Current Mathematics Curriculum Research Articles

Emotional Intelligence And Mathematics Achievement Of Underachieving High Ability Senior Secondary School Students: A Perspective Of Inclusivity In Regular Secondary Schools In Calabar Education Zone, Cross River State, Nigeria

Some high ability students who show great mathematics potentials fails to perform at a level commensurate with their abilities in mathematics. Most of them lack self-efficiency, goal directedness or self-regulation skills which has resulted to poor performance in Mathematics The dwindling performance in Mathematics in both internal and external examinations among high ability students in Nigeria are not because they do not have the intellect but because of prevailing factors of emotional intelligence which influence their performance in schools. The main purpose of the study is to examined the relationship between emotional intelligent and Mathematics achievement of high ability students in Calabar Education Zone of Cross River State, Nigeria. This study adopted correlational survey design which determined emotional intelligence (wellbeing, self control and sociability) as relate to Mathematics achievement of high ability students in Calabar Education Zone of Cross River State, Nigeria. It was guided by three research questions and three null hypotheses. A sample of 400 Senior Secondary II students was selected from public schools using the stratified random sampling technique, school record, and teachers’ nomination checklist. Two instruments, emotional intelligence Questionnaire (EIQ) and Mathematics Achievement Test (MAT), were used for data collection. The reliability of the questionnaire, established using Cronbach Alpha with a coefficient of 81 and .84 while the reliability estimate of the high ability Students’ MAT was established through Kuder Richardson formula K-R20 which yielded .83. The hypotheses were tested using Pearson product Moment Correlation Coefficient at .05 level of significance. The findings of the study revealed that wellbeing, self control, sociability significantly relate with mathematics achievement of underachieving high ability senior secondary school students. Based on the findings of this study, it was recommended amongst others that the attributes of emotional intelligence should be taken into consideration during planning of educational curriculum so as to enrich the current Mathematics curriculum and enhance high ability students’ performance in the subject.
 

Effect of Model-Based Problem Solving on Error Patterns of At-Risk Students in Solving Additive Word Problems

Students with learning disabilities/difficulties in mathematics often apply ineffective procedures to solve word problems due to a lack of conceptual understanding of word problem solving, which results in poor mathematics performance and falling further behind the normal achievements of their peers. Current mathematics curriculum standards emphasize conceptual understanding in problem solving as well as higher-order thinking and reasoning, including all students. The purpose of this study was to evaluate the impact of a computer-assisted model-based problem-solving intervention program (MBPS) on elementary students’ word problem-solving performance by analyzing the error patterns. Results indicate that after the MBPS intervention, participants significantly improved their problem-solving performance and made fewer errors in solving problems across a range of additive word problem situations. Specifically, the participating students made their attempt to represent the mathematical relation, decontextualized from the word problem story, in the model equation before solving the problem, rather than blindly applying an operation or relying on the “keyword” strategy as they did during the preassessment. Implications of the study are discussed in the context of the National Council of Teachers of Mathematics’ calling for teaching big ideas to help students develop a deep understanding of mathematics knowledge.

Research on the teaching of classes on probability distributions and hypothesis testing in high school mathematics departments and universities

Data is a prevalent concept in today's world. We are in an era of Big Data and the field of data science is possibly more important than it ever has been. Associate Professor Chieko Matsumoto, School of Education, University of Fukui, Japan, is an expert in data science who is conducting research on statistics and data science education in upper secondary schools and universities, with a focus on the concept of statistical hypothesis testing. Matsumoto's goal is to quantify what is lacking in the current mathematics curriculum in order to put forward recommendations to overcome challenges facing statistics and data science education. She and her team want to develop teaching materials and practical guidance on statistics and data science education. Their research approach and methods are developed with a focus on probability distributions and hypothesis testing. The researchers will conduct a questionnaire survey of upper secondary school teachers to clarify the various teaching problems and teaching difficulties that teachers encounter when teaching statistical hypothesis testing. The team is yet to obtain permission to conduct a large-scale questionnaire and so the researchers have been conducting small-scale interviews to establish an understanding of teaching difficulties faced by upper secondary school teachers.

Investigating Student Teachers’ Contemporary Mathematics Practices of Engagement, such as "Try This," as They Begin Their Mathematical Lessons.

This study explores the extent to which pre-service teachers are able to implement contemporary practices in teaching mathematics during their practicum. The main focus is on the importance of prior engagement of students in learning mathematical concepts. The total population of 150 student teachers from both the Colleges of Education, Paro College of Education (PCE) and Samtse College of Education (SCE), was targeted for this study. However, only 60 participants could actually return the questionnaires. A mixed-method comprising of both quantitative and qualitative methodologies was used. Research tools such as survey questionnaires (quantitative) along with a few open-ended questions, followed by lesson plans and interviews (qualitative) were used to collect the data. The findings from this study tend to reveal that although the student teachers are in favour of the contemporary ideas/approach of teaching and learning of mathematics, they do not seem to have practiced it while they were in a teaching practicum. The findings cast doubt on whether preservice teachers are able to drive changes for improvement in the teaching and learning of mathematics in mathematics classrooms. The benefit of this study was expected to be very relevant not only for the authorities to consider the effectiveness of the contemporary practices of teaching and learning of mathematics education in those two colleges of education, but also in Bhutanese schools using the current mathematics curriculum.

Developing Mathematical Proof: Back to the Future with Vieta Extended Theorem

The education system is in a constant search for ways to improve the quality of its daily educational work in the classroom, in response to the increasing demand that its graduates reach achievements appropriate for the 21stcentury. The current mathematics curriculum for middle schools in Israel introduces students mainly to proofs in geometry, and seems unaware of the need for algebraic proofs and the insights rooted in proving theorems. This paper suggests interesting and challenging research activity for 8th and 9th grade students, who are taking their first steps in algebra. This activity would require them to go back in time to the 16th century, and follow the work of François Viète, a French mathematician who was one of the fathers of modern algebra. Algebraic knowledge required to prove Vieta’s extended theorem corresponds to the algebraic knowledge of middle school students. The activity suggested in this historic context could be an intellectual experience for the students because it encourages searching for relationships and constancy, understanding the need for proof in algebra, and applying the theorem through solving varied questions and creating new questions. Mathematics teachers who choose this topic and place the students at the center as independent learners, could cultivate and promote mathematical thinking among their students.

The importance and emergence of K-12 data science

The COVID-19 global pandemic has required everyone to make sense of data about community spread, levels of risk, and vaccine efficacy. Yet research shows that students are underprepared in data literacy. Tanya LaMar and Jo Boaler argue that data science education provides an opportunity to address this problem while providing much needed updates to the current mathematics curriculum. The integration of data science can provide a more equitable mathematics pipeline than the calculus-focused pathway that has excluded most students from a future in mathematics. Through data science, students can learn to answer questions that are relevant to their lives and communities, to be critical consumers of the data that surround them every day, and to wield the power of data analysis.

Third Grade Students’ Use of Relational Thinking

Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between numbers, developing awareness of properties and of the structure of the decimal number system and using it in a strategic manner. In this framework, the term relational thinking directs attention towards a way of working with arithmetic expressions that promotes relations between their terms and the use of properties. A teaching experiment has allowed to characterize the way in which third grade students use this type of thinking for solving number equalities by distinguishing four profiles of use. These profiles inform about how students employ relations and arithmetic properties to solve the equalities. They also ease the description of the evolution of the use of relational thinking along the sessions in the classroom. Uses of relational thinking of different sophistication are distinguished depending on whether a general known rule is applied, or relations and properties are used in a flexible way. Results contribute to understanding the process of developing the algebraic component of number sense.

A study on the plane figures of elementary school in the view of transformation geometry

One of the main purposes of geometry learning is the classification of shapes. Thus the activity of classifying shapes from a geometric symmetry (invariant) point of view has sufficient educational significance from Klein's point of view. The concept of translation, line symmetry, and rotational symmetry is introduced as part of activities to raise spatial sense in the current elementary school mathematics curriculum. The above three transformations are basic activities in the concept of congruence. But the current mathematics curriculum tends to deal with three basic concepts and congruence regardless of whether they are related. In fact, three activities and congruent concepts for developing spatial senses was introduced in different the grade-band for each other. In this paper, we shall classify triangles and quadrilaterals from the viewpoint of a symmetry breaking

Mathematics Curriculum Change: Identifying Parental Expectations

Parents’growing concerns about the current approaches to learning mathematics in elementary schoolhave drawn public attention in Canada. Rather than dismiss such concerns, understanding parent perceptions andgarnering their support is essential to ongoing curriculum transformation and students’ success in mathematicslearning. Using phenomenography, we examined parents’ perceptions of the current mathematics curriculum andtheir children’s experiences as expressed in community-based focus groups and individual interviews. Parentsresponded based on their past experiences, their views of children’s current experiences and their future aspirationsfor their children. Our analysis of parents’ perspectives revealed that their concerns and critiques were grounded inthe expectations they held for their children’s mathematics learning. In particular, parental expectations fell intothree categories: students need the opportunity to reach expected goals of mathematics learning; essential supportsmust be in place to reach expected goals; and, home-school communication is necessary for parent understandingand engagement. We suggest that by understanding the specific expectations that underlie parents’ concerns,teachers can engage in conversations that begin with affirming mutual expectations and respecting parents’personal experiences to lead to partnering with parents as they realize their agency in their children’s learning.

The effect of fun and interactive games as a strategy in teaching coordinates to enhance students’ performance in Mathematics

This research is aimed to help students develop their mathematical concept, as well as emphasizing the appropriate use of information technology among Year Three students. The current mathematics curriculum in Year Three primary school in Malaysia was introduced in 2018. This quantitative study used a quasi-experimental method. Thus, this study examines the differences in performance between a controlled group and experimental group from a school in Malaysia. Paired samples test results have proven that the experimental group performed better than the controlled group. It was also found that fun and interactive games can increase students’ understanding and interest towards mathematics. Interactive games can contribute least time to master some mathematical concepts in a fun way. Therefore, the fun and interactive game is a superior instrument that can be utilized by primary students in learning mathematics in order to encourage learning and innovation skills in the 21st century.

Comparing and Validating Four Methods for Scoring Mathematics Writing

Current mathematics curricula and assessments emphasize students’ ability to communicate mathematical reasoning in writing. Limited research exists, however, on what mathematics writing (MW) is and how to assess the quality of MW. Therefore, based on our definition of MW construct, we explored 4 approaches to scoring MW: (a) holistic rubric scoring for overall quality of explanation; (b) analytical rubric scoring across 4 components (i.e., mathematics content, mathematics vocabulary, writing organization, writing grammar); (c) genre-based elements scoring (modified from the scoring form used for the Essay Composition subtest of the Wechsler Individualized Achievement Test); and (d) curriculum-based measurement mathematics-writing sequences (MWS) scoring, including rules for scoring numbers and symbols. Students from 6 classrooms in 3rd-grade, 4th grade, and 5th grade (2 classrooms at each grade level; N = 122) were recruited for the current study. Results indicated all 4 scoring methods were moderately correlated with measures of writing and mathematics. Holistic, analytic, and elements scoring were strongly correlated with each other, with slightly lower correlations for the MWS scoring. Confirmatory factor analysis further demonstrated adequate construct validity. All 4 scoring methods were reliable with an exception of lower reliability for writing components assessed by analytic scoring. Based on the validity, reliability, efficiency, and information provided by each scoring method, we recommend holistic scoring for summative assessments and elements scoring for formative assessments.

Changes Needed in Saudi Universities’ Mathematics Curricula to Satisfy the Requirements of Vision 2030

The aim of this study is to improve the quality of the mathematics curricula in Saudi universities by investigating the required changes in mathematics curricula in order to satisfy the demands of the Saudi Vision 2030. The researcher used qualitative methods to answer the research questions by randomly selecting a sample composed of some faculty members who specialised in curricula and methods of teaching mathematics. In addition, some of undergraduate and postgraduate students. I founded that the current mathematics curriculum in Saudi universities lacks some important requirements and needs to be changed in order to satisfy the demands of Vision by including what is important for the integration of technology into the undergraduate and postgraduate mathematics curriculum. Furthermore, the mathematics laboratory must be an integral part of the curriculum. Moreover, problem-solving ought to be at the centre of a mathematics curriculum. This study concludes with recommendations regarding future research.

Study of the Thoughts of Math Teachers about the Content of Secondary Education Math Class

The purpose of this study is to investigate the opinions of secondary school mathematics teachers on the content of the current mathematics curriculum in Turkey. Based on this general aim, the views of teachers on the appropriateness of the curriculum content and their advice for improving the efficiency of the content have been revealed.Research was carried out as a case study, which is a qualitative research method. The study group for the research consisted of nine mathematics teachers working in Turkish Ministry of Education secondary schools in the city center of Sivas during the spring term of the 2011–2012 academic year. The research data were collected through semi-structured interviews with the teachers in the study group and all of these were carried out by the researcher. Data were analyzed using a categorical content analysis technique via the NVivo computer program.According to the results of the study, teachers believe that the content of the Secondary School Mathematics Curriculum (SSMC) is aligned with the principles that have to be applied while choosing the content. However, they have alleged that the content of the program is not sufficient according to the principles of scheme (readiness), individual differences, validity and economicality. Based on the findings of this study, various solutions are offered for researchers, managers and program development experts.

한국의 수학교육 평가 유형에 관한 연구동향

This study was to analyze the research trend related to mathematics education evaluation in the analysis of the articles on <National mathematics education journal>, <Korea mathematics education journal>. The study explores the future direction of mathematics education assessment research by investigating whether such evaluation was suitable for the expectation about the assessment required in the current mathematics curriculum. This study was to classify the evaluation-related researches based on Korea educational curriculum revision from 1991-2010 to examine the research trend on the mathematics education evaluation in each season in Korea, analyze the articles by 'monitoring of student's progress', 'judgement on instruction', 'giving the value on mathematics achievement of students', 'value judgement of the program' that were the purpose of evaluation presented in 1995 NCTM(National Council of Teachers of Mathematics). As a result, looking at the research trend classified by the time of the educational curriculum revision, the 7th educational curriculum had the most number of the papers announced from 1997-2006. Despite 2007 educational curriculum revision was the short period from announced 2007-2008 before the next educational curriculum was placed, 11 papers(34.4%) were published. According to the category by the purpose of the assessment prescribed in NCTM, it showed that researches of 'monitoring of student's progress(46.9%)' were the most, those of 'value judgement of the program' and 'giving the value on mathematics achievement of students had a similar percentage.

Why the journey to mathematical excellence may be long in Scotland’s primary schools

In the past 30 years mathematics curriculum reform in many countries has attempted to replace procedural approaches to learning the subject with inquiry based learning that hopes to develop mathematical thinking. Scotland’s Curriculum for Excellence can be seen as part of this trend. The success of such moves is highly dependent on the learning experiences devised by teachers which in turn are informed by their own conceptual understanding of the content and processes of the subject. As mathematics curriculum reform has shifted from “an emphasis on knowing things to being able to do things” (Yates &amp; Collins 2010: 89) subject content detail has tended to be removed from curriculum documentation to be replaced by more global outcomes when it is the very detail teachers may need to prompt and augment their own subject knowledge. This study analysed data from national and international surveys of achievement to gauge how well prepared Scottish children are in mathematics. It also examined subject content and advised pedagogies in previous and current mathematics curriculum documents to ascertain how these have changed over time. On this basis, recommendations are made relating to national qualifications, initial teacher education and continuing professional development. The hope is that these can begin to inform future policy development on how best to prepare teachers to deliver mathematics within Curriculum for Excellence in such a way that will meet the high aspirations Scotland has for its young people.

Effects of Problem-based Learning Approach in Learning of Statistics among University Students

Current Mathematics Curriculum concerns are focused on students’ needs to think mathematically rather than just mathematical computation. Students should be able to develop more complex, abstract, and powerful mathematical structures. This can dramatically enable them to solve a broad variety of meaningful problems. Furthermore, students ought to become autonomous and self-motivated in their mathematical activities such as acquiring mathematical concepts, skills and problem solving; meta-cognitively aware of their mathematical thinking; highly motivated in mathematics learning and develop positive attitudes towards mathematical task. To achieve this learning goal, an investigation into efficient learning mode, the problem-based learning (PBL) was undertaken. PBL has been successfully applied in medical, engineering, economics, and accounting field but lack of evidence in mathematics field. This study examined possible outcomes of PBL among postgraduate students who were taking Educational Statistic course. Three statistic tests were employed to assess the students’ performance in statistic learning. The Meta-cognitive Awareness Inventory (MAI), which comprises of 52 items was used to assess the students’ meta-cognitive strategy in solving Educational Statistics problems. Students’ motivation towards the PBL learning was measured by Keller's Motivational Design Questionnaire with 36 items. Comparison of students’ performance based on three tests showed that there is significant diffrence between mean performance (F [2,28]=5.571, p<0.05). In addition, results indicated that there is significant positive effects on students meta-cognitive awareness (t [30]=3.358, p<0.05) and on students motivation level (t [30]=2.484, p<0.05) after undergoing PBL intervention.

Conditions of progress in mathematics teacher education

The progress of mathematics teacher education as a field of study depends on theoretical and empirical work. Both kinds of work are intimately related. Any scientific article that reports an empirical study needs to be based in theoretical constructs, and, at the very end, should contribute to a better understanding of these concepts or, at least, of their power for understanding specific problems, and any theoretical work, to make sense, requires some sort of empirical application. The articles in this issue of JMTE draw on several key theoretical concepts in mathematics teacher education: content knowledge and pedagogical content knowledge (Davis), teachers’ beliefs (Cross, Davis), teachers’ practices (Cross, Ryken), and teacher learning (Ryken). As a subfield of the social sciences, we cannot expect that all the authors share the same view about such notions. However, we must be able to understand how they conceptualize their major theoretical concepts, relate them to each other, note their similarities and differences, and regard the implications of the different choices. Teachers’ knowledge of mathematics includes teacher knowledge of mathematical facts and representations, concepts, procedures, and other information, as well as the ability to solve problems, to construct and use models, to establish connections within and outside mathematics, to reason, to prove, and to evaluate results. In this issue, Davis, in his article titled ‘‘Understanding the influence of two mathematics textbooks on prospective secondary teachers’ knowledge’’ draws on the distinction between factual knowledge and conceptual knowledge that points toward different levels of elaboration. Other dimensions of knowledge in action, which are captured by the notions of problem solving, modeling, proving, and evaluating, are at the core of the current mathematics curriculum orientations for students’ learning and also need the attention of mathematics teacher education researchers. Teachers’ pedagogical content knowledge blends ‘‘pedagogy’’ and ‘‘content’’ in a special way. Davis stresses two aspects, the educative representations that include ‘‘the most powerful analogies, illustrations, examples, explanations, and demonstrations’’, and

Mathematics Teaching and Learning in the Early Years in Aotearoa/New Zealand

This paper presents an overview of events in Aotearoa/New Zealand mathematics education over the past decade or so. We begin with the curriculum reforms of the 1990s that led to the development of the current mathematics curriculum (Ministry of Education, 1992), and document developments in policy, resources and approaches to teaching. There has been a strong emphasis on improving student achievement, and the overview illustrates how developments in the school sector have been accompanied by a focus on early childhood education, adult numeracy, and community involvement in children's learning. We conclude by reflecting on the current curriculum review, and what this might mean for practice.

Inscribing the Winch: Mechanisms by Which Students Develop Knowledge Structures for Representing the Physical World With Algebra

I propose and test an account of mechanisms by which students develop knowledge structures for modeling the physical world with algebra. The account begins to bridge the gap between current mathematics curricula, in which modeling activities play an important role, and theoretical accounts of how students learn to model, which lag behind. After describing the larger study, in which I observed 12 pairs of 8th-grade students introduce and refine algebraic representations of a physical device called a winch, I then focus on 1 pair that generated an unconventional yet sound equation. Because the prevailing genetic accounts of knowledge structures in mathematics education, cognitive science, and information-processing psychology do not explain key characteristics of the data, I begin to construct a new developmental account that does. To do so, I use forms, a class of schemata that combine patterns of algebra symbols with patterns of experience in the physical world, and 2 mechanisms, notation variation and mapping variation. I then use forms and the 2 mechanisms to analyze how the selected pair of students introduced and refined initial, faulty algebraic representations of the winch into an unconventional yet sound equation.

Empowering Classroom Teachers for the 21st Century: meeting the challenge of advancing children's mathematical development1

SUMMARY In this paper, the specific concerns for literacy and numeracy as we enter a new era are addressed through a discussion of an innovative mathematics early intervention programme, which the author and classroom teachers have developed and applied. ‘Mathematics Intervention ‘ is an innovative programme developed by three classroom teachers to identify, then assist, children in year 1 ‘at risk’ of not coping with the current mathematics curriculum. The programme incorporates assessment tools and learning activities based on recent research about children's early numerical learning. It develops the basic concepts of number upon which children build their understanding of mathematics. All three teachers participated in a professional development course, which developed skills that allow teachers to recognise which children have a problem, to identify the underlying problem and to provide appropriate activities to advance their mathematical development. The course highlights the benefits of clinical interviewing as an assessment tool and promotes various strategies that classroom teachers can use to assist the development of numerical concepts. ‘Mathematics Intervention’ is an example of a programme developed and implemented by classroom teachers using new learning processes designed to empower classroom teachers to meet the challenge of advancing all children's mathematical development.