StephenL: Tell me about yourself.
@cbrownlmath: This question always gets me wanting to reply with questions...I will, however, not do so today. A few personal details I am a...Husband, father of 3 grown women, no grandchildren, cancer survivor. I was born and raised in Central California, though it hasn't always been home, it is for now.
I am a mathematics and STEAM educator with over 30 years of experience at this point. My first 14 years were in the High School setting where I taught all the courses a Secondary teacher might from General Math to AP Calculus. During those years I worked on a Master's of Arts Degree in Math Education and then changed roles and became a university faculty member at a small, faith-based, liberal arts university. In 2011 I went back to school and took a Leave of Absence from my teaching job at the university and earned my Ph.D. in Education, Policy & Practice with a focus in Mathematics.
In 2019 I co-authored a book with Sunil Singh of Toronto, Ontario Canada; Math Recess Playful Learning in an Age of Disruption. Wherein we make a radical call for a change in how mathematics is viewed by society in general and the education community in particular. Mathematics is a vibrant, joyful and uplifting endeavor we as a species have engaged in for millennia. Only in the last 100 or so years have we turned it into this dull thing of drudgery that needs to be "gotten through," endured, tolerated. We need to recapture that sense, return again to the idea that mathematics is an adventure.
I am an active researcher and professor of mathematics & STEAM Education, and creativity as well. I have several publications in-press now related to the intersection of creativities and mathematical understandings. I expect to see these having a broad impact on the teaching and learning sciences.
StephenL: You have written several articles on creativity in mathematics. That seems like a contradiction to the mathematics many older adults experienced during their K-12 education. Can you provide an example of how a parent of a young child can create the conditions for a creative exploration of mathematics?
@cbrownlmath: While thinking of mathematics as a creative endeavor may seem foreign to many who have been schooled in math in the last 50 years, it was never seen as such by those who have been busy making it over the past 8 millennia or so. The processes mathematicians follow to arrive at the end result we see are never as clear as what they publish in the public record. For instance, take the result we know as the Pythagorean Theorem. One of the earliest proofs of this idea is credited to a man named Euclid who wrote down his proof as the climax of his first book of the Elements. He wrote this down in a very neat and tidy fashion...it was however not the manner in which Pythagoras thought of it. It came almost 150 years after Pythagoras had died. Now that refinement takes careful, considered, and often deep thought. This is creativity at its purist.
First off parents, be curious yourself, never stop wondering, asking questions about how and why this or that idea in mathematics came to be or must be true??? The most critical thing parents can do to create conditions for creative exploration is to never answer a math question with an answer...but another question, even better one they don't know the answer to themselves. After this attitude of perpetual questioning is the family atmosphere, also provide your child with blocks, springs, gears, pendulums, puzzles, string, paper to draw on (few if any coloring pages where there is an expectation of "coloring in the lines")...let them entertain their fantasies, visions, and musings about reality.
StephenL: What was the writing process like with a co-author? Did you then work with a book editor on the manuscript draft? How did you resolve differences of opinion?
@cbrownlmath: Writing with a co-author was a fun experience for me. I enjoy collaborations, find renewed energy when bouncing ideas off a good friend. I don't recall having many differences but that was probably because we both scoped out various sections of the book to write from our own perspective. This format allowed us to stay out of each other's stories but to provide clarifying questions and suggestions to each other. Our publishers also provided some important guidance during the writing phase. He wanted a book that would bring our message to school administrators as well as math teachers; we had not been thinking big enough you see, and they worked with us, intensely, for more than a few meetings till we were able to incorporate their thoughts more fully.
Yes, we did work with an editor, one that our publishers chose. Well really, several editors because we had imagery embedded within our text and as such some editors worked on our prose, others on our visuals. Finally, it came together under the watchful eye of an executive editor who gave final approval on all the little things here and there. Truth be told, that creative endeavor, messy and smudgy as it was, still went to press with errors. We found several in the first weeks after the printed versions were out and thanks to several kind friends we were able to rectify these and now in the second printing it is relatively error-free.
StephenL: Blocks, springs, pendulums. I get the sense that creativity in mathematics is about inquisitiveness on whatever it is one is learning.
But aren’t you setting students up for disappointment when they enter the classroom and standardized tests and worksheets are more the norm?
And what if that student shares their inquisitiveness by asking questions and gets shut down by the teacher who’s trying to just get through the curriculum?
@cbrownlmath: Ohhhhh you are pushing all my buttons now, aren't you? ;)
In short, yes I suppose I am setting children up for disappointment. Classrooms are inevitably disappointing though. In this era of accountability through relentless assessment, how can anyone expect schooling to be completely non-disappointing? So here my thoughts turn to parents. If you are genuinely interested in helping your child to enter school and not be disappointed after you have raised her to be the ultimate in creative person she can be...start now to get involved in the process of policy debate surrounding schools. It doesn't sound sexy or exciting but changing policy is where the hard work of changing school culture is going to take place.
In the situation you describe where an inquisitive student is shut down by a harried and haggard teacher, first I would hope that the student could tell their parents about that happening and that they could go together and discuss the situation with the teacher. My initial reaction is to want to accuse the teacher of malpractice, but the truth is most teachers are doing their dead-level best to teach all the students in their room...so give them some space to be human too. But never give up advocating for your students to have the opportunity to be fully creative within the classroom situation. Support teachers by working to improve their lot in life through greater autonomy not the overstructured, homogenized attempts at the one-size-fits-all curriculum that so many have to teach now.
StephenL: You mentioned that your editors challenged you to broaden the scope of the book in order to make it more approachable to school administrators whose first language was not math.
What changes did you make to the book as a result of that feedback?
@cbrownlmath: Yes the publisher helped us to see that while we were seeking to be disruptive to the system of education regarding mathematics, we need to do so in ways that school administrators won't shut off from completely for fear of being “too radical.” So one important alteration we made was to link the problems, puzzles, conundrums, paradoxes etc. that are in the book to the "Common Core" Standards in some way. I did this by focusing on the most important, and least often thought of, Standards of Mathematical Practice (SMPs).
The SMPs address the critical concept of purpose in the math curriculum. I see them as saying something like, "Look! Mathematics has within it so many sub-fields that we could never enumerate them all, many are still left out of the Content Standards...but really these eight statements are the PURPOSE for studying mathematics at all in the K-12 curriculum.”
If you look at any single piece of the mathematical content you are likely to be hard-pressed to justify its artificial inclusion in the curriculum at the grade-level that it occurs, without connecting to the SMPs. They remind me of an excellent little article written by a couple of mathematics authors, Al Cuoco and Kenneth Levasseur, in which they describe what they have seen in mathematicians' ways of attacking problems and call for the curriculum to foster these positive habits of the mind.
Sorry, I have gone afield some...in short if you look in the book, after every puzzle, problem, or game you will see a parenthetical note that is meant to inform all who read the book that, what just preceded this spot is an example of the following Standards of Mathematical Practice. In this, we hope to give teachers a means by which they can "justify" the inclusion of such tasks in their classes. Because in this era of senseless accountability and high-stakes testing, EVERYTHING that is taught must be tied to some "standard." It is oppressive.