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ALIVE#

See also: teaching-mathematics, mathematical-resilience-classroom-environment, TIRED

De Geest & Lee (2019) define ALIVE teaching as

  • A accessible
  • L linked
  • I inclusive
  • V valuable
  • E engaging

Perhaps to avoid the perception that classroom activities are TIRED

Nardi & Steward (2003) report students wanting relevance, excitement, variety, and challenge in mathematical activities.

Methods to bring a classroom ALIVE#

  • Be less helpful

  • Build confidence

    Bandura's suggestions for building self efficacy

    • create experiences that require effort and overcoming struggle
    • share role models who have achieved that
    • create a social environment where mistakes are natural and important
    • help interpret emotions during struggle as normal
    • Understand and manage emotions

Making mathematics activities come ALIVE#

Accessible#

Links to the ideas of low-floor-high-ceiling-wide-walls

Linked#

i.e. helping students see a link between mathematical topics that often disconnected in the curriculum. De Geest & Lee (2019) give the example of factors, multiples, HCF and LCM of numbers. Introduced in one year, but not used extensively until later.

Highlighting a connection to some of the work around exploring-australian-curriculum

The examples given here also (IMHO) have echoes of productive-failure

Inclusive#

Suggest making greater use of activities that require use of physical senses

  • hearing patterns in a sequence
  • feeling the length and other measures
  • physical manipulation

Echoing ideas of enactive-mathematics-pedagogy. Reminiscent of the CPU schedule demo in OS. Gives example activity graphing student shoe sizes using their bodies.

Beyond this would the wide walls of low-floor-high-ceiling-wide-walls

Valuable#

Students see the point and value the mathematics they are doing/learning. Picks up on the point that students - through a lack of mathematical knowledge and examples from others about the utility of mathematics - will not see the utility/value of mathematics in the every day world

Suggest "value" for pupils comes through "links to ideas that are interesting to hem, that cause them enjoyment and that they consider to be worth heir attention"

Activity

  • Choose an event that the students may find interesting that may involve real mathematics (from teacher or students)

  • Encourage students to develop questions about the event (pairs)

    • Remind them that mathematics not only deals with numbers and variables, but also with trends, patterns and relationships between things
    • have them categorise three levels of questions: comfortable answering, take some work/struggle to answer, probably not able to answer.
    • Share the questions
    • Students choose and work on their problem.

Engaging#

Engaged students learn efficiently and experience enjoyment. Quote Polya

For efficient learning, the learner should be interested in the material to be learned and find pleasure in the activity of learning (1962, p. 608)

  • reverse what they do

    Rather than answer questions, come up with questions. Instead of giving them instructions, ask them to write the instructions.

  • collaborative learning

References#

De Geest, E., & Lee, C. (2019). Promoting a positive learning environment. In C. Lee & R. Ward-Penny (Eds.), A Practical Guide to Teaching Mathematics in Secondary School. Taylor & Francis Group.