A look at my Teaching growth and practices in late 2015.
My personal relationship with math & computing as a teacher
I have always been aware that I am “good at teaching,” in an informal way. I sensed from an early age that I was good at decoding things in the world, and at explaining those things to other people. This has been a useful skill throughout life: I’ve used it and been recognized for it among friends and family, in school, and as a professional.
Math, Science, and Computing have always been my teaching specialties, and I based my university program and early professional career on them. In 2014, after several years focusing more and more on pure technology, I re-engaged with the education world as a volunteer Computing teacher in Montreal. I was happy to discover I was still “good at teaching.”
But then in 2015 I took the first step from “being good at teaching” to “being an educator.” Note there is a shift there from having a characteristic to embodying a role, a recognition or adoption of a new epistemological stance. My goal now is to no longer be effective simply because of my natural talents and inclinations, but to be effective because I know how learning works and because I focus on precisely the things that help it take place.
My definition of learning math & computing
In September 2015 I defined learning as “To form a factual or working understanding of something new.” I defined teaching as its counterpart: “To directly convey, or orchestrate the learning of, something new.”
I arrived at that ad hoc definition after an educational background in Cognitive Science and a long professional career working alongside professional instructional designers. I was already convinced of the Constructivist model of learning: namely, that the act of learning something is really the active construction or building of new a mental model with connections to other ideas.
In my Fall 2015 seminar I saw that my ad hoc definitions were reasonably accurate, and they map well to Guy Brousseau’s (1988) Théorie des situations didactiques. His framework crystallizes for me the dual role of a Teacher: one, as the didactic instructor/listener, and two, the designer of the adidactic environment in which a student interrogates material and learns from it. This resonated deeply for me. As a child I experienced the power of computers as just this kind of adidactic medium, just as described by Seymour Papert in Mindstorms (1980). This is my vision for Computational Learning today, now informed by Brousseau’s framework.
How my professional identity has evolved
My overarching goal is to have an impact on how Computational Thinking is taught to children and teenagers. I think there are two ways I can achieve that: (1) by becoming the most effective teacher I can be, and (2) by applying my skills behind the scenes via curriculum design, coaching, and teacher education.
These are the two halves of my professional identity, and in late 2015 they are more distinct and better developed than before.
As a teacher, I now see I have to focus on two different phases: (1) devoting more time to preparation (clear development of goals, thoughtful planning of tasks and timing, anticipation of questions and problems) and (2) devoting more attention to students’ ideas in the teaching moment. Coming out of my first reflective Cycle of Enactment I know I used to be overly focused on the “performing” aspect of teaching, and that limited how much my students could get out of my classes. No more; I’ve learned to use patience, elicitation, and orientation to help the students develop the ideas in the room.
As a behind-the-scenes contributor, I have a vocabulary now that I can use with Computing Education colleagues to describe where we should be aiming: High Quality teaching, Ambitious teaching; Epistemological beliefs and stances; Ethnography; Community of Practice. I have models from Mathematics (Lampert, Beasley, Ghousseini, Kazemi, and Franke, 2010) and Science (Thompson, Windschitl, and Braaten, 2013) to draw from.
More practically, I also have a much clearer picture of how I want to design curricula: more open-ended, with multiple solutions and a room built in for orientation and discourse (Stein, Engle, Smith, Hugues, 2008; Jackson, Shahan, Gibbons, Cobb, 2012; de Garcia, 2011). Based on this, I have already begun re-writing Scratch lessons for Kids Code Jeunesse that approach children’s learning in an ambitious way.
Finally, having now been a participant in a teacher-education program, I have literature and first-hand examples of how I would like to run such a program myself. I can see drawing my students’ attention to their evolving epistemological stances (Savard, 2014) via a cycle of enactment; helping them objectively observe and coach themselves and others to start “noticing” (Van Es & Sherin, 2002); helping them develop their instructional focus and their in-class orchestration skills.
Looking to the future: Principles & Practices of High Quality Teaching
At the end of 2015 with just a single cycle of enactment and investigation, plus a turn as a classroom observer, plus the experience of coaching and being coached, I made tremendous improvements in my teaching. Here is what I’ve gained specifically from Lampert’s High Quality Teaching framework.
As an occasional/visiting teacher and teacher educator, several of the Principles of High Quality Teaching are outside the scope of my work. Three stand out as principles that I know I will apply:
- Children are sense makers.
- Ambitious instruction requires clear instructional goals.
- Design the instruction and the environment to support all children to do rigorous academic work and have equitable access to learning.
Sense making (1) is the basis of Constructivism and educational foundation of buzzwords like “student-centered” and “inquiry-based.” While constructivism is no longer a controversial model, it is nonetheless elusive in real life curriculum design and teaching. Many writers and teachers (including myself in this course) fall back on an instinct to tell instead of orchestrating an environment in which students are led, or lead themselves, to discover, interrogate, and make sense of things. Most teachers find it very difficult to leave problems open-ended or to leave questions unanswered. Yet these are essential elements of ambitious “complex tasks” (Jackson, Shahan, Gibbons, Cobb, 2012).
Instructional goals (2) will be the basis for my teaching preparation. My own Enactment and Coaching experiences have taught me that Instructional Goals are paramount, and if they are in place, everything else follows. Even an off-topic question or an unexpected idea from a student can be turned into a productive moment if the instructional goals are clear.
Equitable access (3) is an important aspect of today’s “teach every kid to code” movement, and one that motivates me personally. It is explicitly mentioned in the mission of Kids Code Jeunesse, and I’ve written about it on this blog here (socioeconomic access) and here (gender access). Equally important, too, is cognitive access. Annie Savard’s class taught me the importance of pacing and ordering a lesson in such a way that students all have access to the key ideas at the right time. My vision for Computing Teaching is exactly like that of High Quality Mathematics Teaching, providing everyone with access this way.
I’ve found Lampert’s Cross-Disciplinary Practices to be the Ten Commandments of teaching techniques: they are certainly useful rules for conducting an effective classroom activity, and it was important for someone to capture them … but they are uneven, not organized particularly well, and may not in fact be the best formulation that one could come up with.
For me, Mary Kay Stein’s Orchestrating Productive Mathematical Discussion (Stein, 2008) is the second wave that improves on Lampert. Stein’s Practices have become my blueprint for developing a curriculum for Computational Thinking, where there are many expert practitioners but few well-grounded teachers. Stein provides a clear framework that can bridge novice teachers from the “show and tell” format that often happens naturally to a format that is more focused and ambitious, and based on sound epistemology. The overall approach:
- Set up a cognitively demanding instructional task.
- Ensure that it has multiple possible strategies or responses.
- Keep it on track with well-defined instructional goals.
- Support it with an accurate understanding of the students’ current thinking and practices/skills.
Then, within this, Stein, et al offer a step-by-step teaching routine that any novice teacher can grasp, and that covers the preparation phase of teaching better than Lampert’s Practices: Anticipate, Monitor, Select, Sequence, and Connect.
Brousseau, G. (1998). Théorie des situations didactiques. Grenoble, La Pensée Sauvage.
Papert, S. (1980). Mindstorms: children, computers, and powerful ideas. New York, Basic Books.
Lampert, M., Beasley, H., Ghousseini, H., Kazemi, E., & Franke, M. (2010). Using Designed Instructional Activities to Enable Novices to Manage Ambitious Mathematics Teaching. In M. K. Stein & L. Kucan (Ed.), Instructional Explanations in the Disciplines (pp. 129-141). New York: Springer.
Thompson, J., Windschitl, M. & Braaten, M. (2013). Developing a Theory of Ambitious Early-Career Teacher Practice, American Educational Research Journal. 50 (3), 574-615.
Stein, M.K., Engle, R.A., Smith, M.S. & Hugues, E.K. (2008). Orchestrating Productive Mathematical Discussion: Five Practices for helping Teachers Move Beyond Show and Tell. Mathematical Thinking and Learning, 10(4), 313-340.
de Garcia, L. A. (2011). “How to Get Students Talking! Generating Math Talk That Supports Math Learning”. Math Solutions online newsletter accessed from www.mathsolutions.com
Jackson, K., Shahan, E., Gibbons, L., & Cobb, P. (2012). Launching
complex tasks. Mathematics Teaching in the Middle School, 18(1), 24-29.
Savard, A. (2015). Transition between university students to teachers: Practice in the middle. Canadian Journal of Science, Mathematics and Technology Education, 14(4), 359-370.
Van Es, E.A. & Sherin, M.G. (2002). Learning to Notice: Scaffolding New Teachers’ Interpretations of Classroom Interactions. Journal of Technology and Teacher Education, 10 (4), 571-596