performanslarını değerlendirmek için alternatif ölçme-değerlendirme yaklaşımlarına yönelmek gerekmektedir (Watt, 2005). Araştırma bir çoklu durum çalışması olup maksimum çeşitlilik örneklemi aracılığıyla beş ortaokul matematik öğretmeni belirlenmiştir. Temel veri toplama araçları görüşme, gözlem notları ve dokümanlardır. Durumlar karşılıklı analiz edildiğinde verinin üç ana başlık altında toplanabileceği görülmüştür. Bu başlıklar öğretmenlerin değerlendirme yapmaktaki amaçları, öğretmenlerin kendilerini ölçme-değerlendirme etkinliklerini yapma zorunluluğunda hissetmeleri ve tüm değerlendirme etkinlikleri sonunda öğrenciye verilecek nihai notu nasıl belirledikleri olmuştur. Araştırmanın bulgularına göre öğretmenlerin değerlendirme yapmalarının temel amaçları arasında öğrencilerin öğrenme eksiklerini belirlemek, öğretim sürecinin etkililiği hakkında bilgi edinmek ve velileri öğrenci hakkında bilgilendirmek olduğu görülmektedir. Katılımcıların tüm değerlendirme etkinlikleri sonunda öğrencilerin nihai notunu belirlerken yazılılar ve projelerden ders ve etkinliklere katılım puanlarından yararlandıkları görülmüştür. Öğretmenlerin yapılandırmacı yaklaşımı benimsediklerini, alternatif değerlendirme yöntemlerini hazırlama ve uygulamada zorlanmasa da değerlendirme aşamasında sınıf, okul, öğrenci ve veli profili gibi etkenlerden dolayı daha çok geleneksel ölçme-değerlendirme yöntemlerini kullandıkları görülmüştür. Alternatif değerlendirme yöntemlerini puanlama aşamasında sıkıntı çektikleri için bu konuda bilgilerinin yetersiz olduğu sonucuna varılmıştır. Yapılan görüşmelerde katılımcıların ölçme-değerlendirme yöntemleri konusunda açılacak seminer ve hizmet-içi eğitimlere istekli olmaları, bu alanda yapılacak araştırmalar için göz önünde bulundurulmalıdır.

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.

Investigating Preservice Middle School Mathematics Teachers’ Competencies in Statistics and Probability in Terms of Various Variables

In this study, probabilities of preservice middle school mathematics teachers’ possession of four fundamental cognitive skills required for learning and teaching statistics and probability topics were examined by using the log-linear cognitive diagnostic model, which is one of the cognitive diagnostic models. Moreover, the probabilities of preservice teachers’ possession of these skills were investigated according to gender, university ranking, and grade level variables. Hence, it was examined whether there was a significant relationship between the probabilities of having each skill and these variables. A Statistical Reasoning Test, which was developed by Arican and Kuzu in 2019, measured preservice teachers’ possession of four critical skills was used in collecting the data. These four skills included representing and interpreting data, drawing inferences about populations based on samples, selecting and using appropriate statistical methods to analyze data, and understanding and applying basic concepts of probability. In the 2016-2017 academic year, the test was applied to 456 preservice teachers selected from four different universities in Turkey, and probabilities of their possession of each attribute were calculated. Later, the relationship between the preservice teachers’ test scores and gender was examined by using the Mann-Whitney U test, and the relationship between their test scores and ranking of the attended university and grade level were examined using the Kruskal Wallis-H test. Although probabilities of the preservice teachers’ possession of these four skills did not significantly differ according to gender, some significant differences were detected for university ranking and grade level variables.

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.

An inquiry-based design research for teaching geometric transformations by developing mathematical practices in dynamic geometry environment

This study reports the classroom mathematical practices proposed in an instructional sequence grounding on the principles of inquiry-based learning (IBL) through the use of the dynamic geometry software (DGS) in learning to teach geometric transformations. A 5-week instructional sequence consisting of IBL activities that were guided by the hypothetical learning trajectory (HLT) was designed. The participant 23 preservice middle-school mathematics teachers (PMSMTs) used the geometer’s sketchpad in the sequence. The qualitative data obtained from whole-class discussions, classroom artifacts, and teacher candidates’ products were analyzed by the three-phase methodology of Rasmussen and Stephan based on the Toulmin argumentation model. The findings revealed that three mathematical practices emerged at the end of the 5-week instructional sequence: (1) an in-depth understanding of geometric transformations, (2) operational definitions of geometric transformations and the identification of the relationship among them, and (3) the properties and attributes of geometric transformations. The development of the PMSMTs’ understanding of geometric transformations in the instructional sequence was explained by the systematic nature of classroom mathematical practices. Hence, it was concluded that the PMSMTs’ knowledge and understanding of transformation geometry were enhanced through the instructional sequence based on the specific HLT.

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.

Desenvolvimento do conhecimento didático de professores em Estatística

Este artigo tem como objetivo analisar o desenvolvimento do conhecimento didático de professores em formação continuada, com foco nas representações e investigações estatísticas, dois aspectos fundamentais da Educação Estatística. A formação é relativa à disciplina de Estatística de um Curso de Especialização para professores de Matemática do Ensino Básico, com 13 participantes. Os dados foram recolhidos no decorrer das sessões através de um diário de bordo, gravações de áudio, recolha documental e entrevistas. A disciplina foi estruturada de modo a articular conhecimentos didáticos a partir de atividades direcionadas à prática letiva. Os resultados mostram que os professores aprofundaram seus conhecimentos sobre as representações estatísticas e sobre o modo de as ensinar. Em relação às investigações estatísticas, os professores destacam a importância da valorização destas atividades para a formação de cidadãos críticos capazes de lidar com a informação.

Exploring Self-Efficacy Beliefs Within the Context of Teaching Mathematics with Concrete Models

The purpose of this study was to investigate pre-service mathematics teachers’ self-efficacy beliefs about using concrete models in teaching mathematics. Participants were 31 junior pre-service middle school mathematics teachers. Six instructional sessions based on using concrete models were carried out during a three week period. Data were collected by a survey on pre-service teachers’ efficacy beliefs about using concrete models and semi-structured interviews. Data analysis demonstrated that the instruction had positive contributions on the pre-service teachers’ self-efficacy beliefs. In addition, results revealed that pre-service teachers had confidence in themselves about using concrete models both as learners and as teachers. Moreover, they believed that using concrete models would have positive consequences in teaching process and students’ learning. However, pre-service teachers had relatively low efficacies about classroom management.

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*