e-learning in maths - research, practical tips and discussion

e-Learning in Maths:What does the research

say?and how do we do it?

Thursday 23rd October 2014Stephen McConnachie

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

Why e-Learning?

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?

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

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

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

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

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

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)

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)

Student Agency.

Why e-Learning?

Student Agency.

Why e-Learning?

Actively involved, reflective, connected learners who take responsibility for their own learning

Lots of research Not new Students collaborating build a “shared

understanding” of the knowledge Bounce ideas off each other

Social Learning Theory

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.

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

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

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

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

“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.

“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.

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

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?

Enter SOLO Taxonomy…

Pre-Structural

Uni-Structural

Multi-Structural

Relational

Extended Abstract

Read more about SOLO Taxonomy

Enter SOLO Taxonomy…

Not Achieved

Achieved Merit

Excellence

Enter SOLO Taxonomy…

Requires directed teaching

Requires scaffolded teaching but benefits from constructivist approaches

Requires constructivist approaches

We need both.

My conclusion:

We need both.

Surprise

My conclusion:

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

My conclusion:

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:

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

All objectivist – bad

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

We need both.

Requires directed teaching

Requires scaffolded teaching but benefits from constructivist approaches

Requires constructivist approaches

Conceptual / Procedural knowledge Social learning theory Constructivist learning theory SOLO

What does this actually look like?How do we do this in practice?!

Summary

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?!

TPACK:

TechnologicalPedagogicalContentKnowledge

Activity Types Taxonomy

T

P C

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

TPACK:

TechnologicalPedagogicalContentKnowledge

Activity Types Taxonomy

T

P C

TP

Technological pedagogical knowledge – how to use technology to teach effectively

TPACK:

TechnologicalPedagogicalContentKnowledge

Activity Types Taxonomy

T

P C

TC

Technological content knowledge – how to use technology to do maths

TPACK:

TechnologicalPedagogicalContentKnowledge

Activity Types Taxonomy

T

P CPC

Pedagogical content knowledge – how to teach maths effectively

TPACK:

TechnologicalPedagogicalContentKnowledge

Activity Types Taxonomy

T

P C

TPC

Technological pedagogical content knowledge – how to use technology to effectively teach maths

Grandgenett, Harris and Hofer’s Activity Types Taxonomy for Maths:

TPACK broken down into a practical taxonomy for teachers

Activity Types Taxonomy

bit.ly/mathsATtax

Seven levels Very practical HUGELY useful

Activity Types Taxonomy

The SAMR Model Substitution Augmentation Modification Redefinition

More: SAMR Model explained on TKI

The Journey

YouTube clip: why SAMR

YouTube clip: SAMR with example

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

There is nothing wrong with Substitution

Start small, but start somewhere

e-Learning – where do I start?

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

e-Learning – what should I be aiming for?

e-Learning in Maths:Social, constructive, student-centred

TPACK, Activity Types