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Class Expectations

See also: teaching, my-approach-to-teaching-digital-technologies, my-approach-to-teaching-mathematics

An emerging collection of ideas for identifying and promoting the expectations I'd like to see in a class.

Current status

  • Some combination of Boaler and Ingram - erring toward how Ingram phrases it

Emerging ideas#

We can all achieve at high levels#

Boaler's first norm rephrased.

  • Our brain's can adapt and grow in response to any learning opportunity
  • If you believe you can't, that won't help.
  • If we do it, we'll all do it differently, at different speeds, but we will do it

We value our mistakes and struggle#

Boaler's second rephrased with struggle added. i.e. we don't learn anything new without making mistakes and struggling. It's okay to do this.

You don't find this hard. Congrats. Can you help someone else? Can we find you something more challenging in the work?

We value all questions#

You should have many questions. Always ask why does this make sense?

If you disagree, ask why.

Ideas from elsewhere#

Mathematical Mindsets#

Boaler and colleagues provide

Norm Description
Everyone Can Learn Math to the Highest Levels Encourage students to believe in themselves. There is no such thing as a "math person." Everyone can reach the highest levels they want to, with hard work.
Mistakes Are Valuable Mistakes grow your brain! It is good to struggle and make mistakes.
Questions are really important Always ask questions. Ask: why does this make sense?
Math is about creativity and making sense At its core about visualising patterns and creating solution paths for others to see, discuss and critique
Math Is about Connections and Communicating. Math is a connected subject, and a form of communication. Represent math in different forms---such as words, a picture, a graph, an equation---and link them. Color code!
Depth Is Much More Important Than Speed Top mathematicians, such as Laurent Schwartz, think slowly and deeply.
Math Class Is about Learning, Not Performing. Math is a growth subject; it takes time to learn, and it is all about effort.

Building a Mathematical Mindset community#

Poster from Boaler's ideas and work at Tulare County Office of Education.

Teachers and students believe everyone can learn maths at high levels#

  • Students are not tracked or grouped by achievement
  • All students are offered high level work
  • "I know you can do this" "I believe in you"
  • Praise effort and ideas, not the person
  • Students vocalise self-belief and confidence

Communication and connections are valued#

  • Students work in groups sharing ideas and visuals
  • Students relate ideas to previous lessons and topics
  • Students connect their ideas to their peers' ideas, visuals and representations
  • Teachers create opportunities for students to see connections
  • Students related ideas to events in their lives and the world

The maths is visual#

  • Teachers ask students to draw their ideas
  • Tasks are posed with a visual component
  • Students draw for each other when they explain
  • Students gesture to illustrate their thinking

The maths is open#

  • Students are invited to see maths differently
  • Students are encouraged to use and share different ideas, methods and perspectives
  • Creativity is valued and modeled
  • Students' work looks different from each other
  • Students use ownership words - "my method" "my idea"

The environment is filled with wonder and curiosity#

  • Students extend their work and investigate
  • Teacher invites curiosity when posing tasks
  • Students see maths as an unexplored puzzle
  • Students freely ask and pose questions
  • Students seek important information
  • "I've never thought of it like that before"

The classroom is a risk-taking, mistake valuing environment#

  • Students share ideas even when they are wrong
  • Peers seek to understand rather than correct
  • Students feel comfortable when they are stuck or wrong
  • Teachers and students work together when stuck
  • Tasks are low floor/high ceiling
  • Students disagree with each other and the teacher

Ingram 2019#

Ingram, 2019 offers

  • we share our ideas and listen to each other
  • we talk one at a time
  • we respect each other's opinions
  • we give reasons to explain our ideas
  • if we disagree we ask "why"
  • we try to agree at the end

Mathematical Thinking assumptions (Mason et al, 2010)#

  1. You can think mathematically.
  2. Mathematical thinking can be improved by practice with reflection.
  3. Mathematical thinking is provoked by contradiction, tension and surprise
  4. Mathematical thinking is supported by an atmosphere of questioning, challenging and reflecting.
  5. Mathematical thinking helps in understanding yourself and the world.

References#

Ingram, J. (2019). Discussion and communication. In A Practical Guide to Teaching Mathematics in the Secondary School (pp. 58--66). Taylor & Francis Group.

Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed). Pearson.