Approaches to Study and the Quality of Learning. Some Empirical Evidence from Engineering Education

In the late 1990s failure rates in a first-year introductory calculus course at the Norwegian University of Science and Technology reached peak levels. This paper reports on findings from an action research project that was set up in 2002/2003 to improve the situation. The study confirms that students approach their tasks differently which contributes to qualitatively different learning outcomes. Furthermore, patterns of achievement in mathematics and physics in secondary education keep reoccurring in the calculus course, even though the teaching and learning contexts are different. The paper does not provide any definite answer as to why groups of students get involved in distinctly different learning processes, and it will take further research to decide the nature of commitment to the learning tasks. However, inspired by the notion of ‘practices’ this paper raises a discussion about the role of intentionality in learning processes. When doing mathematics, students are also in a process of being engaged in and developing a practice. It is a major challenge for academic staff to contribute to communities of practice that are conducive to learning.     

Measuring students’ transition into university and its association with learning outcomes

Previously we showed how we measured pedagogy and revealed its association with learning outcomes of sixth‐form college mathematics students. In this project we followed a similar approach to the study of university transition. We particularly sought to identify the students’ perceptions of the transitional experience, and measure the association with learning outcomes. We drew on longitudinal surveys of students entering different programmes in five universities. Following them into their first year or so, allowed us to track their ‘disposition to complete the course’ and their ‘disposition to study more mathematics’, inter alia. We developed and validated two ‘fit‐for‐purpose’ measures of students’ perception of their transition, one we call ‘perception of the transitional gap/jump’ and one we call ‘degree of positive feeling about the transition’. We report some statistically and educationally significant associations between these and the students’ developing dispositions, and discuss the prospects for this approach to studying transition.     

Not Your Usual Maths Course: critical mathematics education for adults

This article describes an action research project that investigated which features of critical theory were useful for teaching everyday mathematics in an evening course for adults. Paulo Freire's philosophy of education and Jürgen Habermas’ theory of knowledge interests are among the main influences on exponents of critical mathematics education such as Ole Skovsmose and Marilyn Frankenstein. Through the use of dialogical processes and critical reflection, students engage in social and political issues in their lives or communities and, as a result of their increased consciousness and mathematical learning, take “transforming action”. This study highlights the value of learning in a positive environment, through dialogical processes and critical questioning. Participants of the study were able to overcome barriers to learning mathematics; engage in everyday issues involving mathematics; and make changes to the way they dealt with mathematics, as a result of increased critical consciousness.     

华罗庚的数学“双基”教学思想及其启示

华罗庚在几十年学习、研究、教授、普及数学和指导师生数学教与学中形成的数学教育思想是珍贵的财富,对于研究中国数学教育的优良传统和开展数学课程改革都具有重要的指导意义.华罗庚认为,数学教学的基本要义是让学生在打好"双基"中走向创造,为此,数学教学要重视"双基"教学,使学生对"双基"达到"懂"、"识"、"熟",并通过自学、独立思考、历经成功和失败、加强训练等"双基"教学方式使学生在打好"双基"中学会创造.     

Explaining Student Achievement: the Influence of Teachers’ Pedagogical Content Knowledge in Statistics

Statistics is an increasingly important component of the mathematics curriculum. StatSmart was a project intended to influence middle-years students’ learning outcomes in statistics through the provision of appropriate professional learning opportunities and technology to teachers. Participating students in grade 5/6 to grade 9 undertook three tests, a pre-test, a post-test and a longitudinal retention test over a period of 2 years. Their teachers completed a survey that included items measuring pedagogical content knowledge (PCK) for teaching statistics. Despite the development of valid instruments to measure both student and teacher content knowledge and teachers’ PCK, linking teachers’ knowledge directly to students’ learning outcomes has proved elusive. Multilevel modelling of results from 789 students for whom there were 3 completed tests and measures from their teachers indicated that students’ outcomes were influenced positively by their initial teacher’s PCK. Extended participation of teachers in the project also appeared to reduce negative effects of changing teachers.     

让学生学会做数学——课改下的数学教学新理念

新课标要求数学教学要让学生学会“做数学”,做数学”的目的最终是要让学生学会“数学化”。“做数学”的实质是把重点从“教”转向“学”,从教师的行为转向学生的活动,并且从感觉效应转向活动效应,使学生在数学的活动中感知数学、认识数学、体验数学和应用数学。     

Students’ and teachers’ perceptions of classroom learning environment in Bhutanese eighth-grade mathematics classes

This paper reports a study of students’ and teachers’ perceptions of their classroom learning environment in Bhutanese eighth-grade mathematics classes. Research suggests that positive perceptions of the learning environment can have a positive influence on students’ learning outcomes, interest and engagement in classroom activities. The study was conducted in 2013, using the survey samples of 608 students and 98 teachers from 22 lower- and middle-secondary schools in western Bhutan. Students’ and teachers’ perceptions of the classroom environment were measured using the Mathematics Classroom Learning Environment Survey (MCLES). Students and teachers mostly perceived their classroom environments favourably on the MCLES scales irrespective of gender, school level and school location. The study is significant for understanding and evaluating the implementation of new mathematics curriculum in Bhutanese schools because it could guide the development of strategies for more-productive mathematics classroom learning. It is also significant from the perspective of Bhutan’s national goal of Gross National Happiness because perceptions and happiness always go hand-in-hand.     

Analysis of STEM Activities in Primary Students’ Science Projects in an Informal Learning Environment

This study adopted a researcher-generated framework to analyze STEM activities demonstrated in primary students’ science projects in an annual extracurricular event held in Hong Kong. Ten students’ project reports were randomly selected from each of the three groups of 24 outstanding, 45 merit, and 68 consolation awarded projects. Content analysis was conducted to code the activities in each project. The coded information was then changed into numerical data for quantitative analysis. The results showed that, in general, more engineering and science activities than technology and mathematics activities were adopted by the primary students in their projects. More projects with the Outstanding Award conducted STEM activities than those projects with Merit and Consolation Awards, and significant group differences existed in the science and mathematics activities. Besides, science activities significantly positively related to engineering and mathematics activities. Furthermore, STEM-related content knowledge of discipline core ideas and crosscutting concepts were reported. This study sheds light on the pattern of STEM activities in students’ science projects, and has implications for promoting STEM integration in primary education.     

Decision Making and Sources of Knowledge: How Students Tackle Integrated Tasks in Science,Technology and Mathematics

This article reports on students' decision making processes and sources of knowledge in an integrated teaching and learning setting. The study was conducted in a Year 9 classroom as students undertook a 10-week solar-powered boat project and were exposed to related concepts from science, technology and mathematics. Data collection involved detailed case studies of three pairs of students, interviews, classroom observation and analysis of the artefacts and portfolios produced by the students. Students were found to access knowledge from a variety of sources, including teacher's notes from formal instruction, informal interactions with the teacher, observation of and interaction with other students, as well as sources outside the classroom. However, the utility of the knowledge sources was influenced by the nature of the task. When students were performing open-ended tasks, they drew on a wider variety of knowledge sources than when they were performing less open tasks. Moreover, subject discipline-based sources often were not as helpful in solving open tasks. The study leads to several important implications for designing teaching and learning in integrated curriculum settings.     

Teachers’ views of the challenges of teaching grade 9 applied mathematics in Toronto schools

Mathematics teachers, mathematics department heads, curriculum leaders, and administrators from 11 schools in four school boards from Toronto, Ontario, Canada, participated in a project to improve the teaching and learning in grade 9 mathematics classrooms. In each of these schools, an implementation team was created, so that at least three teachers from every school could collaborate, in order to improve learning outcomes of their students. This article reports on the challenges identified by teachers when they taught grade 9 applied mathematics. Teachers’ views of challenges fell into five main layers: (a) teacher professional development and pedagogical skills, (b) student learning needs, (c) settlement issues and families’ social and economic background, (d) administrative difficulties and resources, and (e) curricular issues. These challenges were complex and interconnected, demanding special remedial efforts by the administration and teachers. By reflecting on the challenges and practices, these teachers made a long-term strategy to engage in professional development activities to better understand their students’ learning needs and to improve their achievement in provincial tests.     

Outcomes of synergetic peer assessment: first-year experience

Active participation in learning activities and reviewing assessment activity can facilitate learners engaged in these processes. This case study reports student experiences of the process of peer assessment with teacher guidance in a group project for a first-year nursing course with 153 students. Twenty groups of students were assigned roles in exploring one of the two scenarios: one involved analysing diabetes mellitus and the other considered colorectal carcinoma, in each case covering provision of acute nursing care in hospitals and preparing health promotion strategies in a community. Each group also provided comments to the group that worked on the other scenario, based on prearranged assessment criteria. After receiving comments from their peer group, each group was then allowed to revise their drafts prior to final submission. The teacher’s input would be offered, if the peer feedback was inaccurate or insufficient. A survey was conducted to explore the learning experiences, and three semi-structured focus group interviews were conducted to triangulate findings with the survey. The first-year students expressed the need for both peer feedback and the lecturer’s direct guidance.     

The teacher shaping and creating dialogues in project work

The background of the work presented in this article is that for quite some time project work has been a method of working that is more theoretically described than it is put into practice. The aim of this text is to show how a teacher can function as a facilitator or a guide for the students within project‐directed teaching and how this setting can enhance the students’ learning. A qualitative method with a focus on dialogues in the classroom was used in the inquiry process. In this article a dialogue between the students in the realization phase of the work is analysed in depth to illustrate how student interaction framed by project work can enhance the students’ learning. In the study Dewey’s, Vygotsky’s and Bakhtin’s theories are used as a theoretical framework and the activity system is used to visualize the work processes in their intertwined context. The outcome of the study shows that learning is inherent in language, but concludes that it demands a great deal of the teacher to create such learning situations.     

Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases

As part of a larger research project aimed at transforming preK-8 mathematics teacher preparation, the purpose of this study was to examine the extent to which prospective teachers notice children’s competencies related to children’s mathematical thinking, and children’s community, cultural, and linguistic funds of knowledge or what we refer to as children’s multiple mathematical knowledge bases. Teachers’ noticing supports students’ learning in deep and meaningful ways. Researchers designed and enacted a video analysis activity with prospective teachers in their mathematics methods course. The activity served as a decomposition of practice in order to support prospective teachers in engaging in an approximation of the practice of noticing. Our findings showed that prospective teachers evidenced noticing of mathematics teaching and learning as early as the mathematics methods course. We also found that the prompts and structure of the activity supported prospective teachers by increasing their depth of noticing and their foci in noticing, moving from attending primarily to teacher moves (and merely describing what they saw) to becoming aware of significant interactions (and interpreting effects of these interactions on learning). Implications for teacher educators interested in designing and enacting activities to support noticing are discussed.     

Young students’ aesthetic experiences and meaning-making processes in an outdoor environmental school practice

This study uses John Dewey’s theoretical concept of ‘aesthetic experience’ in empirically exploring expressions of cognition and emotion in students’ meaning-making processes. A case study was conducted in one class of Grade 6 students during a single school semester. This article reports results from five outdoor days. The empirical material consists of observations, field notes, logbook entries, interviews and students’ written reflections. The students’ meaning-making processes were analyzed through the Deweyan theory of an initial phase involving anticipation, an activity phase with courses of actions and a concluding phase with reflections that serve as fulfillments. Expressions of aesthetic experience were identified in four important components of the students’ meaning-making processes: prior personal experiences; responses to environments and artifacts; social interaction; and situations allowing for responsibility, trust and independence. A more in-depth process-oriented analysis revealed that aesthetic experiences are vital in continuous meaning-making processes.     

Motivational and affective determinants of self-regulatory strategy use in elementary school mathematics

The aim of the study was to investigate the relationships between elementary students’ reported use of self-regulatory strategies in mathematics and their motivational and affective determinants. Participants of the study were 344 fifth- and sixth-grade Greek students. Students were asked to complete self-reported measures regarding the strategies they use to self-regulate mathematics learning, their achievement goals in relation to mathematics, their self-efficacy concerning mathematics learning and achievement, the value they attribute to mathematics as a subject domain and their enjoyment of mathematics learning. Structural equation modelling confirmed a mediation model, that is, students’ mathematics self-efficacy, value beliefs about mathematics and enjoyment mediated the effects of achievement goals on reported strategy use. Results are discussed in terms of implications for elementary students’ self-regulated learning skills.     

Parental guidance of young children’s mathematics and scientific inquiry in games,cooking, and nature activities

ABSTRACT

This study investigated the influence of guidance instruction and type of activity on parental guidance of young children’s mathematics and scientific inquiry during cooking, games, and nature activities at home. Thirty families participated with their preschool-aged child; half were randomly assigned to an inquiry guidance instruction group and encouraged to support children’s reasoning with open-ended prompts and questions. Families participated in activities for one month, some of which they audio-recorded. Families engaged in processes of comparing, predicting, evaluating and concluding more often after inquiry guidance instruction, and incorporated inquiry processes into all activity types. Mathematics was most frequently observed in games and cooking. The results suggest that parents can use inquiry guidance to support preschoolers’ mathematics and scientific inquiry in a variety of activities performed at home. As children engage in inquiry-based learning during co-constructed activities with parents, they develop conceptual understanding of mathematics and scientific inquiry in a positive social context.     

Parallel Structures of Computer-Assisted Signature Pedagogy: The Case of Integrated Spreadsheets

This article was motivated by the authors’ work on a project with a group of 2nd-grade students in a computer lab of a rural school in upstate New York. From this project, one goal of which was to provide a capstone experience for a teacher candidate in teaching application-oriented mathematics with technology, the ideas about parallel structures of two universes—the teacher's and the students’—that echo Shulman's structures of signature pedagogy have been developed. In the article the authors introduce the notion of computer-assisted signature pedagogy and explore its features through the combined lens of teaching and learning using the concept of Type I/Type II technology integration.     

Developmental Math Pilot: Massive Open Online Course (MOOC), Psychology Concepts,and Group Work

Researchers observed their students’ frequent choices to use technology and the students' weak developmental math course completion rates. These observations piqued researchers' interest to find a new approach to improve students’ math learning—utilizing disruptive innovation. The purpose of this study was to understand students’ perceptions about learning developmental math with a Massive Open Online Course (MOOC) and face-to-face group activities interwoven with psychology of learning concepts. Research findings suggest that MOOCs used in developmental math coursework can improve math success, and group work within face-to-face classrooms can increase connectivity to learning. A MOOC was merged with face-to-face psychology of learning group projects, and students described increased connectivity to their learning. For example, Haley exclaimed, “So definitely learned how to learn all over again this semester and I’m doing awesome … It’s like I’m breezing through!”     

Factors influencing early adolescents’ mathematics achievement: High-quality teaching rather than relationships

This study used data from the Assessment Tools for Teaching and Learning project, which involved data on the academic performance of more than 90,000 New Zealand students in six subjects (i.e. reading, writing and mathematics in two languages). Two sub-samples of this dataset were included for detailed re-analysis to test the general applicability of the Australian model of Quality of School Life (Ainley et al. 1986) in the New Zealand context. The first sample comprised 336 year 8 students from elementary schools and the second sample consisted of 272 year 10 students from high schools. Furthermore, two structural equation models were developed and tested, expressing relationships between students’ quality of school life perceptions, students’ attitudes to mathematics, and their effects on mathematics achievement. The quality of school life questionnaires scales [Ainley and Bourke, in Res Pap Educ 7(2):107–128, 1992] were used as indicators of students’ perceptions regarding learning, teachers and peer relationships. The model proposed that perceived quality of school life would affect students’ attitudes of liking and confidence in mathematics, which would in turn affect their academic performance. After controlling for other variables in the model, students’ perception about their self-efficacy to learn mathematics was more directly related to outcomes than to perceptions of teacher quality or peer involvement. Data analyses revealed no apparent relationships of these factors to mathematics achievement. Moreover, results for both samples led to the conclusion that the perceived quality of learning is connected with ‘confidence in’ and ‘liking mathematics’, which in turn predict students’ mathematics achievement.     

Role of teacher characteristics and school resources in early mathematics learning

The authors investigated the degree to which school-level teacher characteristics and resources are related to the mathematics learning of kindergarten children using a sample drawn from a large US database. Kindergarten-level teacher characteristics were operationalised as collective teacher efficacy, teacher experience and teacher preparation; kindergarten resources were operationalised as efforts that schools make to reach out to parents, classrooms with mathematics manipulatives, and classroom technology. Kindergarten students learned more in mathematics over a year in schools where teachers’ collective efficacy was high. School resources yielded a range of significant yet mixed results in young children’s mathematics achievement. Notably, younger students and students entering kindergarten with lower levels of mathematical skills benefited greatly from classroom resources. Overall, the presence of classroom technology as a school-level resource was positively related with older kindergarten students’ learning. Based upon the findings, organisational and policy implications are discussed.