Graph 3-Coloring on the Invisible Graph

This presentation will explore an activity paradigm for engaging with computational problems in a way that is efficient with respect to set up costs. For the featured example of graph three coloring, one begins with just having some number of people standing around. Each person then secretly chooses two neighbors. This creates an invisible graph, with each person monitoring a small part, but without the entire graph being visible to anybody. The people are the vertices, and each vertex is asked to choose a color
(one of three) acted out dramatically. Each edge is being monitored by somebody, and if the coloring is not proper then people will have to choose new colors, independently. 

Besides engaging with combinatorial optimization, this activity engages with distributed computation, which is a very important topic in modern computing. Similarly, there could be activities based on different problems than graph three coloring. 

An open research question concerns the edge density for the best invisible 3-coloring. If every vertex has degree 2, then it is too simple.

Corresponding Authors: Mike Fellows and Fran Rosamond
Affiliation of corresponding author: Institute for Informatics, University of Bergen, Norway
Time frame: 30 minutes


Jumping kangaroos

Imagine two groups of kangaroos heading in opposite directions meeting at a sheer precipice with nowhere to go but forwards (kangaroos can’t go backwards but can jump over a single kangaroo into a space).

Is there a way for the groups to pass each other if the group sizes are the same? Is there is an optimal solution? Is it possible if the group sizes are different and there is a general optimal solution?

In this activity will explore these questions.

Corresponding Authors: Brett Stephenson
Affiliation of corresponding author: Guilford Young College, Australia
Time frame: 30 minutes


Data and algorithms in creative projects

On the one hand the science of the fundamental nature of reality seems distanced from everyday societal-cultural life, and on the other hand artists are precisely positioned to explore the boundary between culture and knowledge. This presentation begins with two examples where data visualisations from quantum theory experiments have been algorithmically sonified, and the subsequent audio files have been algorithmically visualised, to create a moving image and audio art work.

This is a premise for opening a discussion about the interconnection and transmutability of all things, which has important precedents in Polynesian Philosophy, post-structural notions, engineering, nonlinearity, chaos theory and complexity. This foundation places contemporary knowledge in a uniquely intercultural location, one that has the potential to form a basis for innovation in creative practice.

Several creative projects will illustrate this, and discussion is welcomed.

Corresponding Author: Ian Clothier
Affiliation of corresponding author: Intercreate
Time frame: 60 minutes


Human Pictogram CS-Unplugged

The authors developed a CSU activity called "Finding Sam" for learning information theory.  In addition, they have developed a "Pictogramming" teaching method that can control the behavior of pictograms. With these activities learners can learn various computer science concepts, such as programming, information design, and communication.

In this workshop the authors will present both activities,  "Finding Sam" and "Pictogramming", and discuss their applications.

Corresponding Author: Yoshiaki Nakano
Affiliation of corresponding author: Osaka Electro-Communication University, Osaka, Japan
Time frame: 60 minutes


Universal (Un)plugged Adapters: Re-imagining CS Unplugged for Highschool and Beyond

Computer Science (CS) unplugged activities, and its predecessor MEGA Mathematics, were originally designed to make CS education more accessible to middle school teachers.  Interest from middle school teachers in these activities still continues to grow. However, another important group of learners who can benefit from hands-on, unplugged, CS activities are senior high school and undergraduate students.  At the University of Victoria, we have used unplugged activities in undergraduate classrooms to support more traditional university teaching techniques. In this interactive workshop, we begin by introducing an unplugged activity that was designed for undergraduate students: Computational Biology Unplugged.  We will then work together with participants to brainstorm other activities that can be used to support learning fundamental CS concepts with a focus on activities that are feasible to run in lecture halls or large classrooms where classroom setup often limits easy movement; classrooms where students can only easily work with their immediate neighbours and instructors may not be able to move freely throughout the classroom.  Some options include: retooling existing CS unplugged activities, developing new CS unplugged activities top-down from learning outcomes for a specific course, or turning common problems in CS into learning activities.

Corresponding Authors: Sarah Carruthers (VIU, UVic, TRU), Andrew MacLean (UVic), Todd Milford (UVic), and Urlike Stege (UVic)
Affiliation of corresponding author: Vancouver Island University (VIU), University of Victoria (UVic), Thompson River University (TRU)
Time frame: 60 minutes


Creating a Competency Continuum:  Assessing Mathematical Literacy in Secondary Education

Following educational trends in jurisdictions from around world, the Ministry of Education in British Columbia, Canada has revised the high school curriculum to move away from objective oriented assessment and towards competency driven outcomes. One of the significant challenges of this curriculum change is the absence of an assessment structure that can validly and reliably measure these competencies. In this pilot project, we respond to this challenge through development and testing of an interdisciplinary competency assessment structure, based primarily around the work of the Danish KOM Project and the fuzzy logic portfolio assessment framework developed by Foureli (1997). In partnership with a local alternative high school in Victoria, BC, the Pacific School of Innovation and Inquiry, we introduced an assessment structure, and then, over the course of a month, collected data related to mathematical literacy assessment in this inquiry-focused and project-based learning environment.  We present the initial results of the study, looking specifically at challenges and successes as well as further applications of the structure in the classroom and beyond.

Corresponding Authors: Andrew MacLean (UVic), Sarah Carruthers (VIU, UVic, TRU), Todd Milford (UVic), and Urlike Stege (UVic)
Affiliation of corresponding author: Vancouver Island University (VIU), University of Victoria (UVic), Thompson River University (TRU)
Time frame: 30 minutes


Creative Lessons with Dragon Cards

Dragonistics Data Cards are a set of 240 cards each containing data on a unique dragon. The cards are colourful, interesting and invite play. The data is multivariate including species, gender, behaviour, dangerous breath type, strength, height and age.  This workshop will use wisdom and creativity of the participants to generate a range of learning possibilities, and to have fun with a unique resource.

The dragon cards were originally designed to teach statistics to 8-12 year olds. They are currently used for mathematics and statistics for students from about 6 to 18 years old. A fictional dataset allows control of relationships within the population and gives learners more freedom to use their imagination, and hence creativity, when analysing and problem solving. Existing learning activities include creating graphs with the cards, exploring combinatorial questions and understanding sampling.

The workshop will begin with an interactive and fun learning activity to introduce participants to the dragon cards. We then turn to creating and exploring ideas for wider use of the cards. We are particularly interested in activities for computational thinking, but also broader topics. The remainder of the workshop will involve exploring, and possibly trialling, some of the ideas as well as generating others.

Corresponding Authors: Dr. Shane Dye and Dr. Nicola Petty
Affiliation of corresponding author: Creative Maths
Time frame: 60 minutes


Every?

In this activity we will try to understand the differences and similarities between everyday language and mathematics with respect to statements that make use - explicitly or implicitly - of the word ‘every’.

Does ‘every’ literally mean in every single case? How often is this word used literally? How easy is to use it literally? Why? By exploring such questions we will try to bring to the surface an aspect of mathematical reasoning that lay people, and in particular students, may find it hard to grasp.

Corresponding Authors: Eleni Charalampous
Affiliation of corresponding author: n/a
Time frame: 30 minutes


Playfulness and Curiosity

You are invited to play with two tasks that are under development by the reSolve team. We want you to be playful and curious in engaging with the task. Your feedback about the task is welcomed, especially in how they might be tweaked to challenge and develop learners’ algorithmic/computational thinking.

The reSolve Project is a collaboration between the Australian Academy of Science and the Australian Association of Mathematics. Nearly 90 Inquiry-based lessons have been developed for Foundation to Year 10, along with Special Topics (responding to the STEM agenda) and Professional Learning Modules (to support school leaders in their work). All resources try to honour the reSolve Protocol:

  • reSolve mathematics is purposeful
  • reSolve tasks are challenging yet accessible
  • reSolve classrooms have a knowledge-building culture

The human legacy of the project is the recruitment of 300+ Champions from all sectors across Australia, who participate in a program, delivered by face-to-face workshops and access to online learning.

They will be a resource for professional association affiliates and the Government, Catholic and Independent sectors to to draw upon to lead cultural change in the teaching of Mathematics.

Corresponding Authors: Matt Skoss
Affiliation of corresponding author: Australian Association of Mathematics Teachers
Time frame: 60 minutes


Exploring water to make STEAM

A hands-on experience of ways in which water connects with life, science, art, management and creativity.  Discover and create some of the key patterns of nature by simple and novel exploration of wet stuff.  A door-opener for students who are allergic to formulas and a set of treasures for those who aren’t daunted by the language of maths.

Corresponding Authors: Jonathan Milne
Affiliation of corresponding author: The Learning Connexion
Time frame: 30 minutes