But what is a strategy is doing the mathematics before the students.
In IT circles, it’s called ‘dog fooding’. And refers to developers and techies when, during the construction/development and planning phase, they work through their program through the eyes of the market consumers. As an average joe. As a high end firm. Through this process, developers see the product in terms of its usability, suitability, strengths and challenges. Michael DeFranco of Forbes wrote about dogfooding from an IT perspective, and Jennifer Gonzsales (from Cult of Pedagogy fame) wrote and spoke about it through an educators eyes.
(Side note: if you don’t follow Jennifer Gonzales/Cult of Pedagogy on all platforms and listen to her podcast, do yourself and your teaching a favour. Her approach and content is A+)
While I don’t wholly like the term ‘dogfooding’, in the teaching and learning world it might also be called anticipation.
I first heard about anticipation at a system learning day that was being facilitated by the Numeracy team here in the Parramatta Diocese. In amongst sharing awesome ideas about how to engage the wider community with the school’s Numeracy learning, the team introduced Five Practices for Orchestrating Productive Mathematical Discussions by Margaret S. Smith and Mary Kay Stein, published by NCTM and Corwin Mathematics. Boldly in 2018 I said there has been no book that has impacted my teaching and leadership practice than this one, and to this day I will stand firm on this call.
Smith and Stein define these practices as…
“The five practices were designed to help teachers to use student’s responses to advance the mathematical understanding of the class as a whole by providing teachers with some control over what is likely to happen…as well as more time to make instructional decisions by shifting some of the decision making to the planning phase of the lesson.” (p.9)
In addition to anticipation, monitoring, selecting, sequencing and connecting make up the five practices. Each is just as critical to the integrity as the next or the one prior.
Laura Wheeler created this amazing sketchnote summary of the article and graciously allowed me to use during our professional learning meeting.
Laura’s thoughts and insights are very much worth following, and you can do so here.
At St Luke’s, anticipating can occur in the co-planning phase of task design and this was a concept introduced to teachers during the week. Using a simple, but high yield task called handfuls, teachers anticipated the possible student responses. In short, they did the maths through the eyes of a student in their class. Some prompting questions to help the teachers in this anticipation were:
- What might you expect students to do with the equipment?
- How would student x approach the task?
- What about students who find mathematics challenging? What might they do?
- What red herrings are present in the task that you would expect students to come across?
- What misconceptions might a student bring to the activity?
- What prompts (enabling or extending) will you be ready with to scaffold student’s understanding?
As a part of the co-planning and anticipation, staff collaborated on a Google Doc that represented teaching teams across Kindergarten to Year 4, representing the various abilities in these spaces. The result was a crowd sourced resource for use by all in Foundations to call upon when implementing handfuls as a warm up.
So as an instructional strategy, anticipating the mathematics in the co-planning stage is a key move. This is a much better strategy than hoping to be in the right place, at the right time and seeing the right thing to advance the learning. Anticipating tunes the teacher into the possibilities that may arise in the course of the activity, allowing for an awareness of what students might produce, where they might feel challenged, what instructional decisions to cue when the situation occurs and also to get a feel of if the task is suitable for the students. I acknowledge that by anticipating, you are likely not to imagine the entire range of responses to a particular task, it may mean you are less likely surprised by a response and more control in the moment to make choices that will positively effect the learning.
So for your next task, try anticipating in your planning. It certainly have the potential to value add to your task and ultimately student learning. What did you notice? Did you do the task through the eyes of a particular student or groups of students? Why did you choose that particular child? Was the task too easy or challenging? Let me know how you went by commenting below.