Thinking Competencies: Creativity Through Math

THINKING COMPETENCIES: Creativity through Math with Fred Harwood April 24, 2015

It is the supreme art of the teacher to awaken joy in creative expression and knowledge. Albert Einstein

What are cross-curricular competencies? At the heart of the definition of the cross-curricular competencies is the principle that education should lead to the development of the whole child—intellectually, personally, and socially. In a world of growing diversity and challenge, schools must do more than help students master the sets of knowledge and skills acquired through the standard subject areas. They must prepare students fully for their lives as individuals and as members of society, with the capacity to achieve their goals, contribute to their communities and continue learning throughout their lives.

The cross-curricular competencies are the set of intellectual, personal, and social skills that all students need to develop in order to engage in deeper learning—learning that encourages students to look at things from different perspectives, to see the relationships between their learning in different subjects, and to make connections to their previous learning and to their own experiences, as members of their families, communities, and the larger society.

The conceptual framework described here envisions three broad cross-curricular competencies: thinking competency; personal and social competency; and communication competency.

Thinking competency, which encompasses critical, creative, and reflective thinking, represents the cognitive abilities that students develop through their studies. Personal and social competency represents the personal, social and cultural abilities that students develop as individuals and members of society. Communication competency represents the abilities students need to interact and learn effectively in their world. Together, these three cross-curricular competencies represent a holistic and unifying approach to learning, spanning all courses and grades in the common purpose of enriching students’ learning experience and preparing students for the future.

These cross-curricular competencies are interconnected; and they are not three linear and discrete entities . . .

Creative thinking is the act of generating and implementing ideas that are novel and innovative to the context in which they are generated. A creative thinker is curious and open-minded, has a sense of wonder and joy in learning, and demonstrates a willingness to think divergently and tolerate complexity. A creative thinker uses imagination, inventiveness, resourcefulness and flexibility and is willing to take risks to imagine beyond existing knowledge in order to generate and implement innovative ideas.

Students are enabled to think creatively through opportunities that allow them to take initiative, exercise choice, explore ideas and options, question and challenge, make connections, and imagine and visualize the possibilities. Teachers can foster creative thinking by welcoming students’ unexpected answers, questions, and suggestions; delaying judgment until students’ ideas have been thoroughly explored and expressed; offering students opportunities to work with diverse materials in various ways; and supporting and scaffolding students as they explore new and unusual ideas.

‘It’s never enough to just tell people about some new insight. Rather, you have to get them to experience it a way that evokes its power and possibility. Instead of pouring knowledge into people’s heads, you need to help them grind anew set of eyeglasses so they can see the world in a new way.’— John Seely Brown


3 components of creativityFigure 2.  Adapted from Adams, K. “Sources of innovation and creativity: A summary of the research.”

Some helpful links for future research:      Roger von Oeck’s “Whack on the Side of the Head”

Chic Thompson’s “teaching children to be creative first and critical second”          “What a Great Idea”

John Spencer Blog on “Why Consuming is Necessary for Creating”

“The truth is that consuming well is a part of how we develop a taste for what we like. It’s part of how we gain information. It’s part of how we fall in love with an art or a science or a craft.”

On the Edge of Chaos Where Creativity Flourishes by Katrina Schwartz

Ken Robinson’s drive for getting more of the creative competencies in education:

“Creativity is the process of having original ideas that have value.”

“Creativity is not an option, it is an absolute necessity!”

Revolutionary Ted Talk:

From: “Sir Ken Robinson: Creativity Is In Everything, Especially Teaching”

“Creativity is putting your imagination to work. It is applied imagination. Innovation is putting new ideas into practice. There are various myths about creativity. One is that only special people are creative, another is that creativity is only about the arts, a third is that creativity cannot be taught, and a fourth is that it’s all to do with uninhibited “self-expression.” None of these is true.

Creativity draws from many powers that we all have by virtue of being human. Creativity is possible in all areas of human life, in science, the arts, mathematics, technology, cuisine, teaching, politics, business, you name it. And like many human capacities, our creative powers can be cultivated and refined. Doing that involves an increasing mastery of skills, knowledge, and ideas. Creativity is about fresh thinking. It doesn’t have to be new to the whole of humanity— though that’s always a bonus— but certainly to the person whose work it is.

Creativity also involves making critical judgments about whether what you’re working on is any good, be it a theorem, a design, or a poem. Creative work often passes through typical phases. Sometimes what you end up with is not what you had in mind when you started. It’s a dynamic process that often involves making new connections, crossing disciplines, and using metaphors and analogies. Being creative is not just about having off-the-wall ideas and letting your imagination run free. It may involve all of that, but it also involves refining, testing, and focusing what you’re doing. It’s about original thinking on the part of the individual, and it’s also about judging critically whether the work in process is taking the right shape and is worthwhile, at least for the person producing it.”

Competency: Creative Practice


Innovation is a key component of creativity: if there is no innovation, then there is no creativity.  To be innovative is to have ideas and contribute to, or lead, activities that have not been tried before. As a creative practitioner, innovation should be the constant driver for your work; while originality is your ultimate goal.  Consistent innovation requires a strong disciplinary base of knowledge and skills.

There are two main ways in which something can be new: a new method or a new context.  Secondly, something could be new to you, new to your client or client group, or completely new to the sector, or even the world – as far as you know!

The more of these boxes it ticks, the closer to ‘original’ your work will be.  However, behaving innovatively is not about achieving an ideal; it is about demonstrating, in all your creative practice, that you are constantly striving to be innovative and that you understand where and how your action is innovative. 

Teaching Creativity

A helpful website exhibiting a creativity structure called SCAMPER is found at

Art of Creativity


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