Plenary presentation from conference on 23rd October 2014. Overview of relevant research, practical frameworks for designing and evaluating learning activities (TPACK and the Activity Types taxonomy), and a quick look at the SAMR model.

1. Thursday 23rd October 2014
Stephen McConnachie

2. Students need these skills – the world they are
preparing for is not the world we prepared for

3. 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

4. Multiple representations of the same concept
Caters for different learning styles, allows
students to make connections between
representations
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)

5. Multiple representations of the same concept
Related to that: different media synchronised into
multi-modal presentations
- Created by students OR teachers
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)

6. Multiple representations of the same concept
Related to that: different media synchronised into
multi-modal presentations
Links / hyperlinks within the resources –
networking the activities
Teachers can create a learning path / flow
within the resources themselves
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)

7. 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
Eg web applets / manipulatives
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)

8. 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
It allows for ubiquitous learning, but
boundaries must still be enforced
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)

9. 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
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)

10. 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
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)

11. Student
Agency.

12. Student
Agency.
Actively involved, reflective, connected learners who take responsibility
for their own learning

13. Lots of research
Not new
Students collaborating build a “shared
understanding” of the knowledge
Bounce ideas off each other

14. Li & Ma, 2010:
Using technology in maths education is
effective (raises achievement)
It is even more effective when combined with
a constructivist approach
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.

15. 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?

16. 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

17. 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 Achieved
Multi-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

18. or, “How SOLO helped me to reconcile Constructivism and
Objectivism with regard to e-learning in Mathematics”, to put
it more boringly
Stephen McConnachie
Originally presented at CMA Mini-Conference 2014

19. “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.
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.

20. “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”.
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.

21. 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
“Traditional Maths” “Effective e-Learning”

22. 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?

23. Pre-Structural
Multi-Structural
Uni-Structural
Relational
Extended Abstract
Read more about SOLO Taxonomy

24. Not Achieved
Achieved Merit
Excellence

25. Requires directed
teaching
Requires scaffolded
teaching but benefits
from constructivist
approaches
Requires
constructivist
approaches

26. We need both.

27. We need both.
Surprise

28. We already knew this for Maths in the
classroom
Dan Meyer
Rich tasks
Effective questioning

29. 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.

30. Drilling with a flashy animation and a hip
blinged-up avatar is not effective pedagogy
for developing higher order thinking

31. 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

32. Requires directed
teaching
Requires scaffolded
teaching but benefits
from constructivist
approaches
Requires
constructivist
approaches

33. Conceptual / Procedural knowledge
Social learning theory
Constructivist learning theory
SOLO
What does this actually look like?
How do we do this in practice?!

34. 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…

35. TPACK:
Technological
Pedagogical
Content
Knowledge
T
P C

36. TPACK:
Technological
Pedagogical
Content
Knowledge
T
Technological
knowledge – how
to use technology
P C
Content knowledge
– how to do maths
Pedagogical
knowledge – how
to teach effectively

37. TPACK:
Technological
Pedagogical
Content
Knowledge
T
TP
P C
Technological
pedagogical
knowledge – how
to use technology
to teach effectively

38. TPACK:
Technological
Pedagogical
Content
Knowledge
T
TC
Technological
content knowledge
– how to use
technology to do
maths
P C

39. TPACK:
Technological
Pedagogical
Content
Knowledge
T
P PC C
Pedagogical
content knowledge
– how to teach
maths effectively

40. TPACK:
Technological
Pedagogical
Content
Knowledge
T
TPC
Technological
pedagogical
content knowledge
– how to use
technology to
effectively teach
maths
P C

41. Grandgenett, Harris and Hofer’s Activity Types
Taxonomy for Maths:
TPACK broken down into a practical taxonomy
for teachers

43. bit.ly/mathsATtax
Seven levels
Very practical
HUGELY useful

44. The SAMR Model
Substitution
Augmentation
Modification
Redefinition
More: SAMR Model explained on TKI

45. YouTube clip: why SAMR

46. YouTube clip: SAMR with example

47. http://techtipsedu.blogspot.co.nz/2013/11/samr-model-metaphor-mistakes.html

48. There is nothing wrong with Substitution
Start small, but start somewhere

49. Activities that require students to:
Create
Collaborate
Think critically
Reflect on their own learning

50. Social, constructive, student-centred
TPACK, Activity Types