Beyond Objectives

• # Beyond Objectives

By Marjan Hong, posted November 21, 2016 —

One of my favorite books, Art Linkletter’s Kids Say the Darndest Things! is full of hysterical thoughts, observations, and opinions. I absolutely love how kids view and interpret their world. As a self-professed math geek, I relish children’s many “why“ questions as opportunities for inquiry. And, as a grandmother of six, I’m downright dangerous when opportunities arise to explore my grandchildren’s thinking. A few months ago I overheard a conversation between my son and granddaughter.

Seven-year-old Ava loves all types of crafts, so this past summer her mother enrolled her in a weeklong basic sewing class. Needless to say, she loved it! Soon after that, Ava asked her dad to read Emily Gravett’s The Rabbit Problem to her. On the inside of the book’s front cover, the problem is explicitly stated: If a pair of baby rabbits are put into a field, how many pairs will there be (a) at the end of each month and (b) after one year? The story then begins in January with a single lonely rabbit who invites another rabbit to his field.

Modeling good reading habits, my son asked Ava to make a prediction about how many pairs of rabbits there would be at the beginning of each new month. She easily made predictions for the first few months: February? “One pair.” March? “Two pairs.” April? “Three pairs.” May? “Four pairs.”

I held my breath as they turned the page and read that there were five pairs of rabbits at the beginning of May. “Wait, what?”

My son allowed Ava to absorb the news and flip back a few pages to try to figure out what happened. The reading continued. June? Ava conjectured, “Seven?”

Turning the page, they read that there were eight pairs at the beginning of June. Again she was given the opportunity to flip back through the pages. July? Ava stated, “Thirteen.”

Turning the page, they read that there were thirteen pairs at the beginning of July. My son asked how she got thirteen.

I heard Ava struggle to explain and then offer that the next number should be twenty-one. Again, my son asked her how she determined the next number. After several minutes, Ava explained in the only way she knew how: “It’s like the backstitch!” My son was stunned into silence because he knows nothing about sewing. I was stunned (and elated!) because I do. Once she was able to articulate her connection, Ava could explain the mathematics she observed in the sequence.

I share this story because it illustrates how easily we transition to inquiry-based learning in our interactions with our own children and grandchildren. Obviously, this was not a planned classroom lesson, but it highlights some important elements of inquiry-based learning that deserve a closer look. The story also includes evidence of what I call a beyond-objectives mindset, which is critical to targeting our students’ leaning goals. My son’s objectives were simple: Enjoy one-on-one time and model good reading practices by making predictions. Clearly, his objectives were met. Would it have been OK if Ava had not figured out the pattern of the Fibonacci sequence? I suggest that the answer to this question is a resounding yes, because it was not one of his objectives. However, he made specific choices that provided opportunity to go beyond the objectives, resulting in deeper learning and surprising connections. One critical choice was to refrain from explaining the Fibonacci sequence. Rather, he allowed Ava time to reflect, revisit, and conjecture, thereby supporting her in productive struggle. Another critical choice was to ask for an explanation once Ava correctly identified other terms in the sequence, thereby strengthening her reasoning, which eventually led to mathematical discourse.

As teachers with thirty to forty students from diverse backgrounds and varied mathematical experiences, can we just as effortlessly and successfully transition to a dynamic inquiry-based learning environment in our classrooms? Is it really possible? In the next few blogposts, I would like to explore these questions together and consider what beyond-objectives lessons might look like.

Marjan Hong, marjan_hong@yahoo.com, has worked in mathematics education for nearly thirty years as a teacher, mentor, curriculum specialist, and consultant. She is currently curriculum content developer for Discovery Education. Her passions include access and equity in mathematics education, empowering teachers, and inquiry-based learning.