Approximation vs. Mastery: Nurturing Independence from the Start

“Okay, honey, here it comes…Remember to keep your eye on the ball.” Still gripping the neon-colored softball in my throwing hand, I watched as my oldest daughter lifted her new Wilson glove to eye level, bit her lower lip, and waited. Earlier this summer, she, her sister and some friends all decided to take up softball for the first time. So it was time to learn to catch and throw. Pulling the ball back, I stepped forward and released a gentle throw, carefully trying to aim a little high so as not to sail it toward my daughter’s face. Up went her glove, webbing opened. “Just like I showed her,” I thought. But as the ball got close, I noticed her glove was not quite high enough. Instead of nestling perfectly inside the webbing of her glove, the ball ricocheted off the edge, careening off into the grass behind. “That’s okay, honey,” I called. “Let’s keep practicing.” 

In sports, much like writing, kids get better with practice. And coaching. And like sports, writing is a skill developed in use. My daughters will unlikely be “good” at softball at the end of the summer, or even an entire season. But they’ll likely be better, and hopefully more confident. In writing workshop, one of our important mantras is, “Teach the writer(s), don’t fix the writing”; this is so writers can grow to become more independent. When my daughters play their first softball game, I will not be standing right next to them, telling them exactly what to do and when. Therefore, their coaches and I work to help them develop skills they can use independently at times when these skills will make a difference. The same approach can be applied to the teaching of writing. And this development process begins with coaching (teaching) toward approximation.

As we begin this week to think about nurturing independence in our writers, it is important to remember that in a writing workshop, much like a softball coach, we can be focusing more on “getting some work in play,” and less about “kids getting good at it.” Part of this means understanding that perhaps on several fronts, our students – as they write – will be approximating. And this is what we want.  Approximation is defined as “a result that is not necessarily exact, but is within the limits of accuracy required for a given purpose.” As our students write this year, it will be important for us to remember that they are still learners, and as such, they will be approximating. It will be unlikely they will reach mastery. Understanding this can actually improve our teaching.

In his seminal research on learning, Dr. Brian Cambourne of the University of Wollongong in Australia reminds us that one condition required for people to learn anything is an environment in which approximation is safe and honored. As Cambourne suggests, young writers then need teachers who provide opportunities to approximate without fear. Because, remember, if kids are doing something they already know how to do, they are not learning. Mistakes are essential for learning to occur.

As teachers of writing, we can work to keep ourselves cognizant of the importance of approximation in a few ways:

  • Remember the importance of frequency- Just like repeated practice will be required for my daughters to become better, more skilled and independent softball players, writers need repeated practice at structuring and developing pieces of writing. This notion undergirded the newer Teachers College Reading and Writing Project Writing Units of Study, as the Project realized units needed to be shorter in order to provide more frequency both across units and the school year. Writers cannot write a little or “sometimes” and become better; they need to write a lot to get better. Lots of approximation moves learners closer to mastery.


  • Plan work just outside of students’ zones of proximal development- When young writers work just beyond their ‘zones of proximal development’ (psychologist Lev Vygotsky’s term to describe the difference between what a learner can do without help and what he or she can do with help), growth and improvement become possible. Writing workshops are set up to create a learning environment that provides explicit instruction (minilesson), sustained independent practice time, teaching and guidance from knowledgeable persons (teachers, mentor authors), and supportive peer interactions (writing partners, student-led small groups). These are the structural components necessary for growth to occur. As teachers, if we place our instructional focus on ambitious work that will challenge our writers, pushing them just beyond the limits of where they have been while providing the support they need, we are teaching toward approximation. And this is what will move our writers.
  • Avoid teaching to masteryAcross my years of consulting, I have sometimes heard phrases like, “So-and-so is a weak writer,” or “This kid doesn’t do such-and-such.” It’s likely I used such phrases as a beginning teacher myself. But we must remember: To be a kid is to be in a long phase of approximation. If we gear our teaching toward all students mastering every strategy, writing technique, and language convention, we will likely eventually fall into the trap of fixing the writing, not teaching the writer. We will also squelch independence. Instead of teaching to mastery, we can focus on getting some work into play, and trusting that the unit will help students get better. Encouraging a spirit of approximation, especially at the beginning of the school year, will likely take us far toward nurturing independence from the start, as students will understand that mistakes and imperfection pave the way on personal journeys of growth.


On the next throw, my daughter kept her eye on the ball, opened her glove, and successfully caught the softball. The girls and I practice a little each day, working on when to point fingers down, when to point them up, how to catch across the body, etc. Each day I try to show them something that they can try on their own, and give them space to make mistakes. And honestly, they are getting better. 

As we all prepare to launch a new year, hopefully with a renewed spirit of optimism and possibility for our students, all of us at Two Writing Teachers hope this week to provide you with ways to nurture independence from the start. One way to begin is to make the space, both physical and mental, for writers to try stuff out, make mistakes, push beyond where they’ve been, approximate. By teaching toward approximation, we support student independence and growth.


Let’s chat on Monday, August 12th at 8:30 p.m. EDT, when all of the TWT Co-authors will host a Twitter Chat about nurturing independence from the start. Just search and tag #TWTBlog to participate.

Giveaway Information


  • This giveaway is for a copy of No More “I’m Done!” and No More “How Long Does It Have to Be?” by Jennifer Jacobson. Thanks to Stenhouse Publishers for donating a copy of each of these books — one book for a primary educator and one book for a secondary educator. (You must have a U.S. mailing address to win a print copy of this book.)
  • For a chance to win this copy of  No More “I’m Done!” or No More “How Long Does It Have to Be?”, please leave a comment about this or any blog post in this blog series by Sunday, August 11th at 6:00 p.m. EDT. BE SURE TO WRITE DOWN THE GRADE LEVEL OR GRADE BAND YOU TEACH SO WE CAN PUT YOU IN THE RUNNING FOR THE BOOK THAT MATCHES THE GRADE BAND YOU TEACH. Betsy Hubbard will use a random number generator to pick the winner’s commenter number. His/her name will be announced in the ICYMI blog post for this series on Monday, August 11th.
  • Please leave a valid e-mail address when you post your comment so Betsy can contact you to obtain your mailing address if you win.  From there, our contact at Stenhouse will ship the book to you. (NOTE: Your e-mail address will not be published online if you leave it in the e-mail field only.)
  • If you are the winner of the book, Betsy will email you with the subject line of TWO WRITING TEACHERS – NO MORE BOOKS within five days of receipt. A new winner will be chosen if a response isn’t received within five days of the giveaway announcement.