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Interdisciplinary Learning: Development of Mathematical Confidence, Value, and the Interconnectedness of Mathematics Scales
Abstract
This paper describes the process of developing a survey instrument aimed at measuring aspects of mathematical confidence, value, and the interconnectedness of mathematics as part of a larger study investigating the thinking processes and attitudes towards mathematics of Singaporean secondary school students (aged 12-14) during interdisciplinary learning. Results from exploratory and confirmatory factor analyses on scale items tested revealed six scales with sound validity and reliability properties. The scales are intended for measuring attitudes towards mathematics particularly during interdisciplinary education.
... This is the value of mathematics. Ng and Stillman (2007) describe that value of mathematics as well as mathematical confidence, and the interconnectedness of mathematics are three affective domains directly associated with interdisciplinary learning involving mathematics. They measure the value of mathematics by looking at the perceived usefulness of mathematics by students, i.e. current relevance, usefulness for further education or society. ...
We describe what Research Experiences for Undergraduates (REU) Fellows reported regarding their experiences within a research-intensive programme in STEM Education. Our study employed a mixed methods approach. Quantitative data included a survey by Kardash (2000) to examine Fellows’ research expectations, familiarity with literature, and ability to conduct statistical analyses pre and post the interdisciplinary STEM Education programme. We also analysed qualitative data from the Fellows’ pre-, mid-, and post-evaluation interviews. We discovered significant growth in their confidence levels in studying, conducting, and analysing research (p < 0.001). At the end of their nine- month research experiences, Fellows stated they felt they had gained skills in coding and analysing data, conducting interviews, using technology, writing, and presenting, but most frequently noted their increase of interpersonal collaborations with other future STEM teacher researchers. This research is the first to examine the effectiveness of an academic year interdisciplinary STEM Education REU programme. REU programmes typically are offered two months (8 weeks) between Spring and Autumn semesters and within only one STEM content discipline located in schools of science and engineering, as opposed to education.
... This is the value of mathematics. Ng and Stillman (2007) describe that value of mathematics as well as mathematical confidence, and the interconnectedness of mathematics are three affective domains directly associated with interdisciplinary learning involving mathematics. They measure the value of mathematics by looking at the perceived usefulness of mathematics by students, i.e. current relevance, usefulness for further education or society. ...
To gain insight into ways student’s experiences with mathematics can support them to reach their human potentials, we explored children’s engagement in a collaborative art project. We describe the teacher-developed project and facilitation approaches that supported the exploration. Using a narrative inquiry methodology and artefacts from the experience, we narrate children’s experiences using four dimensions: autonomy, authority, success, and relationships with others. We contend that the children were involved with ideas and peers in ways that resulted in building a positive relationship with mathematics, producing a counter-narrative to one of failure and helplessness typical of mathematics as a discipline. Recommendations for further study focussed on mainly mono-disciplinary contexts are shared.
... This is the value of mathematics. Ng and Stillman (2007) describe that value of mathematics as well as mathematical confidence, and the interconnectedness of mathematics are three affective domains directly associated with interdisciplinary learning involving mathematics. They measure the value of mathematics by looking at the perceived usefulness of mathematics by students, i.e. current relevance, usefulness for further education or society. ...
Since one of the keywords in the interdisciplinary discourse is integration, the aim of the study was to describe the actions of participants that could be considered as part of an integration process involving mathematical and musical discourses. Based on the commognitive perspective developed by Anna Sfard, which argues that communication is a collectively performed patterned activity, here integration is a way to develop a new type of communication. Music and mathematics students participated in an experience, where it was possible to observe how line graphics of random data were interpreted through actions from a musical discourse and how the students developed a new form of communication when talking about chords, which they called “baggies”.
... This is the value of mathematics. Ng and Stillman (2007) describe that value of mathematics as well as mathematical confidence, and the interconnectedness of mathematics are three affective domains directly associated with interdisciplinary learning involving mathematics. They measure the value of mathematics by looking at the perceived usefulness of mathematics by students, i.e. current relevance, usefulness for further education or society. ...
In this chapter, we develop in broad strokes the concept and history of the ‘disciplines’, a prerequisite for understanding disciplinary and interdisciplinary activity, since activity is always mediated by the cultural artefacts history leaves us. We develop the social and cultural theories of activity, practice, and discourse to offer further insights into both academic and professional ‘disciplines’, and their interrelationships, both in the academy, and in practical, joint, ‘interdisciplinary’ activity in everyday, workplace and professional life. The aim is to provide the foundations of a comprehensive theory for researchers of interdisciplinary activity. We build the analysis first of all on classical activity theory and modern developments in this tradition (a) of Vygotsky’s group and their Western interpreters, and (b) of those inspired by Bakhtin who have particularly developed multivoicedness and hybridity in dialogism. We additionally draw on Bourdieu and Foucault to consider the nature of the power structures in the disciplinary fields and discourses respectively, and how they might be resisted. We argue for a new conceptualisation of meta-disciplinary mathematics education that is a requirement of a critical mathematics education, concluding that meta-knowledge of disciplinarity is necessary for negating and becoming, to some extent, free from the discipline. We reflect on the adequacy of this theoretical battery, and its proposed synthesis for researchers in the field.
... This is the value of mathematics. Ng and Stillman (2007) describe that value of mathematics as well as mathematical confidence, and the interconnectedness of mathematics are three affective domains directly associated with interdisciplinary learning involving mathematics. They measure the value of mathematics by looking at the perceived usefulness of mathematics by students, i.e. current relevance, usefulness for further education or society. ...
The purpose of this chapter is to preface, and introduce, the content of this book, but also to help clarify concepts and terms addressed, set the stage by summarising our previous work, and issue some caveats about our limitations. We will close with a discussion of the mathematics in Interdisciplinary Mathematics Education (IdME), which we see as a lacuna in the literature, and even in this book.
... This is the value of mathematics. Ng and Stillman (2007) describe that value of mathematics as well as mathematical confidence, and the interconnectedness of mathematics are three affective domains directly associated with interdisciplinary learning involving mathematics. They measure the value of mathematics by looking at the perceived usefulness of mathematics by students, i.e. current relevance, usefulness for further education or society. ...
This paper attempts to demonstrate that inter-disciplinary mathematics is an old practice, newly rediscovered, and formerly accessible to everyone, but problematised by modern times. Evidence of interdisciplinary mathematics, now often termed STEM, is presented from history and from more recent curriculum documents. Research into the benefits of integrated approaches to STEM education give qualified support to such approaches, and suggests characteristics defining effective interdisciplinary learning. An example of a project-based approach is examined for its contribution to thinking about how inter-disciplinary mathematics might be more generally applied to student learning in Primary and Secondary schools in modern times. Curricular considerations and examples are examined for interdisciplinary possibilities, while some caveats are presented to temper any rush to inter-disciplinarity without due consideration of the consequences.
... This is the value of mathematics. Ng and Stillman (2007) describe that value of mathematics as well as mathematical confidence, and the interconnectedness of mathematics are three affective domains directly associated with interdisciplinary learning involving mathematics. They measure the value of mathematics by looking at the perceived usefulness of mathematics by students, i.e. current relevance, usefulness for further education or society. ...
There are increasing calls for the teaching of STEM within inter-disciplinary settings, as a way of engaging students in authentic tasks and innovation. However there have been concerns raised about the impact of inter-disciplinary curricula on mathematics learning particularly, with a concomitant need to conceptualise how mathematics might productively interact with other disciplines in STEM settings. This chapter explores cases of interdisciplinary STEM activity that arose as part of two major Australian STEM professional learning initiatives. It focuses on the variety of curriculum structures that occurred, the challenges for schools and teachers in implementing such structures, and teacher perceptions of their experiences including student engagement. Cases of inter-disciplinary tasks/investigations are presented to explore the different ways in which mathematics is transacted, and to develop a set of principles that should govern the inclusion of mathematics in inter-disciplinary settings. The cases show evidence of increased engagement and enthusiasm of students for STEM project and investigative work, but indicate the challenge for teachers of generating productive and coherent mathematics learning in inter-disciplinary settings. The results also point to institutional and systemic barriers to the wider take-up of interdisciplinary STEM activities.
... This is the value of mathematics. Ng and Stillman (2007) describe that value of mathematics as well as mathematical confidence, and the interconnectedness of mathematics are three affective domains directly associated with interdisciplinary learning involving mathematics. They measure the value of mathematics by looking at the perceived usefulness of mathematics by students, i.e. current relevance, usefulness for further education or society. ...
Whilst Science, Technology, Engineering and Mathematics (STEM) interdisciplinary teaching and learning in the USA K-12 education still needs greater promotion, middle school students demonstrated that they can, using low-cost, single board computers that promote the teaching of computer science (in this case Raspberry Pis), successfully engage with computer programming of digital images and videos. The context for these students’ engagement was the Advancing Out-of-School Learning in Mathematics and Engineering (AOLME) Project. This chapter describes how the processes of design, model, and implement, supported 40 Latinx middle school students’ development of computational thinking in an out-of-school setting, and how these processes promoted the genuine integrated practice and learning of technology, engineering, and mathematical concepts.
Some findings from an interdisciplinary project work (PW) implemented with Year 7 and 8 students (13–14 years old) from three Singapore schools are reported. These are part of a study examining the impact of PW in terms of its learning outcomes (LO). Of interest are findings associated with LO: the extent to which the PW brings about student-perceived “interconnections” between school disciplines, within mathematics, and between school-based mathematics and real-world problem solving. There was an overall increase in mean scores on the scales measuring perception of interconnectedness of mathematics and inter-subject learning (ISL) and beliefs and efforts at making connections (BEC) after PW. ANOVA showed a significant impact of the PW on ISL but not BEC scores. Qualitative results revealed that these seemingly positive results disguised issues with students’ ability to make the desired interconnections in a meaningful manner.
Gender differences in mathematics learning in the high school serve as a basis for achievement in mathematical disciplines in higher education, as well as in social mobility in Western society. The main findings reported here are that, in the Jewish sector in Israel, even when the level of mathematics is held constant, so that the perceived degree of achievement in mathematics of boys and girls is similar, girls are nevertheless found to report a lower degree of self-confidence in mathematics than boys on a number of different measures. Paradoxically, the educational system in the Arab sector, despite its gender conservatism relative to the general Jewish sector, has succeeded in generating amongst its female students a high degree of perceived achievement and self-confidence in mathematics, which in turn increases their willingness to consider mathematically-based studies and professions in the future.
Any good mathematics teacher would be quick to point out that students’ success or failure in solving a problem often is as much a matter of self-confidence, motivation, perseverance, and many other noncognitive traits, as the mathematical knowledge they possess. Nevertheless, it is safe to say that the overwhelming majority of problem-solving researchers have been content to restrict their investigations to cognitive aspects of performance. Such a restricted posture may be natural for psychologists and artificial intelligence scientists who are concerned primarily with expert systems or machine intelligence, but it simply will not suffice for the study of problem solving in school contexts.
Competence in mathematics has long been identified as a critical skill directly related to educational and occupational choices. Yet compared with men, fewer women elect to take advanced level mathematics courses and to enter mathematically-oriented careers. The present article summarizes the common explanations of this problem and then integrates this research into a theoretical model first proposed by J. E. Parsons et al (in press) for studying students' academic choices and decisions. Drawing on concepts used in decision-making, achievement, and attribution research, this psychological model links academic choice to expectations of success and the subjective value of a particular course. In addition, the model specifies the relations among a set of other variables that are believed to mediate individual differences in both students' expectations of success and their perceptions of the relative value of various academic options. The utility of the model for increasing understanding of course enrollment patterns and career decisions and for designing appropriate intervention strategies is discussed. (3 p ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This paper reports the results of two interventions involving the integrated study of mathematics and technology practice
to girls in Years 6 and 7. The focus of the study was to look at factors that contributed to girls’ disengagement with mathematics
study and seek pedagogical solutions for this. The key mathematics concepts embedded in the two interventions were proportional
reasoning and ratio. A design based research methodology was adopted. The study started with the assumption that by integrating
mathematics study with technology practice students would see the mathematics as authentic and understandable. The results
of the first intervention indicated that a significant proportion of the girls did not develop the hoped for improvement in
perceptions about the value of studying mathematics through technology practice, despite an improvement in their understanding
of proportion and ratio. These results informed the second intervention in which modified tasks and pedagogy were implemented.
The results of the second intervention were similar in terms of cognitive outcomes. However, when students were given explicit
scaffolding in “within” and “beyond” the domain of mathematics integration as well as tasks that they considered authentic,
student perceptions of mathematics study improved.
This study is a description of a high school mathematical curriculum designed to implement the National Council of Teachers of Mathematics Standards. The curriculum is teacher written, application based, uses technology where appropriate, has students working in groups, and incorporates open-ended problem solving. For one year, twenty-two classrooms of mainly ninth-grade students studied this new curriculum. Students took a pre- and post-treatment attitude questionnaire, PSAT examination, and an authors written open-ended end-of-the-year assessment. A control group of six classes of ninth-grade students also took the PSAT and the open-ended End-of-Year Tasks. Paired t-tests found significant attitude improvement in experimental students' mathematical confidence. Analysis of variance (ANOVA) found no significant differences between experimental and control classes on the PSAT. Multivariate ANOVA found significant differences on the end-of-the-year test favoring experimental classes. These results suggest that a Standards-based curriculum can improve students' mathematics attitude and problem-solving skills.
This article examines the idea that perceived self‐efficacy is an important variable in understanding achievement behavior. Self‐efficacy refers to personal judgments of one's capability to organize and implement behaviors in specific situations. Students gain information about their level of self‐efficacy from self‐performances, vicarious experiences, verbal persuasion, and physiological indices. In forming efficacy judgments, people take into account factors such as perceived ability, task difficulty, effort expenditure, performance aids, and outcome patterns. Even when students acquire efficacy information from self‐performances, efficacy judgments are not mere reflections of those performances because educational practices differ in the type of information they convey about students’ capabilities. Some experimental tests of these ideas are summarized along with their educational implications. The self‐efficacy framework is compared with locus of control, attribution, and self‐worth theories of achievement behavior.
A number of national science and mathematics education professional associations, and recently technology education associations, are united in their support for the integration of science and mathematics teaching and learning. The purpose of this historical analysis is two-fold: (a) to survey the nature and number of documents related to integrated science and mathematics education published from 1901 through 2001 and (b) to compare the nature and number of integrated science and mathematics documents published from 1990 through 2001 to the previous 89 years (1901–1989). Based upon this historical analysis, three conclusions have emerged. First, national and state standards in science and mathematics education have resulted in greater attention to integrated science and mathematics education, particularly in the area of teacher education, as evidenced by the proliferation of documents on this topic published from 1901–2001. Second, the historical comparison between the time periods of 1901–1989 versus 1990–2001 reveals a grade-level shift in integrated instructional documents. Middle school science continues to be highlighted in integrated instructional documents, but surprisingly, a greater emphasis upon secondary mathematics and science education is apparent in the integration literature published from 1990–2001. Third, although several theoretical integration models have been posited in the literature published from 1990–2001, more empirical research grounded in these theoretical models is clearly needed in the 21st century.
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