Understanding confidence intervals in context
Sue Finch and Ian Gordon, The University of Melbourne
15 November 2023
A small body of research has investigated student and researcher understanding of confidence intervals. This has mostly focused on the interpretation of the confidence coefficient, the meaning of the width of the confidence interval, and the lexical ambiguity of the term “confidence”.
Most of this research has used fixed response option questions or simple hypothetical scenarios to assess students’ or researchers’ knowledge.
We present an analysis of 150 graduate students’ written explanations based on an assessment task. Students were shown a graphical presentation of confidence intervals in a meaningful context, where they consider analysis of the relevant data and respond to a common misunderstanding of the interpretation of results presented.
A correct understanding of the meaning of a confidence interval or a simple examination of the data provided to the students would allow correction of the misunderstanding. However, many students failed to perceive the misunderstanding, or to provide a coherent response.
In contrast, on fixed response option questions, most students chose a correct interpretation of a confidence interval. We discuss the implications for teaching the applied interpretation of this fundamental statistical concept.
The academic perceptions and experiences of mathematical communication
Oliver Murfett, The University of Melbourne
2 November 2023
In this undergraduate research program, the experiences and perceptions of academics in relation to mathematical communication are identified. Using a phenomenographic research design, these experiences are then categorised in an attempt to provide some insight into the communication that academics perceive. We will also discuss how the findings could relate to the teaching within the school, and research that could be done to extend these results. The hope is that this new understanding of the variations in how academics experience mathematical communication can be used to provide a framework for thinking about teaching mathematical communication in the classroom.
The 1001 uses of randomised online questions
Dr Laure Helme-Guizon, Deputy Director of first-year Mathematics and Statistics, School of Mathematics and Statistics, UNSW Sydney
20 October 2022
The school of Mathematics and Statistics at UNSW Sydney uses Möbius to create randomised online questions. For a given question, different students may get different numbers, different functions, different data sets (in Stats), different situations/scenarios and the sub-questions could be different.
So, if you have 1000 students in a course, 1000 unique versions of your formative or summative activity are generated. Therefore, students can discuss the methods but cannot blindly copy the answers. Students can also regenerate a question many times and use the variations to get more practice.
The answers can be auto-marked, except for the essay boxes which need to be marked manually. The limitations in what can be auto-marked are mostly your coding skills and your imagination: for instance, you can give half marks to a slightly incorrect result or write a marking algorithm which accepts
the word “parallelogram” despite typos.
I will explain in the talk how we use Möbius for weekly formative self-paced lessons, for class test/midterms, for competency tests, for assignments (coupled with a Turnitin submission) and for final exams.
Getting students to link algebra with geometry: a Linear Algebra lab redesign project
James Clift and Nick Sgro-Traikovski, School of Mathematics and Statistics, The University of Melbourne
5 October 2022
This semester we have been redesigning some content in Linear Algebra computer labs to allow students to better visualise the more abstract concepts in the subject. Our project involved redesigning lab questions and designing new applets using MATLAB and GeoGebra to guide students towards an understanding
of how algebraic and geometric ideas are linked. In this seminar, we will demonstrate some of the applets, discuss how they were made, reflect on the lab redesign process and offer some suggestions for developing computer lab materials in other subjects.
A report on NextGen tutorial classes in Calculus 2
Dr TriThang Tran, School of Mathematics and Statistics, The University of Melbourne
17 June 2022
Have you been wondering about those digital whiteboards in G11 and G14 of Peter Hall? In Semester 1, Calculus 2 (along with a couple other subjects) participated in a trial of these "NextGen" tutorial rooms.
For Calculus 2, the trial was a hybrid trial, with some classes using making use of the nextGen rooms, some classes in traditional whiteboard rooms, and some classes still entirely online. The purpose of this talk is to share how the trial went for Calculus 2. I'll focus on how we went about re-developing
tutorials to make use of the new technology available in a meaningful way. While the trial is still very much in progress, I'm hoping that this talk will be useful for those that are interested in trying out the NextGen rooms in their own subjects (either next semester or beyond).
Taking care with context: Curating suitable data for teaching statistics
A/Prof Sue Finch (Joint work with Prof Ian Gordon), School of Mathematics and Statistics, The University of Melbourne
29 April 2022
Providing a rich context has become a sine qua non of principled teaching of applied statistics and statistical literacy. With increasing opportunities to access secondary data via online sources, there should be increasing opportunity to work with rich context. What do instructors need to consider
when looking for genuine data sets? We share our story of investigating the base R ‘datasets’ package as a source for introductory tertiary level statistics teaching, and what we found when we looked at the source information for four of these (potentially useful) datasets in detail.
The failure to describe and retain important contextual information, raises questions about the credibility of the data involved for statistical inference. The curators, distributors and users of these data need to examine, where possible, the primary sources in order to accurately preserve
the context and optimize pedagogical opportunities.
Student Relationship Engagement System (SRES): what is it and what can we do with it?
Dr Anthony Morphett, School of Mathematics and Statistics, The University of Melbourne
24 March 2022
SRES (Student Relationship Engagement System) is an online database for storing student data – assignment marks, class attendance, etc – and sending automated, customised emails to targeted students – for instance, everyone who missed a class recently, students who failed the assignment, or students
who got full marks on the assignment. SRES was developed by academics at the University of Sydney, and it is available to us thanks to the Faculty of Science. In this presentation, I’ll give a demo of SRES and show how I’ve been using it in Calculus 2 – namely, for recording students’ attendance at tutorials,
and then contacting students who are at risk in the lead-up to census date.
Next Generation Tutorial Room Pilot Update/Demo
MSLC staff, School of Mathematics and Statistics, The University of Melbourne
10 November 2021
Abstract: Over the last few weeks the MSLC staff have tested various vendor options for large touchscreen smart boards for pilot deployment in a small number of our tutorial spaces. In our testing we have considered various ways this technology could be deployed in tutorials across our full range of
subjects. In this seminar we discuss the various relevant features of the boards and show particular examples of how tutorial and lab activities can be redesigned to make use of these technologies.
Automated Assessment in Mathematics and Statistics - Part 2
Anthony Morphett, School of Mathematics and Statistics, The University of Melbourne
27 October 2021
Abstract: We have used WebWork for automated assessment in some of our large undergraduate subjects for several years now. In this talk, we’ll discuss some of the ways that we use automated, randomised assessment in Calculus 2 and Linear Algebra. This includes scaffolding students through simple proofs
and helping develop their mathematical communication as well as practice at routine exercises. I will also demonstrate a new automated assessment platform, Wiris, which is likely to become available as part of the suite of technologies offered by Learning Environments.
Automated Assessment in Mathematics and Statistics - Part 1
John Banks, School of Mathematics and Statistics, The University of Melbourne
13 October 2021
Abstract: We have implemented automated assessment using WebWorK for 3 years now across several subjects (7 subjects in 2021). This talk gives a survey of the ways this has been done in various subjects, focussing particularly on the integration of written and online assessed work in MAST10005 and the
use of “step-wise questions” to support learning of multi-step techniques where students experience difficulty choosing the appropriate approach at various steps in the process.In a follow up talk, we will discuss a new automated assessment platform Wiris which is likely to become available as part of
the suite of technologies offered by Learning Environments.
Introducing Students to the Community of Mathematicians and Statisticians
Chris Duffy, School of Mathematics and Statistics, The University of Melbourne
29 September 2021
Abstract: Faced with a cohort of MathEd students who didn’t really understand the broader context of the work they were doing in the classroom, I devised an assignment activity to introduce these students to the community of mathematicians and statisticians. I then realised that this activity was
(near) zero effort method to introduce students of all kinds to the broader context of their technical studies.
Swan Delta 2019: Reflections of Change
Paul Fijn, School of Mathematics and Statistics, The University of Melbourne
This seminar highlighted some of the ideas, innovations, challenges and research presented at the Swan Delta conference, and how Paul intended to incorporate some of these elements into his teaching. Some key themes explored included interdisciplinarity, effective use of technology and evaluation of
Taking the aaarrrggghhh out of teaching statistics with R: Using R Markdown
Sue Finch, School of Mathematics and Statistics, The University of Melbourne
This seminar discussed the various challenges posed by different software packages in teaching Statistics and by R in particular, and described a structured innovation designed to foster the right pedagogical goals, using R Markdown (including providing exercises and solutions). It presented feedback
from participants in a trial course and outlined what was successful, and some possible improvements.
Getting ready for the new Canvas LMS - a report on the Semester 2 pilot subjects
John Banks and Lawrence Reeves, School of Mathematics and Statistics, The University of Melbourne
The University's LMS migrated from Blackboard to Canvas for all subjects in 2020. Three Mathematics and Statistics subjects used Canvas in Semester 2 2019 and this seminar was a report on those pilots.
WebWork - What worked?
Tom Wong, School of Mathematics and Statistics, The University of Melbourne
This seminar reported on a pilot of the online homework system WebWork in the first year subject Introduction to Mathematics (MAST10012). It also considered suggestions of what could be improved next time and things to consider if implemented in other subjects.
Making assessment part of active ongoing learning
Jen Palisse, School of Mathematics and Statistics, The University of Melbourne
This workshop explored alternate assessment methods to allow students to take more ownership of their learning. The main example was a high school level exercise concerning the introduction of index laws in Year 8 where students had to generate the index laws for themselves before proceeding with
further exercises to reinforce the rules. This approach aims to give students ownership of their own learning as the mathematics that they are using is their mathematics, not the teacher's.
WebWork: An exploration in implementing an online homework system
Thomas Wong, School of Mathematics and Statistics, The University of Melbourne
This seminar explored the idea and feasibility of using an online homework system (WebWork) to
complement the existing assignment system. WebWork has been used to partially automate assignments in pre-calculus algebra, single and multivariable calculus, differential equations, linear algebra, discrete mathematics, probability, statistics, and complex
Origami in mathematics education: from Kindergarten to Graduate school
Michael Assis, School of Mathematics of Statistics, The University of Melbourne
Presented relevant resources and many practical applications for the inclusion of origami in teaching at all levels of mathematics education.
Using Class OneNote as a teaching/learning tool in small to mid-sized classes
Alysson Costa, School of Mathematics of Statistics, The University of Melbourne
Reported on the comprehensive use of OneNote for lectures/assignments/tutorials/discussions as trialled in a third year subject.
Interactive activities to engage a large introductory statistics class
Sharon Gunn and Anthony Morphett, School of Mathematics and Statistics, The University of Melbourne
Presented a suite of interactive activities to engage students with statistical concepts.
CALC 101 - A survival guide for first year lecturers
Thomas Wong, School of Mathematics and Statistics, The University of Melbourne
Reported on two techniques to assist first year teaching - a LaTeX typesetting requirement for assignment submissions and the use of an online forum for students to promote student interaction.
Wolfram computing tools in primary, secondary and tertiary education
Craig Bauling, Wolfram Technologies
The Inaugural Seminar in this series was held in November 2016 and concerned the introduction of Mathematica tools into primary and secondary school teaching in Victoria.