Technology: Boots, Warts & All
AMA 5 April 2014
GREG OATES
Department of Mathematics,
The University of Auckland
Complex, Inter-Related Factors affecting
Successful Technology Integration
“DOING Maths”
VS
“LEARNING Maths”
VS
“Delivery & Management”
“Doing Maths” vs “Learning Maths”
vs “Delivery & Management”
Doing Maths: Technology as a tool-Research Mathematicians;
Commercial & workplace, e.g. Excel, Matlab, Maple
(past=slide rules, log tables etc)
Learning Maths: Teachers, educators. Pedagogical Technical
Knowledge (PTK); CAS-calculators; Internet & Software
options; Geogebra, Desmos, Mathematics, Autograph,
Wolfram Alpha, Khan Academy, BYOD
Maths delivery & Management: Powerpoint, Tablet PC’s,
data-projectors; Interactive Whiteboards; Learning
Management systems (Onenote; Moodle; Cecil);
Response systems (eg clickers)
Learning Maths: PTK
:
The necessary knowledge of the principles and
techniques required to teach mathematics using a
given technology (Thomas & Hong, 2013).
Mathematicians tend to have a “tool”=oriented view
of technology, hence calculators seen as toys,
limited awareness of learning opportunities, e.g.
visualisation (rule of four); Exploration; skills
building through repetitive exposure; (PTK),
lessens arithmetic errors.
Drijvers, 2012
Learning Maths PTK:
Thomas & Hong, 2013
Boots & All:
Explosion of options/possibilities; BYOD
What’s Available? (not even touching on statistics)
•Calculators: Scientific, Graphics, CAS, e.g. TI-nSpire –links
between teacher & students;
•Delivery: Data Projectors, Interactive Whiteboards, overhead
data-cameras; Tablet PC’s, lecture recordings;
•BYOD: Flipped Classrooms & Blended Learning: Huge range of
options Doceri, Smartphones to make recordings; Internet access
via tablets, computers, smartphones: Wolfram Alpha, Khan
Academy, Freeware: e.g. Desmos, Geogebra; Math Way (need to
purchase for full functionality); Other Commercial , eg Autograph
•Access: now potentially less of problem? – many platforms work
on Smartphones (apps); Have calculators lost their advantage of
portability?
Boots & All: UoA
LUMOS Project Maths 102
•Lectures: Desmos, Wolfram Alpha, smart-phone response app;
•Assignments: Promote active use of technology –e.g. marked
correct if use technology (issues of how students show answers);
ask for graphs using technology;
•Group Tutorials: Tasks designed to be technology-active;
BYOD; only one out of five tutorials in computer lab (Desmosstudents highly familiar even in just 4 weeks); Tutorial with
Smartphone video as task; (total 10% of coursework)
•Assessment: Test (10%) & five Skills quizzes (10 questions
each quiz, worth 1%) done online using MathXL; Exam (60%) still
traditional except CAS calculators permitted (fewer have);
•Learning: Encouraged to use web; Learning support quizzes
(with study plans) on MathXL
Warts
Rots Brain, Destroys Skills: This view is
a distraction, non-productive: Ineffective use
certainly can have this effect– this is the BIG CHALLENGE:
How to promote, develop effective use –Instrumental Genesis?
Access: Cost of many options still high, even freeware cant be
accessed without a phone or computer; Often not allowed in
summative assessment (e.g. exams); Which technology to
choose?
Syntax & Instrumentation: Can take a while for teachers &
students to learn (advantage of Desmos is that it doent take long
at all)–learning technology can get in the way of the mathematics;
PTK: Growing challenge for teachers, especially with BYOD, how
to keep up with the affordances, instrumentation of so many
different technologies?
Online Learning
& Assessment
Summer Project 2012/2013: UoA – Michael Walden & Simeon
Pattenwise: Looked at wide variety of online learning &
assessment platforms (not e.g. Math Way-primarily learning);
Settled on MathXL (advantages described earlier);
Technology–Active Assessment: They looked at a large
number of questions traditionally asked in Maths 102 exams:
Classified as Technology –Trivial; -Neutral, Active
Trivial: (Does not imply the question is trivial)
e.g. Determine the gradient & y-intercept of 5y + 3x - 2 =0.
Even without technology, this is largely a routine procedural
question. (Skemp’s instrumental vs relational understanding).
How might we transform or ask such a question as technology-active?
Example: Asking
Technology-Active Questions
Find
71
3 3

x3 dx
6
How can technology help?
4
Scientific calculator - limited
to arithmetic value;
GC - sketch a graph,
2
helps with visualisation;
CAS - will just give answer
(Wolfram Alpha, Geogebra,
0
2
4
TI-nSpire etc); Can also
Show area under curve – calculate as move across.
6
8
Example: Asking
Technology-Active Questions
Suppose you know that the definite integral for a certain
function f(x) between a and b equals 15, i.e.

b
a
f ( x) dx  15
What can you say about the integral of f(x) + 4 between the
same limits, i.e.
  f ( x)  4dx  ?
b
a
Thank You
Promos:
*MEU Post-Grad Courses: b.barton@auckland.ac.nz
*Maths Olympiad: p.kane@auckland.ac.nz
*Teacher Study Awards (close early June): Information
meeting to be held at Epsom Campus – AMA to email.