Mathematics Network Conference

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 2 About the Bridging Mathematics Network No formal structure Range of interests: bridging courses, re-entry issues Academic “fringe dwellers” Conference tends to precede MERGA conferences Inclusive atmosphere

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 3 About the Bridging Mathematics Network Conferences 2002 Auckland (Unitec) ~50 2000 Perth (Murdoch) <20 1998 Toowoomba (USQ) 1997 Auckland < 65 “Australasian Bridging Mathematics Network” 1996 Adelaide < 32 1995 Darwin (Batchelor) Sydney “Australian Bridging Mathematics Network” 1993 Brisbane (QUT) 1992 Canberra (ANU) “Bridging Mathematics Group” 1991 Bathurst (CSU) “NSW Bridging Mathematics Group”

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 4 Seminar Contents Who wants to cross the bridge? Crossing the bridge: distance education, ESL A current issue: Graphic Calculators Tricks in Powerpoint

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 5 Who Wants to Cross the Bridge? Mature age students (varied, inc. “maths phobics”) International students (ESL) Indigenous students Other Equity Groups

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 6 Adults Returning to Study Maths (Mary Jane Schmitt, TERC) Tertiary Education Research Centre Cambridge Massachusetts Extending Mathematical Power (EMPower) Project K-12 Adults and out-of-school youth Multi-level classes

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 7 Adults Returning to Study Maths (Mary Jane Schmitt) “Describe in complete sentences a pattern in your life that involves numbers. Say how the pattern plays out over time, in terms of a week, or a year, or longer. What predictions might someone else make by studying your pattern?”

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 8 Adults Returning to Study Maths (Mary Jane Schmitt) First Lesson: “Every year on Oct. 19 is my b-day. As soon as I get in from class I call a friend (Carter) around 1:30-1.45. I wake up at 10:30 everyday . . .”

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 12 Adults Returning to Study Maths (Stuart Laird, Auckland) ... a student coming across symbolic mathematics for what is effectively the first time does it not like a blank book waiting to be written on, they have literally to construct the apparatus with which they will perceive …

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 13 Adults Returning to Study Maths “And how is education supposed to make me feel smarter? Besides, every time I learn something new, it pushes some old stuff out of my brain. Remember when I took that home winemaking course, and I forgot how to drive?” Homer Simpson

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 14 Adults Returning to Study Maths: “Maths Phobia” (Phil Kane, Manukau) “I just don’t have the brain for maths” Interviews with bridging maths students about school: Lack of relevance Teaching emphasises process over understanding Diverse learning styles/speeds not allowed for

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 15 Adults Returning to Study Maths: “Maths Phobia” (Geoff Coates) Maths learning is highly sequential over a long period Maths is often not a teacher’s first skill Students obliged to study maths for job purposes It helps if someone in family has a maths background

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 16 Toowoomba High School Survey (Mehryar Nooriafshar, USQ) I regard mathematics to be . . . Nooriafshar, Mehryar. (2002). Factors Contributing to Making the Learning of Statistics an Enjoyable Experience. (Unpublished paper). University of Southern Queensland.

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 20 Breaking the Cycle: Primary Teachers (Jane Ewing, UTS) Action points: Put maths in true social context A strong maths foundation crucial to future Ensure Primary Teachers are numerically proficient

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 21 Breaking the Cycle: Primary Teachers (Jane Ewing, UTS) Academic Malpractice: “What do you promise the student will learn? If you don’t provide sufficient education to enable the student to learn you might be guilty of breach of contract, negligence, or misleading and deceptive conduct.” Lyndal Taylor (Chair, Int’l Bar Assoc. Academic Forums)

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 22 Crossing the Bridge: distance education (Janet Taylor, James Taylor, USQ) 75% of USQ students are off campus Five Generations of distance education (James Taylor): Print based correspondence 4. Computer mediated communication using human response systems 5. Computer mediated communication using automated response systems

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 23 Crossing the Bridge: distance education (James Taylor, USQ) USQ has developed an e-content management system Works within PeopleSoft Cross-media publishing from a single source XML Maths typesetting by MathML?

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 24 Crossing the Bridge: distance education (Kathy Egea, CQU) Face-to-face delivery minimises student anxiety Computer-based diagnostic test Dynamic: chooses pathway based on student answers and reflection (easy vs not easy) Prototype met approval of experts and students “the test was not a test”

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 25 Crossing the Bridge: distance education (Janet Taylor, USQ) Access to Technology (internet/email): Over 80% of USQ external undergrads have email 71% of external Tertiary Prep (TP) have email 32% of Equity Group external TP have email Equity Group access levels static since 1998 Others have risen 30 percentage points since 1998

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 26 Crossing the Bridge: indigenous distance education (Ashton Eibeck, Nulloo Yumbah, CQU) Access: Establish internet sites in regional Access: areas Access: Intensive Residential Schools Anxiety: Reflective Journals Too Much Text: video clips of teaching on CD ROM Feedback: self-test with password for next topic

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 27 Crossing the Bridge: ESL students (Mike Baldwin, Waikato) Setting writing activities in statistics course Better interaction when asked to rate their confidence in understanding question and accuracy of answer

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 28 Crossing the Bridge: ESL students (Mike Baldwin, Waikato) Should ESL students learn only in English? Yes: concepts learned in one language stay there Yes: translation method inefficient No: quality of thinking is superior in own language “It is impossible to attach English to something you do not understand.”

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 29 Technology: Graphic Calculators (Greg Oates, Auckland) Graphic Calculators (GC) introduced on voluntary basis in Level I Maths subject 2001 Syllabus unchanged Minimal training in GC use Formative assessment calculator neutral

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 30 Technology: Graphic Calculators (Greg Oates, Auckland) Survey of GC use at end of course (before exams) 215 responses (out of 320) Uptake: 81 used GC, 63 bought one via Dept. Uptake: 60% of others nominated cost as reason Uptake: 19% didn’t want one or felt GC was no use

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 31 Technology: Graphic Calculators (Greg Oates, Auckland) Usefulness: 75% of users felt GC helped with Usefulness: homework Usefulness: Many felt non-GC users were Usefulness: disadvantaged Used for: 88% used GC to check answers sometimes Used for: 78% used to conduct matrix operations Used for: 34% copied GC demonstrations in lectures

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29 October, 2002 Copyright © 2002 The University of Adelaide Slide Number 32 Technology: Powerpoint (Stuart Laird, Auckland) Useful teaching aid? Easy to access online and run? Easy to prepare? Example 1: Slope Fields

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Consider This allows us to calculate a gradient at any point (x,y) (0,4) (1.5,1) (1.5,5) (2,7) Note: Here the gradient depends only on x

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Euler’s method works by approximating the curve by a series of straight line segments

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The population of Australian adult men is Normally distributed with a mean of 175 cm and a standard deviation of 7 cm. 154 161 168 175 182 189 196 What proportion of men are taller than 182 cm?

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The population of Australian adult men is Normally distributed with a mean of 175 cm and a standard deviation of 7 cm. 154 161 168 175 189 196 What proportion of men are taller than 182 cm? 182