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My Teaching Philosophy#

See also: teaching, not-how-bad-you-start

Nascent attempt to articulate my teaching philosophy. Initially focused on listing ideas that resonate.

Misc aphorisms#

teaching-as-gather-weave-augment

Broad statements

  • No such thing as best practice
  • gather and weave what is available, suggesting you need to improve the quality of what's available casa
  • "To teach is to model and demonstrate. To learn is to practice and reflect."

Mathematics (and possibly apply to Digi Tech)

  • Have a strong/attractive vision of mathematics

    High school mathematics gives the wrong impression in students and teachers. See: mathematical-mindset, mathematical-structure, what-do-mathematicians-do - Lessons need to reinforce and re-connect that vision all the time - Students need to engage in mathematics

    Engaging in real mathematics helps create a better mathematical identity and better results later in life (very broad claim - see explicit-versus-inquiry) - Numerous pressures on teachers to do otherwise

    The push for explicit teaching and other generic approaches that are boiled down to standardised steps. Leading to simple, non-mathematical, generic, boring L&T activities. In turn reinforcing the wrong impression of mathematics. - Ready made casa - specific to mathematics - are required to make it easy to do this

    They need to be low-floor-high-ceiling-wide-walls, generative, flexible, scalable through adaptation.

Internship philosophy#

Following was written as part of a report on my internship whilst studying by Grad Dip.

I like that I used the wicked design problem idea. Though, today, I wouldn't have gone with connectivism. I'd go with pragmatism. i.e. Box's quote "That all models are wrong, but some are useful". Pragmatism was the philosophy underpinning my PhD.

This echoes arguments Dron and Anderson (2023) make in terms of bricalogogy. Which in turn resonates strongly with the Bricolage Affordances Distribution (bad) mindset I've written about.

The original#

My philosophy of teaching is currently based on the idea of teaching as a wicked design problem and both learning and teaching best understood through the theory of Connectivism. As defined by Rittel and Webber (1973), a wicked problem cannot be solved from a purely scientific-rational approach due to an absence of a clear problem definition and the widely varying perspectives of people involved. Any problem – like teaching – that involves a diverse group of people in activity that requires a change of behaviour or understanding is likely to be a wicked problem. Connectivism uses the metaphor of a network with nodes and connections as a central metaphor. Within this metaphor learning is a process that results in the modification of networks and the development of a network.

Flowing from this foundation is the belief that teaching is best seen as an on-going process of reflective practice and action research exploring the differing perspectives of all those involved in learning and teaching. This process links directly with the three dimensions of the Queensland College of Teachers Professional Standards. The nature of this linkage and evidence of existing connections between my practice and the three dimensions are provided in the following sections.

Informing ideas#

Shades of gray, CAS and wicked design problems#

Teaching occurs within a complex adaptive system. It is a wicked design problem.

5 messages math teachers should share with students early

  1. I believe in every one of them, there is no such thing as a math brain or a math gene, and I expect all of them to achieve at the highest levels.
  2. I love mistakes. Every time they make a mistake their brain grows.
  3. Failure and struggle do not mean that they cannot do math—these are the most important parts of math and learning.
  4. I don’t value students working quickly; I value their working in depth, creating interesting pathways and representations.
  5. I love student questions and will put these onto posters that I hang on the walls for the whole class to think about

Norms to reinforce

  1. Everyone can learn math to the highest levels.
  2. Mistakes are valuable.
  3. Questions are really important.
  4. Math is about creativity and making sense.
  5. Math is about connections and communicating.
  6. Depth is much more important than speed.
  7. Math class is about learning, not performing

Biesta#

As described here

In Biesta’s words: “The educational task consists in arousing the desire in another human being for wanting to exist in and with the world in an grown-up way, that is as subject” (p. 7, italics in original). Being-a-subject and adulthood mean to be able to shape the world together with others, without giving up the world due to excessive creative will or, conversely, abandoning any creative will and even shattering oneself as a subject. Biesta writes: “The middle section between world destruction and self-destruction is the field on which an adult form of (co) being with others and others can be reached” (p. 15). Adulthood also includes an elaboration of one’s desires encouraged (but not enforced) by pedagogical actions and the experience of the difference between the subjectively desired and the generally desired. In this respect, education is centrally about interruptions of one’s own state of mind (interruption), it creates a sanctuary for contemplation (suspension), and offers support and assistance (sustenance) for those to be educated.