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

**Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding.**

Based on work with Dr Sonica Froneman

From 2008-2009 it was a hard time in universities for new students coming in from the new curricula.

How can we measure reasoning abilities? What do we want students to be able to do?

Mathematical reasoning is an important process through which mathematical understanding develops.

Students should be able to transfer mathematical knowledge from familiar to unfamiliar contexts (Englebrecht, Harding and Phiri, 2010)

Critical outcomes of the school curriculum:

Learners should demonstrate an ability to think logically and analytically and be able to transfer skills from familiar to unfamiliar situations.

Curriculum based on “active and critical..” approach

Creative reasoning must not only be seen as a mathematical reasoning needed for solving difficult mathematical problems but rather as mathematical thinking that needs more than just reproducing algorithms or imitative solutions to problems.

Must create the right environments for creative reasoning to be developed.

This takes time. No time in school given the size of the curriculum. Teachers are sometimes too eager to simply help the student with the answer.

Research question:

Are students able to solve problems that require creative reasoning? Can we measure it?

Used the framework of Lithner to evaluate the reasoning abilities of the students based on scientific research.

Look at creative, and imitative reasoning.

Memorised reasoning is when you have to recall an answer: A definition, memorised proof.

Algorithmic reasoning is when you can recall a procedure.

Creative reasoning is:

- Novel
- Flexible
- Plausible
- Has a mathematical Foundation

**Classification of the questions**

- Dependent on the students’ previous history regarding the solution of the problem
- Main classification involves a distinction between algorithmic or memorized reasoning and creative reasoning

Lithner, Palm et al, said that if there are 3 tasks in the students’ resources of a problem that are similar to the one that they are going to do, then you can classify the question as familiar algorithmic reasoning.

If there are 3 tasks which are exactly the same, then it’s memorised reasoning

Otherwise it is creative reasoning

The creative reasoning come in two kinds: Local, or global creative reasoning

If it’s local, then it only has some of the four elements of creative reasoning. If they are all there, then it is global.

In this research all the questions were local, rather than globally creative (if they were creative).

647 first year students enrolled for mainstream mathematics module at North West University

Instrument: First mathematics test written early in march. This was part of the normal assessment – not a test compiled with the aim of the research.

**Research procedure:**

Marks obtained by each question and sub-question recorded

**Analysis of data:**

- Included the textbook, manuals, study guides and class work as a reference to what students have had the opportunity to learn
- Authors explain the framework of Lithner to the lecturers of the module
- Five mathematics lectures individually classified the questions
- Discussed their classification

**Discussion of results**

The non-creative questions scored on average around 60%+, the creative question was roughly 33% on average.

**Summary:**

- Students performed well on questions that require imitative reasoning, not those that require any creative reasoning (here local).
- There are opportunities at school level to develop reasoning skills but deep learning is impeded by obstacles such as: time constraint and the drive for good pass rates.
- Assessment should include opportunities to develop creative reasoning elements
- It is possible to measure reasoning skills – still in a process of development

**Way forward:**

- Creative reasoning does not happen automatically for the majority of students, therefore we as lecturers will teach consciously for creative reasoning
- We use the classification of Lithner as a taxonomy to set tests and assignments to make sure that all the reasoning categories are included.

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