Geoff Woolcott, PhD Associate Professor of Mathematics and Science - - PowerPoint PPT Presentation

Geoff Woolcott, PhD Associate Professor of Mathematics and Science Education School of Education Southern Cross University AUSTRALIA

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Compare DNA sequences from related species find the specific DNA sequence of target species

Cognitive Load Theory based in modern cognitive psychology A scientific view based in modern integrative biology

http://www.enrichmentcorner.com. au http://jmrc.arts.unsw.edu.au http://froemming.wordpress.com

Such connectivity can be interpreted in a less-used conceptualisation of information as matter and energy organised in a pattern (e.g. Bates, 2005). All structures can connect with the environment through information pathways or systems of

• connectivity. The changes in such information pathways can be referred to as information

processing.

Information and information processing

Probabilistic models (e.g. for differentiation of signal and noise, Shannon & Weaver, 1963) Connectionist rather than behaviourist educational theories (e.g. Sweller’s Cognitive Load Theory, 2003) Computational models (e.g. for describing biology, Chaitin, 2011)

A broad view of learning and memory in terms of information Learning and memory, in a very broad sense, can be said to involve three temporally- connected but separable stages in the information flow that is matter and energy connections and interactions. 2. Processing of resultant information changes within the structure 1. Environmental input to or output from a structure 3. Changes in the observed state of the structure as a result of such information processing In this broad view, information as matter and energy does NOT need to be organised in a

• pattern. The description of information as matter and energy, whether or not a pattern is

involved, serves to identify distinct spatial entities and their learning and memory systems. My subsequent research has been built around this conceptualisation of information, which lends it self to complex systems approaches based in the natural sciences. This research, however, also embraces Tomasello’s (1999) view of cultural accumulation and ‘cultural ratcheting’ as a distinctively human characteristic enabled by the social connections made through education and teaching. I sometimes use the umbrella term of “how people learn stuff” to describe my overall research aim, but my focus is broader-how people connect with their world. Obviously learning is a key feature!

Connectivity and systems approaches (1)

Examining spatiotemporal links in mathematics concept learning A two-year project supported internally by the School of Education at SCU

Connectivity and systems approaches (2)

It’s part of my life: Engaging university and community to enhance science and mathematics education A three-year project supported by a $1 million grant awarded by the Australian Government’s Office for Learning and Teaching (now the Department of Education and Training)

Connectivity and systems approaches (3)

Student-centred service integration and identification of risk factors in undergraduate university education A two-year project supported internally from SCU

Connectivity and systems approaches (4)

Bite size maths: Building mathematics capability of low SES students in regional/remote Australia A one-year project supported by $140,000 grant awarded by the Australian Government’s Higher Education Participation Program

Connectivity and systems approaches (5)

Collaborative networks, impact and sustainability

Examining spatiotemporal links in mathematics concept learning Network analysis (bi-modal) of inferred relationships between measurement items for a Year 3-6 individuals, based on shared outcomes/concepts

Connectivity and systems approaches (1)

Longitudinal tracking of concept development: Inferred connectivity of the incorrect Year 6 Item 10 with items in Years 3-5. Solid lines are based on incorrect to incorrect connections and and dashed lines on incorrect to correct

• items. Items are indicated by filled squares with an item number.

Presentation of this work at a Vancouver conference in 2014 connected me to the Spatial Reasoning Study Group (www.spatialresearch.org) organised by Prof Brent Davis (University of Calgary), working on spatial research networks.

Understanding Collaborative Research Networks - The Spatial Reasoning Study Group

Figure 3. A network map representing the directed connections of citations between disciplines. The red circles represent the consensus Modal Disciplines. The blue squares represent by size the number of papers from differing disciplines that were cited in the source papers of the Modal Disciplines (2-mode greater than 100 ties with nodes weighted by degree). Darker lines show larger numbers of connections. (Arrows going from blue to red not included.)

Understanding Collaborative Research Networks The Spatial Reasoning Study Group

Using structural holes to construct collaborations – the SRSG new grant: Connecting mathematics learning through spatial reasoning. Australian Research Council Discovery Project funded through 2017-2020 ($300,000). Project partners Prof Joanne Mulligan (lead CI), Associate Professor Geoff Woolcott, Prof Michael Mitchelmore (CI) (Macquarie University) and Prof Brent Davis (PI) (University of Calgary, Canada).

Office of the Chief Scientists STEM funding program Australian Maths and Science Partnership Program (AMSPP) Priority projects early 2013 Regional universities network (RUN) maths and science digital classroom: A connected model for all of Australia, led by USQ. ($1M) Evaluating and selecting STEM resources: capacity building for teachers in rural and regional schools, led by the UTAS, with SCU, Deakin, Edith Cowan, USA & government and industry partners. ($0.4M) AMSPP second round projects 2014 Inspiring Science & Mathematics Education (iSME), led by SCU with the University

• f Wollongong, Charles Darwin

University and the Australian Academy of Technological Sciences and Engineering (ATSE) ($1M) AMSPP funded through the Australian government Office for Learning and Teaching (OLT) It’s part of my life: Engaging university and community to enhance science and mathematics education. Enhancing the Training of Mathematics and Science Teachers (ETMST), a RUN project led by SCU. ($1M)

Connectivity and systems approaches (2)

It’s part of my life: Engaging university and community to enhance science and mathematics education

RUN location features

• Regional - rural or peri-urban
• High unemployment
• Large population identifying as young

indigenous

• Large numbers of people identified as

low socio-economic RUN university features

• Diverse student representation
• Large geographic coverage
• External/internal course delivery
• Research focus within region
• Strong links with community

The Regional Universities Network (RUN) Southern Cross University Central Queensland University Federation University Australia University of New England University of Southern Queensland University of the Sunshine Coast

• Current curriculum have a genuine focus on trying to bring real world mathematics/science into

the classroom, to enhance classroom studies, but the ideal mathematics/science classroom should be about the real world of mathematics/science.

• We are trying to show pre-service teachers and school students that mathematics and science

is ‘out there’ in the real world and that our classrooms should reflect this. The project is designed as a complex system and many of the outcomes considered as

• emergent. This has enabled the construction of a model that compares this project with the four
• ther large projects in a funding scheme that accounts for 25 of Australia’s 36 universities.

The project has developed an novel Enhancement-Lesson-Reflection (ELR) process. Enhancement: Interactions with mathematics and science researchers and education specialists – in recent times through video recordings. The Enhancement involves collaborative team discussions in order to produce a plan for a teaching a ‘Teaching Lesson’ based on familiar real- world interactions, generally in a student-centred problem-solving context. Reflection: The Teaching Lesson is followed by self-reflection or collaborative reflection around affect-based critical moments in teaching – how you felt while you were teaching and why you felt that

• way. This serves as a non-judgemental focus for

teacher improvement.

We have developed protocols that can be upscaled – they are currently being utilised in course structures by all six university partners.

The iterated ELR process can be described as design-study implementation (Penuel et al., 2016). At the end of each ELR sequence, data collected during the process is analysed in order to determine how to re-configure the discussions/lessons in the following iteration. This allows the process to be more effective in ensuring delivery of lessons related to the project goals and strategies.

The process may seem simple but it is both DISRUPTIVE and IMMERSIVE – it is both challenging and confronting since it requires a change to teaching practices.

Local – Regional (place) focus Institutional – Diversity (person) Classroom student Scientist & mathematician Classroom teacher PST educator

Increased numbers Broader intake pool Science & maths content plus thinking & creating Sustainable STEM dynamic upskilling & leadership Provide dynamic UEC content, thinking & creating Border crossing + Self pedagogy + direct contact Global National State Regional Local Institutional

student scientist teacher PST educator

Intervention networks Decisions & info sharing Shared principles e.g., Agents, training

Comparing emergent outcomes from 25 universities within a complex system framework.

This work connected me to most of the key researcher in Australian mathematics and science education, with a major funded meeting about future research directions to be held in June 2017. It has also allowed me to work with neighbouring countries who are currently interested in improving their STEM education. I have already run extensions to this project with teachers and pre-service teacher in Vietnam and Cambodia and extensions of iSME with members of the Southeast Asian Ministers of Education Organisation (SEMEO). Hopefully it will also provide some avenues for research collaborations within North America and Europe. Where I am directing my attention right now

STEM leadership models. Adding value to research through collaborative inquiry in regional, national and international scenarios with A/Prof Marilyn Chaseling (SCU), Prof David Townsend (University of Lethbridge, Canada) and members of the Southeast Asian Ministers of Education Organisation (SEMEO) and the Australian Academy of Technology and Engineering (ATSE) The Asia-Pacific STEM School (modelled on the Latin American School for Education, Cognitive and Neural Sciences). Support will be required from a Foundation with a dedicated research fund for STEM education.

Neal & Neal, 2013

Connectivity and systems approaches (3)

Student-centred service integration based on identification of risk factors in undergraduate university education.

Based on Bronfenbrenner’s Bioecological Model of Human Development , a Developmental Social Ecology (Bronfenbrenner & Morris, 2006)

CLIMATE FLORA FAUNA BELIEFS NORMS VALUES NGO’s SCHOOL FAMILY NEIGHBORHOOD CHURCH CLUB

MACROSYSTEMS EXOSYSTEMS MESOSYSTEMS MEGASYSTEMS MICROSYSTEMS

A

Basal information. “A” is a girl that was admitted at a public early intervention center in a rural area of the Province of Buenos Aires. She had delayed maturation in many cognitive, emotional, social and motor competences, and belonged to a single-mother and a poor house in terms of income and unsatisfied basic needs. Rationale of the network. Based on the narrative of professionals of the center I draw the network (see what I wrote for each node and connector. Basically, green is no risk, blue is neutral and red is risk. Dotted and continuous lines (connectors) mean implicit and explicit narratives. S: strongness; W: weakness. The girl has not an Adequate level of School-adjustment (W) The family is supported at eary care center (S) The relationship between center and school is adequate (S) The community, including Teachers, stigamitized family and girl (W) Stimgatization affects the capacity of interventions

• f the early care center (W)

Professor Sebastian Lipina, Argentina

Neal & Neal, 2013

Neal & Neal, 2013

Using proximal features of the micro system to construct social ecology networks that include risk factors in undergraduate education at SCU – additional risk factors provided from relative risk analysis

Factors shared by fail and success consensus Factors exclusive to success consensus Factors exclusive to fail consensus

Excel listing of fail and success network features to be used in potential intervention based

• n supporting student agency

.62 .64 .24

Analysis of student subject choices in the first year of university

Connectivity and systems approaches (4)

Bite size Maths: Building mathematics capability of low SES students in regional/remote Australia This MOOC grew out of my 2012 doctoral thesis in Education and internal projects in mathematics, and cognitive load and instructional design at SCU (Raina Mason and Graeme Cooper)

The MOOC and associated interactive modules are constructed on three simple and well-tested effects from cognitive load theory: the worked example effect; the modality effect; and, the completion effect.

Each module includes feedback of some form, based on a Study Process Questionnaire (SPQ) We hope to develop this process using Kalyuga’s online adaptive models, but using spatial reasoning as the basis for MOOC/module content, and with an industry partner.

Connectivity and systems approaches (5)

Collaborative networks, impact and sustainability – mapping my own research networks

Connections through Open Access Data There is a growing awareness that data from publically funded projects is valuable and should be made discoverable Networks and sustained impact: Connections and relationships within a project are what enhance the capacity for research, supporting productivity and sustainability. Relationships through dynamic network groups Embedding collaborative activities across through active engagement of participants across institutions and disciplines, as well as training.

I ntegration Continuum

COOPERATION COORDINATION COLLABORATION

Low trust — unstable relations Medium trust — based on prior relations High trust — stable relations I nfrequent communication flows Structured communication flows Thick communication flows Known information sharing ‘Project’ related and directed information sharing Tactical information sharing Adjusting actions Joint projects, joint funding, joint policy System s change I ndependent/ autonomous goals Semi-independent goals Dense interdependent relations and goals Power remains with

• rganisation

Power remains with

• rganisations

Shared power Resources — remain own Shared resources around project Pooled, collective resources Commitment and accountability to own agency Commitment and accountability to own agency and project Commitment and accountability to the network first Relational time frame requirement — short term Relational time frame medium term — often based on prior projects Relational time frame requirement — long term 3-5 years I ntegration Continuum

COLLABORATION High trust — stable relations Thick communication flows Tactical information sharing System s change Dense interdependent relations and goals Shared power Pooled, collective resources Commitment and accountability to the network first Relational time frame requirement — long term 3-5 years

Keast, 2014

Connectivity and systems approaches - Grant futures

Mapping knowledge flows from the real world to the mathematics classroom, A/Prof Geoff Woolcott Online spatial reasoning: An adaptive MOOC, with Emeritus Prof John Sweller and Prof Slava Kalyuga (UNSW), Dr Raina Mason (SCU) and industry partners FARMING TOGETHER: SNA Evaluation Component for the $14M Farm Cooperatives and Collaboration Pilot Program (led by SCU), with Prof Robyn Keast (SCU), Prof Jo Barraket, Director of the Centre for Social Impact, Swinburne, and Dr Daniel Chamberlain, The Australian Prevention Partnership Centre, La Trobe FarmCENTRAL: A Knowledge Mobilization Project for the $14M Farm Cooperatives and Collaboration Pilot Program (led by SCU), with The University of New England and the University of Sydney and other invited partners Integrated service management using client-centred and place-based network models with Prof Robyn Keast (SCU), A/Prof Peter Tsasis (York University, Canada), Dr Piotr Modselewski (University of Warsaw, Poland), Dr Daniel Chamberlain (La Trobe), Dr Ben Farr-Wharton (UTS) and industry partners STEM leadership models. Adding value to research through collaborative inquiry in regional, national and international scenarios with A/Prof Marilyn Chaseling (SCU), Prof David Townsend (University of Lethbridge, Canada) and members of the Southeast Asian Ministers of Education Organisation(SEMEO) and the Australian Academy of Technology and Engineering (ATSE) STEM short courses for teacher professional development and initial teacher education The Asia-Pacific STEM School (modelled on the Latin American School for Education, Cognitive and Neural Sciences)

The overarching range of possibilities or potentialities that may occur within a UIPS over a given time period is the Universal System Memory Potential (Memory Potential). Universal System Memory Expression (Memory Expression) is the observed state of a UIPS - how Memory Potential is expressed. In a UIPS, Universal System Learning Potential (Learning Potential) occurs when there is a change in Memory Potential due to communication of information into or out of the UIPS. The universe, and all of its energy and matter components, can be seen as discrete spatial components of information, each here called a Universal Information Processing System (UIPS). Processing refers to any changes that may, or may not, take place in that system over a given time interval.

A universal view of learning and memory

Within each human the range of potentialities is the Memory Potential. For example, there may be a variety of changes in connectivity within the body that can occur due to its matter and energy state

• ver a given time period.

Memory Expression is the observed state of the UIPS - how the organism is seen by an observer in a given time period. For example, growth of the body may be observed over a period of 20 years. Memory expression is a subcategory of Memory Potential. In the human UIPS, Learning Potential occurs when there is a change in the Memory Potential due to communication of information into or out of the UIPS. For example, loss of information as heat (Learning Potential) may lead to changes in Memory Potential in the body. Each human can be viewed as a UIPS, as each human is an identifiable spatial entity that may, or may not, be subject to informational changes in a given time period.

The human Universal Information Processing System (UIPS)

• In initial trials, we were able to test the process using face-to-face collaborative meetings, but this is

not sustainable in the long term – mathematicians/scientists and educators have research and teaching commitments.

• We are, therefore, developing a set of video resources. In these videos we pose a set of 5 questions

to a mathematician or scientist, based around how he/she solves problems, and their expertise and mathematical/scientific thinking in every-day life.

• Responses to these questions were videoed and made into short video vignettes, either based around a

single question or around the entire set of questions. The questions 1. How do you, as a mathematician/scientist, begin to solve a new research problem? 2. How have you applied your problem solving to a specific problem in the your university region? 3. How is your problem solving similar to how people solve problems in their every-day lives? 4. How is your problem solving different to how people solve problems in their every-day lives? 5. How would you teach someone to think like a mathematician/scientist? These short videos have become a valuable part of the ELR process, particularly when used in conjunction with the affect-based critical moment protocol. This combination is being embedded in our pre-service teacher curriculum.

An important feature of these videos is showing mathematicians and scientists as living full and interesting lives.

REFLECTION THE AFFECT-BASED CRITICAL MOMENT PROTOCOL

A key breakthrough for pre-service teachers is self-assessment or peer- assessment that uses a critical moment process that does not rely on student learning or teaching performance evaluations by an outside party.

A step through of the reflection process questions

An integrated service system model based on social ecology network conceptualisations