Elephant Delta Day 3 – Renee LaRue from West Virginia University on Optimization in first semester calculus: A look at a classic problem

Photo of Renee LaRue available here.

Co-author Nicole Engelke Infante

Classic problem: Fence along a barn. Minimize amount of fencing given a fixed amount of fencing.

Literature: 4 versions of this problem. More difficult when students have to set up problem from words.

Carlson and Bloom (2005) Problem-Solving Framework

Tall and Vinner (1981) Concept image

7 students (pilot with 3 students), just before final exam involving optimization.

Recordings of students thinking aloud.

Questions about rectangles – what happens to perimeter if area changes?

5 students solved without intervention, 3 perfectly, 2 forgot about barn. Other 2 needed much help.

Responses showed gaps in reasoning.

Six key maths concepts that played a role:

1. Use 2x + y or 2y + x? 2l + 2w = 2y + 2x (matching variables to what they think they must mean).
2. Function notation. Haphazard use of equal signs. Student said you can’t write 2x + y as f(x) because y = f(x).

Johann Engelbrecht from University of Pretoria on Conceptual or procedural mathematics for engineering students – views of two qualified engineers from two countries

Opening photo of co-author Owe’s colourful toenails – a different colour for each of the 10 Delta conferences!

Photo available here

Paper available here

Traditionally, engineers demand from mathematics fluent use of techniques.

With technology, is this as important as conceptual insight?

Procedural (mechanical) knowledge in mathematics, e.g. ‘For this function, what is the equation of the tangent line at this point?’

Conceptual knowledge link relationships between verbal, visual, symbolic representations. E.g. Match graph of derivative to a written description.

SA – Sweden project.

Quantitative analysis: Junior students in 3rd semester; senior students in 7th semester.

Qualitative analysis: interviews with Swedish and SA engineers.

Swedish engineer

• Procedural maths needed as a basis for mathematics (concerns that he understood procedural knowledge as basic maths background for applications, equivalent to learning the language of maths).
• Conceptual understanding = engineering judgement, broader than maths.
• New engineers should be able to be independent, deal with a whole problem, be self-confident.

Elephant Delta day 3 – Emilie Naccarato from University of Northern Colorado on Expectations and implementations of the flipped classroom model in mathematics courses

Emilie Naccarato presenting, co-author Gulden Karakok

Goal: talk about themes occurring in flipped classrooms in tertiary maths in USA

Flipped class:

• Some course content on technology accessed outside class
• More time in class for related, meaningful activities
• Same contact, face-to-face hours
• (notice the loose way a flipped class can be arranged – many ways to arrange)

Existing studies

Descriptions of implementation and student perceptions.

Looking at student performance in flipped vs traditional courses. Big differences in studies – no consensus on what works best (but implementations vary a lot).

Need to link expectation and goals of a flipped class to the implementation – can’t simply compare all versions of a flipped class.

How do you assess differences when learning goals and implementations are so different?

You need alignment. Schoenfeld (2000) emphasized “identifying important topics and specifying what it means to have a conceptual understanding of them. With this kind of information … [they] could then decide which aspects of understanding were most important, which they wanted to assess, and how.” (p.…

Elephant Delta Day 4 – Nouzha El Yacoubi from University Mohammed V Rabat, Morocco on The impact of mathematics on the Africa socioeconomic takeoff

Information, knowledge, science and technology give real power and is more essential for wealth creation of nations than capital or land.

Freeman Dyson:

Technology is a gift of God. After the gift of Life, it is perhaps the greatest of God’s gifts. It is the mother of civilization, of Arts and of Sciences. Technology continues to grow to liberate mankind from the constraints of the past. The most revolutionary aspect of technology is its mobility.
Anybody can learn it. It jumps easily over barriers of race and language. And its mobility is still increasing.

The world is in perpetual change: Science, technology and media are converging.

The widening gap in the economy between the developed and developing countries is essentially a manifestation of science and technology. Within Africa this is clear.

South Korea’s investment in engineering graduates increased enormously from 1970-1990.…

Elephant Delta day 4 – Fransonet Reyneke from University of Pretoria on First level statistics students’ performance in a large classroom environment under the magnifying glass

Fransonet Ryneke from University of Pretoria

Over the last 10 years students in first year engineering have been in the 60-70% pass-rate bracket. Tried many interventions with little success.

New interventions:

• Blended learning model
• Student centred
• Flipped classroom

If you want to innovate something, there must be a what, how and why!

What?:

• APLIA Online homework system: 3 attempts to do homework.
• Flipped classroom using APLIA as a pre-class assignment
• MindTap and APLIA clickers

Just APLIA on its own didn’t make much difference, but APLIA with the flipped homework made a huge difference – a 12% increase.

A pre-class and a post-class assignment, youtube videos.

They write a clicker exam. Students answer all go into an excel file. The clicker seemed to make a difference in the final marks too.

 How clear is this post?

Elephant Delta day 4 – Prof João Frederico da Costa Azevedo Meyer from Universidade Estadual de Campinas on Mathematical Disciplines for Undergraduate (and Graduate) Mathematics and Statistics: Challenges for Cooperating and Operating with Social Needs

Different points of view lead to different views. Talking from the point of view of an applied mathematician – this will lead to a particular biased applied mathematician’s point of view, a utilitarian point of view, as well as an environmental scientist’s point of view.

He speaks as a customer. His students need certain skills, knowledge, etc. He is the one who needs the results of mathematical education at technical schools and university activities.

A lot of abstraction leads to unrealistic ideas: Who cares about the trigonometric functions applied to a 30 degree angle?

Fenando Pessoa: The preacher of his own truths…

Do students share our enthusiasm with what is taught in the classroom?

In fact, do WE share any enthusiasm?…

Elephant Delta Day 3 – Jeff Waldock from Sheffield Hallam University on Designing and using informal learning spaces to enhance student engagement with mathematical sciences

Jeff Waldock

Department of Engineering and Mathematics

Sheffield Hallem University, UK

Engagement: try to feel ‘belonging’, part of a community of staff and students. Aim: How to develop this more effectively.

Developing patterns of social behaviour.

Need IT-enabled space.

Community = having a common purpose. Space supports this aim. Communicate this idea frequently to students.

Design of Open Learning Space

(maybe in a corridor …)

• Sense of belonging
• Encourage staff-student, student-student interactions
• Keep students engaged in gaps between classes.
• Key words: active, collaborative, social
• Activities: Peer-supported learning (PSL/PAL), group work, individual work, social/professional activities (e.g. strategy board games), informal staff-student contact (small amounts of interaction makes a big difference).
• Activities enabled by: an attractive space people want to use, meeting rooms with white boards, tut rooms with white boards, IT enabled, card access to students after hours – trust needed (and security)
• Room numbers in binary to make the space look mathematical.

Elephant Delta Day 3 – Shirley Wagner-Welsh from Nelson Mandela Metropolitan University on An Investigation into the Effect of Mathematics Self-Efficacy and Mathematics Anxiety on Mathematics Performance

At Nelson Mandela Metropolitan University Very diverse socio-economic circumstances, mostly non-native English speakers. 23 Different languages on campus.

Why this study? There has been a large issue of poor performance and lack of engagement in mathematics.

Possible issues:

• Topics are introduced at a fast pace
• Students may not have the necessary prerequisites
• Independent learning is required

Two other issues:

Mathematics self-efficacy:

Self-efficacy is people’s judgements of their capabilities to organise and execute courses of action required to attain designated types of performance (Bandura 1986).

Mathematics self-efficacy affects performance.

This can tell us why students sometimes don’t put in the necessary effort. If a student DOES have a high level of mathematical self-efficacy they tend to work longer on problems.

There does seem to be a link between mathematics self-efficacy and gender: Higher in males (grade 10-12 and pre-service teachers – Malpass, O’Neil and Hocenar: Self‐regulation, goal orientation, self‐efficacy, worry, and high‐stakes math achievement for mathematically gifted high school students) – in another study this was not found.…

Elephant Delta Day 3 – Dr Jyoti Jhagroo from The Auckland University of Technology on Multicultural lecturing: some challenges

Dr Jyoti Jhagroo from AUT.

This is a personal reflective narrative as a student and teacher in the school/higher education contexts.

It is a hermeneutic phenomenological study with 10 immigrant students

• Considerations of cultural constructs: Languages, Beliefs and Experiences (though of course there are much more).
• Students lived experiences in their mathematics classrooms with considerations for teacher education.
• Explore some ideas of multiplications from different cultures and consider their implications for teaching and learning in a multicultural context. Take some ideas to take forward for teacher education

As a student with a personal narrative, Jyoti had been indoctrinated into the ideas of what mathematics education were about. It should be:

• Culture-free
• Factual
• Based on theorems
• Present, practice, perfect

As a teacher: a shift from a monocultural context to a multiculural context:

• Some students spoke a different language at home, potentially held different beliefs and different experiences of mathematics
• However, it seemed that the mathematics education practices and attitudes are often projected as culturally neutral ideologies.