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e-Learning in Maths:What does the research
say?and how do we do it?
Thursday 23rd October 2014Stephen McConnachie
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Students need these skills – the world they are preparing for is not the world we prepared for
Why e-Learning?
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Students need these skills – the world they are preparing for is not the world we prepared for
They need to be fluent with the technological skills, but also the technological resilience, and being comfortable operating in online communities working toward a common goal
Why e-Learning?
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Multiple representations of the same concept
Why e-Learning?
From Kramer & Schmidt, 2001 “Components and tools for on-line education” (p195)As quoted in Pachler & Daly, 2011 “Key Issues in e-Learning: Research and Practice” (p21)
Caters for different learning styles, allows students to make connections between representations
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Multiple representations of the same concept Related to that: different media synchronised into
multi-modal presentations
Why e-Learning?
From Kramer & Schmidt, 2001 “Components and tools for on-line education” (p195)As quoted in Pachler & Daly, 2011 “Key Issues in e-Learning: Research and Practice” (p21)
- Created by students OR teachers
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Multiple representations of the same concept Related to that: different media synchronised into
multi-modal presentations Links / hyperlinks within the resources –
networking the activities
Why e-Learning?
From Kramer & Schmidt, 2001 “Components and tools for on-line education” (p195)As quoted in Pachler & Daly, 2011 “Key Issues in e-Learning: Research and Practice” (p21)
Teachers can create a learning path / flow within the resources themselves
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Multiple representations of the same concept Related to that: different media synchronised into
multi-modal presentations Links / hyperlinks within the resources –
networking the activities Interaction / interactivity – allows students to
construct and collaborate
Why e-Learning?
From Kramer & Schmidt, 2001 “Components and tools for on-line education” (p195)As quoted in Pachler & Daly, 2011 “Key Issues in e-Learning: Research and Practice” (p21)
Eg web applets / manipulatives
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Multiple representations of the same concept Related to that: different media synchronised into
multi-modal presentations Links / hyperlinks within the resources –
networking the activities Interaction / interactivity – allows students to
construct and collaborate Ubiquitous* learning – sickness, sports trips,
homework
Why e-Learning?
From Kramer & Schmidt, 2001 “Components and tools for on-line education” (p195)As quoted in Pachler & Daly, 2011 “Key Issues in e-Learning: Research and Practice” (p21)
It allows for ubiquitous learning, but boundaries must still be enforced
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Multiple representations of the same concept Related to that: different media synchronised into
multi-modal presentations Links / hyperlinks within the resources –
networking the activities Interaction / interactivity – allows students to
construct and collaborate Ubiquitous* learning – sickness, sports trips,
homework Ubiquitous access to learning communities
Why e-Learning?
From Kramer & Schmidt, 2001 “Components and tools for on-line education” (p195)As quoted in Pachler & Daly, 2011 “Key Issues in e-Learning: Research and Practice” (p21)
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Multiple representations of the same concept Related to that: different media synchronised into
multi-modal presentations Links / hyperlinks within the resources –
networking the activities Interaction / interactivity – allows students to
construct and collaborate Ubiquitous* learning – sickness, sports trips,
homework Ubiquitous access to learning communities Modelling – virtual laboratories / environments
Why e-Learning?
From Kramer & Schmidt, 2001 “Components and tools for on-line education” (p195)As quoted in Pachler & Daly, 2011 “Key Issues in e-Learning: Research and Practice” (p21)
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Student Agency.
Why e-Learning?
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Student Agency.
Why e-Learning?
Actively involved, reflective, connected learners who take responsibility for their own learning
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Lots of research Not new Students collaborating build a “shared
understanding” of the knowledge Bounce ideas off each other
Social Learning Theory
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Li & Ma, 2010:
Using technology in maths education is effective (raises achievement)
It is even more effective when combined with a constructivist approach
Constructivist Learning Theory
Li, Q., & Ma, X. (2010). A meta-analysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review, 22(3), 215-243.
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Mathematics has traditionally been taught procedurally; that is, as a list of steps for students to follow in order to reach the correct answer
(McLeod et al., 2012)
Do you agree?
Constructivist Learning Theory
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Procedural learning: “knowing how to do something or recalling the algorithm to solve a problem”
Conceptual learning: “knowledge of the interrelationships of the basic elements that make up larger structures”
- Anderson et al., as cited in McLeod et al., 2012
Constructivist Learning Theory
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Types of knowledge(Anderson; McLeod)
SOLO Taxonomy(Biggs & Collis)
SOLO Taxonomy “major category”(TKI, n.d.)
NCEA achievement levels(NZQA, n.d.)
Pre-structural Not Achieved
Procedural knowledge
Uni-structural“Surface” thinking
AchievedMulti-structural
Conceptual knowledge
Relational“Deep” thinking
Merit
Extended abstract
Excellence
McLeod, J., Vasinda, & S., Dondlinger, M. (2012). Conceptual visibility and virtual dynamics in technology-scaffolded learning environments for conceptual knowledge of mathematics. Journal of Computers in Mathematics and Science Teaching 31(3), 283-310.
New Zealand Qualifications Authority [NZQA]. (n.d.). Level 1 Achievement Standards – Mathematics and Statistics Retrieved from http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/subjects/mathematics/clarifications/level-1/level-1-achievement-standards-mathematics-and-statistics/
Te Kete Ipurangi [TKI] (n.d.). Chapter 1: Curriculum. asTTle V4 Manual 1.0. Retrieved from http://assessment.tki.org.nz/content/download/259/1546/file/chapter1.pdf
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Maths, e-Learning and SOLO
or, “How SOLO helped me to reconcile Constructivism and Objectivism with regard to e-learning in Mathematics”, to put it
more boringlyStephen McConnachie
Originally presented at CMA Mini-Conference 2014
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“Knowledge has a separate, real existence of its own outside the human mind. Learning happens when this knowledge is transmitted to people and they store it in their minds.” – Roblyer, 2006
Maths as we know it – a defined set of skills that necessarily build on each other in a more-or-less linear progression of knowledge.
Objectivism
Roblyer, M. D. (2006). Chapter 2: Foundations of Effective Technology Integration Models: Theory and Practice, Integrating Educational
Technology into Teaching (4th ed.), Upper Saddle River, New Jersey: Prentice Hall, Inc.
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“Humans construct all knowledge in their minds by participating in certain experiences. Learning occurs when one constructs both mechanisms for learning and his or her own unique version of the knowledge, colored by background, experiences, and aptitudes.” – Roblyer, 2006
“The good ICT” – students creating, collaborating, constructing. What is perceived to be “21st Century Learning”.
Constructivism
Roblyer, M. D. (2006). Chapter 2: Foundations of Effective Technology Integration Models: Theory and Practice, Integrating Educational
Technology into Teaching (4th ed.), Upper Saddle River, New Jersey: Prentice Hall, Inc.
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To put those side by side:
“Traditional Maths” “Effective e-Learning”
Objectivism: Requires directed
learning Instructional Design
models Specific skills Drilling
Constructivism: Requires collaborative
learning with students creating together to construct knowledge, tie it into their prior knowledge and experience and represent it in a way that is meaningful to them
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Is there more to Maths e-Learning than just flashy animations that drill skills?
Are we “doing e-learning wrong” by using flashy animations that drill skills?
How do we reconcile these two?
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Enter SOLO Taxonomy…
Pre-Structural
Uni-Structural
Multi-Structural
Relational
Extended Abstract
Read more about SOLO Taxonomy
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Enter SOLO Taxonomy…
Not Achieved
Achieved Merit
Excellence
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Enter SOLO Taxonomy…
Requires directed teaching
Requires scaffolded teaching but benefits from constructivist approaches
Requires constructivist approaches
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We need both.
My conclusion:
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We need both.
Surprise
My conclusion:
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We already knew this for Maths in the classroom Dan Meyer Rich tasks Effective questioning
My conclusion:
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We already knew this for Maths in the classroom Dan Meyer Rich tasks Effective questioning
We now need to apply it to our e-learning programmes.
My conclusion:
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Drilling with a flashy animation and a hip blinged-up avatar is not effective pedagogy for developing higher order thinking
All objectivist – bad
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Airy-fairy thinking activities are all well and good but if students don’t have the basic skills they don’t have the basic skills
All constructivist – bad
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We need both.
Requires directed teaching
Requires scaffolded teaching but benefits from constructivist approaches
Requires constructivist approaches
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Conceptual / Procedural knowledge Social learning theory Constructivist learning theory SOLO
What does this actually look like?How do we do this in practice?!
Summary
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If only there was some really practical framework that scaffolded activity design…
…that was based on solid research but was written in everyday language, that teachers could just pick up and use tomorrow…
How do we do that?!
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TPACK:
TechnologicalPedagogicalContentKnowledge
Activity Types Taxonomy
T
P C
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TPACK:
TechnologicalPedagogicalContentKnowledge
Activity Types Taxonomy
T
P C
Technological knowledge – how to use technology
Content knowledge – how to do maths
Pedagogical knowledge – how to teach effectively
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TPACK:
TechnologicalPedagogicalContentKnowledge
Activity Types Taxonomy
T
P C
TP
Technological pedagogical knowledge – how to use technology to teach effectively
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TPACK:
TechnologicalPedagogicalContentKnowledge
Activity Types Taxonomy
T
P C
TC
Technological content knowledge – how to use technology to do maths
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TPACK:
TechnologicalPedagogicalContentKnowledge
Activity Types Taxonomy
T
P CPC
Pedagogical content knowledge – how to teach maths effectively
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TPACK:
TechnologicalPedagogicalContentKnowledge
Activity Types Taxonomy
T
P C
TPC
Technological pedagogical content knowledge – how to use technology to effectively teach maths
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Grandgenett, Harris and Hofer’s Activity Types Taxonomy for Maths:
TPACK broken down into a practical taxonomy for teachers
Activity Types Taxonomy
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bit.ly/mathsATtax
Seven levels Very practical HUGELY useful
Activity Types Taxonomy
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The SAMR Model Substitution Augmentation Modification Redefinition
More: SAMR Model explained on TKI
The Journey
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http://techtipsedu.blogspot.co.nz/2013/11/samr-model-metaphor-mistakes.html
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There is nothing wrong with Substitution
Start small, but start somewhere
e-Learning – where do I start?
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Activities that require students to: Create Collaborate Think critically Reflect on their own learning
e-Learning – what should I be aiming for?
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e-Learning in Maths:Social, constructive, student-centred
TPACK, Activity Types