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My approach to teaching mathematics

See also: teaching-mathematics

This will never be finished. Perhaps not even particularly useful, but I need to start making concrete some initial ideas.

Probably also applicable to other subjects.

Philosophy/assumptions#

Starts with my-teaching-philosophy - essentially bricolagogy.

Deal with the

  • practicalities of school teaching as a system of systems
  • including the constraints of the curriculum, common approaches to teaching, conceptions of mathematics
  • the huge diversity of students on numerous fronts, including the mathematical literacy/ability

Tasks#

  • Identify specific set of norms

  • Link to school expectations

  • Design themes/structures for units

  • Refine activities

  • Figure out effective, digital methods for production and support

Principles#

  • create exciting mathematics environments
    • curiosity, connection making, challenge, creativity, collaboration
  • give students the positive messages they need
  • pique students' curiosity and interest
  • driving questions
  • integrate assessment-for-learning - data-informed-teaching

Aiming to help students develop a mathematical-mindset / mathematical-mindsets. Weave in principles from other work (e.g. the GiST 7 principles and Gutstein's reading and writing the world with mathematics (RWWM)).

Informed by abc-learning-design-and-acad, needs-for-learning-design-systems, evolution-of-design-for-learning, norman-activity-centered-design

Beyond the norms/principles there will be a range of other insights/practices underpinning this approach. Possible examples include: lesson planning using productive failure; designing collaborative learning informed by complex instruction and thinking classrooms; assessment for learning; and leveraging digital technologies.

Resource practices#

Curriculum design#

Take units of work and draw on mathematical big ideas and RWWM to create a structure for the unit's mathematical knowledge and skills (K&S) that is meaningful/accessible to students. Develop graphical organisers and other assessment for learning practices/resources that have the students actively engaged with the structure and their progress.

Search for problems/inquiry tasks

Activity Types#

Expectations#

math expectations - set, model, reinforce expectations

starters#

Move beyond just simple revision to integrate number talks etc. designed to engage students more broadly in fundamental mathematical K&S.

math-connections-activity-type#

Help students see connections within and outside of mathematics

Including stories about the history/use of mathematics (emphasising the purposeful development of abstract ideas). Linked to ideas of using stories to help students understand mathematics.

recognising/modelling tasks -- pick one of these - perhaps notice-and-wonder#

  • What about anyqs?

e.g. "Which one doesn't belong" (HT: Janelle), contemplate-then-calculate, What Can You Do With That (WCYDWT), or Math Watch

rich tasks;#

Tasks with a a low floor, wide walls, and high ceilings

"wax on, wax off" (Explicit teaching)#

I suspect there will still be call (if only due to personal inertia) for explicit teaching/worksheets. Focused on mathematical K&S and perhaps other topics (e.g. brain science, growth mindset, the learning pit etc.). Hence give it a label that makes the purpose explicit.

closers#

Exit tickets or others.

homework#

Focused on reflection, conceptual understanding, connections etc (not procedural)

Other possible strategies#

  • Liljedahl's

  • lesson planning advice three/five non curricular, followed by scripted curricular

  • Random group work (Liljedahl, 2014) and ideas for thinking classroom (Liljedahl, 2020)

  • Richland et al (2012) report on research focused on the two most common types of problem. But also note research that found the making connections type problems can be turned into a using procedure.

  • Using procedures - students solve problems they've been taught to solve.

  • Making connections - problems where students struggle and are focused on making connections between concepts.

Activity Types#

Associated ideas: Project Zero's Thinking Routine toolbox

The vague idea is to develop a small collection of common activity types - related by pedagogical purpose - that can be

  1. Integrated into lessons as required, regardless of the broader pedagogical framework/approach
  2. Perhaps eventually form the basis for a form of activity based learning design for mathematics

Math expectations#

class-expectations

Purpose to reinforce the type of mindset/perception of students and mathematics

  • growth mindset stuff
  • sense of belonging in mathematics (Good, Rattan & Dweck, 2012)

Homework#

One of Boaler's suggestions

  • What was the main idea you learned today?
  • What is something you are struggling with or have questions about?
  • How could the ideas from today's lesson be used in life?

References#

Liljedahl, P. (2014). The Affordances of Using Visibly Random Groups in a Mathematics Classroom. In Y. Li, E. A. Silver, & S. Li (Eds.), Transforming Mathematics Instruction: Multiple Approaches and Practices (pp. 127--144). Springer International Publishing. https://doi.org/10.1007/978-3-319-04993-9_8

Liljedahl, P. (2020). Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning. Corwin Press. http://ebookcentral.proquest.com/lib/griffith/detail.action?docID=6358633

Richland, L. E., Stigler, J. W., & Holyoak, K. J. (2012). Teaching the Conceptual Structure of Mathematics. Educational Psychologist, 47(3), 189--203. https://doi.org/10.1080/00461520.2012.667065