Creativity: The essence of mathematics

Reference: Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236-260.

Abstract: For the gifted mathematics student, early mastery of concepts and skills in the mathematics curriculum usually results in getting more of the same work and/or moving through the curriculum at a faster pace. Testing, grades, and pacing overshadow the essential role of creativity involved in doing mathematics. Talent development requires creative applications in the exploration of mathematics problems. Traditional teaching methods involving demonstration and practice using closed problems with predetermined answers insufficiently prepare students in mathematics. Students leave school with adequate computational skills but lack the ability to apply these skills in meaningful ways. Teaching mathematics without providing for creativity denies all students, especially gifted and talented students, the opportunity to appreciate the beauty of mathematics and fails to provide the gifted student an opportunity to fully develop his or her talents. In this article, a review of literature defines mathematical creativity, develops an understanding of the creative student of mathematics, and discusses the issues and implications for the teaching of mathematics.

Notes: I have heard some University lecturers in Engineering complain that their students "nail it" in the exams, but in the end fail to really comprehend the core ideas, and are unable to apply them later on. Some teachers have gained prominence by incorporating some "active learning" approaches to teaching Mathematics and Physics... but what I have not seen (enough, anyway) is this idea of targeting the creative dimension of mathematics.

Idea evaluation: Error in evaluating highly original ideas

Reference: Licuanan, B. F., Dailey, L. R., & Mumford, M. D. (2007). Idea evaluation: Error in evaluating highly original ideas. The Journal of Creative Behavior, 41(1), 1-27.

Abstract: Idea evaluation is a critical aspect of creative thought. However, a number of errors might occur in the evaluation of new ideas. One error commonly observed is the tendency to underestimate the originality of truly novel ideas. In the present study, an attempt was made to assess whether analysis of the process leading to the idea generation and analysis of product originality would act to offset underestimation error in the evaluation of highly original new ideas. Accordingly, 181 undergraduates were asked to evaluate the originality of marketing campaigns being developed by six different teams where the level of idea originality was varied. Manipulations were induced to encourage active analysis of interactional processes and the originality of team products. It was found that active analysis of product originality and appraisal of interactional processes reduced errors in evaluating the originality of highly novel ideas. The implications of these findings for the evaluation of new ideas are discussed.

Notes: There is a clear bias in creativity research to study the production or generation of ideas (can ideas strictly be "generated" or ideas more like energy?), while only a few studies focus on the evaluation or assessment of ideas.

The expatriate-creativity hypothesis

Reference: Fee, A., & Gray, S. J. (2012). The expatriate-creativity hypothesis: A longitudinal field test. Human Relations, 65(12), 1515-1538.

Abstract: While prior research suggests that the cognitive changes triggered by cross-cultural experiences can enhance an individual’s creative-thinking abilities, this is yet to be verified through empirical field research. We draw on schema theory, and the principle of psychological dissonance experienced during cultural adaptation, to argue that expatriates undergo wholesale cognitive changes that can lead to enhanced creative-thinking abilities. We test this hypothesis by measuring changes in the creative-thinking abilities of a sample of expatriates over the first 12 months of their placement. When compared with a control group of non-expatriates, the expatriates showed significant increases in overall creative-thinking abilities and cognitive flexibility, although not originality, elaboration, or ideational fluency.

Notes: TBD

Teaching for creativity: from sage to guide to meddler

Reference: Erica McWilliam (2009) Teaching for creativity: from sage to guide to meddler,Asia Pacific Journal of Education, 29:3, 281-293

Abstract: This paper serves three purposes. First, it makes a case for seeing creativity as a keylearning outcome in our times, and thus the core business of education. It then goes on
to examine the nexus of creativity and pedagogy, showing the conceptual work done to
demonstrate creativity as a learnable set of dispositions and capabilities. Finally and
most importantly, the paper argues the value of a pedagogical approach the author calls
“Meddling-in-the-Middle”, in augmenting and enhancing the repertoires of “Sage-onthe-Stage” and “Guide-on-the-Side” in order to build students’ creative capacity.
Examples are given of what these meta-approaches might look like in relation to the
teaching of Shakespeare. The author concludes by arguing the important connection
between Meddling pedagogy and creative capacity building.

Notes: A culture of teaching that values obedient attentiveness or busy work for its own sake,rather than the attention and busy-ness that speaks of productive engagement, is death to
proactive, self-managing learning. Fortunately, active engagement, rather than listening
and regurgitating, reflects the learning preferences of the present generation of learners,
who are more likely in informal environments to try things out rather than follow
instructions “from above”. If teachers can understand the value of being “usefully
ignorant” about learning options and possibilities, at the same time as they are expert in
their disciplinary field and their pedagogical practice, who are active and inventive in the
classroom, who challenge and support, who do not make things too easy, and who are not
the only source of authority, who use processes of discovery, critique, argument and
counter-argument effectively, who enjoy learning themselves and who do not rush to
rescue their students from complexity – such teachers will contribute immeasurably to the
creative capacity of their students now and in the future.

Metaphors we think with: The role of metaphor in reasoning

Reference: Thibodeau, P. H., & Boroditsky, L. (2011). Metaphors we think with: The role of metaphor in reasoning. PLoS One, 6(2), e16782.

Abstract: The way we talk about complex and abstract ideas is suffused with metaphor. In five experiments, we explore how these metaphors influence the way that we reason about complex issues and forage for further information about them. We find that even the subtlest instantiation of a metaphor (via a single word) can have a powerful influence over how people attempt to solve social problems like crime and how they gather information to make ‘‘well-informed’’ decisions. Interestingly, we find that the influence of the metaphorical framing effect is covert: people do not recognize metaphors as influential in their decisions; instead they point to more ‘‘substantive’’ (often numerical) information as the motivation for their problem-solving decision. Metaphors in language appear to instantiate frame-consistent knowledge structures and invite structurally consistent inferences. Far from being mere rhetorical flourishes, metaphors have profound influences on how we conceptualize and act with respect to important societal issues. We find that exposure to even a single metaphor can induce substantial differences in opinion about how to solve social problems: differences that are larger, for example, than pre-existing differences in opinion between Democrats and Republicans.

Note: The best series of studies that I'm aware of in terms of understanding how people shape their reasoning when exposed to controlled metaphors. I'm glad it's being cited often in the last four years: https://scholar.google.co.nz/scholar?cites=10748680439318539033 

Teaching Creativity in Engineering

Reference: Daly, S. R., Mosyjowski, E. A., & Seifert, C. M. (2014). Teaching Creativity in Engineering Courses. Journal of Engineering Education, 103(3), 417-449.

Abstract
The ability to engage in a creative process to solve a problem or to design a novel artifact is essential to engineering as a profession. Research indicates a need for curricula that enhance students' creative skills in engineering.

Our purpose was to document current practices in engineering pedagogy with regard to opportunities for students' creative growth by examining learning goals, instructional methods, and assessments focused on cognitive creative skills.

We conducted a critical case study of engineering pedagogy at a single university with seven engineering courses where instructors stated the goal of fostering creativity. Data included instructor and student interviews, student surveys, and course materials. For qualitative analysis, we used frameworks by Treffinger, Young, Selby, and Shepardson and by Wiggins and McTighe.

One aspect of creativity, convergent thinking (including analysis and evaluation), was well represented in the engineering courses in our case study. However, instruction on generating ideas and openness to exploring ideas was less often evident. For many of the creative skills, especially those related to divergent thinking and idea exploration, assessments were lacking.

An analysis of pedagogy focused on goals, instruction, and assessments in the engineering curriculum revealed opportunities for growth in students' creative skill development. Designing assessments that motivate students to improve their creative skills and to become more aware of their own creative process is a key need in engineering pedagogy.

Notes: Interesting in principle, the conclusion seem contentious, i.e.: that more/new assessments are needed -and that assessments motivate students.

Humberto Maturana and Francisco Varela’s Contribution

Reference: Hallowell, R. (2009). Humberto Maturana and Francisco Varela’s Contribution to Media Ecology: Autopoiesis, The Santiago School of Cognition, and Enactive Cognitive Science. Proceedings of the Media Ecology Assocation, 10.

Abstract: This paper provides an overview of the major body of work in the biology of cognition produced by the Chilean biologists Humberto Maturana and Francisco Varela. In addition to a review of their work together, Varela’s “enactive” approach to cognition is discussed. Insights from these studies are related to the field of media ecology. In their early work together Maturana and Varela developed the idea of “autopoiesis” (self- production) as the primary feature that distinguishes living things from non-living things. From their theory of autopoiesis in biology, they develop a naturalistic, non-transcendental and observer-dependent interpretation of cognition, language, and consciousness. They argue against any absolutely objective world; instead they claim that we bring forth a world with others through the process of our living in human created worlds that arise through language and the coordination of social interaction. Implications of this view for media ecology are considered.

Notes: I first read Maturana and Varela's work as an undergraduate student of design (thanks to Fernando Shultz mainly), and what surprises me today, twenty years later, is how marginal these ideas still are, across science and in design circles. For example, even in a South American online forum where design issues are discussed, a simple comparison is quite telling:

• 39 results for "philippe starck" site:foroalfa.org
• 4 results for "humberto maturana" site:foroalfa.org

In other words, a clown is ten times more popular with designers than an intellectual who has deep contributions for understanding fundamental issues behind humans and design.

What does it mean to be design-led?

Reference: Beverland MB and Farrelly FJ (2007) What does it mean to be design-led? Design Management Review 18(4).

Notes: An interesting question, unfortunately the paper fails to address it in a meaningful way, or even address the core issues of design-led strategies. The positive aspects include:
1. What does it mean for design to be the "dominant logic" of a company?
2. Good design strategy doesn't mean good design, as obvious from Fisher and Paykel appliances: interesting briefs, awful user interfaces. Refreshing to see in this paper examples that are not the usual Apple, etc.
3. The authors get close to a very important issue but miss it with the Ford Ka case: design-led has key implications mainly outside the design departments, it is about enabling understanding of design in areas such as engineering and marketing.
4. Perhaps their most valuable insight is that design-led does not mean designer-led.

Abductive theory construction

Reference: Timmermans, S., & Tavory, I. (2012). Theory construction in qualitative research from grounded theory to abductive analysis. Sociological Theory,30(3), 167-186.

Abstract: A critical pathway for conceptual innovation in the social is the construction of theoretical ideas based on empirical data. Grounded theory has become a leading approach promising the construction of novel theories. Yet grounded theory–based theoretical innovation has been scarce in part because of its commitment to let theories emerge inductively rather than imposing analytic frameworks a priori. We note, along with a long philosophical tradition, that induction does not logically lead to novel theoretical insights. Drawing from the theory of inference, meaning, and action of pragmatist philosopher Charles S. Peirce, we argue that abduction, rather than induction, should be the guiding principle of empirically based theory construction. Abduction refers to a creative inferential process aimed at producing new hypotheses and theories based on surprising research evidence. We propose that abductive analysis arises from actors’ social and intellectual positions but can be further aided by careful methodological data analysis. We outline how formal methodological steps enrich abductive analysis through the processes of revisiting, defamiliarization, and alternative casing.

Notes: A clear and well framed analysis of the role of abductive reasoning in research.

Research into Design Across Boundaries

Title: ICoRD’15 – Research into Design Across Boundaries Volume 2 Creativity, Sustainability, DfX, Enabling Technologies, Management and Applications

Editor: Chakrabarti, Amaresh (Ed.)

Description: This book showcases over 60 cutting-edge research papers from the 5th International Conference on Research into Design – the largest in India in this area – written by eminent researchers from across the world on design process, technologies, methods and tools, and their impact on innovation, for supporting design across boundaries. The special features of the book are the variety of insights into the product and system innovation process, and the host of methods and tools from all major areas of design research for the enhancement of the innovation process. The main benefit of the book for researchers in various areas of design and innovation are access to the latest quality research in this area, with the largest collection of research from India. For practitioners and educators, it is exposure to an empirically validated suite of theories, models, methods and tools that can be taught and practiced for design-led innovation.

Link: http://www.springer.com/gp/book/9788132222286

Notes: A collection of recent ideas presented in Bangalore earlier this year.