Secondary School Mathematics Teachers Research Articles

A systemic analysis of secondary school mathematics teachers' attitudes toward assessment of learning

Aware of the various issues involved in assessing learning, but also of the difficulties encountered in classroom practice of this pedagogical act, we set out in this article to explore and analyze the assessment practices of secondary school mathematics teachers and the conceptions they underlie. The study was conducted from a systemic perspective. We therefore targeted three aspects in our study: the conceptual, the institutional, and the docimological. Analysis of the attitudes declared by a random sample of mathematics teachers enabled us to confirm that pedagogical, and in particular cognitive, issues do not represent a priority for them in assessment practices. They focus more on the organizational aspect of examinations, with a remarkable lack of concern for docimological considerations to give credibility to the assessments carried out.

Prospective secondary teachers’ noticing of students’ thinking about the limit concept: pathways of development

AbstractResearch has shown that there is a need to examine prospective teachers’ development trajectories related to noticing expertise. An important content in the Spanish high school curriculum (16–18 years old) is the limit concept. Given the importance of this concept in the curriculum and the difficulties some prospective teachers have, developing their noticing of students’ mathematical thinking of this concept in teacher education programs is crucial to achieve high school student mathematics achievement. This study examines how prospective secondary school mathematics teachers (PTs) notice students’ mathematical thinking about the limit concept as they participated in a teaching module. PTs had to anticipate and interpret students’ mathematical understanding and make instructional decisions to support students’ conceptual progression using information about high school students’ understanding of the limit concept. We examined PTs changes related to how they anticipated, interpreted and made instructional decisions during the teaching module. We identified a change in how PTs conceived the understanding of the dynamic limit concept: from all-or-nothing dichotomy to progression; and a change in the instructional decisions they made: from decisions focused on changing the type of discontinuity to conceptual decisions. These changes allow us to characterise development noticing pathways. Our findings also help to identify the teaching module characteristics that support the development of PTs noticing.

Secondary school teachers’ interest and self-efficacy in implementing STEM education in the science curriculum

This study examines the role of Namibian secondary school science, technology, engineering and mathematics (STEM) teachers’ interest in STEM education and self-efficacy in implementing STEM education in science education curricula. Furthermore, it aimed to distinguish male and female Namibian teachers’ interests and self-efficacy regarding STEM education and investigate how different teaching subjects affect them. To achieve this goal, a survey was completed with (n=200) secondary school teachers, both males and females. Data were analyzed quantitatively using exploratory factor analysis and analyzed covariance. The results show that most teachers were highly interested and confident in implementing STEM subjects into science curricula. While Namibian teachers indicated a high level of interest, they also revealed a high lack of interest in STEM, implying that at least some teachers felt bored and meaningless in implementing STEM education. However, gender plays a significant role in teachers’ negative self-efficacy, with male teachers being less confident than female teachers in implementing STEM education. Moreover, teachers in the present study have high positive and negative self-efficacy levels regarding implementing STEM education. Therefore, these findings highlight the need for a paradigm shift, especially in the Namibian science curricula, to promote STEM subjects and to improve science education. Potential implications from this research also suggest that teachers’ participants benefit significantly from learning within a community by engaging in solutions to real-world problems.

Enabling teachers to enact core elements of mathematics in the classroom: a retrospective design-research analysis of interrelated course conceptions and their development phases

Mathematics education in secondary schools should not only provide content knowledge but also an understanding of the fundamental processes by which new mathematical knowledge is created – students should experience how mathematics ‘works’ as a discipline. Initiating this, however, has been shown to be a major challenge for teachers. We therefore undertook a developmental project to design courses that would better prepare pre-service teachers for this task. In this article, we conduct an analysis of the project from a design-research perspective, which provides as a result the theoretical output of the project in the form of an articulated design principle.

Investigating boundaries and boundary crossing between mathematics and visual art teaching in a collaborative setting

Our study explores boundaries and boundary crossing between communities of mathematics teaching (MT) and visual art teaching (AT). We focus on teacher collaboration, draw on communities of practice and examine the existing boundaries and the way collaborating members handle them. We present data from 17 group meetings of secondary school art and mathematics teachers who try to develop ways of linking ΜΤ and ΑΤ. Results indicate the emerging boundaries by means of discontinuities regarding mathematical practices and tools used in MT and AT, and the disciplines’ teaching and curriculums. Via analysis of the central boundary – the analytical or visual ways of thinking – we present members’ boundary handling that indicates the development and developmental process of integrated practice. The study incorporates boundary crossing processes and learning mechanisms in which the two separate ways of thinking are gradually transformed into an integrated one and reveals possible ways of integration in teaching and learning.

Needs Assessment of Senior High School Teachers in Mathematics Instruction

This study attempted to assess the needs of Senior High School Teachers in Mathematics instruction at the Schools Division Office of Cabanatuan City. Specifically, it sought to describe the following; the professional qualification, the familiarity with Mathematics essential knowledge, the pedagogical strategies employed; and the significant relationship between the profile of the respondents with familiarity with Mathematics essential knowledge and pedagogical strategies employed, the educational infrastructure in terms of teacher’s guide and adequacy of Mathematics materials in terms of instruction. As an output, the identified needs of the SHS Mathematics teachers were collected for future use. The study utilized descriptive-correlational research as it describes and examines the relationship between variables without making any causal claims. Based on the results of the study, the following conclusions are drawn: the majority of the respondents have Master’s Degrees in Education with a specialization in Mathematics, have 1 to 10 years of teaching experience, attended 5 to 7 various seminars in their field of self-identified specialization, all of the respondents teach Mathematics subjects and some of them are also teaching non-mathematics subjects. No respondents are freed from Non-Teaching Assignments; the familiarity of the respondents with essential knowledge in Mathematics Instruction is EXCELLENT, pedagogical strategy most employed by the respondents is Assessment; there is no significant relationship between the profile of the respondents and their competence on General Mathematics essential knowledge; the DepEd – issued Teacher’s Guide is generally rated by respondents as strongly agree or Excellent, the availability and sufficiency of Mathematics Materials inside the classroom is SATISFACTORY. Based on the study conducted, the needs of SHS Mathematics teachers in the public secondary schools of Cabanatuan City must be concentrated on provision of more usable and sufficient Mathematics tools and materials. Mathematics-related seminars focusing on content are also found to be a necessity among teachers.

Comparing the teaching quality of alternatively certified teachers and traditionally certified teachers: findings from a large-scale study

The present study investigates whether alternatively and traditionally certified teachers differ in their teaching quality. We conducted doubly latent multilevel analysis using a large-scale dataset with student ratings on the quality of instruction provided by 1550 traditionally and 135 alternatively certified secondary school mathematics teachers in Germany. Findings show no evidence of differences in teaching quality between alternatively and traditionally certified teachers. Independent of the type of certification, novice teachers scored lower on classroom management than experienced teachers. Findings suggest that beginning teachers—whether alternatively or traditionally certified—need to be better prepared for classroom management before starting to teach.

Investigating the effect of instruction designed according to the ARCS model enriched with web 2.0 tools on students' mathematics achievement and motivation

This study aimed to investigate the effect of instruction designed according to the ARCS model enriched with Web 2.0 tools on the mathematics achievement and motivation of secondary school students and to examine student opinions regarding the applied instruction process. A mixed-methods approach was employed in the study since both quantitative and qualitative data were collected. To support quantitative data with qualitative data, a sequential explanatory design was chosen from mixed-methods designs. The research was conducted in the 2022–2023 academic year with the participation of 40 7th grade students enrolled in a public school in Niğde province. The research process was planned for 10 weeks, including a pretest administration in the first week, an eight-week intervention, and a posttest administration in the last week. In the experimental group, a mathematics instruction plan designed according to the ARCS model enriched with Web 2.0 tools was implemented, while in the control group, only the existing mathematics instruction plan was implemented. Quantitative data were collected using the ratio, proportion and percentage achievement tests and the mathematics motivation scale. Qualitative data were collected through focus group interviews with experimental group students. Data analysis was conducted, which included independent samples t-tests, paired samples t-tests, MANOVAs, and content analysis. The findings obtained from this study revealed that teaching with the ARCS model enriched with Web 2.0 tools had a positive effect on students' academic achievement. When the sub-dimensions of motivation were analyzed, no significant difference was found between the groups in the posttest motivation scores, but most of the participant students in the focus group interviews expressed positive opinions about the process and mentioned the effectiveness of the process. This study provides important information about the effectiveness of integrating Web 2.0 tools into the ARCS model in secondary school mathematics education in terms of the effectiveness of the teaching process and its contributions to students' achievement.

Podporné mechanizmy školy ako inštitúcie v inkluzívnom matematickom vzdelávaní

This paper offers an interdisciplinary perspective of researchers from the fields of therapeutic pedagogy and mathematics didactics in identifying the support mechanisms of the school as an institution in inclusive mathematics education. Qualitatively analysing the written accounts of mathematics teachers in Slovak primary and secondary schools in mainstream education, it brings together the suggestions from these teachers on the support mechanisms of the school in inclusive mathematics education for pupils with special needs. The research findings may be helpful in the pre-service training of teachers of subjects other than mathematics in the context of teaching pupils with enhanced support.

Training on the Use of Montessori-Based Mathematics Learning Media for Primary and Secondary School Teachers in Thousand Islands

Learning media has an important role in learning mathematics because mathematics is an abstract science and requires a deep understanding of concepts. Students have difficulty in understanding mathematics due to the teacher's monotonous explanation in class without any learning media or epraga tools. Fun learning media is interactive learning media, which allows students to use the media themselves and interact both with other students and with teachers. One example of interactive learning media is Montessori learning media. Based on observations at partner locations, it was found that mathematics teachers in elementary and secondary schools have never used Montessori learning media, therefore training on the use of Montessori-based learning media is needed for elementary and secondary school teachers so that classroom learning runs optimally in accordance with learning objectives. Training on the use of Montessori-based learning media has a positive impact on teachers, it can be seen from the final questionnaire of the training participants provide positive feedback, to this training activity, namely with data interpretation of 96%.

A Comparative Study of Secondary School Mathematics Teaching Materials from the Perspective of Reasoning--Taking "Pythagorean Theorem" as an Example

Education has always been a hot topic of discussion. From the results of junior high school mathematics assessments in recent years, there are differences in mathematical abilities between Eastern Europe and Europe and America. Since reasoning is crucial to understanding mathematics, we compare the "Pythagorean Theorem" in textbooks from China, the United States, and Singapore, examining the theorem's different types of reasoning and how it relates to previously acquired knowledge. The reasoning categories proposed by Shi Ningzhong, Harel, and Sowder serve as the fundamental basis for categorizing the varieties of reasoning in this research. The introduction of proofs for the hook and Pythagorean theorem is investigated for each edition of the textbook, and concerning the deductive reasoning ability, the People's Education Press edition (PEP) and Zhejiang Education edition (ZJE) editions are in the first tier, followed by Singaporean textbooks and American textbooks. In terms of the correlation between the Pythagorean theorem and what has been learned, the ZJE involves the most points of correlation. Finally, we discuss the implications of these results for teachers' explanations of the Pythagorean theorem: teachers can briefly introduce the geometric deductive proof process of the Pythagorean theorem to stimulate students' interest in learning mathematics.

Normative Evaluation Scale of Pedagogical Content Knowledge with Emphasis on Proving knowledge of Secondary School Mathematics Teachers

Normative Evaluation Scale of Pedagogical Content Knowledge with Emphasis on Proving knowledge of Secondary School Mathematics Teachers

Micro-Teaching Application Situations of Secondary School Mathematics Teacher Candidates based on Student Misconception/Difficulty

Misconception/student difficulty is one of the student characteristics that should be known by teachers. Teachers should have effective knowledge and strategies to overcome these misconceptions and difficulties. In this sense, microteaching practices have an important place in the context of pre-service teachers’ ability to increase their knowledge and strategies and their developing professional experience. The aim of this research is to examine the microteaching of primary school mathematics teacher candidates in the context of student misconceptions and difficulties. The research design is in the qualitative reserch model and the case study method was used. The research data were obtained from the analysis of semi-structured interviews with pre-service teachers, prepared lesson plans and micro-teaching video recordings. The obtained data were analyzed by content analysis method. According to the results of the research, although different strategies such as pre-service teachers, group work and class discussion were used, the most frequently used strategy was the strategy of putting students on the board and dealing with misconceptions/student difficulties through sample questions.

Investigating the statistical reasoning skills of secondary school mathematics teachers

Bu çalışmada ortaöğretim (lise) matematik öğretmenlerinin istatistiksel akıl yürütme becerilerinin, alan bilgileri kapsamında değerlendirilmesi ve istatistiksel akıl yürütmeye dair alan bilgilerini ortaya koyma yaklaşımlarının incelenmesi amaçlanmıştır. Çalışma kapsamında öğretmenlerin istatistiksel akıl yürütmeye dair alan bilgisi ve istatistiksel akıl yürütme alan bilgisini ortaya koyma yaklaşımları; değişebilirliğe ilişkin akıl yürütme, dağılıma ilişkin akıl yürütme, informel çıkarımsal akıl yürütme ve dağılımın kapsadığı merkez ile ilgili akıl yürütme çeşitlerine göre incelenmiştir. Çalışmada nitel araştırmalar içerisinde yer alan özel durum çalışması yöntemi kullanılmıştır. Çalışmanın katılımcılarını 17 ortaöğretim matematik öğretmeni (10 erkek, 7 kadın) oluşturmaktadır. Söz konusu öğretmenler amaçlı örnekleme yöntemleri arasında yer alan tipik durum örnekleme yöntemi kullanılarak belirlenmiştir. Veri toplama aracı olarak istatistiksel akıl yürütme becerilerini alan bilgileri doğrultusunda ortaya koyan istatistiksel akıl yürütmeye dair alan bilgisi formu (İAY-AB) kullanılmıştır. Söz konusu form Gökçe (2019) tarafından hazırlanmış olup; beş adet açık uçlu sorudan oluşmaktadır. Verilerin analizi Gökçe (2019, s. 97) tarafından hazırlanan derecelendirme ölçeği kullanılarak ve alt problemlere göre ayrı ayrı ele alınarak yapılmıştır. Derecelendirme ölçeğindeki göstergeler baz alınarak veriler içerik analizine tabii tutulmuştur. Elde edilen bulgular doğrultusunda ortaöğretim matematik öğretmenlerinin istatistiksel akıl yürütmeye dair alan bilgilerinin beklenen düzeyde olmadığı, geliştirilmesi gerektiği tespit edilmiştir. Çalışma sonucunda katılımcıların önemli bir bölümünün istatistiksel akıl yürütmeye dair alan bilgilerini ortaya koyma yaklaşımlarında kullandıkları dört akıl yürütme becerisini bir arada içeren sorularda düşük ve orta düzeyde akıl yürütme becerisine sahip oldukları görülmüştür. Bu çalışmanın sonuçlarından hareketle istatistiksel akıl yürütme becerilerinin gelişimine yönelik etkinlikler planlanarak, bu etkinliklerin öğretmenler üzerindeki etkileri gözlemlenebilir.

Mathematics teachers’ conceptions about infinity: A preliminary study at the secondary and high school level

The literature indicates that students consistently exhibit limited conceptions of infinity in various contexts. Furthermore, it is more resistant in geometric than arithmetic contexts. On the other hand, there is a smaller amount of literature that explores teachers' conceptions and how these conceptions may be similar to those of their students. Therefore, this work presents the results obtained from applying a five-item instrument with secondary and high school mathematics teachers who are in public or private service in the state of Puebla, Mexico. This study had a dual purpose: to show that teachers also possess limited conceptions of infinity, as students do, thereby expanding the existing literature on this topic; and secondly, to emphasize that the results shown here will enable subsequent work to design an intervention for a profound conceptual change regarding infinity among teachers.

Study on the Tripartite Collaborative Training Mechanism for Secondary School Mathematics Teachers

Based on the principle of "local colleges and universities serving the local community", the university has established a tripartite collaborative training mechanism with the local secondary schools and government with clear rights and responsibilities, stable coordination and win-win cooperation. Based on the theoretical teaching and practical guidance of teacher education, and oriented to the improvement of educational and teaching ability, the university is striving to build a cooperative community integrating the training of secondary school mathematics teachers, the training of in-service secondary school mathematics teachers, and the research and service of backbone teacher education.

Diagnostic Assessment Knowledge and Practices among Secondary School Mathematics Teachers in Dodoma, Tanzania

This study examined how secondary mathematics teachers understand and implement diagnostic assessments in their mathematics classes. To understand how mathematics teachers conceptualize diagnostic assessment and how they put it into practice, the study conducted in-depth interviews with 20 secondary school mathematics teachers using a phenomenography research approach and analyzed them thematically. The results showed that most mathematics teachers are unfamiliar with the concept of diagnostic assessment, misunderstand its role in the teaching and learning process, and refrain from using it because they don't know how to do so efficiently. Due to the overcrowding in classes and the widespread failure of national examinations, the few people who understood the concept admitted to not implementing it. The study recommends professional development for mathematics teachers to improve their conceptual understanding of diagnostic assessment as well as their capacity to integrate it in classrooms to improve the teaching and learning of mathematics and hence improve students' performance in the subject.

Analisis Pemahaman dan Pelaksanaan Asesmen Nasional pada Guru Matematika Sekolah Menengah di Kecamatan Dampit Kabupaten Malang

Evaluations are carried out by independent institutions periodically, comprehensively, transparently and systematically to assess the achievement of national education standards. The aim of this research is to describe the understanding of secondary school mathematics teachers in the Dampit sub-district regarding the National Assessment system and to describe the implementation of the National Assessment by secondary school mathematics teachers in the Dampit sub-district. This research uses a qualitative approach with a descriptive type. This research was conducted at SMP Negeri 2 Dampit, SMP Diponegoro Dampit, SMAN 1 Dampit, and SMA Diponegoro Dampit, Malang district. Researchers collected data through questionnaires and interviews with mathematics teachers in the schools that were sampled. The results of this research for understanding the national assessment are quite good and its implementation is good, however it should be noted that there are still many obstacles in implementing the national assessment, such as parents of students protesting because their children were not included in the exam during the AN implementation. The government's socialization of the national assessment is not evenly distributed to teachers, so there are still many points in the national assessment that confuse teachers, especially mathematics teachers. Mathematics teachers carry out national assessments based on the principal's instructions, so the socialization from the government has not been felt directly by teachers

Educational Game Design Experiences of Secondary School Preservice Mathematics Teachers

In this study, it was aimed to reveal the mathematical games designed by secondary school preservice mathematics teachers and their views on this process. The participants of the study, in which a case study, one of the qualitative research designs, was used, consisted of 45 pre-service secondary school mathematics teachers who took the Teaching Mathematics with Games course. The data obtained from the study were subjected to descriptive and content analysis. According to the results obtained from the study, while the majority of the games were designed as board/card games, the most preferred learning area was numbers and operations. In addition, according to the grade levels, the most games were designed for the 8th grade and the least for the 5th grade level. In the process of mathematical game design, pre-service teachers mostly aim to provide meaningful learning, develop procedural skills, reinforce what has been learned, and make learning mathematics fun. In addition, although the pre-service teachers experienced some difficulties during the game design process, it was determined that this process affected them positively in cognitive, affective, and pedagogical terms.

Teachers in Math Lessons in the Digital Age: The Real Face of Distance Education

The COVID-19 pandemic has made distance education compulsory for all students in primary, secondary, and higher education in Türkiye. This situation has brought about many changes in teaching methods, material use, assessment and evaluation processes, and course durations. This study investigates the effects of these changes on secondary school mathematics teachers and their experiences and difficulties adaptation processes. This study conducted using a qualitative approach as a case study, included 75 secondary school mathematics teachers working in Türkiye in the 2020–2021 academic year. The data collection process was conducted online with a semi-structured interview form via Google Form. The obtained data were evaluated by content analysis. According to the findings of the research, teachers tend to provide skill-based questions as homework during the distance education process, rather than the lesson. Teachers who have negative judgments about assessment-evaluation processes find the course durations in distance education insufficient. Teachers who use different motivation tools in the distance education process, on the one hand, think that the process improves them; on the other hand, they expressed their concerns in terms of professional development. Teachers need more support and training to cope with the difficulties they face in the distance education process. In addition, they should be supported to improve themselves in online assessment and evaluation strategies and increase student participation.