National Mathematics Research Articles

Mathematics curricula in francophone countries

This paper presents a qualitative study of four Grade 1 and Grade 2 national mathematics curricula coming from francophone countries: Côte d’Ivoire, Djibouti, Canada (Québec), and France. A comparative analysis was performed to identify differences that potentially lead to inequities among the countries. We identified all the concepts present in the Grade 1 and Grade 2 mathematics curriculum using the mathematical literacy framework developed by the OECD through its PISA assessment: quantity, change and relationship, data and uncertainty, and space and shape. Then we looked across countries to find the major differences among them. The findings show three categories of possible inequities among the different curricula: some mathematical concepts are not presented in culturally relevant ways to students, some concepts present in the mathematics curricula are not mathematical concepts, and some important mathematical concepts are not part of the mathematics curricula. Our results show that these inequities appear in all four national curricula analysed here. Those findings highlight the need to question the political inequities among mathematics curricula around the world in order to give a chance for all students to learn strong and meaningful mathematics.

A COMPARISON OF PUBLIC AND PRIVATE HIGH SCHOOLS LEARNERS’ PERFORMANCE IN MATHEMATICS IN DISTRACT LAYYAH PUNJAB, PAKISTAN

The key purpose of the current study was to inspect the mathematics teaching and education performs of high schools educators and to recognize the break between present mathematics teaching performs in distract Layyah Punjab Pakistan and the finest teaching performs advocated through literatures. In teaching to understand this purpose, the researcher chosen a samples of 100 high school learners and 100 teachers. The sample of study were taken in two phases. In 1st phase 25 high school males schools and 25 government females schools were designated. Likewise 25 private males’ institutes and 25 females’ private institutes were also designated. 10 learners from every of the sample institutes were designated by mean of methodical random sampling method. The study was quantitative data gathering and examination expired parallel and the results accompaniment every other. The quantitative facts were composed with the help of two surveys tool 1 for learners and the other for educators. The reliability coefficient resulting in a pilot study designated that surveys were dependable sufficient to be used in the full study for data gathering. The outcomes presented a thoughtful gap among present and professed coaching and knowledge performs. It was too originated that educators did not even know what class room performs were recommended in instruction policy documents and the National Mathematics Curriculum. In the survey, it was piercing out that the argument and protest method is extremely used by the educators, though the class room comment exposed that the educators frequently used the drill and practice method. Educators give learners a guide for remembering numerous ideas and then practice it. Though numerous educators have spoken intangible considerate of mathematics, it is missing in class rooms. Problem solving teaching technique is claimed to be the best and operative repetition with the standard stated in Nationwide Curriculum Mathematics (2006), data presented that this repetition is infrequently used in mathematics class rooms. It is decided that Pakistani high school mathematics educators do not usage numerous of the finest mathematics instruction performs recommended in the literature. The study likewise observed that certain of the finest mathematics instruction practices are used in private institutes, which is illustrated in the teacher survey. It was recommended that teachers orientate themselves on the usage of the best mathematics instruction performs in high school class rooms. With the purpose of emerging a profounder conceptual considerate amongst learners. Moreover, educators may be given the chance to progress their individual knowledge and considerate of the best performs for coaching mathematics as recommended in national education policy and curriculum pamphlets. Furthermore, it is recommended that upcoming study may be lead to inspect how pre-service and in-service preparation makes middle school mathematics educators to usage the best performs in coaching mathematics.

The emergence of computational thinking in national mathematics curricula: An Australian example

The emergence of computational thinking in national mathematics curricula: An Australian example

Preservice Special Education Teachers’ Experience of a Math Methods Course: Examining the Development of Personal and Pedagogical Efficacy

Students with disabilities have scored well below their same-aged peers on national mathematics standardized tests for decades. This problem is compounded by special education teachers who lack strong content knowledge, experience math anxiety, and have poor self-confidence in their ability to teach math. This qualitative study explores three preservice special education teachers' experiences in a Math Methods course designed to encourage students to view mathematics through a growth mindset. After the course ended, individual interviews were conducted, and findings revealed personal growth in confidence and pedagogical knowledge. Components that influenced their decision included Socratic conversations centered around a mathematical mindset book study, a focus student project, and extra hands-on application time resulting from the use of the flipped instruction model. This information contributes to educator preparation literature as teacher educators work to best support future P-12 educators to impact their future students and help overcome barriers to learning.

PRECISION OF MATHEMATICAL VERBS IN GRADE 12 LEBANESE NATIONAL EXAMS

This study aims at analyzing a recent copy of the Lebanese mathematics national exams in terms of precision of action verbs as well as classification of free-response items according to Porter’s rubric related to language associated with performance outcomes and two-dimensional Bloom Revised Taxonomy. Results showed that the verbs were classified at different levels. The levels were all tackled in the exam which shows variety of questions except for the highest Porter level. The higher thinking level questions as specified by Porter and Bloom constituted around 30% of the exam. Similar studies targeting all national mathematics exams are recommended.

Factors influencing teachers’ grading standards in mathematics

ABSTRACT National assessments can be used to explore the strictness of teachers in grading students by comparing student grades to their scores on standardised tests. Several factors influence teacher-given grades, including student gender, school type, geographical regions, and socioeconomic status. In this paper, we used data from the Italian institute INVALSI, responsible for the organisation of national mathematics assessments, to investigate how these factors influence teachers’ grading standards. We considered a sample of 36,589 Grade 13 Italian students from 2,062 classes at 990 high schools. The relationships between the variables were analysed using hierarchical linear modelling. The findings reveal that teacher-given grades are related to student-level variables (e.g. gender, socioeconomic status, and score on the INVALSI test) and school-level variables (e.g. school type and location). When the difference between teacher-assigned grades and scores on the INVALSI test was considered, only student gender, school type, and location accounted for the gap in student achievements. Therefore, student socioeconomic status has a lower influence on their performance on the INVALSI test, suggesting that using standardised assessments might improve equity in assessment.

Preparing Secondary Mathematics Preservice Teachers for Rural Schools in Colombia

AbstractThis article describes a qualitative research case study that aimed to explore the complexity levels and types of mathematical thinking and national mathematics standards that a group of preservice teachers (PSTs) used to write mathematics word problems for secondary school students. The context was a teacher preparation course at a public university located in a rural region in Colombia, South America. The collected data included PSTs’ community reports, audio recordings of small-group discussions, and mathematics word problems. The data analysis process encompassed inductively created codebooks, several rounds of coding, and the inter-rater technique. The findings of the study demonstrated that most word problems written by the PSTs aligned with a few national mathematics standards and different potential levels of mathematical thinking. However, there was a disconnect between these levels of mathematical complexity and the types of funds of knowledge identified. The article ends by sharing implications for mathematics teacher education and suggestions for future research.

Reconsidering conceptual knowledge: Heterogeneity of its components

Cognitive arithmetic classically distinguishes procedural and conceptual knowledge as two determinants of the acquisition of flexible expertise. Whereas procedural knowledge relates to algorithmic routines, conceptual knowledge is defined as the knowledge of core principles, referred to as fundamental structures of arithmetic. To date, there is no consensus regarding their number, list, or even their definition, partly because they are difficult to measure. Recent findings suggest that among the most complex of these principles, some might not be “fundamental structures” but rather may articulate several components of conceptual knowledge, each specific to the arithmetic operation involved. Here, we argue that most of the arithmetic principles similarly may rather articulate several core concepts specific to the operation involved. Data were collected during a national mathematics contest based on an arithmetic game involving a large sample of 9- to 11-year-old students (N = 11,243; 53.1% boys) over several weeks. The purpose of the game was to solve complex arithmetic problems using five numbers and the four operations. A principal component analysis (PCA) was performed. The results show that both conceptual and procedural knowledge were used by children. Moreover, the PCA sorted conceptual and procedural knowledge together, with dimensions being defined by the operation rather than by the concept. This implies that “fundamental structures” rather regroup different concepts that are learned separately. This opens the way to reconsider the very nature of conceptual knowledge and has direct pedagogical implications.

예비 중등 수학교사들의 함수 개념의 도입 방식 탐색

The purpose of this study is to analyze and present what aspects of the concept of function that prospective mathematics secondary teachers emphasize when designing a class that introduces the concept of function using curriculum and textbooks. For this purpose, virtual instruction and reflections on virtual instruction were analyzed. The results are as follows. The prospective mathematics secondary teachers thought of function as correspondences and processes. Their conception of function was consistently observed during virtual instruction and reflections on virtual instruction. The prospective mathematics secondary teachers’ conception of function was closely related to the form of expressing functions. These results are considered to be empirical evidence that suggests implications for the prospective mathematics secondary teachers’ education and research to introduce the concept of function based on the dependent relation between variables presented in the 2015 revision of the national mathematics curriculum.

An analysis of item response theory using program R

The test is one of the instruments used to assess the extent of student understanding in learning. Multiple choice is a type of test commonly used in testing students. In addition to testing students' understanding, the quality of the tests used also needs to be tested. This study aims to determine the characteristics of the national mathematics test items in Baubau in the 2015/2016 academic year and the test information function with the item response theory approach. This research is an ex-post-facto study with a sample size of 574 students using a random sampling technique. Data was collected through documentation and analyzed using the LTM R package program. Findings indicated that there were four items (I1, I2, I4, and I8) for the 1-PL model, six items (I1, I2, I4, I7, I8, and I10) for the 2-PL model, and seven items (I1, I2, I3, I4, I7, I9, and I10) (3-PL) that fit the model (FM). The percentage of good (G) item parameters using R was 90% for (b) (1-PL), 90% (b) and 100% (a) (2-PL), and 90% (b), 10% (a), and 70% (c) (3-PL). The percentage of good quality items in each model for the 1-PL model was 40% or four items, the 2-PL model was 60% or six items, and the 3-PL model was 0%, or none was included in the good quality item category.

Evaluation of the Curriculum of Junior High School Mathematics Subject Using Spatial Analysis in the Regions of Pekanbaru

<p style="text-align:justify">Evaluation of the K-13 curriculum (2013 Curriculum) on the value of the national mathematics examination “Nilai Ebtanas Murni” (NEM) in every State Junior High School needs to be carried out thoroughly in order to improve the quality of education. This study uses spatial analysis to evaluate the curriculum and determine the development of NEM scores in the school year. Furthermore, the kriging interpolation method via surfer software was used to generate scores. The results showed that the 2015 K-13 mathematics curriculum did not give good results based on the 36-68 NEM score interval for the entire Pekanbaru area. In addition, the curriculum only gives good results for a small area in the north and south. In 2016, the curriculum which was accompanied by the entry of the new education unit level curriculum “Kurikulum Tingkat Satuan Pendidikan” (KTSP) showed a significant change in the NEM value. Although most of these areas experienced an increase in scores, the intervals still ranged from 36-68. The total revision of the K-13 curriculum carried out and used in 2017 showed a significant increase in scores for all regions with an interval of 68-84 scores. In conclusion, this study shows that the revision of the K-13 curriculum is the right step to produce quality mathematics learning.</p>

Demystifying Area and Perimeter: A Practitioner’s Guide to Strategies That Work

An understanding of concepts related to geometric measurement is considered to be critical to the development of individuals’ mathematics knowledge. Specifically, the National Mathematics Advisory Panel’s 2008 report listed the skills of area and perimeter as foundational for algebra readiness. Yet, this content knowledge continues to be an underdeveloped skill area for many school-age children and especially those with learning disabilities. This article provides educators with the following four strategies that are grounded in research and can be implemented during instruction on area and perimeter: (a) instruction using manipulatives, (b) focusing on salient variables within problems, (c) utilizing visual-chunking representations, and (d) incorporating contextualized scenarios and experiences.

Differential relationships between mathematics self-efficacy and national test performance according to perceived task difficulty

ABSTRACT We explore the effect of students’ perceived task difficulty on the mathematics self-efficacy – performance relationship. Specifically, we expand on previous reciprocal effects studies through including students’ self-efficacy for different levels of task difficulty in an empirical investigation. We examined students’ self-efficacy for easy, medium difficulty, and hard tasks and performance on a national mathematics test in a longitudinal study of 95 Norwegian students from grade 8 to grade 9. We found differential relationships between self-efficacy for different levels of task difficulty and national test performance. In support of the ‘skill development’ model, grade 8 national test performance predicted grade 9 self-efficacy for medium and hard, but not easy, tasks. While mastery experiences are likely to arise more easily on easier tasks, such experiences are likely to matter more on harder tasks. Our findings highlight the importance of supporting students’ engagement with challenging tasks to strengthen both their performance and self-efficacy.

한국, 싱가포르, 호주 수학 교과서의 행렬 단원 비교

The national mathematics curriculum revision process is underway in the background of the era where rapid technological development, uncertainty and volatility are expanded. In this process, consideration of matrix as a learning content emerged as one of the key issues, and conflicts among diverse educational participants are escalating. This study attempted to obtain implications for revising the presentation of matrix in textbooks by comparing the perspectives reflected in mathematics textbooks in Korea, Singapore, and Australia. First, the study compared and analyzed the learning contents, concept introduction and contents development methods in the textbooks from the three countries, and found that Korean textbooks cover more learning elements and tend to focus on calculation, while the other two textbooks from Singapore and Australia value the meaning of matrix as a useful means of expressing data. In addition, the results of comparing tasks based on the cognitive level framework developed by integrating the TIMSS cognitive domain and Jan de Lange’s framework showed that more than 80% of the tasks included in the Korean textbooks remained at the level of reproduction and connection, while Singapore and Australian textbooks provided various opportunities to learn such as making conjecture, justification and mathematical modeling through 70% and 45% of the tasks at the level of reflection, respectively. Drawing on the implications from the analysis, it is suggested to have fewer focus on content elements and more emphasis on conceptual understanding, mathematical reasoning, and mathematical modeling rather than calculation.

데이터 기반 확률교육을 위한 수학과 교육과정 재구조화 방향 탐색

The aim of this study is to explore how to restructure the probability content standards in the national mathematics curriculum by pursuing the goals of developing probabilistic thinking competence and probabilistic problem solving. We named the perspective pursuing these goals as Data-Driven Probabilistic Education (DDPE) in that data sensitivity plays a significant role in probabilistic thinking and problem solving, and moreover relations between data and probability matter in statistics and machine learning fields. We further investigated into how to facilitate probabilistic thinking and probabilistic problem solving as well as what to adapt the meaning or grounding sense of the two major goals in the context of DDPE. Findings suggested some alterations to be made in the content standards and directions of teaching and learning in the curriculum document. First, to understand the probability concept based on data sensitivity, to understand randomness, and to solve probabilistic problems using modelling approach are suggested to be included in the contend standards. Second, we suggest to include contexts in which decisions about risk are made in the teaching and learning directions to enhance competence of dealing with volatility and uncertainty using probabilistic thinking competence. Third, rather than writing general statements on using technological tools, it is suggested to present specific ways or procedures of probability simulation using a computer in relation to understanding stages of probability concepts and solving probabilistic problems as guides to teaching and learning to realize DDPE.

Out of the Woods Yet? The Continuing Impact of National Standards on New Zealand Music Education

Several years have passed since the removal of National Standards, however the current provision and enactment of music education in New Zealand remains unknown. Using a case study, this article seeks to illustrate the current practice of music education at one high decile primary school. This study finds that despite the removal National Standards, reading, writing and mathematics have continued to be prioritised, dominating classroom timetables, initial teacher education and the allocation of resources and professional development. With limited opportunities for music-making in the classroom, I argue that practice has stagnated and without targeted policies, music will continue to be marginalised within the curriculum.

Elementary Computational Thinking Instruction and Assessment: A Learning Trajectory Perspective

There is little empirical research related to how elementary students develop computational thinking (CT) and how they apply CT in problem-solving. To address this gap in knowledge, this study made use of learning trajectories (LTs; hypothesized learning goals, progressions, and activities) in CT concept areas such as sequence, repetition, conditionals, and decomposition to better understand students’ CT. This study implemented eight math-CT integrated lessons aligned to U.S. national mathematics education standards and the LTs with third- and fourth-grade students. This basic interpretive qualitative study aimed at gaining a deeper understanding of elementary students’ CT by having students express and articulate their CT in cognitive interviews. Participants’ (n= 22) CT articulation was examined usinga prioricodes translated verbatim from the learning goals in the LTs and was mapped to the learning goals in the LTs. Results revealed a range of students’ CT in problem-solving, such as using precise and complete problem-solving instructions, recognizing repeating patterns, and decomposing arithmetic problems. By collecting empirical data on how students expressed and articulated their CT, this study makes theoretical contributions by generating initial empirical evidence to support the hypothesized learning goals and progressions in the LTs. This article also discusses the implications for integrated CT instruction and assessments at the elementary level.

The role and significance of the World Federation of National Mathematics Competitions in the International Mathematics Education Community

The role and significance of the World Federation of National Mathematics Competitions in the International Mathematics Education Community

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.

Comparative Analysis of Question Item Parameters and Students' Ability between Dichotomy and Polytomic Score Versions; Research on Mathematics National Exam Test Participants

The purpose of this study was to determine the differences in the estimation of item parameters and students' abilities between the dichotomous scoring version and the polytomy scoring version. The data used in this study is the response of participants in a particular year national mathematics exam test which is presented in two versions of the scoring form, namely dichotomy and polytomy. In the dichotomous scoring version, each item is scored individually. Alternatively, each item that is scored separately on the dichotomous version, is aggregated into the same indicator, and then summed to obtain the polytomy version. Estimation of item parameters and students' abilities in the dichotomous scoring version was carried out using the 3 PL (Logistics Parameter) model using MLE estimation and the polytomy scoring version using the GPCM (Generalized Partial Credit Model) using EAP. Both were analyzed using PARSCALE software. Comparative analysis of the two scoring versions by looking at the average results of the estimated difficulty level, graph analysis, calculating correlations, and the results of the value of the information function. The results of the analysis show that the average difficulty level of the dichotomous version is 0.166, with a standard deviation of 1.137, while the average difficulty level of the polytomy version is 0.033, with a standard deviation of 0.940. The value of the dichotomous scoring version of the information function is higher than the polytomy scoring version. These results indicate that the math exam test with the dichotomous scoring version is better than the polytomy scoring version. graph analysis, calculate correlations, and result in value information functions. The results of the analysis show that the average difficulty level of the dichotomous version is 0.166, with a standard deviation of 1.137, while the average difficulty level of the polytomy version is 0.033, with a standard deviation of 0.940. The value of the dichotomous scoring version of the information function is higher than the polytomy scoring version