The 'It's all about maths' symposium focused on connecting mathematics across the curriculum...
Using Digital Tech to learn maths: Transforming the learning?
Keynote: Dr Nigel Calder
"Digital technologies are everywhere in our lives. We use them to communicate, research, process, record and for for entertainment. They influence the way we interact in the world, the way we live. We use them in work and play. How might they change the learning process?" (Nigel Calder)
Technology might take the student 'somewhere', but it might not always optimise the learning. It is about the pedagogy and the learning, thus pedagogy is critical and it is not a matter of having apps or having technology, the reason becomes the critical thing. Apps should be about purpose/pedagogy for learning.
Affordances - What are they?
"Affordance implies the complementarity of the animal and the environment. They are not just abstract physical properties" (Gibson, 1979)
Visual affordance: Tinkerplots, Multiplier
Interactive apps: Sketchpad (look at: ‘geometry for young learners’ site), Touchcounts 1.0, Maths shake.
Tech gives non-judgemental feedback which might facilitate: risk-taking, an investigative approach, collaborative approaches, engagement, alternative learning trajectories, reshaping of the learning.
Moyer-Packenham and Westenskow (2013) identified app affordances as focus constraint, creative variation, simultaneous linking, efficient precision, motivation. These affordances interact and appear to be mutually influential of each other.
A five-stage developmental process when learning to integrate a particular technology:
- Recognizing (knowledge)
- Accepting (persuasion)
- Adapting (decision)
- Exploring (implementation)
- Advancing (confirmation)
Teacher knowledge for learning with technology: (when considering apps)
- Focus on the mathematics and learning outcomes
- Facilitating teaching and learning
- Re-organising learning - seeing connections
- Mathematical thinking and problem solving
- Self-correction and reasoning
- Making mathematics attractive and motivating
- Recording thinking and opportunities for collaboration
Aspects that underpin all themes:
- Student-centred
- Encouraging ownership of learning, eventual self-assessment and direction
- Get students to explain their thinking, it is powerful
- Teacher open to new technologies, ongoing learning
- School support with access to devices, reliable wifi, technology
- Herding cats... this is kind of what we do... it is not an easy job
- Task and apps should focus on the learning
- Foster creativity and self-directed learning
- Use them to optimise the learning situation
- Facilitate learning
- Give insights into students strategies and mathematical thinking
- The apps are built for purpose
Workshop 1: Making the most out of e-ako
Having a class in e-ako maths enables you to monitor your whole class' progress. Pathways are unlocked so you can look ahead and see what your students will see, but students will still need to follow the pathway. You can unlock steps by emailing Andrew.
Tip: Collate all students' names on a spreadsheet with a class email account. You can do this from eTap. Save as CSV file. Student names can then be important as bulk.
Workshop 2: Problem solving with juniors
Explore problem solving in a junior context
Task design
Integrating digital technology
How to problem solve with juniors?
1. Launch the problem (try and get them to read out problem themselves - literacy link here)
2. Independent think time
3. Small group sharing
4. Reporting back
5. Student self-assessment
Hints for Launching the Problem:
- Staging the problem - acting it out
- What do we know about the context of this problem
- Retell this problem to your partner
- What information do you know? How are you going to use it?
- Where is the question? What is the problem asking you to do?
- To expose students to a range of thinking
- To foster mathematical communication skills
- To increase students’ confidence
- To clarify common misunderstandings
- To provide a foundation for the extension of a problem
- To highlight the mathematics inherent in the problem
Sharing back
Get students to role model and show what they did
Self-Reflection Questions to consider
- What did you notice
- What are the students' next steps
- What went well
- Goals for next time
Sites that provide pictures and video clips useful for maths problems:
- Enriching mathematics
- Put your students in a pickle
- The Mathematics Shed
- 101questions
- Have you got maths eyes
Workshop 3: Developing student agency through a growth mindset
Agency and Growth Mindsets are both big in their own right. The aim here is to put the learner in the driving seat. However, when you are in the passenger seat for the first time, it is a very weird feeling, as you have to let go of the controls. Giving students control is a risk, but they are also taking the risk as a learner...
Give students ways to talk and think in a 'Growth Mindset' way, rather than them saying "I can't do it, I will never get to do it". The word 'yet' is powerful to use.
How can we encourage students to develop student agency and a growth mindset?
Move away from making all the decisions, what books they are going to read, what maths equipment / tools they are going to use.
Teachers also have to develop a growth mindset:
- Use technology to make both their own and students' learning richer
- Risk trying new learning
- Bring their own student passion into learning activities
- Let go of the need to control all variables
- Find ways to change even under adversity
- Value relationships with students
- Make a difference in student lives
- Network and connect with others for resources, assistance and support
Learning Mindsets/beliefs:
- Growth Mindset: Value mistakes and use them. Talk more about struggles and strategies to overcome them
- Sense of Belonging: Student Voice (What can I do as a teacher to help you more? What can you do to help yourself?). Ethic of Care
- Relevance: students will be more engaged if learning is relevant and they are given a choice
- Self-efficacy: when students understand their goals, they can monitor their learning and it is going to be more meaningful for them
Student Self Assessment 'tools' to support self managing:
Using Digital Tech to learn maths: Transforming the learning?
Keynote: Dr Nigel Calder
"Digital technologies are everywhere in our lives. We use them to communicate, research, process, record and for for entertainment. They influence the way we interact in the world, the way we live. We use them in work and play. How might they change the learning process?" (Nigel Calder)
- Overview
- Affordances
- Influences on the learning process
- Research projects
- Some effective apps
Technology might take the student 'somewhere', but it might not always optimise the learning. It is about the pedagogy and the learning, thus pedagogy is critical and it is not a matter of having apps or having technology, the reason becomes the critical thing. Apps should be about purpose/pedagogy for learning.
Affordances - What are they?
"Affordance implies the complementarity of the animal and the environment. They are not just abstract physical properties" (Gibson, 1979)
Visual affordance: Tinkerplots, Multiplier
Interactive apps: Sketchpad (look at: ‘geometry for young learners’ site), Touchcounts 1.0, Maths shake.
Tech gives non-judgemental feedback which might facilitate: risk-taking, an investigative approach, collaborative approaches, engagement, alternative learning trajectories, reshaping of the learning.
Moyer-Packenham and Westenskow (2013) identified app affordances as focus constraint, creative variation, simultaneous linking, efficient precision, motivation. These affordances interact and appear to be mutually influential of each other.
A five-stage developmental process when learning to integrate a particular technology:
- Recognizing (knowledge)
- Accepting (persuasion)
- Adapting (decision)
- Exploring (implementation)
- Advancing (confirmation)
Teacher knowledge for learning with technology: (when considering apps)
- Focus on the mathematics and learning outcomes
- Facilitating teaching and learning
- Re-organising learning - seeing connections
- Mathematical thinking and problem solving
- Self-correction and reasoning
- Making mathematics attractive and motivating
- Recording thinking and opportunities for collaboration
Aspects that underpin all themes:
- Student-centred
- Encouraging ownership of learning, eventual self-assessment and direction
- Get students to explain their thinking, it is powerful
- Teacher open to new technologies, ongoing learning
- School support with access to devices, reliable wifi, technology
- Herding cats... this is kind of what we do... it is not an easy job
- Task and apps should focus on the learning
- Foster creativity and self-directed learning
- Use them to optimise the learning situation
- Facilitate learning
- Give insights into students strategies and mathematical thinking
- The apps are built for purpose
Workshop 1: Making the most out of e-ako
Having a class in e-ako maths enables you to monitor your whole class' progress. Pathways are unlocked so you can look ahead and see what your students will see, but students will still need to follow the pathway. You can unlock steps by emailing Andrew.
Tip: Collate all students' names on a spreadsheet with a class email account. You can do this from eTap. Save as CSV file. Student names can then be important as bulk.
Workshop 2: Problem solving with juniors
Explore problem solving in a junior context
Task design
Integrating digital technology
How to problem solve with juniors?
1. Launch the problem (try and get them to read out problem themselves - literacy link here)
2. Independent think time
3. Small group sharing
4. Reporting back
5. Student self-assessment
Hints for Launching the Problem:
- Staging the problem - acting it out
- What do we know about the context of this problem
- Retell this problem to your partner
- What information do you know? How are you going to use it?
- Where is the question? What is the problem asking you to do?
- To expose students to a range of thinking
- To foster mathematical communication skills
- To increase students’ confidence
- To clarify common misunderstandings
- To provide a foundation for the extension of a problem
- To highlight the mathematics inherent in the problem
Sharing back
Get students to role model and show what they did
Self-Reflection Questions to consider
- What did you notice
- What are the students' next steps
- What went well
- Goals for next time
Sites that provide pictures and video clips useful for maths problems:
- Enriching mathematics
- Put your students in a pickle
- The Mathematics Shed
- 101questions
- Have you got maths eyes
Workshop 3: Developing student agency through a growth mindset
Agency and Growth Mindsets are both big in their own right. The aim here is to put the learner in the driving seat. However, when you are in the passenger seat for the first time, it is a very weird feeling, as you have to let go of the controls. Giving students control is a risk, but they are also taking the risk as a learner...
Give students ways to talk and think in a 'Growth Mindset' way, rather than them saying "I can't do it, I will never get to do it". The word 'yet' is powerful to use.
How can we encourage students to develop student agency and a growth mindset?
Move away from making all the decisions, what books they are going to read, what maths equipment / tools they are going to use.
Teachers also have to develop a growth mindset:
- Use technology to make both their own and students' learning richer
- Risk trying new learning
- Bring their own student passion into learning activities
- Let go of the need to control all variables
- Find ways to change even under adversity
- Value relationships with students
- Make a difference in student lives
- Network and connect with others for resources, assistance and support
Learning Mindsets/beliefs:
- Growth Mindset: Value mistakes and use them. Talk more about struggles and strategies to overcome them
- Sense of Belonging: Student Voice (What can I do as a teacher to help you more? What can you do to help yourself?). Ethic of Care
- Relevance: students will be more engaged if learning is relevant and they are given a choice
- Self-efficacy: when students understand their goals, they can monitor their learning and it is going to be more meaningful for them
Student Self Assessment 'tools' to support self managing:
When teachers and students focus on improvement rather than on whether they're smart, kids learn a lot more when they had a deeper understanding of themselves as learners, so they could build their own autonomy to change and gain confidence in their academic abilities
Reflection:
My aim with attending this symposium was to learn further how I can take sensible steps to provide and maintain a teaching and learning environment through my planning. I wanted to make sure that I select the right approaches to address the needs of all my students. This day was worthwhile and I walked away with lots of new ideas to implement with my students.
Next Steps:
To put my learners in the driver seat by developing learner agency in our learning environment. To step back a bit and let the students taking a little bit more ownership.
~ "Pure mathematics is, in its way, the poetry of logical ideas" - Albert Einstein ~
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