Presentation by Robert Prince, UCT at the Teaching and Learning of Mathematics Communities of Practice meeting at UJ, 29 – 30 August 2018

The Diagnostic Mathematics Information for Student Retention and Success (DMISRS) Project

The problem: Only 27% of students entering full-time university in 2006 graduated in minimum time.

40% leave higher education.

41% of engineering and 48% of science 2006 entrants graduated in 5 years.

Educational diagnostic testing is assessment before instruction begins.

DMISRS – a collaboration by mathematicians to improve graduation rates.

• Make use of NBT data to inform students and lecturers about what areas of weakness and strength are.
• Share practices, leverage best practices.
• Extend the reach of academics beyond a physical classroom.
• Create supportive environments for maths learning [maybe using positive psychology]. What kinds of things will make our classrooms more welcoming to students.

Objectives

1. Get more institutions on board to collect diagnostic information in the same style/language.

Professor Rajendran Govender from the University of the Western Cape presented the objectives and future plans of the Universities South Africa (USAf) Teaching and Learning of Mathematics Community of Practice (TLM CoP) at the 2-day meeting at the University of Johannesburg, 29 – 30 August 2018

• In accordance with the principles guiding a community of practice, the TLM CoP provides an opportunity for academics and relevant other university staff members to collaborate, network and share knowledge on issues of common interest or concern.
• The objectives of the TLM CoP are to promote and strengthen the teaching and learning of Mathematics in public universities in South Africa by:

1.Developing and recommending strategies for the sector to ensure improved access and success in the teaching and learning of Mathematics, thus contributing directly to the transformation needs of South Africa. (session dedicated to this at the next meeting)

2.Providing a shared, common platform from which successful initiatives may be disseminated.…

Siyaphumelela Conference 2017, The Wanders Club, Johannesburg

Andre Freedman, Capital Community College

Bernadine Chuck Fong, Carnegie Math Pathways

Workshop goals:

• Learn about the design, goals, implementations of Carnegie Math Pathways
• Experience Pathways lessons
• Engage in design tasks to improve student success in maths and college
• Engage in conversations about professional learning to address issues and concerns that are specific to local contexts

Faculty had to learn new ways to teaching maths, there had to be ‘buy in’ for it to be successful.

How to radically transform outcomes for all mathematics students?

• Completion
• persistence
• quality of learning (e.g. students can explain what a function is years after taking a maths course)
• identities of learning (students see themselves as someone who can do maths).

Make maths a Gateway not a Gatekeeper.

How?

• Acceleration: Rather not have 3 developmental courses (pre-algebra, algebra1, 2) before taking the required course
• Problem-centered curriculum
• Student-focused, collaborative pedagogy
• ‘Productive Persistence’ interventions / practices to give students belief that they can succeed
• Language and literacy supports
• Train faculty so they can feel comfortable about the new approach
• Use networking to support staff to get running and sustain change
• Keep cohort together for 2 semesters in classes of 30 – 40, or as one institution did teach the 2 semesters in one term (quarter of a year) with about 5 hours a day and one other course -success rate was very high at 78%.

Attendance: The mismatch between academics and students. Who is right?

R. Nazim Khan, University of Western Australia

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

Students don’t attend from the 1^st lecture – how do they know if the lecturer is good or not? Something else is afoot.

Lectures are recorded, students watch the recordings rather than attending.

Low attendance is correlated to high failure rate.

Reasons for low attendance:

• Maths is not their major
• Lecturing is not done well
• Students believe they can pass without attending
• When students have jobs and work comes up, they prioritise work over attendance
• Attendance is higher when there is assessment in class
• Research on attendance …

This study:

Does attendance affect performance? Who attends class? Attitudes on attending, staff and students?

Business statistics course, records of attendance, survey, marks, demographics, high school marks.…

A tale of two journeys

Barbara Miller-Reilly and Charles O’Brien

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

20 years ago Charles was a young business man with a fear of maths; Barbara was a teacher of mathematics-avoident adults and working on a PhD.

Recently Charles asked Barbara for help with maths again. They decided to co-author a paper on their journeys.

Barbara:

• Left teaching to look after her 3 children
• Did part-time teaching, e.g. course on Maths Anxiety, where she learnt many skills
• Started job-share university work
  • Developed maths and statistics learning
  • Researched programmes encouraging girls in STEM
  • Started PhD in early 50’s

Charles

• Lower stream in maths at aged 13
• Failed all maths tests in high school
• Left his brokering job due to fear of maths
• Wondered if he has a maths version of dyslexia
• Said maths was like skiing on blue ice with no edges, blindfolded.

Understanding of limits and differentiation as threshold concepts in a first year mathematics course

Greg Oates (Robyn Reaburn, Michael Brideson, Kumudini Dharmasada)

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

Misconception from school: a graph can never cross an asymptote (Greg had never seen such a graph before university).

Beware of demonstrations that cement misconceptions like walking halfway to the wall repeatedly, the tortoise and the hare.

Threshold concepts – once you understand it, you can’t go back. Meyer & Land, 2003.

Bachelard 1938  -topics that are epistemological obstacles, hard to get.

Are limits threshold concepts?

Students see trickery when limits are taught.

Study

• 1^st year calculus
• Pre-survey
• Interviews
• Repeat survey in 2^nd semester
• In survey, responses were true, false, never seen before, forgot
• Only 14 responses from 270 students
• 4 said you can’t cross a vertical or horizontal asymptote
• 7 said the limit of sin x / x as x tends to 0 could probably be rewritten so the denominator is not l

In interviews, the way students talk about limits, asymptotes, infinity showed that it is a threshold concept.…

Chris Rasmussen, chris.rasmussen@sdsu.edu, maa.org/cspcc

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

There are 4 regular  international conferences on undergraduate mathematics:

RUME (USA), DELTA (Southern hemisphere), one in the UK, one in Europe

How do you make sense of Ax = b where x and b are vectors? (Larson & Zandieh, 2013). There are multiple representations:

• Linear combination, vector addition
• System of equations, intersection of 3D lines
• Transformation, one vector mapped to another

Chalk Talk practices include

• Verbalising everything written on the board
• Board choreography
• Using pointing gestures to highlight key issues, and connections
• Using rhetorical questions to signal transitions, reflection or to check for understanding

Students in lecture-oriented classes has 1.5 times the chance of failing compared to inquiry-oriented classes. Inquiry-based learning is especially good for women. The continued use of traditional lecturing without some form of active learning can be seen as a way to limit the success of many students. …

The exploitation of videos in teacher training

Marcia Jussara Hepp Rehfaldt, University of Vale do Taquari, Brazil

5^th year of a research project on primary mathematics education. Using videos to teach mathematical modelling to teachers in training.

Steps for creating videos

1. Mathematical modelling practices were developed by researchers and recorded on video, e.g. how to choose a team.
2. Editing the image and created slides on an online platform
3. The narrative and final editing were carried out.

The narrative was tabulated. Each of 14 screens was described by what was said and displayed.

What was done with the video?

• Training courses with undergraduate students in teaching
• Teachers in 6 schools
• Online training courses – no professors wanted to go to the northeast state of Brazil after kidnappings

After the video, sent questionnaire to participants and analysed using Tagcrowd software to find most mentioned words (word cloud).

• Common words: mathematica, tendancias, contribuiu, video, clara, ensino, aprendizagem, alunos.

A novel approach to mathematics examination design and marking

David Easdown (University of Sydney, Australia), Ruth Corran (American University of Paris, France), Brad Roberts (University of Sydney)

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics in Gramado, Brazil, November 2017, “Brazil Delta 2017’

The new approach to marking evolved over 3-4 years, prompted by policy changes regarding assessment.

Old method of assigning grades: norm-referenced: use professional judgement to decide what a passing grade was, map to the students in the class. Policy said a maximum of 5% can achieve the top bracket grade (over 85%).

Intermediate method: Instead of grades, assessment classifies students’ test performance as ‘masterful’, ‘excellent’, ‘credible’ or ‘routine.’ Less greyness around borderlines compared to previous norm-referenced scale.

Policy change meant the raw mark achieved on an assessment would be their score. Tests need to be developed so that a student who deserved to pass would score 50% of the marks on the test, but only those who deserved a distinction would achieve the marks.…

Modelling in education! Modelling and statistics in research

By Marcelo de Carvalho Borba (mborba@rc.unesp.br; Facebook Marcelo Borba)

and João Frederico C. A. Meyer (joni@ime.unicamp.br)

Keynote presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics, ‘Brazil Delta 2017’ for short, 27 November 2017

How to teach modelling to teenagers? There has just been the 10^th conference on Modelling in Education in Brazil – we can say this topic has become a trend.

Modelling may help to answer the question, “Why am I studying this?”

Bringing modelling to teacher education may help teachers to use modelling in school teaching and keep students interested in STEM career paths.

Annual Perspectives of Mathematics Education, the yearbook of the National Congress of Mathematics Teachers in America had Modelling as a theme for the yearbook – a sign that this is a topic becoming of greater interest.…