*Artsy*

A few years ago, I completed a questionnaire to determine my personal operating style. I’m green. Creativity. At first, IÂ questioned the validity of the assessment. I didn’t see myself as creative. I’m notâ€¦ *artsy*.

But taking a closer look, the results made sense. I scored very highly in the four strategies that made up creative thinking in this system: brainstorm ideas, challenge assumptions, reframe problems into opportunities, and envision possibilities. To be clear, this was an assessment of *preferences*, not *proficiencies*.*Â *Also, there are trade-offs; to choose one thing is to reject another. For example, my 98 in *reframe* and 91 in *envision*Â meant zero — zero! — in *tune-in to feelings*Â and ten in *empathize with others*.Â These results did not suggest that I *can’t*Â tune-in and empathize; they did suggest that I don’t *want* to. Preferences, not proficiencies.

More importantÂ to this post, this assessment tool offered a different definition of creativity: “the generation of a wide variety of options, ideas, alternatives and fresh ways of approaching difficult situations and everyday challenges.” BC’s Ministry of Education defines creative thinking, one of the core competencies, as “the generation of new ideas and concepts that have value to the individual or others, and the development of these ideas and concepts from thought to reality.”Â There are similaritiesÂ between these two definitions: both talk of the generation of novel ideas; neither talk of art.

# Broccoli with Cheese Sauce

The MoE also has this to say: “Core competencies are evident in every area of learning; *however, they manifest themselves uniquely in each discipline.*”

Over the last few years, I’ve sat through many presentations where examples of creative thinking across subject areas have been shared. The examples from mathematics almost always make me cringe. The math song is a common offender. (Usually the topic tips towards the procedural — BEDMAS, the quadratic formula, etc. — but that’s a different post.) Here, creative thinking manifests itself *outside* of mathematics. It happens *in* language/fine arts. (Maybe. Talk to a language/fine arts teacher.) You can substitute provincial capitals for divisibility rules and the nature of creative thinking within the task remains unchanged. Math is merely the context.

Worse, the message is that math is unappetizing in and of itself.Â Broccoli. The cheese sauce that isÂ the math song (or poster, or skit, or diorama, or â€¦) comes at a cost. Limited time means tension — time spent on products versusÂ time spent solving interesting problems and having interesting conversations. Note: in my mind, the opportunity cost isn’t coverage of content; it is engaging students in the “doing” of mathematics.

Yesterday, I attended a meeting where the MoE repeated the message: “By doing the curricular competencies, students will be developing their core competencies.”Â The math song attempts to have students developÂ a core competency without doing theÂ curricular competencies.

# Et tu, Desmos?

The connection between creativity and art is strong:

I’d like to suggest a better title:

CreativeÂ *Math*Â is clearly evident. Just click on one of the staff picks and look to the left. FocusÂ not on the equations themselves, but on the thinking behind them. Not on “front mathematics,” but on “mathematics in back.” (A lovely metaphor from Reuben Hersh that I first came across in Tracy Zager’s *Becoming The Math Teacher You Wish You’d Had.)*

To most math teachers, this titleÂ makes no difference. Just me nitpicking. But it matters where teaching includes designing curriculum/learning experiences. If teachers think of creativity in terms of *art*, theyÂ may look to Pinterest when planning; if theyÂ think of creativity in terms of *ideas*, theyÂ mayÂ dive deeper into Desmos.

Last year, one of my highlights was being invited into a classroom to observe Marbleslides: Lines in action.

I observed students experimenting with new ideas byÂ changing the variables one at a time. They asked “what ifâ€¦” questions. They made — and checked — predictions. “New ideas” here means new to the students themselves. These new ideas had value, evident in cheers and high fives. “Right here, right now” value, not “real-world,” career, or “when you take Calculus” value.

(The Desmos Teaching Faculty designed the activity with students in mind who were familiar with equations for lines in slope-intercept form and the idea of domain.Â In the classroom that I visited, the students were not. We worried that introducing restrictions on the domain at the same time as slope-intercept formÂ would overcomplicate things. It didn’t.)

# More Mathematical Manifestations

I don’t faultÂ my fellow educatorsÂ for associating creativity with art. It’s a natural thing to do. We in mathematics education need to articulate better what creative thinking looks like in mathematics. I’ve had some success in askingÂ teachersÂ to sort curricular competencies by core competency. (HereÂ they are, in random order. Venn diagrams work nicely; I let that idea come from teachers themselves.)

There’s still the leap required to go from making these connectionsÂ to designing curriculum/planning learning experiences with these connections in mind. Rather than listing activities that elicit creativity, like Marbleslides above, it may be helpful to think about the attributes of these tasks.

Marbleslides is immediately accessible and highly extendable (“low floor, high ceiling”). It invites a wide rangeÂ of responses (multiple *solutions*). (The teacher can view novel solutions at a glance on the dashboard.) Open questions, like *Which one doesn’t belong?*,Â share these attributes, as does Quarter the Cross.

A rich task can have a single solution, but invite a wide range of approaches (multiple *strategies*). To me, this has less to do with the task/problem itself and more to do with pedagogy. A curriculum that values creative thinking has pedagogical implications. Consider a typicalÂ *What’s the best deal?*Â task. A step-by-step-worked-examples-now-you-try-one approach to teaching leaves littleÂ roomÂ forÂ creativity. The strategy — calculate and compare unit prices — is predetermined.Â What if students were presented with the problem before the strategy? The class would generate several different ways to solve the same problem. They’d see and discuss a wide range of ideas. Note: this doesn’t preclude the teacher from later bringingÂ a particular strategy (e.g., compare unit prices) to the conversation, if necessary. Ask “Why does this strategy make sense?” or “What’s the best strategy?” and students develop another core competency: critical thinking.

*Mathematics* is creative. Is math *class*?

In herÂ ShadowCon talk, Tracy ZagerÂ shared a word cloudÂ generated from the language mathematicians use to describe their work. *Creative* sticks out. AndÂ *invent*, *curiosity*, *play*, *imagination*, *wonder*, etc. The image generated from the language society/teachers use to describe mathâ€¦ not so much.

But I know that there are places where *school* math is creative. In Surrey Schools (#sd36learn), in the “MathTwitterBlogoSphere” (#MTBoS), and beyond. When I wrote “We in mathematics education need to articulate better what creative thinking looks like in mathematics” above, I really meant “*I* need to articulate betterâ€¦” So, I need your help. DidÂ I get it right in this post? Artsy or not, what does *mathematical* creativity look like in your classroom?