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1.
Abstract

In this paper, we describe how we integrated complex analysis into the second semester of a geometry course designed for preservice secondary mathematics teachers. As part of this inquiry-based course, the preservice teachers incorporated their geometric understanding of the arithmetic of complex numbers and complex-valued functions to create a game using Geometer’s Sketchpad. We detail a game created by a pair of preservice teachers that exemplifies their creativity and knowledge of complex-valued functions. Given inquiry-based courses have inherent challenges we also present projects that were not as exemplary.  相似文献   

2.
Abstract

Successful mathematics learning requires the efficient processing of the information that defines the arithmetic tasks. Information processing relates to the ways in which individuals make sense of, or interpret, the information to which they are exposed.

The present study examines four aspects of information processing and their relationship for whole number computation for third and fifth grade students. The aspects included students’ ability to (1) manipulate numerals, (2) encode number sentences , (3) recognise order among numbers and (4) perform an arithmetic procedure.

Information processing in each area correlated with computational skill. At risk students were less efficient in their information processing. As well, the complexity of the numerical information affected how well the students could use it. The more complex the numerical information was, the greater the load it placed on the learner. The implications for diagnosing low mathematics achievement are discussed.  相似文献   

3.
Abstract

Impulsivity is an important and co‐determining factor in the arising of learning difficulties. Impulsive children make many mistakes in arithmetic because of inattention and because they don't use the selfcontrol necessary to correct possible mistakes. In this investigation we examine whether a self‐instructional training program, applied in the teaching of arithmetic, has influences on the impulsivity (measured with help of the MFFT) of pupils who have a quick reaction time and who make many errors. The study involved 52 pupils selected from schools providing special education to children with learning disabilities and educable mentally retarded children. Sixteen of them could be categorized as impulsive children.

The effectiveness of the training program is statistically investigated by means of t‐tests for correlated samples. The results show that training with a self‐instruction strategy can be effectively employed in teaching addition and substraction to educable mentally retarded and learning disabled children with arithmetic deficits. Besides, the impulsive children show after the training a more reflective cognitive style when compared to their cognitive style before the training was started.  相似文献   

4.
John P. D’Angelo 《PRIMUS》2017,27(8-9):778-791
Abstract

We offer many specific detailed examples, several of which are new, that instructors can use (in lecture or as student projects) to revitalize the role of complex variables throughout the curriculum. We conclude with three primary recommendations: revise the syllabus of Calculus II to allow early introductions of complex numbers and linear algebra, include complex variables and some infinite-dimensional linear maps in linear algebra courses, and spice up complex variable courses by better connecting them with the mathematics used in engineering in physics.  相似文献   

5.
ABSTRACT

While the use of numbers in governance has a long history, the kinds of numbers we now produce enable a range of new possibilities for monitoring, regulation and policy decision-making. Global policy actors are now calling for a steep increase in investment in education data. The growing trust in numbers has been critiqued by education policy scholars and social scientists, who have pointed to the reductionist nature of numbers and the dangerous decontextualisation of information which are leading to detrimental policies. The entry of big data poses even more complex epistemological and ontological challenges, many of which we do not fully understand as yet. This paper acknowledges these challenges, and at the same time speculates that big data might afford unique possibilities for new relational theories that may lead to better policy decision-making.  相似文献   

6.
Abstract

The present study examined phonological processing skills (phonological memory, phonological awareness, and rapid automatised naming, RAN) in relation to early Chinese reading and early Chinese mathematics for young children. Early Chinese reading was assessed with single character reading and multi-character word reading, and early mathematics was assessed with procedural arithmetic and arithmetic story problems. Among 86 Chinese kindergarteners, phonological processing skills explained 20% of the variance in character reading and 28% of the variance in word reading; they accounted for 8% of the variance in arithmetic and 11% of the variance in story problem performance. Specifically, findings further highlight the general importance of phonological awareness in early Chinese single character reading, word reading, simple arithmetic and story problems, and the specific role of RAN in single character reading and simple arithmetic.
  • Highlights

  • Phonological awareness and rapid automatised naming explained unique variance in Chinese single character reading and procedural arithmetic.

  • Only phonological awareness significantly accounted for unique variance in Chinese word reading and arithmetic story problems.

  • The associations of phonological awareness with procedural arithmetic and arithmetic story problem were maintained even beyond other variables.

  相似文献   

7.
Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The integrated theory of numerical development posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of the magnitudes to which they refer, and this magnitude understanding is central to general mathematical competence. We investigated relations among fraction magnitude understanding, arithmetic and general mathematical abilities in countries differing in educational practices: U.S., China and Belgium. Despite country-specific differences in absolute level of fraction knowledge, 6th and 8th graders' fraction magnitude understanding was positively related to their general mathematical achievement in all countries, and this relation remained significant after controlling for fraction arithmetic knowledge in almost all combinations of country and age group. These findings suggest that instructional interventions should target learners' interpretation of fractions as magnitudes, e.g., by practicing translating fractions into positions on number lines.  相似文献   

8.
Abstract

In recent years there has been sustained emphasis in many countries on preparing academic staff for their teaching role. However, the necessary emphasis on teaching has distracted attention from the fact that university teachers are facing many other complex demands. University teachers are being appointed from a greater range of backgrounds and types of experience and performing an increasingly diverse range of roles. Moreover, while the emphasis has tended to be on the needs of full‐time tenurable staff, the numbers of casual and contract staff have grown. While much has been achieved, staff development provision is not coordinated, resources are not necessarily provided, centralized schemes do not link with departmental activities and responsibilities are often ambiguous.

The paper identifies some of the influences on preparation for academic roles being faced today and argues that new frameworks are needed. It suggests that a holistic view should be adopted: one which places as central the staff members and their roles, and which emphasizes negotiation and flexibility in response to the diversity of academic activities. The paper outlines the dimensions of such an approach.  相似文献   

9.

The financial constraints imposed upon local government over the past decade have forced many authorities to make savings rapidly and in conditions of considerable uncertainty. Education, as the largest spender and with falling pupil numbers, has often provided the bulk of these savings. In many authorities these have been made in an unplanned, piecemeal fashion and have seriously damaged the service. This paper considers the possibility of a ‘cuts culture’ in which continuing contraction is planned for as part of corporate policy. It raises important questions about the nature of schooling, the relationship between schools and the community and control over the financing of education. It suggests that a case might be made for substantial change, but not unbridled, insensitive reform. The importance of defending, as well as reforming the system is stressed, and the organizational implications of this are considered.  相似文献   

10.
Summaries

English

The concept of a mathematical function is applied widely in science to describe phenomena in which time, frequency, distance, temperature, and other continuous variables depend on one another. Two tasks were designed to test students’ conceptualization of such relations. Each task involved one independent and one dependent variable in a real‐world context (bacterial growth, spacecraft design). Information about the function was provided in the form of a table of paired values that exhibited a clear non‐linearity. The almost 400 subjects, ranging in age from 11 to 18 years, were required to make interpolations between the given values and to explain their procedure. A brief demonstration of graphical curvilinear interpolation was given between the presentation of the two tasks.

Student responses were classified into four categories according to the method of interpolation: curvilinear, combined curvi‐ and rectilinear, rectilinear, and intuitive (estimates, guesses, unsystematic or erroneous calculations). Most of the youngest subjects used the intuitive approach, while most of the older subjects used the rectilinear approach (either in the form of arithmetic averaging or straight lines on a graph). Only a small percentage of the subjects used curvilinear interpolation, considered to be the most appropriate procedure. The numbers of students using a systematic interpolation procedure was increased modestly by the demonstration. Interviews of some students revealed that many were imitating procedures they had seen in their classes, but they did not understand the reasons behind these procedures.  相似文献   

11.
V. Rajaraman 《Resonance》2016,21(1):11-30
Floating point numbers are an important data type in computation which is used extensively. Yet, many users do not know the standard which is used in almost all computer hardware to store and process these. In this article, we explain the standards evolved by The Institute of Electrical and Electronic Engineers in 1985 and augmented in 2008 to represent floating point numbers and process them. This standard is now used by all computer manufacturers while designing floating point arithmetic units so that programs are portable among computers.  相似文献   

12.
Robert Sachs 《PRIMUS》2017,27(8-9):845-855
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13.
Abstract

Background: International large-scale assessments (ILSAs) are a much-debated phenomenon in education. Increasingly, their outcomes attract considerable media attention and influence educational policies in many jurisdictions worldwide. The relevance, uses and consequences of these assessments are often the focus of research scrutiny. Whilst some argue that the assessment outcomes provide an effective basis for informed policy-making, critics claim that the use of international assessment data can result in a range of unintended consequences, such as the shaping and governing of school systems ‘by numbers’.

Purpose: This article explores and analyses the arguments about the uses and consequences of ILSAs. In particular, the discourse about the assessments’ consequential validity will be discussed and evaluated.

Sources of evidence: Literature relating to the uses and consequences of large-scale assessment was analysed, with a focus on research on the consequential aspects of validity.

Main argument: Much research suggests that ILSAs have unintended consequences that affect and influence educational policy. However, the influences on educational policy are complex and interwoven: for example, it is not clear-cut whether effects such as converging curricular are, necessarily, direct consequences of large-scale assessments. Further, it is suggested that a beneficial consequence of large-scale assessment is the infrastructure they provide for studies in the social sciences, although caution must be applied to causal claims, in particular because of the cross-sectional design of the assessments.

Conclusions: The considerable literature discussing the uses and consequences of large-scale assessments tends to point out potential negative aspects of the studies. However, it is also apparent that large-scale international assessments can be a valuable resource for studying global trends and evolving systems in education. Despite the extensive debates around large-scale assessment outcomes both in the media and in educational policy arenas, empirical educational research all too often appears underused in the discussion.  相似文献   

14.
In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number “1”, dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823–1891), “God made the integers; all else is the work of man,” has spawned a lively modern philosophical discussion, and this discussion begins by trying to get a philosophical handle on “1.” This approach remains under heavy discussion, and is more-or-less unresolved (Frege in Die Grundlagen der Arithmetik (English: The foundations of arithmetic). Polhman, 1884). In this note, we consider the many facets of “one” in it many guises and applications. Nonetheless, “one” has multiple meanings, from the very practical to the abstract, from mathematics to science to basically everything. We examine here a mere slice of mathematical history with a focus on the most basic and applicable concept therein. It troubles many, particularly students, even today.  相似文献   

15.
BackgroundEven experienced teachers make inconsistent classroom decisions in unexpected situations. From the cognitive load theory perspective, the effective handling of the novel, unexpected events by teachers depends on the cognitive load of the task, the teaching context in which the unexpectedness appears, and the available cognitive capacity.AimsTeachers’ reactions to unexpected mathematical events, in particular the unexpectedness of the arithmetic calculation, was modeled, investigated experimentally, and explained within the theoretical framework of cognitive load theory.Sample64 mathematics teacher trainees took part in the experiment.MethodsIn a dual-task arrangement, participants verified alternative answers to simple mathematical questions while memorizing task-irrelevant information. The answers represented low (schematic good responses), and high (unexpected good responses) processing load conditions, and control condition (incorrect responses). The memory load was low or high representing levels of extraneous load. The participants’ cognitive capacity was estimated by a complex working memory span task.ResultsThe verification of unexpected but correct answers was slow and more error-prone as compared with the processing speed and accuracy of schematic answers, presumably due to elevated processing (intrinsic) load. The increase in memory load resulted in slower and more inaccurate verifications. However, working memory capacity was found to mediate the extraneous load effect.ConclusionsThe results stress the importance of well-organized schemas for effective reactions to unexpected classroom events. Furthermore, it highlights the importance of accurately understanding and being aware of the impact of cognitive load on teachers to improve teaching practice.  相似文献   

16.
Abstract

The technique for creating diagnostic tutors for arithmetic has been established for over a decade, but progress towards the creation of an educationally viable system has been disappointingly slow. The SUMIT intelligent teaching assistant (ITA) for arithmetic was designed explicitly to meet the requirements of classroom arithmetic teaching. Unlike earlier arithmetic tutors, SUMIT is intended to function as a teacher's assistant, rather than a surrogate teacher. It is fully interactive and is able to give adaptive help, diagnose misconceptions, generate graded sequences of sums, and summarize or replay whole user sessions for each of the “four rules of number.” This article outlines the design philosophy and the system architecture of the SUMIT system, and it reports a range of empirical studies of the type, incidence, and diagnosis of “bugs” for each operation, together with a series of evaluation studies of the classroom effectiveness of the system. It is concluded that construction of ITAs may provide cost‐effective and valuable educational resources.  相似文献   

17.
ABSTRACT

Over a number of years, universities have needed to become more adept at managing change as internal and external factors affect their longer term financial sustainability. That sustainability is, for many institutions, closely linked to how straightforward (or otherwise) it is to recruit student numbers of the right quality from often diverse markets. However, the scale of a university's financial challenge isn't always enough on its own to dictate how bravely an institution drives its change agenda, nor the nature and pace of change.  相似文献   

18.
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19.
One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs.  相似文献   

20.
Abstract

In this article, two intervention studies are described that were set up to investigate whether encouraging elementary students to generate drawings of arithmetic word problems facilitates problem-solving performance. The interventions consisted of 60 to 90 min of practice and showed the usefulness of self-generated drawings for solving word problems. The subjects in the first study were first and second graders, and in the second study, fifth graders. The results indicated that the fifth graders improved problem solutions after the intervention, whereas the first and second graders did not. Unlike the first and second graders, the fifth graders generated lots of drawings of word problems. The findings suggest that the nature of the difficulties children experience when solving arithmetic word problems influences their decision to generate drawings.  相似文献   

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