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Design for a mathematical mindset#

See also: mathematical-mindset, teaching-mathematics-for-a-growth-mindset

Nascent set of ideas about how to go about designing interventions that support the development of a mathematical-mindset

Learning theories and growth mindset#

Campbell et al (2020) map 6 behaviours of a growth-mindset against four learning theories to provide guidance on what learning interventions should do/avoid to encourage a growth mindset (part of a mathematical mindset). The following provides a summary of their table.

Challenges#

A growth mindset actively looks for challenges that will help them improve. A fixed mindset avoids challenges that might expose weaknesses.

Behaviourism (success follows observation of an expert on similar problems)

  • Reward level linked to challenge level
  • Minimal penalty for mistakes
  • Multiple attempts and self-pacing
  • Avoid strong negative feedback

Constructivism

  • Use wide selection of resources, low floor, high ceiling
  • Model and reward value of questions when stuck
  • Ask students to set challenging problems
  • Balance amount of feedback to all students

CoP

  • Have experts explain how they've dealt with and benefited from failure/challenge
  • Key CoP members remember their failures/challenges and model how to deal with challenge

Connectivism

  • Provide resources that include more complex problems, explain common mistakes, and use a variety of problem solving methods
  • Model help-seeking behaviour as a way of learning (not a sign of weakness)
  • Ensure students are able to find and make sense of information resources

Persistence#

A growth mindset continues to persist with difficulties, understanding they can succeed through continuing to work hard and different ways of working.

Behaviourism

  • Feedback on low achievement should emphasise the possiblity of improvement
  • Suggest alternative strategies and allow repeated attempts
  • No public display of low achievement

Constructivism

  • Activities operate in ZPD
  • Link to pre-requisite content
  • Give partial credit

CoP

  • Share community member stories of persistence, preferably members compatible with individuals

Connectivism

  • pair low-achievement feedback with alternative resources
  • Mitigate situations where there is a predominance of low-achieving members (avoid normalisation)

Effort#

Growth mindset understands learning is hardwork, not a sign of failure (needing to do more, longer)

Behaviourism

  • Encourage and reward repeated attempts that integrate feedback to change
  • Make public the benefits of time on task to improvement
  • Provide differentiated activities to engage all
  • Minimise comparisons with peers who achieve with little effort
  • Avoid teaching practices (e.g. reuse of past test questions) that reward low effort rote learning

Constructivism

  • Use rubrics listing sub-steps of expert behaviour, including optoinal steps
  • Ask learners to rate how much effort a task required
  • Include extension options on assignments
  • Avoid distant deadlines without interim deadlines
  • Avoid using a single type of assessment

CoP

  • Members share stories of a variety of effortful practices used
  • Share stories how habit development helps learning become less effortful as expertise is generated

Connectivism

  • set tasks requiring a variety of resources and multiple steps
  • Encourage self-reflection
  • Assignment tasks comparing solutions from different sources
  • Avoid the effort gathering and using resources receiving the credit without student learning

Praise#

Growth mindset favours praise for effort, not for the individual.

Behaviourism

  • Praise successful completion, rather than achievement
  • Avoid praising effort that did not lead to success
  • Avoid pubic praise to high achievers

Constructivism

  • Praise efforts to overcome obstacles
  • Avoid praise for level achievement (rather than the work)

CoP

  • praise when students ask for help
  • showcase different styles of high quality work
  • avoid highly praised celebrity-status community members

Connectivism

  • Praise sourcing notes and examples
  • Avoid reliance on single best resources

Success#

Success of others is an inspiration, not threatening

Behaviourism

  • Set tasks observing of feedback from failure being used to achieve success
  • Reward referring to the work of others

Constructivism

  • Peer tutoring from a more advanced peer
  • Value different ways of constructing knowledge

CoP

  • Showcase diverse examples of success from others
  • Avoid limiting the quantity of individuals achieving the highest level of success

Connectivism

  • Make it easier to engage in collaborative solving of mathematical problems - sharing ideas
  • Have students source, rate and comment on popular YouTube videos
  • Minimise adverse network effects from prevalence of high success individuals

Learning goals#

Growth mindset sees learning as a process of improving performance, not a showcase of performance.

Behaviourism

  • Feedback in form of written comments, not grades
  • Record grades but only release after students have engaged with feedback and made corrections/completed post-test etc
  • Avoid public/competitive results

Constructivism

  • Provide opportunities to demonstrate learning from mistakes e.g. After receiving feedback, students make corrections and resubmit with notes on how they will avoid similar errors

Connectivism

  • Create voluntary tutoring groups where past students engage with current

References#

Campbell, A., Craig, T., & Collier-Reed, B. (2020). A framework for using learning theories to inform 'growth mindset' activities. International Journal of Mathematical Education in Science and Technology, 51(1), 26--43. https://doi.org/10.1080/0020739X.2018.1562118