How can we communicate our thinking?

The math teachers I work with often express frustration with their learners' inability to communicate their thinking when it comes to solving problems. If learners are stuck, they often struggle to articulate what they have tried. If the problem has been solved, learners have trouble explaining their efforts. Too often, learners respond to a teacher's question about their thinking with, "I don't know." This does not present teachers with the assessment data necessary to evaluate what learners can do or are trying to do, which makes it difficult to plan what comes next.


I encountered this same problem while working with fifth-graders on fraction computation. They were practiced in giving answers and even showing work but when I asked them to share their thinking they often said, "I don't know." This provided me with an opportunity to try a response suggested by Ellin Oliver Keene in a session at the 2009 MRA Conference: "Pretend that you did know - what would you say?" The fifth-graders found that this framing supported their communication efforts by freeing them to take a risk because they were "pretending."


While this got them talking about their thinking, they still needed more support to organize their efforts. I thought it would help to demonstrate what a reasoning recount might look like. I was introduced to the recount text form through Margaret Mooney's book, Text Forms and Features. Here is the model reasoning recount I wrote based on the prior efforts of the class to think about adding fractions.

Recently, I have been collaborating with Jennifer Brokofsky via Twitter and email about ways to connect reading, math, and writing. The figure below represents our current thinking.  I hope this vignette further demonstrates the link. We recognize that this is work in progress, and your support would be appreciated. Please share your thinking in the comments.

Why all the questions?

“The important thing is not to stop questioning.”

Albert Einstein

By now you may have noticed that each Delta Scape blog post title is in the form of a question. Why is that? I am glad you asked. Like most of what I do as an educator, it is intentional and built around ideas gleaned from multiple sources.

In the reading comprehension literature, asking questions is identified as one of the core strategies effective readers use. The questions readers ask serve two purposes: (1) Questions help readers to monitor if what they are reading makes sense; and (2) Questions propel readers deeper into the text. A person who reads a passage and asks, “What just happened?” or “What happens next?” is likely to be more highly engaged than someone who is just reading the words.

Questions are also an essential part of the Understanding by Design approach to unit planning. These essential questions take three forms: (1) big-idea questions; (2) key-content questions; and (3) making-sense questions. The goal is to design the unit by determining the essential questions that will frame an authentic and engaging learning experience.

In How to Solve It, Polya uses questions as a means to support problem solving in mathematics. Examples of questions a mathematician might consider during each phase of the problem solving process are provided in the book’s introduction. If you get a chance to watch Polya’s video, Let Us Teach Guessing, you will see him modeling the use of questions to work through a problem and make sense of it.

Asking Better Questions by Morgan and Saxton is another good resource. On page 27, they write: “Learning springs from curiosity, from the need to know.” The questions learners ask contribute to this need and their level of engagement. In order to support teachers and learners in increased involvement in any learning experience, the authors introduce the Taxonomy of Personal Engagement. I use a version of this taxonomy in the courses that I teach as a means of supporting my learners in monitoring their engagement and considering questions they could ask that would improve their involvement in the task at hand.

I hope this answers the question why all my posts have a question in the title. If not, feel free to ask your questions in the comments. Sorry, I couldn’t resist.