Who is doing the thinking?
Numeracy, ICT and Pedagogy
Karen Butler – Lecture to third year primary BEd students at Flinders University
EDUC3625 Lecture Monday 12 October 3-4pm, Lecture Theatre 1.01
About me. My name is Karen Butler and I am a Manager for the Digital Learning and Communication Team. As such I have a unique opportunity to see teaching practice across the state, so some of what I will show you will relate to this role and other examples will be from my own teaching experience. I was teaching year 7s at Grange Primary School three years ago. I have been teaching primary students for a very long time!
When Trudy asked me to present today she asked me to address the assignment where you need to annotate and implement one activity from a lesson related to integrating numeracy and ICT in any learning area and for any year level.
As I was preparing, I asked myself a question. One that I often asked when I was preparing for teaching my year 6/7s, – Who is doing the thinking? Who is doing the learning? And if the answer was something along the lines of – me, I am learning about migration history in Australia since 1901, or I am learning about properties and application of knowledge about triangles – then I realised I needed to change my approach and get the students to do the thinking by asking questions and negotiating personalised and investigative tasks. Of course the answer to this same question today is also “me.” So while I thank you, for giving me the opportunity to synthesize my understandings of these topics, in order to present to you, it occurs to me that I am in fact doing something which is the antithesis of good pedagogy – ie imparting, transferring information to you the learner in a lecture format.
So I invite you to use this time as a hook. As a way to tune in to learning about pedagogies, numeracy and ICTs and to commit to reflecting on your practice as a teacher-to-be. As such I have created the hashtag #educ3625 for your thoughts on Twitter and a Today’s Meet –https://todaysmeet.com/educ3625 which will be open for one month. Why one month and not a year? Because we often find people will consider they have all the time in the world to get to it, and never do, if it’s open for longer. A month gives a sense of urgency. So please, if you have an internet enabled device, tweet to me at @klbutler65 or contribute to the Today’s Meet. Today’s Meet is an excellent tool to use because it does not exclude under thirteens and is an opportunity to teach digital etiquette in real time. Include your questions, thoughts, aha moments, so what moments or yeah but moments. Be honest, be thoughtful and take this opportunity collaborate with your colleagues. I shall also post links to resources in both TM and Twitter so that learning can continue beyond this 50 minutes. My BIG QUESTION for you, your mission, should you choose to accept it to consider what the sweet spot looks like when ICTs, Numeracy and Pedagogy productively collide.
Consider this scenario…An example of moving from “information to understanding”
During 2010 my year 6 students were asked to make a documentary for the New Media Awards. The theme was “sustainability”. I could have provided them with a lot of information about sustainability, facts, figures and statistics. I could have taken control of the process and produced a whole class film based on these facts and figures. That would have been easier to manage and control. However instead, I posed the question “what is sustainability?” From here we used mind mapping tools to discover what the term meant. Then each student posed questions related to the topic. The students formed documentary groups based on their questions. Some asked – How much water do we really need? Others asked – What is the most sustainable form of transport? Others looked at rubbish and asked How can we reduce waste? As part of their documentary assessment they had to show evidence of researching and using mathematics in their presentation. The hook into the learning was the chance to work with others to make the documentary. The New Media competition provided the chance to create a text for a real audience. The tuning in to the information involved mindmapping and research, collecting, curating, analysing and sharing information.
Synthesising all this information was the process involved in creating a 2 and a half minute documentary that had enough factual information and entertainment value to inform viewers. We didn’t have iPads, and if we had it would have been a much easier process. However we used the tools available to us at the time and we used them intentionally, with consideration of the learning and not necessarily of the tools. The task was redefined through a process of inviting students to make meaning from the information that was relevant to their interests, abilities and motivations.
Check out one of the six groups of students’ movies and consider the kinds of numeracy that was required to create this text. (movie as part of e-book located at https://itunes.apple.com/au/podcast/learning-through-new-media/id619604109?i=140563098&mt=2 or on YouTube at https://www.youtube.com/watch?v=gQ7bp8beQGU )
How can you use technology in intentional and purposeful ways across the curriculum and to support numeracy development?
Frameworks for Technology Use
To approach technology in schools from a useful, ethical paradigm and not be seduced by fads, fast paced change and the newest, coolest, shiniest “things” there is a need for conceptual frameworks for understanding the powerful application of technology in schools. I understand you have been using the TPACK Framework, which although not uncontested is useful for our purposes. The TPACK model offers a way of organizing thinking about technology integration by identifying three core components and acknowledging the complexity of interaction between them. These primary knowledge types are content knowledge and pedagogical knowledge, combined with the constantly shifting ground of technological knowledge. While this is a useful tool and the authors, Koehler and Mishra, 2009, acknowledge that separation of the components is an analytical exercise.
Teaching successfully with technology requires continually creating, maintaining, and re-establishing a dynamic equilibrium among all components. It is worth noting that a range of factors influences how this equilibrium is reached. (Koehler and Mishra 2009)
Teachers are therefore working with three shifting, dynamic and ever changing components. Curriculum documents do not necessarily provide the path to a “consistent” approach. Teachers are also constantly dealing with the shifting political grounds of curriculum implementation and design. As the federal and state politics involved in implementing a national curriculum influence the way a curriculum is written and implemented, it can be difficult for teachers to productively interpret curriculum documents into meaningful practice.
Within the public rhetoric and debate there are arguments for a syllabus versus a framework and a back to basics approach versus a more forward thinking innovative curriculum. The temptation therefore could be to disengage and to revert to a default position, sticking to what can be known and measured, namely as Atweh and Goos (2009) suggest in their paper on the Mathematics Curriculum – A Move Forward or Back to the Future
…the dominant view appears to be that technology is to be used to facilitate the traditional content and skills rather than affect the knowledge and possible learning that can occur where the use of technology becomes central. (p10)
It is important therefore for teachers, particularly in South Australia where there is no prescribed syllabus, to engage deeply with curriculum content, technology knowledge and strong pedagogical understandings in order to ensure they are providing a rich, 21st century schooling experience.
Another model often used in conjunction with the TPACK model and one that makes integrating technology extremely practical is the SAMR model.
Ruben Puentedura (2013) outlines four stages of technology use in education:
These four stages make up the SAMR model. At the substitution stage the technology is selected as a replacement for an earlier practice or technology – for example using an electronic whiteboard in the same way you would use a non-interactive whiteboard, i.e. to record notes as you are explaining something to students. At the augmentation stage the technology acts as a replacement technology with greater functionality – for example recording as you write notes on an Interactive Whiteboard and making the recording available to students. At the modification stage the technology used facilitates a redesigning of the task, for example getting students to use a whiteboard app on a tablet device to record their explanations of a topic. Finally at the redefinition level the technology facilitates the invention of new tasks, formerly unimaginable, for example the students could record their understandings on a tablet whiteboard app and then share these with a global audience on the web and receive feedback and comment from other learners. The first two stages are together referred to as the Enhancement level while the last two together are referred to as the Transformation level.
This way of thinking about technology is not new. Trudy Sweeney developed a rubric for using the Interactive Whiteboard in 2008 that was very similar. I used this extensively with teachers when I was teaching at Grange Primary School and working as a coordinator providing professional development in the use of the Interactive Whiteboards. When I started to say to myself I would prefer ten mobile devices to a new interactive whiteboard, where students can experience more interactive tasks through anywhere, anytime, collaborative learning – it was clear I was moving my thinking up the SAMR ladder.
Importantly however, one stage is not privileged over another but recognizes that each level must be used to serve the learning. This is important because users will often begin with substitution and when they achieve success in this area, are much more likely to try other ways of using the technologies. Not privileging one over the other allows teachers to enter the technology landscape at a level with which they can achieve success and be inspired to tackle more complex integrations of technology. These two models provide useful ways of thinking and talking about technology integration.
We will be looking at the three domains of the TPACK Framework in terms of Transforming Tasks and TfEL as Pedagogy, Numeracy as Content and ICT general capabilities with using apps and iPads as Technological knowledge. The SAMR model can help in assessing the validity of using apps in a particular way, this is important to your assignment three when selecting apps to use in your lessons.
Pedagogical Knowledge: Teaching for Effective Learning; making connections across the curriculum.
When you examine the allocated times for each subject area in the Australian curriculum you could be forgiven for thinking there are not enough hours in a day.
English/literacy R–7 300 minutes / 5 hours per week
Mathematics/numeracy R–7 300 minutes / 5 hours per week
Science R–3 90 minutes / 1½ hours per week
4–7 120 minutes / 2 hours per week
So approximately two and a half days on these “essentials” and the rest of the week devoted to “everything else” – that is – five other curriculum areas, seven general capabilities and three cross curricular priorities. Clearly you cannot do this without integrating the learning in response to your students needs and interests. And to integrate effectively without losing the rigour of the subject- specific content requires strong pedagogical knowledge.
With this in mind I would like to focus on the fact that South Australian public schools have a mandated pedagogy framework. It is referred to as the Teaching for Effective Learning Framework. It can be accessed electronically through policy documents from DECD or via the Pedagogy and Leadership Team. This document would be an excellent resource for you to apply in assignment three.
The DECD and the TfEL NP Smarter Schools Pedagogy research conducted through the Pedagogy and Leadership team reflects that teachers’ beliefs and assumptions about their role can have an impact on their practice. The three orientations to practice and the teacher’s’ role are
content coverage and control
high relationship – low expectations
responsive – learning and student centred pedagogy
- to ensure students learn meaningfully
A responsive pedagogy builds multiple entry points to the learning so that students can experience engaging, powerful and intellectually challenging learning.
It was also found that the ways teachers knowledge of pedagogies has an impact on their approach to teaching either perceiving “teaching as script” or “teaching as design”
teaching as script
- places emphasis on a controlled sequential progression and following a pre-planned approach
teaching as design
- characterised by responsive personalised approach to learners needs in order to achieve the desired learning outcomes.
Teachers who have a “teaching as design” approach demonstrate a more highly developed pedagogical repertoire. As there is no syllabus, teachers in South Australia are expected to design responsive learning experiences for their students, based on a sound knowledge of the curriculum and with an understanding of how ICT tools can be leveraged to support high quality pedagogical practices.
Another finding was that students mindsets about intelligence can impact their dispositions to learning. Approximately 40% of all SA students reported a “fixed” mindset ie they consider that intelligence cannot change and is fixed – for example, believing you are either smart or not, good at maths or not.
This means that students may perceive themselves as unable to learn certain aspects of the curriculum. They may either expect or experience learning as a transfer of knowledge or be involved in activities that require low risk and hence not enough intellectual stretch. In these circumstances students are not learning the skills required to participate fully in an information and technologically rich society. The TfEL framework identifies three areas where teachers could focus their practice to mitigate this situation. These are:
2.3 – negotiate learning,
3.3 – explore the construction of knowledge and
4.3 – apply and assess learning in authentic contexts.
So what could integrated learning look like in a classroom that values these aspects of pedagogy and learning? The Pedagogy and Leadership Team have come up with a set of “Transforming Tasks” activities that addresses how we might, as practitioners, modify what we are doing in order to increase the intellectual rigour of tasks.
These are based around four strategies
1.From closed to open
2.From information to understanding
3.From tell to ask
4.From procedure to problem solving.
Accessible here http://www.acleadersresource.sa.edu.au/index.php?page=into_the_classroom
Digital Storytelling Apps support a more open response to a task.
These apps privilege student voice
What are your dispositions to teaching and learning? How could you reflect on your practice using these ideas? When designing your learning sequence, consider who is doing the thinking in the activities in which you are engaging students. Consider how your tasks are developing critical and creative thinking.
Content Knowledge: Numeracy
Numeracy is a contested term, so it is important that educators can clearly articulate what we mean by numeracy, based on a thorough grounding in research and curriculum documentation.
Australian Curriculum (2015) V 7.5 states that
…students become numerate as they develop the knowledge and skills to use mathematics confidently across other learning areas at school and in their lives more broadly. Numeracy involves students in recognising and understanding the role of mathematics in the world and having the dispositions and capacities to use mathematical knowledge and skills purposefully.
The Organisation for Economic Cooperation and Development (OECD, 2012) defines numeracy as: …. the ability to access, use, interpret and communicate mathematical information and ideas, in order to engage in and manage the mathematical demands of a range of situations in adult life.
Numeracy is defined in the South Australian Certificate of Education (SACE) as: … the ability to understand, analyse, critically respond to and use mathematical knowledge, skills, concepts and technologies in a range of contexts
However, conduct a search in the iTunes App store for numeracy and what you will find are boundless apps for teaching maths fluency. The Australian Curriculum v7.5 (ACARA 2014) has listed the proficiencies required to “do “ mathematics – these are “understanding” “fluency” “problem solving” and “reasoning”.
Fluency is defined as
Students develop skills in choosing appropriate procedures, carrying out procedures flexibly, accurately, efficiently and appropriately, and recalling factual knowledge and concepts readily. Students are fluent when they calculate answers efficiently, when they recognise robust ways of answering questions, when they choose appropriate methods and approximations, when they recall definitions and regularly use facts, and when they can manipulate expressions and equations to find solutions. (ACARA 2014)
It appears no-one has told App developers that fluency in mathematics does not constitute numeracy. This could be related to a media emphasis on high stakes testing such as NAPLAN. Take a look at a question from NAPLAN “numeracy” and you may find that many of these questions test mathematics fluency rather than numeracy. As Dan Meyer (2010)
suggests, the “numeracy” questions have all the information you need to solve a problem. When in life is it ever the case that you have all the information, control of all the variables, presented to you to solve a problem. Pedagogies that ask students to engage in asking questions and working to solve real world problems are more beneficial to support students to develop higher order thinking and growth mindsets around learning.
For our purposes we will use the definition of numeracy in the Australian Curriculum –
Numeracy encompasses the knowledge, skills, behaviours and dispositions that students need to use mathematics in a wide range of situations. (ACARA 2014)
When using Tablet apps to teach numeracy you may want to engage students in more than fluency practice, because if that is all you are requiring them to do you are not teaching them to be numerate. To be numerate students need to be able to apply their mathematics skills in multiple contexts and identify and use varied strategies to solve problems.
To access the numeracy continuum and all the continua for the General Capabilities you should go to http://www.acleadersresource.sa.edu.au/ . This is a site created by the Pedagogy and Leadership Team and supports teachers to make the Australian Curriculum work for them in the SA context.
How would you support students to develop numeracy across various curriculum areas? How would you choose apps to teach numeracy? Apps that allow students to explore more than one “right” answer are preferable to drill and practice apps.
Tools to support demonstration of learning
Educreations interactive whiteboard
Technological Knowledge – Tools, Tasks and Learning
Digital technology can support students and facilitate the learning process in many ways, for example by offering computer simulations for exploring, experimenting, and collecting empirical data …; tools for building and running dynamic models …); tools for storing,editing, organizing, visualizing, and sharing data…; and last but not least, tools for communication and exchanging information with others (e.g., chat tools, e-mail, online forums, message boards, threaded discussions)…Kolloffel, B &. Eysink,Tessa H. S & Ton de Jong (2010)
Similarly, the New Media Consortium, a panel of global technology experts, delivers a report every year on technology trends in education and in the 2015 report it is stated that
There is growing support for empowering learners as creators that demonstrate their mastery in forms that surpass traditional tests and worksheets. Emerging instructional frameworks are encouraging teachers to use digital tools that foster creativity along with production skills. (p14)
and encourages the use of ‘Digital Strategies”
Digital strategies are not so much technologies as they are ways of using devices and software to enrich teaching and learning, whether inside or outside of the classroom. Effective digital strategies can be used in both formal and informal learning; what makes them interesting is that they transcend conventional ideas to create something that feels new, meaningful, and 21st century. (p34)
In order to use ICT effectively we therefore need to consider its purpose and intentional use. We need to aim towards redefining learning as suggested in the SAMR model and transforming tasks to support critical and creative thinking, as outlined in the TfEL framework. Without effective pedagogy and learning design, ICT tools will have little to no impact on learning outcomes.
Subject Specific Apps
History – Timeline 3D
Science – iNaturalist
DigiTech – (See visual programming)
Media Arts – (see Digital Storytelling)
Design – Maker’s Empire, Sculpt, Foldify
Geography – Skitch
Health and PE – Coach’s Eye, Buddhify
Mathematics – Numbers,
How would you assess a unit of work that integrated all of these elements? This is one of the issues facing teachers when integrating subject areas. How can you assess individual elements when the demonstration is a culmination of integrated areas?
This is why ongoing formative assessment is crucial. One of the ways teachers assess is to use either student generated rubrics or rubrics that are single point and based on curriculum content/standards. Single point rubrics are much more effective. They explicitly detail what is expected to achieve a particular outcome and then students can consider what needs improvement and what is over and above what is expected. For more about rubrics try reading this article http://www.brilliant-insane.com/2014/10/single-point-rubric.html
An example for the Scratch Junior task is as follows
Assessment – One Point Rubric
This assessment could be completed while moving among the children and discussing their work. Assessments need to be based on both the Achievement Standard and the Content Descriptors. A single assessment task will not provide all the evidence you need no matter how rich the task may seem. Therefore it is important to cumulatively gather work samples and notes so that a summative assessment is based on strong evidence at the completion of a learning event.
So what exciting tasks do you have in mind for your students that use the TPACK, the TfEL and the Australian Curriculum. I would be fascinated to see your work. Stay in contact.
Contribute your thoughts here
( For a list of useful tools and apps, some of which have been demonstrated today please refer to this document – https://docs.google.com/document/d/11tqdPiFsyoEb6T_9xjHPv4wo0slP3-8YpkNXI72dkpU/edit?usp=sharing )
ACARA (2014) Australian Curriculum, General Capabilities, Numeracy
Atweh, Bill, and Merrilyn Goos. “The Australian mathematics curriculum: A move forward or back to the future?.”Australian Journal of Education 55.3 (2011): 214-228.
Butler, Karen (2013) Learning through New Media e-book published on iTunes https://itunes.apple.com/au/podcast/learning-through-new-media/id619604109?i=140563098&mt=2
Crick, R D, Goldspink, C and Foster M (2013) Telling Identities: Learning as Script or Design? Graduate School of Education, University of Bristol, Incept Labs, Sydney Australia, South Australia Department of Education and Child Development
Grange Primary School (2010) Water For All Forever – video posted on YouTube 22 September 2015 accessed online 22 September 2015 https://www.youtube.com/watch?v=gQ7bp8beQGU
Gonzales, Jennifer, (2014) Your rubric is a hot mess; here’s how to fix it posted October 9 2014; accessed online 21 Spetember 2015 at http://www.brilliant-insane.com/2014/10/single-point-rubric.html
Government of South Australia Department of Education and Children’s Services 2010 Teaching for Effective Learning FrameworkKoehler, M. J., & Mishra, P. (2009). What is technological pedagogical content knowledge? Contemporary Issues in Technology and Teacher Education, 9(1), 60-70.
Ingle Farm East Primary School (2015) Bee Movies posted on YouTube 10th August 2015 accessed online 22 September 2015 https://www.youtube.com/watch?v=tlyEu7vfao0&index=1&list=PLF5HEj4xFkVEw4D1AaNM9qj7gJ888Db6D
Kolloffel, B &. Eysink,Tessa H. S & Ton de Jong (2010) Comparing the effects of representational tools in collaborative and individual inquiry learning, in Computer-Supported Collaborative Learning (2011) 6:223–251 DOI 10.1007/s11412-011-9110-3
Meyer, Dan (2010) https://www.ted.com/talks/dan_meyer_math_curriculum_makeover?language=en accessed online 9 September 2014.
New Media Consortium (2015) NMC Horizon Report K-12 Edition 2015.http://cdn.nmc.org/media/2015-nmc-horizon-report-k12-EN.pdf
Olijnyk, David (2013) Minecraft Botanic Gardens of The Future – video posted on YouTube 22 May 2013 accessed online 21 September 2015 https://www.youtube.com/watch?v=Glgdz-LQsa4
Puentedura , R. (2013 May 29). Paths to Technology Integration: SAMR & TPCK in Context http://www.hippasus.com/rrpweblog/archives/2013/05/29/PathsToTechnologyIntegration.pdf accessed online at January 30 2014
Sweeney, T. (2008). Transforming learning with interactive whiteboards: Towards a developmental framework. Australian Educational Computing, 23(2) pp. 24-31
South Australian, Department of Education and Children’s Services (2010) South Australian Teaching for Effective Learning Framework Guide: A resources for developing quality teaching and learning in South Australia.
South Australian, Department of Education and Child Development (2015) Australian Curriculum Leaders Resource – http://www.acleadersresource.sa.edu.au/