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CSER Math Connections with Community

See also: maths-in-schools, teaching-mathematics

Summary/reflections on the third module in the CSER Math in Schools MOOC.

Maths and numeracy in our world#

Suggests maths and numeracy is all about connections across strands and an intrinsic part of cultures etc.

Where do you see mathematics in your local community?

A prompting question for this section. My answer (currently) harks back to the goompi-model and its conception of what mathematics is (start with definitions). Where the mathematics is seen in the community is where people have built the cultural/personal means to connect the real world with the mathematical world. Often those connections wht and representations of mathematical knowledge will not mirror exactly academic mathematical knowledge. And likely many people will not be aware of any resemblance between what they do and mathematics.

The location#

Gives examples of mathematics at home and in the local area. General point about being aware of what is specific about the community and leveraging that. e.g. travel times to school in a regional community.

Fits with the reality of the Goompi model.

The people#

Fits with the cultural bias but also reality from the Goompi model. About being aware of what the culture and people need/bring with mathematics, but also showing students how people like them (or who they want to be like) value/use numeracy/mathematics.

The global context#

Points to some resources. And then onto some big discussion of the various cultural symbols/different approaches to mathematics/measurement across time and cultures.

Makes mention of pi-day

Maths & numeracy outside/on country and place#

Using physical reality to connect with mathematics. Explicitly links with work from Prof Chris Matthews, specific examples

  • geocaching - search for hidden location using GPS
  • measuring garden conditions
  • citizen science - collecting data
  • measurements

People in maths careers#

Shows a view from the "Careers with STEM" folk - standard stock music with graphics

We need maths for shopping, cooking, sport, and then into careers. Careers mapped against the AC and some of their people. Links to more of the posters etc.

Links to AMSI produced video with more detailed example - see the AMSI schools project and Careers in Maths

Mathematicians across the world#

Provides a list of famous mathematicians as examples to inspire students/demonstrate impact etc. The detail is a bit light.

  • Pythagoras
  • Muhammad ibn Musa al-Khwarizmi - Hindu-Arabic numerals, arithmetic, algebra
  • Ada Lovelace
  • Katherine Johnson
  • Raye Montague
  • Terence Tao
  • Cheryl Praeger (Toowoomba native, UWA mathematician)

Classroom Activities#

  • Role models in mathematics

    Mentions (doesn't cite) research that projects where students research maths role models have positive impacts. Links to a Spotlight on Women in Maths in Australia project

  • Who uses maths and numeracy

    Students research careers they are interested in and list the maths/numeracy skills required in those careers.

The M in STEM education#

Standard rhetoric about jobs market/innovation requiring STEM skills

By 2030, workers will spend 77% more time using science and maths skills" - Foundation for Young Australians (2017)

What is they're currently spending 0 time?

77% of 0 is 0 🤭

STEM as a way to develop "21st century skills".

Implementing STEM education#

Multiple approaches, but some common features

  • integration of at least two learning areas
  • programs designed around real-world contexts/problems

Consider focusing on the "ways of thinking" underpinning the learning areas. e.g. design, systems, computational thinking.

Is STEM is a band-aid for the limitations of the formal educational system?

STEM promotions pushes the use of real-world contexts/problems which merge separate (but only STEM) learning areas. i.e. pushing back against the traditions in schools to have pretend problems and to separate subjects into separate classes.

Add in the T in STEM standing for technologies. Which, if you follow certain views of technology includes just about every subject at school.

There also seems to be a tension between the careers rationale for STEM and the focus on STEM as a "way of thinking"/way of develop "21c skills". First, STEM is really multiple ways of thinking. Second, the focus on jobs is potentially problematic. If you take the goompi-model abstraction STEM and its components are a set of abstractions. If we want 21c skills, don't we want people able to draw creatively and appropriately on all of those abstractions? Not just STEM, not just those apparently responsive to current economic need.

Why not focus on providing students with learning experiences that develop their ability to draw on all of these abstractions in ways meaningful to their reality?

See stem-crisis

Evaluate the M in your STEM#

Basically, if teaching STEM evaluate the mathematics

STEM in schools#

Misc resources

Rich context in maths#

Australian curriculum cross-curriculum priorities#

Mentions three that reflect national, regional and global contexts.

Aboriginal and Torres Strait Islander Histories and Cultures#

  • explore representations of number and patterns, including counting systems of First Nations Australian Peoples
  • investigate time, place, relationships and measurement concepts within First Nations Australian Peoples' contexts
  • investigate, analyse and evaluate statistical data of First Nations Australian Peoples to deepen their understanding of their lives.

With further detail along three organising ideas

  • Country/place
  • Culture
  • People

Asia and Australia's Engagement with Asia#

  • gain an understanding of the applications of mathematics in Asia
  • understand the contributions of past and current mathematicians from the Asia region
  • explore examples of maths from the Asia region for fields such as number, patterns, measurement, symmetry and statistics,
  • including calculation, money, art, architecture, design and travel.
  • investigate data collection, representation and analysis can be used to examine issues relevant to the Asia region.

Sustainability#

  • develop the proficiencies of problem-solving and reasoning for exploring sustainability issues and their solutions.
  • apply spatial reasoning, measurement, estimation, calculation and comparison to investigate local ecosystem health
  • cost proposed actions for sustainability solutions
  • measure, monitor and quantify the change in social, economic and ecological systems over time 
  • use statistical analysis to predict futures based on findings that can also inform decision-making for future solutions.

Rich Contexts#

Draws on work from ATSIMA and ACARA to support embracing/embedding

  • Material culture

    Shell necklaces, nets and traps, weaving & baskets, strings & cordage, objects & technologies, spears & spear throwers, commercialised substances (fish toxins)

  • Cultural expressions

    • Sharing/communicating information (data) through story, symbols
    • Cultural accounts, cycles of time
    • Counting stories/rhymes
    • Story and dance of processes on Country/Place
    • Maths expressions/operations through story
    • Dance and algebra

  • Instructive games and toys

    • Size of sets of objects, sharing, patterns
    • Counting, addition, subtraction
    • Length, size, mass, angles, position, movement, shape
    • Prediction/likelihood outcomes
    • Chance events and experiments
    • Probability dependent and independent events, random and non-random

  • Weather & seasons

    • Part-whole reasoning
    • Repeating patterns/cycles
    • Variables, predicting, likelihood, chance
    • Environmental indicators as data
    • Time and seasons/calendars

  • Caring for country/place

    • Resource management - optimisation and sustainability (e.g., through fire, biodiversity, digital technologies)

      e.g. proportion of landmass used between First Nations and current grain belts. - Animal tracks/behaviour, hunting circles, animal populations - Shapes and objects, fractal/growing patterns, symmetry - Travel, maps, measurement, scale - Food, cooking, traditional grain belt, nutrition, hunting

  • Navigation & mapping

    • Land, cultural, star maps
    • Travel routes - night sky
    • Orthogonal representations
    • Geospatial technologies

  • Knowledge systems

    • Counting/number systems, grouping, body-tallying
    • Kinship
    • Time
    • Classification
    • Subitising, quantifying

  • Architecture

    • Dwellings - environment, climate
    • Geodesic design influencing contemporary housing

  • Data sovereignty Linked to UN Declaration. See Indigenous Data Network. See as a way to avoid cultural bias.

    • Reconciliation, 'closing the gap'
    • Cultural bias
    • Dating methods, genetic sequencing, measurement errors, social impact
    • Radio/carbon dating (exponential equations)
    • Time scales - pre/post colonisation

Maths professional communities#

Teacher Professional Associations#

Organisations#

PLNs#

Podcasts - AMSI MathsTalk and Mr Barton's Maths podcast

Twitter chats - #mathchat and #mathstalk

Module task - Connection with community#

  • Reflection ✅ #CommunityConnect

    What can I do to connect maths

    1. To my students inner circle
    2. To our community
    3. To the world

  • Careers with maths - find a career that uses maths

  • Rich contexts - Share a further example of how one rich context can be incorporated into teaching, include

    • The mathematics covered
    • An explanation of how the rich context is addressed
    • Any links to resources
    • Reflection/evidence of using it

What can I do to connect maths#

Inspired by the last module, I'm keen to leverage the Goompi Model as a guide for planning, graphic organiser, and a source of student input. The idea being to build up (shared) knowledge of the the parts of "reality" of interest. Perhaps leveraging that knowledge (with students) to develop generative themes to underpin design for learning. From there weave connections between mathematics and that "reality" in various ways through stories, resources (e.g. prompts for Notice and wonder tasks), and activities.

Students inner circle#

Connecting with the students "reality of interest" is a start. To engage friends and family perhaps the main strategy would be to aim to use mathematics to enable students to construct new or interesting insights or cultural/creative artefacts around their "reality of interest". Objects that will encourage and help the individual student share with their friends/family.

Build on a class norm about the importance of asking questions with a regular activity that encourages students to ask questions of a mathematical type about their realities of interest.

To our community#

As a member of the community, demonstrate the asking of mathematical questions by identifying mathematical questions from the local community (e.g. which is the cheapest place to buy petrol?) and integrate the refinement and answering into lessons. Develop community-specific prompts (e.g. images of a local landmark) for notice and wonder or contemplate then calculate tasks. Leverage local data as examples/tasks in mathematics. For example, use weather data from local climate station to explore measures of central tendency etc to answer questions like "Which January was hotter (1964 or 2024)?".

To the world#

Make use of past resources from PI Day to raise student awareness of students from other countries engaging with the same mathematics. Perhaps working towards students being more actively engaged with PI day. Link inner-circle and community interests to world-wide projects (e.g. UN Sustainable Development Goals). Moving towards enabling the students to use mathematics to read/write their world.