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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 ”. - PowerPoint PPT Presentation
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Technology: Boots, Warts & AllAMA 5 April 2014
GREG OATESDepartment of Mathematics,
The University of Auckland
Complex, Inter-Related Factors affecting Successful Technology Integration
“DOING Maths”VS
“LEARNING Maths”VS
“Delivery & Management”
Technology as a tool-Research Mathematicians; Commercial & workplace, e.g. Excel, Matlab, Maple (past=slide rules, log tables etc)
Teachers, educators. Pedagogical Technical Knowledge (PTK); CAS-calculators; Internet & Software options; Geogebra, Desmos, Mathematics, Autograph, Wolfram Alpha, Khan Academy, BYOD
Powerpoint, Tablet PC’s,data-projectors; Interactive Whiteboards; Learning Management systems (Onenote; Moodle; Cecil); Response systems (eg clickers)
“Doing Maths” vs “Learning Maths” vs “Delivery & Management”
Doing Maths:
Learning Maths:
Maths delivery & Management:
Learning Maths: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
PTK :
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?
• 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 (Desmos-students 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
Boots & All: UoALUMOS Project Maths 102
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?
Warts
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, ActiveTrivial: (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?
Online Learning& Assessment
How can technology help?
Scientific calculator - limitedto arithmetic value; GC - sketch a graph, helps with visualisation; CAS - will just give answer(Wolfram Alpha, Geogebra,TI-nSpire etc); Can also Show area under curve – calculate as move across.
Example: AskingTechnology-Active Questions
7
3
331 dxxFind
0 2 4 6 8
6
4
2
Suppose you know that the definite integral for a certain function f(x) between a and b equals 15, i.e.
Example: AskingTechnology-Active Questions
15)( b
adxxf
What can you say about the integral of f(x) + 4 between the same limits, i.e.
?4)( b
adxxf
Thank You
Promos:*MEU Post-Grad Courses: [email protected]*Maths Olympiad: [email protected]*Teacher Study Awards (close early June): Information meeting to be held at Epsom Campus – AMA to email.