Secondary School Mathematics Curriculum Research Articles

Reasoning Skills in Mathematics Teaching: A Meta-Synthesis on Studies Conducted in Turkey

This research aims to analyze the results of studies conducted in Turkey on reasoning skills in mathematics teaching and to reveal what kind of trend there is in this field. Within the scope of this study, databases were searched with the keywords "reasoning"(muhakeme, akıl yürütme) and "reasoning skill" (Muhakeme becerisi, akıl yürütme becerisi), and the results were examined in accordance with the inclusion criteria regarding mathematics teaching. One hundred sixty-three studies were included. Each of the studies included in the meta-synthesis study was analyzed descriptively according to type, year, method, sample type and size, data collection tools, statistical analysis, learning field, keywords, reasoning type and purpose. In addition, the studies’ results were content analyzed and tabulated by coding the differences and similarities between them with a holistic approach. It has been determined that studies on the learning fields in the mathematics curriculum are mostly carried out in the field of learning numbers and operations in the secondary school mathematics curriculum. When evaluated in terms of reasoning types, almost half of the studies were conducted on mathematical reasoning. It has been observed that after mathematical reasoning, the most focus is on proportional reasoning. When the aims of the studies included in the research were examined, it was determined that the most focused ones were "examining the factors affecting reasoning skills", "measurement of reasoning skills" and "the effect of teaching practices on reasoning skills". In the studies examined, it was seen that there were 33 teaching practices whose effects on reasoning skills were examined.

What Does Symmetry Look Like? A Qualitative Research Based on Mental Images

Symmetry, located within the field of transformation geometry, is a mathematical concept that plays an extremely important role as a problem-solving technique. Despite this, it seems that it is rarely used in solving mathematical problems in secondary school. This research was carried out to reveal the mental images of secondary school students regarding the concept of symmetry in the secondary school mathematics curriculum. In the study conducted based on a qualitative perspective, the metaphors developed by the students regarding the concept of symmetry and the visuals they drew were examined. The study was conducted in the spring semester of the 2022-2023 academic year with 223 students studying in the 5th, 6th and 7th grades at a public school in Ankara, selected according to the convenient sampling method. Content analysis was used to analyze and interpret the data obtained from the students. Looking at the results of the research; It turns out that secondary school students generally perceive the concept of symmetry as "having similar functionality", "visually overlapping" and "perfect and meeting in differences".

Examining the Effect of Teaching with Ethnomathematics on Students' Problem-Solving Skills on Transformation Geometry

This research aims to examine the impact of teaching with ethnomathematics on students' problem-solving skills in transformation geometry and their skills in problem-solving steps. The study was carried out with an experimental design, one of the quantitative research methods. The sample was determined as 42 eighth-grade students in two classes using the purposive sampling method. One of these classes was randomly assigned as the experimental group and the other as the control group. In the research, the "Problem-Solving Test (PST)" was used as a data-gathering tool, and the "Problem-Solving Skill Scoring Key" put forward by Baki (2006) was used in the analysis of the data. According to this key, student responses were graded and the results were noted for the data analysis phase. The results obtained were analyzed with the SPSS20 program. It was seen that teaching using ethnomathematics elements improved students' skills in the steps of understanding the problem, preparing a plan, and plan implementing at the end of the research. The instruction did not have a significant effect on student skills at the evaluation stage. At the same time, teaching using ethnomathematical elements increased students' problem-solving skills and solution skills in daily life problems and traditional problems. In this context, it is recommended to integrate cultural elements into the secondary school mathematics curriculum, and in this way, it is thought that it can contribute to the development of students' problem-solving skills.

Promoting citizenship education in the mathematics curriculum: The Malawi secondary school experience

Background: Malawi recognises the importance of citizenship education (CE) as evidenced by its stated goals of education. In secondary schools, CE is offered explicitly in an elective subject called Social Studies. Consequently, some students do not study it. Mathematics is a compulsory subject; therefore, integrating CE would benefit all learners.Aim: Investigating the extent to which the Malawi secondary school mathematics curriculum promotes CE.Setting: Urban classroom with two experienced mathematics teachers.Methods: The first phase involved document analysis of the intended curriculum’s ability to promote CE. The second phase focussed on analysing mathematics lessons and how they extent they promoted CE.Results: The findings show that the curriculum promotes CE to a large extent, but this varies in the specific curriculum materials and the mathematics topics. The teaching also varies; learner-centred lessons offered more opportunities for CE than teacher-centred lessons.Conclusion: We argue that providing for CE in mathematics should go beyond listing in the school curriculum. There should be more clear guidance on how to integrate it into mathematics teaching.Contribution: Our study contributes in at least two ways: (1) Adds to literature on mathematics and CE drawn from Malawi context, which differs from contexts in most literature. (2) Adds to methodology by introducing a rating for CE in curriculum materials and analysis of lessons for CE through the lens of learner-centred continuum.

The Awareness of Prospective Mathematics Teachers on the Mathematics Curriculum

This research aims to examine the pre-service mathematics teachers' awareness of the special aims, application principles, and learning areas of the mathematics course curriculum. In this study, which was conducted with 30 primary school mathematics teacher candidates selected by convenience sampling technique, the case study design, one of the qualitative research approaches, was preferred. The data of the research were collected with an opinion form that included three open-ended questions questioning the specific aims, application principles, and learning areas of the mathematics curriculum. Descriptive analysis was used in the analysis of the obtained data. As a result of the research, it was seen that the participant teacher candidates mostly emphasized the items related to the use of mathematics in daily life within the scope of the program's special objectives. It can be said that the candidates mostly care about taking into account the individual differences of students in mathematics teaching, the use of materials, and the principle from concrete to abstract in mathematics education. In addition, it has been determined that all participants have knowledge of the learning areas in the secondary school mathematics curriculum and at which grade levels these learning areas are taught. As a result, it can be said that the awareness of the teacher candidates who will be the implementers of the training programs is high.

МЕТОДИЧЕСКИЕ ОСОБЕННОСТИ УЧЕБНИКОВ А.П. КИСЕЛЕВА

The article examines the life and work of mathematician and educator A.P. Kiselev, whose textbooks were used in Russia for more than 50 years. Based on an analysis of Kiselev’s works, the key pedagogical features of his textbooks are identified, including rigorous presentation of material, scientific style, and a variety of practical exercises. Kiselev was among the first to introduce elements of mathematical analysis into secondary school mathematics curriculum. Kiselev’s textbooks defined the structure and content of school courses in arithmetic, algebra and geometry for many decades, and contributed to the systematization and unification of mathematical knowledge in secondary education. The author succeeded in combining fundamental mathematical knowledge with accessible presentation. His books embodied the principles of intra-subject (between arithmetic, algebra and geometry) and inter-subject (between teaching of mathematics, physics and drafting) continuity. A.P. Kiselev’s textbooks were in demand not only in the USSR, but also in other countries.

Espial of Concept Difficulties in the New Africans’ Secondary School Mathematics Curriculum: CTCA Recommended

The value of teaching-learning the subject mathematics has been one of the foremost challenges and concerns of educators. This study employed a mixed method design aimed at investigating difficult concepts in the new senior secondary mathematics curriculum as perceived by students in Ghana and Nigeria. Guided by two research questions and the sample was 1,252 SS 1-3 students from 34 public and 66 private senior secondary (SS). The students are from both urban (62.9%) and rural (35.1%). The mean age of the students was 15 years, the class streams are science, commercial, and arts classes. The instruments were validated and the reliability was established using Cronbach’s Alpha method, and a reliability index of 0.78 using the test-retest method. The data obtained were analyzed using mean ranking in the IBM-SPSS 23 and Ms. Excel for qualitative analysis into themes and graphical representations. From the data gathered, we found 39 topics that students perceived to be difficult in the new mathematics curriculum. It was recommended amongst others that the CTCA should be used for the teaching-learning of mathematics in African schools based on its effectiveness in STEM related subjects in African and beyond

Analysis of Secondary School Mathematics Curriculum Learning Outcomes by TIMSS-2019 Cognitive Domain Skills

Analysis of Secondary School Mathematics Curriculum Learning Outcomes by TIMSS-2019 Cognitive Domain Skills

Examination of Secondary School Mathematics Curriculum in Terms of 21st Century Skills

Abstract
 The curriculum is the whole system that enables them to develop and renew their school education system. With the transition to the constructivism model in the schools of the world countries, many countries have revised their curricula according to this model. The mathematics curriculum taught in secondary education in Turkey was first revised by the Ministry of National Education in 2005 and then renewed in 2018. The aim of this research is to examine the secondary school mathematics curriculum in 2018 (achievements and activities) within the context of 21st century skills. Achievements and activities determined will be evaluated and examined in terms of learning and renewal skills. In line with this purpose, the research analyzed how much 21st century skills were included in the learning outcomes of the 2018 secondary school mathematics curriculum and its effects in the textbooks In addition, in the research, it was analyzed how much problem solving, critical thinking, creative thinking and communication skills of the P21 framework learning and innovation skills were included in the 2018 secondary school mathematics curriculum achievements and textbooks. The research model was conducted with document analysis, one of the qualitative research methods. In the document analysis, 21st century skills were selected by taking into account the P21 framework for 21st century skills. These skills are grouped in three areas: learning and innovation, information, media and technology, and life and professional skills. At the end of the research, it was determined that, due to the nature of the mathematics course, problem solving skills are included in almost all achievements and activities, while skills other than problem solving skills are not included in the achievements, these skills are included in the coursebook activities.
 Keywords: 21st century skills, Secondary school mathematics curriculum, Mathematics curriculum, P21

An assessment of the level of knowledge of secondary school mathematics subject matter among final year pre-service mathematics teachers as a basis for teaching school mathematics

The study sough to establish whether final year pre-service mathematics teachers have mastered secondary school mathematics subject matter as a basis for teaching mathematics at secondary school level immediately after graduation. Based on the assumption of 80% of scores (Guskey & Anderman, 2013) and above in the test administered as accepted cut off point to signify mastery of secondary school mathematics curriculum, the finding of the study revealed that 48.57% of the final year pre-service mathematics teachers have scored 80% and above in the test, which signifies their level of knowledge of secondary school mathematics subject matter, while 51.43% of the final year pre-service mathematics teachers have scored less than 80% in the test, which signifies their inadequate mastery of school mathematics subject matter. The finding shows that over 50% of the final year pre-service mathematics teachers cannot be relied upon to teach secondary school mathematics curriculum with confidence, this is because majority of the final year pre-service mathematics teachers’ (51.43%) have demonstrated inadequate mastery of the subject matter for which they have been trained to teach immediately after graduation. Based on the findings, the following recommendation were put forward; to ensure adequate mastery of school mathematics subject matter among final year pre-service mathematics teachers as a predictable tools for employment, and to serve as a basis for teaching mathematics at secondary school level, mathematics teacher education training should include all secondary school mathematics curricular in their training to ensure adequate mastery of the subject matter among the pre-service teachers.

Designing and Developing Video Lessons in Mathematics Using Code-Switching: A Design-Based Research

Unlike books and audio clips, videos provide stronger visual cues. They are made to help learners comprehend the events particularly when situations call for language interpretation. This design-based research developed a module in the form of video lessons covering the least-mastered competencies in Mathematics for Grade 9 students. This study identified the least-mastered competencies through a survey. Using the snowball sampling method, the researcher chose fifty public school teachers as participants in the study. The module was designed and developed with five video lessons, each lesson covering one competency. During the implementation stage, the lecturer employed code-switching to facilitate instruction. Forty Grade 9 learners had utilized the said module, which was evaluated by both learners and experts according to various criteria. Overall, the module was rated “acceptable” by both learners (M=4.44) and experts (M=4.65). Moreover, the module was deemed “highly acceptable” in terms of learning outcomes (M=4.58), and style and presentation (M=4.61). Code-switching as the medium of instruction, was also evaluated and rated by learners as “highly acceptable” in terms of attention (M=4.62), attitude (M=4.53), and success (M=4.74). The developed module achieved its objectives and opened opportunities for technology integration to cater to 21st-century learners. This approach to education caught the learners’ attention in helping them improve their knowledge and critical thinking ability, which are the goals of the secondary school mathematics curriculum. The output of this research may be used by other Mathematics educators as instructional material, and further assessment of its effectiveness is recommended.

The Effectiveness of a Technology-Based Isometrical Transformation Flipped Classroom Learning Strategy in Improving Students’ Higher Order Thinking Skills

Isometric Transformation is one of the essential topics in the Malaysian Secondary School Mathematics Curriculum. In general, Malaysia’s achievements in Trends in International Mathematics and Science Study (TIMSS) and Program for International Student Assessment (PISA) were found to be less encouraging, especially in the field of Geometry. This fact clearly implies that the mastery of Higher-Order Thinking Skills (HOTS) of Malaysian students is still low, especially in the topic of Isometric Transformation. Therefore, this study was conducted to develop Flipped Classroom Learning Strategy (FCLS) activities and evaluate their effectiveness in increasing Malaysian secondary school students’ HOTS in Isometric Transformation. This study was conducted in two stages whereby the first stage involved the development of FCLS activities, while the second stage was run to evaluate the effectiveness of FCLS activities in enhancing students’ HOTS for the topic of Isometric Transformation. The development of activities involved three phases. The first phase was the needs analysis phase which involved a preliminary survey towards students’ learning difficulties at each level of HOTS in the topic of Isometric Transformation. The second phase was the design and development stage of FCLS activities, involving the learning activities inside and outside the classroom in line with the topic of Isometric Transformation. The last phase was the evaluation phase which involved the content validation and evaluation on the suitability of FCLS activities by 11 experts. Next, the second stage was a quasi-experimental design which involved 131 Form 2 students from two secondary schools in Johor. The study sample was divided into two groups which were the treatment group and the control group. The study was conducted over eight weeks. Mann-Whitney test results showed a significant difference (p =.000 <.05) in the overall level and also for all of the four levels of HOTS for both control and treatment groups. The results of this study showed that the teaching and learning process that used FCLS activities successfully created an effective learning situation in improving students’ HOTS in the topic of Isometric Transformation. In conclusion, these FCLS activities should be used as guidelines for educators to increase HOTS in mathematics education.

Comparison of 5th to 8th Grade Mathematics Curricula in Turkey and Greece

This study compares the Turkish secondary school mathematics curriculum and the 5-8th grades mathematics curriculum in Greece, which has an essential place in the history of mathematics in terms of their general structure and content (learning areas, sub-learning areas, achievements, and course hours). In this study, we have used the document analysis method and curricula as a data collection tool. As a result of the research, we have seen that although the Turkish mathematics curriculum is structured as a single document, the Greek mathematics curriculum has a detailed document covering the aims, general objectives, and basic concepts of the interdisciplinary approach. While primary school is 6 years and secondary school is 3 years in Greece, both are 4 years in Turkey. The number of achievements in the Greek mathematics curriculum is higher than in Turkey, but the course hours are less than in Turkey. In addition, sets, linear equations, and similarity learning areas are included in the Turkish curriculum, but not in Greece. Similarly, sub-learning areas such as Functions and Trigonometry are included in the Greek curriculum, but not in Turkey. In line with these results, it can be ensured that the mathematics course hours are different at each grade level, and the course hours increase as the grade level increases in the mathematics curriculum conducted in Turkey, as in the Greek mathematics curriculum. In addition, as in previous curricula, a broader curriculum including activities, educational materials, and mathematical illustrations that will contribute to students' understanding of the subject can be developed in line with re-achievements.

Teachers' Views and Experiences Regarding Acquiring Analytical Thinking Skills in the Middle School Mathematics Curriculum

In this research, the level of acquiring analytical thinking skills in the secondary school mathematics curriculum was examined according to the opinions and experiences of the teachers. The research was carried out by the phenomenology pattern, one of the qualitative research designs. The research was performed with the voluntary participation of eight mathematics teachers working in public secondary schools in the central district of Bursa in Türkiye. In the selection of teachers, it was considered that they had experience with the curriculum, had at least five years of professional experience, and received in-service training on the curriculum. The opinions and experiences of the teachers about the curriculum were obtained using a semi-structured interview form. The data were analyzed by content analysis, and themes were created. According to the results, the teachers found the curriculum insufficient for gaining analytical thinking skills. According to the teachers' opinions and experiences, the mathematics textbooks' questions and activities are insufficient for gaining analytical thinking skills. According to teacher experiences, leaving students alone with non-routine questions supports their analytical thinking skills. In addition, the modeling technique helps to embody the analytical thinking process. The teachers stated that the applications in the textbooks were prepared to assume every student would learn at the same pace and similarly. In addition, it has been revealed that students wanted to work by rote, not wanting to tire their minds and getting used to ready-made it difficult for them to acquire high-level thinking skills such as analytical thinking. Some suggestions have been developed according to the results obtained.

Content Areas and Performance of Students in the Old Mutual Mathematics Olympiad in Malawi

The Old Mutual Mathematics Olympiad (OMMO) in Malawi is a national mathematics competition open to all final year secondary school students. In this paper, we analyse the results of the preliminary round of the competition from 2015 to 2020. We developed seven content areas for the OMMO based on core elements of the Malawi secondary school mathematics curriculum. We found that the OMMO is dominated by questions on the core element Number and numeration, particularly topics like number systems, indices and logarithms, linear equations and number patterns. We also analysed the general performance of students in these areas. We found that students performed well in topics like inequalities, trigonometry and mensuration and did very poorly on proportions, sets, coordinate geometry and geometric constructions, among other topics. These findings suggest that mathematics Olympiads can help diagnose areas that are difficult for students and hence enhance the teaching and learning of Mathematics, especially in Malawi and other countries with a similar mathematics curriculum. To take care of under-represented areas, future OMMO examinations need to be structured to adequately cover all the core elements.

A systematic review of experimental researches on the learning fields of numbers and operations in middle schools: The case of Turkey

Numbers and operations in the mathematics curriculum are very important regarding the number of learning acievements and course hours. In this review, experimental studies related to the sub-learning fields of the number and operations were reviewed according to methodological characteristics and Turkey's demographic features. For that purpose, 90 theses and 23 articles published between the years 2006-2021 were reviewed through a systematic literature review method. In the study, all sub-learning fields of the number and operations learning field occupying an important place in the secondary school mathematics curriculum, were reviewed. In addition, different aspects of the most and least studied learning fields were investigated.The results revealed that "Fractions" was the most investigated sub-learning field both in theses and articles, and regarding dependent variables, academic achievement and attitude towards mathematics were the most studied variables. Asa consequence, it was recommended that the researchers should focus on less-studied subjects of the 8th-grade curriculum and fill the areas deemed incomplete.

An Analysis of 2018 Secondary School Mathematics Curriculum According to Number Sense Components

Sayı hissi son yıllarda üzerinde çalışılan konulardan biridir ve önemi sıklıkta vurgulanmaktadır. Öğrencilere sayı hissinin kazandırılmasında ise en önemli görev öğretmenlere düşmektedir. Öğretmenlere kılavuzluk eden kaynaklardan biri ise öğretim programlarıdır. Dolayısıyla öğretim programlarında sayı hissine gereken önemin verilmesi gerektiği düşünülmektedir. Bu çalışmanın amacı 2018 yılı ortaokul matematik öğretim programının sayı hissi ve bileşenlerine göre incelenmesidir. Bu amaç doğrultusunda temel nitel araştırma deseni kullanılmıştır. Araştırmanın veri kaynağı Millî Eğitim Bakanlığı’nın 2018 yılında yayınlamış olduğu Ortaokul Matematik Dersi Öğretim Programıdır. Araştırmanın verileri betimsel analiz yoluyla analiz edilmiştir. Çalışma sonucunda öğretim programında yer alan 215 kazanımın 62’sinin sayı hissi ile ilişkili olduğu belirlenmiştir. Ayrıca sınıf düzeyi arttıkça sayı hissi ile ilişkili olan kazanım sayısının azaldığı tespit edilmiştir. Sınıf düzeylerine göre sayı hissi ile ilişkili kazanım sayısının en fazla olduğu sınıf düzeyi ise 5. sınıftır. Öğrenme alanlarına göre incelendiğinde ise öğretim programında yer alan sayı hissi ile ilişkili kazanımların büyük çoğunluğunun sayılar ve işlemler öğrenme alanından olduğu görülürken veri işleme ve olasılık öğrenme alanlarında yer alan tüm kazanımların sayı hissi ile ilişkili olmadığı tespit edilmiştir. Programda yer alan sayı hissi ile ilişkili kazanımların sayı hissi bileşenlerine göre incelenmesi sonucunda tüm sınıf düzeylerinde ve tüm öğrenme alanlarında en fazla kazanımın “sayıların anlamı” bileşeninde olduğu sonucuna ulaşılmıştır. Matematiğin daha iyi anlaşılması ve matematik başarısının artırılması için matematik öğretim programı kazanımlarında sayı hissine daha çok yer verilmesi ve sayı hissinin kavram olarak programda yer alması önerilmektedir.

Investigation of Activity Designs Prepared by Pre- Service Mathematics Teachers for Aspects of Entrepreneurship Education

The aim of this study is to examine examples of activities prepared by pre-service mathematics teachers for entrepreneurship education based on their knowledge of the aspects of entrepreneurship education and the achievements in this area in the secondary school mathematics curriculum. In the national and international literature, there are very few studies on entrepreneurship skills in mathematics education and on developing these skills. In addition, there are no secondary school mathematics curriculum acquisitions or application examples prepared in accordance with such acquisitions. The participants of this study included 20 pre-service teachers enrolled in the third-year undergraduate course “Connection in Mathematics Teaching” who volunteered to participate. Over the course of two weeks, four lessons of approximately 40 minutes, or 160 minutes in total, were taught to pre-service teachers addressing the following questions: “What are entrepreneurship and entrepreneurial skills? How are they related to mathematics? What can be done about the achievements in mathematics and the mathematics curriculum?” The subjects were explained and examples of applications from the researcher’s own work were given. After these explanations, the pre-service teachers were given an assignment. The data of the research consist of the completed assignments and audio recordings of individual interviews after homework analysis. The data were analyzed by content analysis.

Effect of Constructivist Instructional Strategy on Students Achievement in Secondary School Mathematics Curriculum in Rivers State, Nigeria

The study examined effect of constructivist strategy on students Achievement in Senior Secondary Mathematics in Rivers State. The research was guided by three research questions and corresponding hypotheses. The population is all the thirty four thousand, one hundred and sixty eight (34,168) of all Senior secondary II (SS11) students in Rivers State during the 2018/2019 Academic year. A sample size of 280 students in four intact classes were selected through purposive sampling technique. Two of each of the classes were used as experimental and control groups. Non randomized pre-test, post test control group design was used for the study. Instrument used for the study was Mathematics Achievement Test (MAT) made up of 25 items drawn from simple statistics and Lesson Packages. The instrument was validated by experts and reliability coefficient of the instrument was obtained through test-retest method. The scores obtained were subjected to Pearson product moment correlation coefficient analysis and the result yielded 0.82. Analysis of Covariance (ANCOVA), Mean and Multiple Classification Analysis (MCA) were used in analyzing the data. Findings reveals that constructivist strategy was more effective in facilitating students achievement in Mathematics than expository method. The result did not show a significant difference in students’ achievement in Mathematics in terms of gender and school type. The study therefore recommended among others the use of constructivist strategy in the teaching and learning of Mathematics in schools.

Manifesting of pedagogical content knowledge on trigonometry in teachers practice

Although trigonometry is an important section in secondary school mathematics curricula, many teachers find it challenging to teach as a result of insufficient pedagogical content knowledge (PCK). Therefore, the aim of this article was to report on how PCK on trigonometry manifests itself in teachers' practice. This exploratory case study was underpinned by the mathematics knowledge for teaching (MKT) model of Hill et al. (2008). Twelve teachers were purposefully selected from six township schools. Qualitative data were collected through semi-structured one-on-one interviews, lesson plans, assessment tasks, and lesson observations; and analyzed using content analysis. The findings show that four elements of PCK on trigonometry manifest themselves in teachers’ practice, namely knowledge of subject matter, knowledge of teaching strategies, knowledge of students’ conceptions and knowledge of curriculum, but varied in levels of sufficiency. Awareness of these variances forms a useful basis for planning developmental opportunities that could address shortcomings in PCK on trigonometry in teachers’ practice. This study adds to few studies in PCK in mathematics by providing empirical evidence on how PCK on trigonometry manifests itself in teachers’ practice.