Deborah Kent (Drake University) Omar Khayyam’s Geometrical Solution of the Cubic: An Example of Using History in the Teaching of Mathematics

Second talk at the Diversifying the curriculum conference in Oxford.

The following was taken down live, and as such there may be mistakes and misquotes. It is mostly a way for me to keep notes and to share useful resources and thoughts with others. As such, nothing should be used to quote the speaker from this article

From https://www.drake.edu/math/faculty/deborahkent/

From https://www.drake.edu/math/faculty/deborahkent/

 

 

 

 

 

 

 

 

How to generate interesting conversations with students surrounding mathematical diversity.

Historical figures (From wikipedia):

Omar Khayyam 18 May 1048 – 4 December 1131) was a Persian mathematician, astronomer, and poet. He was born in Nishapur, in northeastern Iran, and spent most of his life near the court of the Karakhanid and Seljuq rulers in the period which witnessed the First Crusade.

As a mathematician, he is most notable for his work on the classification and solution of cubic equations, where he provided geometric solutions by the intersection of conics.

June Barrow-Green (The Open University) Towards a diversity resource for undergraduate mathematics

First talk at the Diversifying the curriculum conference in Oxford.

The following was taken down live, and as such there may be mistakes and misquotes. It is mostly a way for me to keep notes and to share useful resources and thoughts with others. As such, nothing should be used to quote the speaker from this article

from https://en.wikipedia.org/wiki/June_Barrow-Green

from https://en.wikipedia.org/wiki/June_Barrow-Green

 

 

 

 

 

 

 

 

 

 

 

When reading through the Open University’s textbook “Pure Mathematics M208”, in the historical margin notes, the only female mathematician was Emmy Noether. The vast majority of characters were white European men.

The question is how do we create a resource which can tackle issues of diversity in mathematics? This is a recent project begun by June Barrow Green.

It is important to avoid tokenism when thinking about diversity.

Athena Swan – ECU Gender charter – a very useful resource for statistics about women in STEM

What do we mean by diversity: Ethnicity, gender, culture/ Images of mathematicians, who are the students?…

By | June 18th, 2019|Conference, Diversifying the curriculum|0 Comments

Getting ideas into action: Statway and Quantway networked improvement communities

Siyaphumelela Conference 2017, The Wanders Club, Johannesburg 28 June 2017

SIyaphumelela

Getting ideas into action: Statway and Quantway networked improvement communities

Bernadine Chuck Fong, Carnegie Math Pathways

Andre Freedman, Capital Community College

It’s an exciting time to be tackling problems that appear to be worldwide. The Carnegie Foundation is in California, home to many disruptive changes / technologies, e.g. Uber, Google.

An example of the problem: When asked which is bigger, a/5 or a/8 many students respond saying 8a = 5a so 8 = 5. For many, mathematics is about following algorithms and although they may pass algebra courses they can’t apply the knowledge.

Diagnostic tests can leave students feeling depressed, like they do not belong in higher education. A principle in the development of a disruptive transformation of mathematics in American colleges was to meet students where they are.

15% of students needing developmental maths complete the required college maths or stats course after 2 semesters.…

By | June 30th, 2017|Conference, Uncategorized|0 Comments

Digital Storytelling

From Health Professional to Film Producer in One Easy Workshop: Creating Digital Stories

Penny Gill, CPUT

Presentation at the SANRC First Year Experience (FYE) conference, J0hannesburg 24 – 26 May 2017

A digital story is

–        a short, first person multi-media video narrative that documents human life experiences ideas or feelings through story-telling.

–        an exciting way to captivate students, amplifies student voice, encourages critical thinking, can give access to a global audience.

To get students to make a digital story:

–        obtain ethical approval

–        Use a computer literacy questionnaire and offer support if needed

–        Consider copyright and confidentiality

–        Obtain permission from students to use videos in conferences and presentations

–        Students write a 500 word story

–        The video must be 4-6 minutes or less

–        Brainstorm ideas to fit purpose and audience – mindmaps/community maps can help

–        30-40% of time is thinking, planning and synthesising (organising)

–        Plan sequence of story using a storyboard: pictures with words/music  saying what this

scene must achieve.…

By | May 28th, 2017|Conference|0 Comments

Conference: Homological Methods in Algebra and Geometry at AIMS-Ghana

Dear all,

We are writing to inform you about a school and workshop titled “Homological Methods in Algebra and Geometry”. The first week will consist of three minicourses. The second week will comprise of research talks on these topics. The school and workshop are funded and supported by AIMS-Ghana and the ICTP.

Dates: 1st -12th of August 2016
Location: AIMS-Ghana, Biriwa, Ghana
Website: http://aimsictp2016.weebly.com/

The goals of the conference are twofold: on the one hand, to inspire the communication of state-of-the-art research within these flourishing areas and the exchange of ideas between them. On the other hand, to give African postgraduates and researchers the opportunity to get in touch with international experts in order to help them enter one of these fields.

Some funding is available to cover travel and local costs of participants. Preference will be given to those based in the region. Please consult the website for information on how to apply and register.…

By | March 5th, 2016|Conference|0 Comments

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).
By | December 1st, 2015|Conference, Elephant Delta 2015, Uncategorized|0 Comments

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.
By | December 1st, 2015|Conference, Elephant Delta 2015, Uncategorized|0 Comments

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

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.…

By | December 1st, 2015|Conference, Elephant Delta 2015, Uncategorized|0 Comments

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

Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

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.…

By | November 27th, 2015|Conference, Elephant Delta 2015, Uncategorized|1 Comment

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

Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

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?
By | November 27th, 2015|Conference, Elephant Delta 2015, Uncategorized|1 Comment