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).

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 3^rd semester; senior students in 7^th 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.

Emilie Naccarato presenting, co-author Gulden Karakok

https://sites.google.com/site/emiliernaccarato/_/rsrc/1410927046099/home/Me.jpg?height=320&width=213

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.…

Jeff Waldock

Department of Engineering and Mathematics

Sheffield Hallem University, UK

Photo link here

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.

Paper published in IJMEST http://www.tandfonline.com/doi/abs/10.1080/0020739X.2015.1076895

Diana Quinn presented, co-authors Amie Albrecht, Brian Webby, Kevin White

University of South Australia

 Photo link available here

Cautious about moving courses online. Courses to be open access too.

Format of courses to be kept standard to make it easier to navigate.

Moodle tip: Can set only to accept pdf uploads.

Used Moodle tool ‘Dialogue’ one-on-one dialogue between student and staff.

Coordinators selected staff to attend professional development. They later coordinated online courses.

Workshops and tutorials for staff.

Well-lit, quiet rooms with good equipment where staff could create videos.

Virtual tours on Camtasia.

Courses ticked off for meeting regulations (according to rubric criteria) months before implementation.

Outcomes

Participant ages 14 – 74!

High pass and failure rates – bi-modal distribution.

Many no-shows who paid $1 000 fee to join!

Some engaged but did not submit assessments – just wanting to learn for themselves.

Kolb’s cycle

Action research

Over 10 cycles of development over 3 years they learnt much about how maths students learn.…

Simon Goldstone, Maritz Snyders presenting, co-author , Margariet Walton

Image taken from here

maritz.snyders@nmmu.ac.za

Nelson Mandela Metropolitan University

Online tutorials can be done in students’ own time or in classes.

Disadvantages

If alone, no immediate support.

Limited scope of questions.

Can’t see how students lay out working.

Feedback not explanations, more like a repeat of the textbook.

Online Tutorial Project Design

300 – 400 students, various programmes.

Started after first semester test.

Marks from Moodle assessments counted to course assessment.

Students must write out full solutions and post online, mostly using phones or scanning. Only get marks for online questions if full solutions are uploaded. Spot checked to make sure uploads were valid. (Not just ‘Henry’s Solutions’ on every page!)

Camtasia software was used to record tutorial videos.

https://upload.wikimedia.org/wikipedia/en/e/eb/Camtasia_Studio_screenshot.png

Other software: Respondus (lets you write solutions in Microsoft Word format) but this has a site licence of US$3 000, no known open source alternative that is as good – institutional site licence), Microsoft Snipping Tool, Adobe, MS Word (Equation Editor better than Maths Type).…