An alternative learning experience in transition level mathematics

An alternative learning experience in
transition level mathematics
Screen captured lectures, collaborative activities, and more

Dann Mallet
QUT Mathematical Sciences

Mallet (QUT Math Sci)

Transition mathematics trial

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Outline

Outline

1

Introduction and context

2

Collaborative learning ideas

3

Recording lecture videos

4

SCORM packages

5

Results – engagement



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Outline

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2


3


4

SCORM packages

5




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The unit – MAB105 Preparatory Mathematics

The most elementary maths unit QUT oﬀers
Among the most diverse cohorts (unit does not belong in any course)
“Like” high school mathematics, steep learning curve
Fundamental to vast number of degree programs
Recently lost favour, but being reborn!



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The unit – MAB105 Content

Properties of the number system
Basic algebra
Functions and equations, graphs
Linear functions – equations and applications
Systems of linear equations
Non-linear functions
quadratic, exponential, logarithmic, trig: properties, applications

Introduction to calculus
rates of change, derivatives, rules of diﬀerentiation, optimization,
applications



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The unit – MAB105 Learning outcomes
1

Solve straightforward equations and draw and interpret graphs of one
independent variable.

2

Understand the concepts involved with functions and functional
notation and in particular know the properties associated with
quadratic, exponential, logarithmic and trigonometric functions and
applications of same.

3

Understand the concepts involved with rates of change, derivatives,
maxima, minima and integration.

4

Engage in analytical thinking skills and communicate clearly and
concisely in mathematical language.



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The unit – MAB105 Assessment

Semester/Year

Items & weighting

2008
2009
2010
2011
2012
2013

Participation/Assignments 40%, ES Exam 60%
Assignments 20%, MS Exam 20%, ES Exam 60%
PST 40%, ES Exam 60%

Fairly “standard” mathematics assessment style: heavy on exam and
assignment



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The unit – MAB105: Enrolments

MAB105 Enrolments 2008-2013

150
100

2/13

1/13

2/12

1/12

2/11

1/11

2/10

1/10

2/09

1/09

2/08

50
1/08

Enrolments

200

Semester


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The unit – MAB105: Results

Percentage of all students

MAB105 Grade distribution (all students) 2008-2013

30
20
10
0


K

1

2

3 4
Grade

5


6

7

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How has MAB105 evolved?

Long transition – my involvement: since 2001
First press: handwritten OHTs, textbook, lectures.
A
Introduced booklet of LTEX ed notes (AC Farr, DG Mallet)
text aligned, inbuilt worksheets, reduced dependence on f2f
A
Introduced set of LTEX ed lecture slides (ﬁll in the gap style) (AC
Farr)

text/notes aligned, reduced dependence on f2f

Introduced workbook-style version of booklet (AC Farr)
further reduced dependence on f2f



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The next step – motivation

“Tertiary institutions will be challenged not only to meet growing demand by expanding
the number of places offered, but also to adapt programmes and teaching methods to
match the diverse needs of a new generation of students.”1
“Today in education, we are witnessing an unbundling of previous network structures.
And a rebuilding of new network lock-in models.”2
“We are living in a constantly changing environment. This situation should force
teachers to constantly re-think their pedagogical philosophy.”3
1
2
3

OECD, 2013, Education at a glance 2013: OECD indicators. OECD Publishing. http://dx.doi.org/10.1787/eag-2013-en
G. Siemens, Associate Director, Technology Enhanced Knowledge Research Institute, Athabasca University
I. Czaplinski, 2012, Affordances of ICTs: An environmental study of a French language unit offered at university level. UQ.



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The next step – motivation

People are doing new, cool things in delivering learning experiences
QUT built collaborative learning spaces
Students don’t show up “just for lectures/tutorials”
Also, national/international agendas...



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The next step – a summary

So what has been done? How much effort was it? What happened?
Here’s what students experienced this semester:
No f2f lectures
Weekly workshops of various styles
Problem sheets
Expert exemplars
Clean and annotated slides
Lectures in video form

Effort = slightly less.
Results:
w.r.t students? wait til after exam. Seminar 2 in January
w.r.t. me? greater planning, better “product”, more reflection



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Outline

1


2


3


4

SCORM packages

5




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Overview

What can we do here? Well, besides mathematics...
Team building
Communication
Technology

Let’s take a look at some examples from this year...



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Team building

Activity: BOMDAS (you know
it? can you do it?)
Purpose: Team formation,
communication, community
building, intro/warm up
Possibilities: competitive,
enduring identification

Workshop 1

MAB105

Preparation and instructions
Before commencing the activity, make sure you are in groups of no more than 6 people. You may
use pen and paper, whiteboards, glass boards, COWs, calculators and your heads.
1. Give your group a name – decide carefully, you’ll be using it for the rest of semester.
2. Nominate one person in the group to be note-taker. The note-taker will keep a record of
discussions and decisions, as well as the final group response.
3. Nominate one person to be the scribbler. They will do any necessary writing and calculating
on the whiteboard.
4. Nominate another person to be the reporter. The reporter will report back to the class on the
group’s response to the task.
5. All group members should then read the task below.
6. Then the group should work together to attempt to come up with the best possible group
responses.
7. Finally, the reporters from each group will report back to the class to see which group has
come up with the best responses.

Background
Let’s say you were given the numbers 5, 6 and 7 and the operations of addition and subtraction. If
you must use each number and operation once, and only once, then the largest possible result is
7+6−5 = 8
and the smallest possible result is
5 + 6 − 7 = 4.

The task

Unexpected: definitions of
terms

Using each of the numbers 2, 3, 4, 5, 6 and 7 once, and only once, and each of the operations of
addition, subtraction, multiplication, division and exponentiation (raising to a power) once, and
only once, your group is to attempt to make
1. the largest number possible and
2. the smallest number possible.
When reporting back to the class, the reporter needs to the provide two numbers, as well as discuss
two decisions that the group made while attempting to find the numbers.

CRICOS No. 00213J



1

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Communication

Workshop 3

MAB105


Activity: communication of
factorising/solving

Before commencing the activity, make sure you are in groups of no more than 6 people. You may
use pen and paper, whiteboards, glass boards, COWs, calculators and your heads.
1. If your table has a group name from the first workshop, reuse it. Otherwise, make up a new
group name and write your names along with the group name on the piece of paper you are
given.
2. Using the COW, navigate a web browser to goanimate.com, and have one of the group either
login using an existing account or sign up for a new one.
3. The group can either work together on the problems (for example, split the problems up with
everybody attempting only one), or you might wish to attempt them all yourself.

The task
Attempt each of the following problems either on a whiteboard, on paper or in your notebooks.
1. Factorise the expression 16a5
2. Solve the equation 3( x

36a3

1) = 2x + 4 for x

3. Factorise the expression 2t2 + 20t + 18
4. Factorise the expression 4x2

Purpose: Communication,
exploring unknown difficulties,
fun

4x + 1

Now, use Go!Animate. Use the “Quick Video Maker” and select a template, setting and characters.
In your group, choose one of your attempts at the above problems and use the two characters in
your Go!Animate video to explain what you did to arrive at your answer. If you weren’t able to
reach the answer, then use your characters to discuss the difficulties you had. You have a total of 10
lines of dialog (parts of a conversation) each of which can be only 180 characters long so you need
to be concise but descriptive to get the point across.
You might want to pretend your characters are a teacher and a student, or a really smart friend
explaining the answer to another friend. Or whatever you like.
You might choose the problem you are most confident about because you can explain it better, or
perhaps you choose the one you are least confident about because thinking about it in this different
way might help you understand it better and identify your difficulties.

Possibilities: showcase, reuse in
future

The point!
This workshop could have just involved solving equations and factorising expressions. But by
explaining and describing your maths in words, you slow down and think about exactly what you
are doing. You will also see how your written attempts at problems can appear to somebody – other
people don’t necessarily know what’s going on in your head, so it’s important to write your maths
clearly and explain it fully. This is especially important for exams because, in order to give you
marks, the marker needs to know what you mean when you write a response.
CRICOS No. 00213J


1

Unexpected: typing maths:
difficult


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Communication

Students attempt questions,
then attempt to explain solns
via GoAnimate!
i.e. translate their maths into
words

Dann

Team temporary

Kier

Epic ninja battle

They see how poorly/well they
communicate their
mathematics by attempting to
translate it



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Technology

Activity: Modelling with
MoCOWs, BoM website

Workshop 7

MAB105


Purpose: Real data, visualise,
interpret, model/apply

Use the MUCOW computer to obtain river height data, import it into a spreadsheet, then plot the
data. Next, attempt to develop a mathematical model, in the form of a trig function, to describe the
data.
• Go to the Bureau of Meteorology website, and the page where rain and river data is available:
www.bom.gov.au/qld/flood/rain_river.shtml
• Choose a river data set (e.g. Bremer R at Ipswich # ).
• Click on the link to the plot to check whether or not sufficient change occurs in the river height
over time to generate a visible sine curve. Then go back to the previous page.
• Click on the link to the data. This should bring up a rather long table of data values.
• Select the data and copy it. Then paste it into Microsoft Excel. Note that you may need to
paste into a text file first and then into excel

Possibilities: Lots

• Produce a scatter plot of the data.

The task
1. How high does the river go at its maximum (on average)? How low?
2. How long (time) does it take for the river to pass from its zero height up to the maximum
height, down through zero to the minimum depth and finally back to zero (on average)?
3. Use your answers to the above questions to generate a function of the form
h(t) = a sin(bt)
to model the height of the river. Here h(t) is the height of the river and t represents time.
4. Generate a new column in your excel spreadsheet that gives values of your model h(t) for the
times already available in your spreadsheet.
5. Plot these on the same scatterplot as the river data.
6. Does your model look similar to the data? What differences do you notice? How might you
overcome these differences to create a better model?

CRICOS No. 00213J



1

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Outline

1


2


3


4

SCORM packages

5




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Specs

Slides were created
using an Apple MacBook Air (11in) and Apple iMac (27in)
running Mac OS X 10.7-8
MacTex 2012, Beamer
Occasionally Wolfram|Alpha

Lecture videos were recorded
using a Samsung XE700T1A Slate PC
running Microsoft Windows 7 and
PDF Annotator 3 and Camtasia Studio 8

Hardware and software provided by the Mathematical Sciences School



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Recording process

Recording process
A
1. Produce slides using LTEX (beamer)
2. Open slides using PDF Annotator, adjust size, prepare tools

3. Open Camtasia Studio, prepare recording window
4. Record!
5. Annotate the slides using stylus and speak (teach!) as usual

Figure : Demo video


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Editing process

Editing process
1. After recording, open recording package in Camtasia Studio
2. Edit sound, cut video/sound, add video, subtitles, annotations,
pointers, graphics, etc
3. Quizzes can be added to the video
4. Save project and produce ﬁnal product (video ﬁle or SCORM package)



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SCORM packages

Outline

1


2


3


4

SCORM packages

5




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SCORM packages

SCORM packages
What is SCORM?

SCORM = Sharable Content Object Reference Model
A set of standards and speciﬁcations for web-based e-learning
Allows “sequencing”: constraining the learner’s path through the
materials
Gatekeeping: completion of materials/score threshold
Blackboard has SCORM compatibility!!!



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SCORM packages

SCORM packages
SCORM and MAB105

Take the video lectures recorded with Camtasia Studio
Embed quizzes at important points
Export as SCORM package
Import into Blackboard. For MAB105:
No restriction on number of attempts
Scoring of quizzes reported to Grade Centre
No completion/score restrictions



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SCORM packages

SCORM packages
Importing into Blackboard

Importing into Blackboard
After producing the SCORM package in Camtasia Studio:
1. Go to relevant Blackboard page (e.g. Learning Resources)
2. Click “Build Content”
3. Choose/click “Content Package (SCORM)”
4. Browse for ﬁle to upload
5. Choose the zip ﬁle of the SCORM package
6. Choose options
naming, detailed notes/info, track views (YES!)
number of attempts, scoring, completion etc



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Outline

1


2


3


4

SCORM packages

5




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Blackboard site access

Bb site total access counts by day

Bb site total access counts by week

800

Assessment due

600

Number of accesses

Number of accesses

2,000

400
200
0
Jul 15 Aug 1

Sep 1
Day

Oct 1

1,500
1,000
500
0
O 1 2 3 4 5 6 7 8 9 10 V 11 12 13 S
Week #

Usage is heavy in ﬁrst 9 weeks (actually: looks like chlamydial
infection curve)



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Blackboard site access by day of week

Access peaks between upload and f2f time
Blackboard site access by day

Workshops

Upload

Hours

200

100

0


S

M

T

W T
Day


F

S

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Student Blackboard site access intensity

# of Students

1/2 class probably only accessing site to do assessment
Student Blackboard site access intensity

30
20
10
0

0-5

5-10

10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 65-70

Hours access over the semester


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Still to come

Usage of individual videos (# accesses, time spent)
A look at student results
more...



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An alternative learning experience in transition level mathematics

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