Distributive law as object of learning through direct and inverse tasks

2017 ◽  
Vol 6 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Lucian Olteanu
Keyword(s):  
Teaching And Learning ◽  
Design Research ◽  
Variation Theory ◽  
Educational Design ◽  
Content Type ◽  
Algebraic Expressions ◽  
Distributive Law ◽  
Asking Questions ◽  
Similarity And Difference ◽  
The Relationship

Purpose The purpose of this paper is to report how the use of a direct and an inverse task gave students an opportunity to discern the structure of a distributive law that they could apply to expand or to factorise algebraic expressions. The paper discusses a teaching sequence (of about 40 minutes) in a Grade 8 (14-15 year-olds) algebra class and it focusses on how the use of inverse tasks opens the dimension of variation. For instance, if the distributive law has always been used as a(b+c), factorising the expressions ab+ac means opening up the dimension of distributive law. The analysis showed that two central processes, transformation and variation, improved communication in the classroom. Design/methodology/approach The data used come from a longitudinal study conducted in Sweden. The methodology is grounded in educational design research. Two secondary school teachers conducted a lesson with variation theory as a guiding principle, supervised by a researcher. The relationship between teaching and learning was analysed in the enacted object of learning. The critical aspect for students’ learning was identified by asking questions to probe the students’ understanding. Findings The use of a direct and an inverse task gave the students an understanding of the structure of the distributive law that they could apply to expand or to factorise algebraic expressions. The teacher opened up a dimension of variation by similarity that gave the students the opportunity to discern the commonality in direct and inverse tasks as well as to relate the direct and inverse tasks to each other. Without an identification of similarity that might help students to compare underlying meanings, or to match one representation to another, students may not experience variations because there is not concordance among the relationships between the representations. Research limitations/implications Teachers can produce new knowledge as well as communicate successfully in the classroom when creating teaching activities that promote the discernment of similarity and difference that might help students to compare underlying meanings, or to match one representation to another. Practical implications The study represents an example of research which has the aim of improving teachers’ practices by using research results from mathematics education whilst keeping in mind that learning must be improved. Social implications The central educational problem is to have students make sense of sophisticated ways of reflecting on the general laws used in mathematics in relation to the algebraic ways of acting and reflecting. Variation theory sees learning as the ability to discern different features or aspects of what is being learned. It postulates that the conception one forms about the object of learning is related to the aspects of the object one notices and focusses upon. Originality/value The commutative law for algebraic generalisations is not characterised by the use of notations but, rather, by the way the general is dealt with. Algebraic generalisations entail: the grasping of a commonality related to the discernment of whole-parts relationships, the generalisation of this commonality to two types of transformations: treatments and conversions, and the formation of direct and inverse tasks that allows one to discern the relationship between the whole, the parts, the relations between the parts, the transformation between the parts and the relationship between the parts and the whole.

Unpacking the combined effects of job scope and supervisor support on in-role performance

2017 ◽  
Vol 36 (9) ◽  
pp. 1170-1179 ◽  
Author(s):  
Rabia Mushtaq ◽  
Usman Raja ◽  
Mohammad Bashir Khan
Keyword(s):  
Social Support ◽  
Job Performance ◽  
Design Research ◽  
Strong Relationship ◽  
Supervisor Support ◽  
Job Design ◽  
Role Performance ◽  
Content Type ◽  
Work Settings ◽  
The Relationship

Purpose The purpose of this paper is to explore how the relationship between job scope and in-role performance is contingent upon the level of social support (i.e. supervisor support) received in the workplace. Design/methodology/approach A total of 640 questionnaires were distributed to employees of Pakistani companies, yielding 328 useable responses for analysis. Regression analysis was used to test for both hypotheses. Findings The results support the role of supervisor support as a moderator in the relationship between in-role performance, a dimension of job performance and job scope. The findings show that a higher job scope would facilitate higher job performance from employees who receive high levels of supervisor support. Practical implications The results provide useful insights for managers and consultants, especially HR professionals involved in job design and redesign. Organizations that encourage high levels of social support can help employees improve their job performance as they foster an environment where employees can get direct assistance and advice from their supervisors. Originality/value This paper makes three key contributions to the literature on job design. First, this inquiry shows that a strong link does exist between job scope and job performance; previous studies have failed to find a strong relationship. Second, it highlights how social context, especially in highly challenging work settings, can shape employees’ proficiencies and behaviors. Third, this paper offers a novel perspective in job design research by incorporating a contextual moderator (i.e. supervisor support).

Speculations on the post-pandemic university campus – a global inquiry

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jay Deshmukh
Keyword(s):  
Higher Education ◽  
Teaching And Learning ◽  
Design Research ◽  
Research Study ◽  
Physical Space ◽  
Well Being ◽  
Virtual Classroom ◽  
Human Interaction ◽  
Ongoing Research ◽  
Content Type

PurposeThe pandemic-induced global shift to remote learning calls for rethinking the foundations of design for higher education. This watershed moment in global health and human interaction has accelerated changes in higher education that were long emergent and amplified specific deficiencies and strengths in pedagogical models, causing institutions to reevaluate current structures and operations of learning and campus life as they question their vision and purpose. Since physical space has largely been taken out of the equation of university life, it is evident that fresh design research related to this new normal is required.Design/methodology/approachThis qualitative research study speculates on new possibilities for the future of campus, based upon insights and inferences gained from one-on-one interviews with faculty and students in multiple countries about their personal experiences with the sudden shift to the virtual classroom. The longer the mode of physical distancing stretched through Spring 2020, these phone and web-enabled dialogues – first with faculty (teachers) and then with students (learners) – lead to a deeper, more nuanced understanding of how the notion of the campus for higher education was itself morphing in ways expected and unexpected.FindingsAt the heart of this study lies the question – Has COVID-19 killed the campus? This study suggests that it has not. However, campuses are now on a path of uneven evolution, and risk shedding the good with the extraneous without eyes-wide-open rethinking and responsive planning. This two-part qualitative analysis details the experiments and strategies followed by educators and students as the pandemic changed their ways of teaching and learning. It then speculates out-of-the-norm possibilities which campuses could explore as they navigate the uncertainty of future terms and address paradigm shifts questioning what defines a post-secondary education.Research limitations/implicationsThis paper draws inferences from discussions limited to the first 100 days of the pandemic. This on-the-ground aspect as the pandemic continues is its strength and its limitation. As Fall 2020 progresses across global campuses, new ideas and perspectives are already reinforcing or upending some of this paper's speculations. This researcher is already engaged in new, currently-ongoing research, following up with interviewees from Spring 2020, as well as bringing in new voices to delve deeper into the possibilities discussed in this paper. This follow-up research is shaping new thinking which is not reflected in this paper.Originality/valueDesign practitioners have long-shaped campuses on the belief that the built “environment is the third teacher” and that architecture fosters learning and shapes collective experience. Educators recognize that a multiplicity of formal and informal interactions occur frequently and naturally across campus, supporting cognitive and social development, collegiality and well-being. Even today's digital-native-students perceive the inherent value of real interpersonal engagement for meaningful experiences. This research study offers new planning and design perspectives as institutional responses to the pandemic continue to evolve, to discover how design can support what lies at the core of the campus experience.

How teachers’ practice knowledge is used and challenged in a Learning Study using Variation Theory as a tool

2015 ◽  
Vol 4 (3) ◽  
pp. 274-287 ◽  
Author(s):  
Anja Thorsten
Keyword(s):  
Teaching And Learning ◽  
Design Methodology ◽  
Research Process ◽  
Point Of View ◽  
Variation Theory ◽  
Learning Study ◽  
Content Type ◽  
Video Recordings ◽  
Field Notes ◽  
Practice Knowledge

Purpose – The purpose of this paper is to discuss how teachers’ practice knowledge is used as a tool in a Learning Study and how teachers’ practice knowledge is challenged by using Variation Theory as a tool in the process? Design/methodology/approach – The analysis is based on data from the research process in a Learning Study. The data consists of meeting notes of ten research meetings, field notes of the research meetings and from the enactment of the lessons, video recordings of the lessons and reflective notes after and between the meetings. The analysis is qualitative and the findings are described in themes. Findings – Teachers’ practice knowledge was used and challenged in different ways in the process. This is described in five themes. Teachers’ practice knowledge was visible in the process since it enabled relevant questions to be addressed and subtle signals from students to be taken into account. It also ensured that the activities used were suitable for the students. The theory provided a focus on the object of learning and a language to talk about teaching and learning. It also challenged teachers’ assumptions about teaching and learning and allowed them to be discussed. Originality/value – The paper addresses both teachers’ practice knowledge and Variation Theory in relation to a Learning Study. It focusses on how practice knowledge of teachers can be used and challenged in the same process. The perspective is from the inside, from a teacher researcher’s point of view.

Pedagogical and learning theories in lesson and learning studies – revisited

2016 ◽  
Vol 5 (4) ◽  
pp. 295-299 ◽  
Author(s):  
Ulla Runesson
Keyword(s):  
Lesson Study ◽  
Teaching And Learning ◽  
Theoretical Perspective ◽  
Learning Theories ◽  
Variation Theory ◽  
Learning Study ◽  
Theoretical Frameworks ◽  
Content Type ◽  
And Mathematics ◽  
Point Of Departure

Purpose The purpose of this paper is to discuss two theoretical frameworks, Pirie and Kieren’s work (Pirie and Kieren, 1994) and variation theory of learning (Marton, 2015) in relation to lesson/learning study and mathematics teaching and learning. Design/methodology/approach The point of departure is the article: “Folding back and growing mathematical understanding: a longitudinal study of learning” (Martin and Towers, 2016) where it is demonstrated how Pirie and Kieren’s work (1994) and particularly the notion “folding-back” can be used as the theoretical framework in lesson/learning study. By dealing with similar arrangements and different theories, the two frameworks are contrasted. Findings It is suggested that the theory appropriated must be in resonance with the aim and focus of the study the theoretical perspective taken since it has implications for what becomes the focus of the process and subsequently the results of lesson/learning study. Originality/value This paper contributes to the discussion about how a more theory-informed lesson study and a broader theoretically framed learning study would improve and change the scope and progress of the two.

A social semiotic approach to identifying critical aspects

2015 ◽  
Vol 4 (3) ◽  
pp. 302-316 ◽  
Author(s):  
Tobias Fredlund ◽  
Cedric Linder ◽  
John Airey
Keyword(s):  
Teaching And Learning ◽  
Meaning Making ◽  
University Teaching ◽  
Variation Theory ◽  
Physics Teaching ◽  
Content Type ◽  
Powerful Approach ◽  
Semiotic Approach ◽  
Variation Theory Of Learning ◽  
Critical Aspects

Purpose – The purpose of this paper is to propose a social semiotic approach to analysing objects of learning in terms of their critical aspects. Design/methodology/approach – The design for this paper focuses on how the semiotic resources – including language, equations, and diagrams – that are commonly used in physics teaching realise the critical aspects of a common physics object of learning. A social semiotic approach to the analysis of a canonical text extract from optics is presented to illustrate how critical aspects can be identified. Findings – Implications for university teaching and learning of physics stemming from this social semiotic approach are suggested. Originality/value – Hitherto under-explored similarities between the Variation Theory of Learning, which underpins learning studies, and a social semiotic approach to meaning-making are identified. These similarities are used to propose a new, potentially very powerful approach to identifying critical aspects of objects of learning.

Developing definitions of research information metadata as a wicked problem? Characterisation and solution by argumentation visualisation

2016 ◽  
Vol 50 (3) ◽  
pp. 303-324 ◽  
Author(s):  
Mathias Riechert ◽  
Sophie Biesenbender ◽  
Werner Dees ◽  
Daniel Sirtes
Keyword(s):  
Content Analysis ◽  
Information Exchange ◽  
Large Scale ◽  
Design Research ◽  
Wicked Problem ◽  
Research Information ◽  
Content Type ◽  
Solution Strategies ◽  
The Relationship ◽  
Further Development

Purpose – The purpose of this paper is to focus on the development of definitional standards for research information as a wicked problem. A central solution strategy for such problems, increasing transparency by argumentation visualisation, is being evaluated. Design/methodology/approach – Qualitative formal content analysis is used in order to examine whether the process of definition standardisation in the project can be characterised as a wicked problem. Action Research is used to assess the effect of argumentation visualisation in the project. Findings – The results of the content analysis confirm the interpretation of the standardisation process as a wicked problem. The implementation of argumentation visualisation shows to increase the meetings’ focus and effectiveness. Research limitations/implications – The relationship between information exchange, transparency and acceptance of the development result should be addressed in future empirical analyses. Visualisation solutions require further development in order to accommodate needs of the stakeholders. Practical implications – Argumentation visualisation is of high value for finding a consensus for definitional standards and should be considered for managing and exchanging information. Originality/value – Applying solution strategies from design research on wicked problems to large-scale standardisation efforts opens up new possibilities for not only handling such projects but also providing new avenues of research for both the design and research information communities.

scholarly journals Improving teacher learning: variation in conceptions of learning study

2018 ◽  
Vol 7 (1) ◽  
pp. 50-61 ◽  
Author(s):  
Guy Durden
Keyword(s):  
Initial Teacher Education ◽  
Variation Theory ◽  
Learning Study ◽  
Conceptions Of Learning ◽  
Structured Interviews ◽  
Content Type ◽  
Design Elements ◽  
Teacher Understanding ◽  
Phenomenographic Study ◽  
The Relationship

Purpose The purpose of this paper is to identify teachers’ conceptions of learning study in order to provide the basis for an application of phenomenography/variation theory (PVT) to the improvement of teachers’ learning about learning study. Design/methodology/approach A phenomenographic study based on semi-structured interviews with 18 beginner teachers of business and economics in England taking part in a learning study during their initial teacher education. Findings The study identified five conceptions of learning study and five associated critical aspects. Results raise questions about the relationship between the process and instructional design elements of learning study. Originality/value The study offers a framework for exploring differences in the quality of learning studies and the relationship between teacher conceptions of learning study and the degree of conceptual change in students in a learning study. It also enables facilitator/researchers to design and manage interventions to develop teacher understanding of learning study that are consistent with the principles of PVT.

scholarly journals Open Source Online Learning in Rural Communities

2018 ◽  
pp. 61-84 ◽  
Author(s):  
Gary L. Ackerman
Keyword(s):  
Decision Making ◽  
Rural Communities ◽  
Open Source ◽  
Teaching And Learning ◽  
Design Research ◽  
Technology Planning ◽  
Educational Design ◽  
Educational Design Research ◽  
Technology Leaders ◽  
The Right

Anyone is free to use open source software without the need to purchase the right to install it. Despite its appeal to school and technology leaders in rural communities, they are less likely to install it than others. In this chapter, three cases in which open source technology was installed to support teaching and learning in three rural communities are described. In each, the systems were deployed and refined using decision-making grounded in educational design research. The projects are detailed, and the method of technology planning is assessed. Unanswered questions are also addressed.

scholarly journals ReleQuant – Improving teaching and learning in quantum physics through educational design research

2015 ◽  
Vol 11 (2) ◽  
pp. 153-168 ◽  
Author(s):  
Berit Bungum ◽  
Ellen K. Henriksen ◽  
Carl Angell ◽  
Cathrine W. Tellefsen ◽  
Maria Vetleseter Bøe
Keyword(s):  
Teaching And Learning ◽  
Quantum Physics ◽  
Design Research ◽  
Design Principles ◽  
Research Literature ◽  
Physics Teaching ◽  
Educational Design ◽  
Teaching Module ◽  
Educational Design Research ◽  
Wave Particle Duality

Quantum physics and relativity are demanding for teachers and students, but have the potential for students to experience physics as fascinating and meaningful. Project ReleQuant engaged in educational design research to improve teaching and learning in these topics in Norwegian upper secondary schools. The paper focuses on the first cycle of development of a teaching module on quantum physics and how design principles were developed. We construct the design principles by reviewing relevant research literature and conducting three pilot studies. The process resulted in the following principles for designing the quantum physics teaching module: 1) clarify how quantum physics breaks with classical physics; 2) use simulations of phenomena that cannot be experienced directly; 3) provide students to use written and oral language; 4) address and discuss wave-particle duality and the uncertainty

Multilevel analysis of the relationship between principals’ perceived practices of instructional leadership and teachers’ self-efficacy perceptions

2017 ◽  
Vol 55 (1) ◽  
pp. 49-69 ◽  
Author(s):  
Mehmet Sukru Bellibas ◽  
Yan Liu
Keyword(s):  
Student Engagement ◽  
Instructional Leadership ◽  
Classroom Management ◽  
Self Efficacy ◽  
Teaching And Learning ◽  
Mixed Model ◽  
School Level ◽  
Content Type ◽  
Service Training ◽  
The Relationship

Purpose The purpose of this paper is to investigate the extent to which principals’ instructional leadership predicts teacher self-efficacy, in order to identify whether a relationship exists between principals’ perceived instructional leadership practices and teachers perceived self-efficacy in classroom management, instruction, and student engagement, while controlling for several principal, teacher, and school characteristics. Design/methodology/approach The data employed in this study were both teacher- and school-level data sets obtained from the Teaching and Learning International Survey, which was administered by the Organization for Economic Co-operation and Development in 2013. A two-level mixed model was employed in the analysis of the data by adding adjusted weights at both levels for the complex survey data. Findings The results indicated a significant and positive relationship between principals’ perceived instructional leadership practice and teachers’ self-efficacy in all three aspects. Also, gender, experience, tenure status, and formal in-service training of teachers were found to be the key factors that have significant effects on teachers’ self-efficacy perceptions. Practical implications Findings suggested that international effort for mandating instructional leadership in schools is a worthwhile strategy, which can help teachers develop a greater sense of ability in classroom management, instruction, and student engagement. Originality/value This study is the first of its kind to examine the relationship between instructional leadership and teachers’ perceived self-efficacy in multiple areas related to teaching.

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