Mathematics Curriculum Change Research Articles

CULTURAL HISTORICAL ANALYSIS OF IRANIAN SCHOOL MATHEMATICS CURRICULUM: THE ROLE OF COMPUTATIONAL THINKING

In this paper, six mathematics curriculum changes in Iran will be reviewed, spanning from 1900 until the present time. At first, change forces, barriers, and the main features of each curriculum reform will be represented. The first five curriculum changes are described briefly and the sixth and most recent curriculum reform will be elaborated. In this paper, we call the last reform as contemporary school mathematics curriculum change. This recent (contemporary) curriculum reform will be explained in more detail, followed by a discussion of the effect of globalization and research finding in the field of mathematics and mathematics education (in the Iranian mathematics curriculum). In total, three key ideas are distinguished as an effect of globalization which is “New Math”, “International Comparative Studies”, and “Computational Thinking”. Finally, the paper comments on the necessity of paying more attention to information and communication technology as part of globalization; in particular, recall policy-makers to consider “Computational Thinking” as an important component of future curriculum design.

The effect of changes in mathematics curriculum in improving students’ reasoning skills and mathematical problem solving

This study aims to describe the effect of changes in mathematics curriculum on mathematical reasoning skills and problem solving for junior high school students in Bima, Indonesia. Curriculum changes in Indonesia are motivated by several factors, including because students still have not been able to maximize the power of reasoning and problem solving so that the previous applied mathematics curriculum is deemed necessary to be refined so that the power of reasoning and solving mathematical problems can be maximized by students. The data in this study were obtained through giving a test to the eighth grade junior high school students in Bima. The evidence of validity of instruments was obtained from an expert judgment in the form of agreement on the feasibility of the each item of instruments. The estimation of reliability of instruments using the Kuder-Richadson formula (KR-20) with the reliability coefficient for reasoning and problem solving instruments are respectively 0.72 and 0.73. The results showed that there were no significant differences in mean scores of mathematical reasoning and problem solving between students of The Previous Mathematics Curriculum group and students of The New Mathematics Curriculum group indicated by the F 0.02 value with a significance value of (p) 0.162 in the two test group MANOVA or there is no effect of changes in mathematics curriculum on students’ reasoning abilities and mathematical problem solving. This study also found that students from both groups obtained the lowest average score on reasoning indicators drawing conclusions, while the lowest average score of the two groups of students in solving mathematical problems was on the aspect of understanding problem information.

Analysing the correlation between secondary mathematics curriculum change and trends in beginning undergraduates’ performance of basic mathematical skills in Ireland

The phenomenon in which students enter university under-prepared for the mathematical demands of their undergraduate courses, regularly referred to as the ‘Maths Problem’, has been widely reported in Ireland, UK, Australia, and the US. This issue has been of particular concern in Ireland recently, with beginning undergraduates’ performance of basic mathematical skills showing signs of significant decline in recent years. New mathematics curricula, commonly referred to as ‘Project Maths’, were gradually introduced into the Irish secondary school education system from 2010 onwards. These new curricula aim to place greater emphasis on student understanding of mathematical concepts, use of contexts, and applications of mathematics. This study analyses, through mathematics diagnostic test data gathered between 2008 and 2014, the change in the basic mathematical skills of beginning undergraduates over the time period in which the new mathematics curricula were introduced to secondary education in Ireland. It was found that students’ basic mathematical skills have declined over the time period during which the new mathematics curricula were introduced. Significant declines in beginning undergraduates’ performance of basic mathematical skills were observed during the period 2008–2014, particularly among students who have achieved Higher Level C grades and Higher Level D grades.

Teachers’ Perceptions of Learners’ Proficiency in Statistical Literacy, Reasoning and Thinking

This paper explores teachers’ perceptions of their learners’ proficiency in statistical literacy, reasoning and thinking. Research in Statistics education has prompted a move away from the teaching of statistical skills, towards focusing on the development of statistical literacy, reasoning and thinking. The recent South African Grade 10–12 Mathematics curriculum change reflects this move. A specific challenge for South Africa is that teachers should understand the new intended outcomes of statistics when assessing learners. The participants (n = 66) included Grade 12 Mathematics teachers (females = 40%) from a district in the Free State, South Africa, selected through convenience sampling. A quantitative research approach was used by administering a 13-item Likert scale questionnaire with the Grade 12 Mathematics teachers. The responses were summarised descriptively as frequencies and percentages. The results indicated that two in three teachers perceived their learners to obtain acceptable proficiency in statistical literacy as defined by the literature. In contrast, only one in three teachers perceived their learners usually or almost always to be proficient in statistical reasoning and statistical thinking as defined by the literature. The findings of this study showed that about half of the Mathematics teachers do not see the connection between the action words in the curriculum, and the aspects of statistical reasoning and statistical thinking to be assessed. The large percentage of teachers uncertain about the proficiency of their learners in statistical reasoning and statistical thinking leads to the conclusion that teachers need to be provided with pre-service or in-service training strengthening their Subject Matter Knowledge and Pedagogical Content Knowledge related to the key intended outcomes of statistics assessment, that is, proficiency in statistical literacy, reasoning and thinking.

Educational change leadership through a new zonal theory lens: Using mathematics curriculum change as the example

This paper outlines actions that educational change leaders can take to better meet their curriculum change obligations and responsibilities. In order to do this we extend Vygotsky’s (1978) zonal theory and its many extensions and elaborations by positioning educational change leadership within this theory. We rename the zones to Zone of Principal Responsibilities, Zone of Principal Support, Zone of Professional Learning, Zone of Teacher Resistance and Zone of Principal Illusion, and we introduce the Zone of Curriculum Change and represent these zones in diagrammatical form. We use our research on mathematics curriculum change in one school as an example of how our new zonal theory lens supports educational change leadership. Our findings illuminate possible actions and reactions of the principal and the teacher that ultimately suggest a way forward for turning around unsuccessful curriculum change. Our new zonal theory provides opportunities for change leaders to reduce teacher resistance with evidence that the action and reaction of the principal and the teacher are not independent of each other but are, in fact, co-constructed.

The Use of Cartoons as a Tool to Support Teacher Ownership of Mathematics Curriculum Change

In South Africa teachers are faced with the introduction of yet another revised curriculum. Higher education institutes are developing programmes to help teachers through the transition. This article describes such an intervention. The research addresses the question: how could mathematical reasoning cartoons be used as a tool to support teacher ownership of curriculum change? The article reports on three action research iterations in which qualified and experienced mathematics teachers are introduced to the use of reasoning cartoons during a short learning programme targeting the development of teachers’ ownership of curriculum change. Rainer and Matthews's ownership of learning framework is adapted and used as a theoretical lens to provide indicators of teachers’ ownership of curriculum change. Data were collected from audio-taped discussions in groups and teachers’ written reflections concerning the introduction of reasoning cartoons, using the tenets of exploratory talk, into their classes. The results indicate that, after the first iteration, where cartoons developed commercially in the UK were introduced, teachers demonstrated that they could move from a didactic to a dialogic environment where spaces were created for all participants to speak and to listen. When cartoon content was drawn from the current South African curriculum, the teachers were able to introduce a largely teacher-centred approach to implementing the curriculum. However, it was only when the teachers took ownership of their own cartoon construction that they manifested the majority of indicators of ownership of curriculum change. The research suggests that teachers can use a mediating artefact to enable them to embrace curriculum changes imposed from the top down.

Mathematics curriculum change: Parliamentary discussion over the past two decades

This paper explores views of mathematics that have been offered in parliamentary exchanges over the past two decades. It makes connections between the development of mathematics curriculum and the political and ideological arrangements in which curriculum is nested. In tracing how school mathematics debates in parliamentary sessions are set within specific social, cultural and economic contexts, we draw attention to an increasing national drive for competitiveness and to heightened allegations of falling standards.

Cross-national comparisons of mathematics curriculum materials: what might we learn?

In most of the world, there is a broad public interest in cross-national comparisons. Despite the myriad difficulties inherent in such comparisons, and despite the fact that most studies explicitly acknowledge limited generalizability, news media representatives, policy makers, politicians and educators often take the findings at face value as providing solid scientific evidence of the achievement of students in the countries studied. This often leads in turn to superficial commentaries and unhelpful recommendations. Our task as scholars of mathematics education is to demonstrate the nuanced complexity of such comparisons. The papers in this issue of ZDM succeed in this regard. Using a range of scholarly perspectives (mathematical, psychological and socio-cultural), the authors offer many insightful observations regarding curriculum and curriculum materials in East Asian countries (especially China) and the USA, with careful attention to the central role of curriculum in the teaching and learning of mathematics in schools. In this commentary study I discuss a few of these insights and develop one illustrative example of how cross-national comparative analyses such as these could be used to sensibly inform policy discussions related to changes in mathematics curriculum, teaching, or teacher preparation.

The Mathematics Curriculum in The Netherlands: Measuring curricular alignment using TIMSS-99

After a drastic mathematics curriculum change in The Netherlands in 1993, a study on the alignment of intended, implemented, and attained curriculum was carried out using TIMSS-99. For benchmarking, identical instruments were used in a neighboring country (Flanders), and for science. Two innovative methodological features were: (1) the teachers' judgments on concrete items through an item-based instrument, and (2) the use of the partial overlap of the TIMSS test and the Dutch intended mathematics curriculum. Comparing the results, the mathematics curricular alignment in The Netherlands had reached an acceptable level, 6 years after 1993.

Criteria for authentic assessment of mathematics: Understanding success, failure and inequality

The notion of the desirability of authentic assessment has become widespread across many areas of the curriculum and at various levels of education, including higher education (Torrance, 1995). Within mathematics education, there has been considerable international interest in discussing the characteristics of more authentic means of assessment and attempting to design and implement them (see, for example, Niss, 1993a, 1993b; Romberg, 1995). The term authentic, when used in the context of curriculum and assessment, has rich and multiple connotations that are not always distinguished from one another or clearly analysed. Cumming & Maxwell (1999) provide a useful categorisation, identifying and distinguishing four major interpretations of authenticity, each based on different underlying theories of learning: performance and performance assessment; situated learning and situated assessment; complexity of expertise and problem-based assessment; competence and competence-based assessment. Within the mathematics education literature, however, the underlying theory of learning is usually left implicit and the term authentic is used as if it were unambiguous. In this paper I intend to explore the meaning of authenticity in relation to recent changes in mathematics curriculum and assessment. In particular, I shall consider the forms that assessment criteria may take and the implications for both individuals and groups of students. The examples I employ relate specifically to the use of ‘open-ended tasks’, introduced in many curriculum reform movements internationally (Pehkonen, 1997). The principles for interrogating the nature of assessment criteria and their implications are, I believe, more generally applicable. At the level of the assessment task itself, authenticity tends to refer to the nature of the mathematical activity involved — but this may be judged according to some idealised version of the nature of mathematics (for example, ‘Mathematics is a creative activity, so authentic tasks should allow space for students to be creative rather than to repeat memorised procedures’), relative to a view of what students will find meaningful, often involving some ‘realistic’ aspect or, according to Cumming & Maxwell (1999), reflecting adult activity. Authenticity is also often considered at the level of the entire assessment system. In this case, it is usually taken to mean that assessment procedures match the aims, content and breadth of the curriculum; the assessment system is thus an authentic representation of the curriculum it is assessing. This aspect of authenticity is often asso

A Role for Technology in Mathematics Education

New technology poses challenges to mathematics educators. How should the mathematics curriculum change to best make use of this new technology? Often computers are used badly, as a sort of electronic flash card, which does not make good use of the capabilities of either the computer or the learner. However, computers can be used to help students develop mathematical habits of mind and construct mathematical ides. The mathematics curriculum must be restructured to include activities that allow students to experiment and build models to help explain mathematical ideas and concepts. Technology can be used most effectively to help students gather data, and test, modify, and reject or accept conjectures as they think about these mathematical concepts and experience mathematical research.

Change in mathematics education since the late 1950's ? Ideas and realisation West Indies

The story of mathematics curriculum change in the countries of the Eastern Caribbean region in recent years is one neither of unblemished success nor of unmitigated gloom. There is now in every island a small cadre of people with adequate training and experience to guide the future development of the mathematics curriculum in their territories. There is also a body of teachers trained in the skills of diagnostic testing, and the writing, production and use of teaching materials appropriate to the deficiencies found in their pupils. There is also a wider variety of commercially-published material available on which those teachers who have acquired skills of curriculum-building can draw. On the other hand, many constraints remain, and those of socio-economic origin are largely outside the power of educators alone to change. For far too many children, mathematics remains a mysterious subject, unquestioningly acknowledged as important, but apparently of little direct relevance to the rest of life. A start has been made, but so much more remains to be done.

Classroom Applications of the Inexpensive Hand-Held Calculator

Are we in the early stages of another revolution in the teaching of mathematics? It certainly seems that the age of the inexpensive, hand-held calculator has arrived. Will your approach to teaching change when almost every student brings a hand-held calculator to class? Will the traditional mathematics curriculum change? It is true that only the passing of time will really determine the answers. Nevertheless, many mathematics educators (if not publicly, then privately) are claiming the hand-held calculator in the classroom will significantly change (and improve) the teaching of mathematics at all levels. In the discussion that follows, a hand-held calculator is used to explore several easy and interesting mathematical topics suitable for beginning college students, particularly students in developmental or beginning algebra courses popular at many community colleges, two year colleges, and large state universities. With appropriate modifications, these ideas could also be presented to students in standard precalculus and beginning calculus courses. The calculations exhibited in this article can be obtained by using the inexpensive Texas Instruments Model 1200 calculator. Similar results can be obtained by using any eight digit, floating decimal calculator with a repeat-multiplication capability, many priced from only 5 to 10 dollars. Other calculators may require different procedures and yield slightly different calculations. Consider the formula for compound interest given by,

Classroom Applications of the Inexpensive Hand-Held Calculator

Are we in the early stages of another revolution in the teaching of mathematics? It certainly seems that the age of the inexpensive, hand-held calculator has arrived. Will your approach to teaching change when almost every student brings a hand-held calculator to class? Will the traditional mathematics curriculum change? It is true that only the passing of time will really determine the answers. Nevertheless, many mathematics educators (if not publicly, then privately) are claiming the hand-held calculator in the classroom will significantly change (and improve) the teaching of mathematics at all levels. In the discussion that follows, a hand-held calculator is used to explore several easy and interesting mathematical topics suitable for beginning college students, particularly students in developmental or beginning algebra courses popular at many community colleges, two year colleges, and large state universities. With appropriate modifications, these ideas could also be presented to students in standard precalculus and beginning calculus courses. The calculations exhibited in this article can be obtained by using the inexpensive Texas Instruments Model 1200 calculator. Similar results can be obtained by using any eight digit, floating decimal calculator with a repeat-multiplication capability, many priced from only 5 to 10 dollars. Other calculators may require different procedures and yield slightly different calculations. Consider the formula for compound interest given by,

Effecting Mathematics Curriculum Change in the Secondary School

Effecting Mathematics Curriculum Change in the Secondary School