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

Dr Harry Wiggins – University of Pretoria (http://www.up.ac.za/en/mathematics-and-applied-mathematics/article/1942109/mr-hz-harry-wiggins)

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. Equations will also be put into more readable format ASAP.

The problem:

How should we teach a mixed ability class?
Children already come to us differentiated. It just makes sense that we would differentiate our instruction in response to them (Tomlinson 1999)

We teach with an average student in mind.
Our teaching is content driven, and we don’t take our students into account.

Unfortunately (sometimes) – this leaves the academically strong students starved and bored in class.

Academically stronger students face a higher level of boredom at school than their peers.
More recent studies indicate that a lack of challenge in the classroom is largely responsible for this boredom of academically stronger students.

  • Dumbed down curriculum
  • Lack of meaningful content

When tasks are not sufficiently challenging, the brain does not release enough neurochemicals to create learning…

Student enrichment:

Any learning experience that replaces, supplements or extends the restrictive boundaries of course content, textbook and classroom and that includes depth of understanding, breathe of understanding and relevance to the student and to the world in which he or she lives.

Advantages of student enrichment:

  • Provides students greater freedom for latitude of inquiry
  • Fosters mathematical thinking and problem solving skills
  • Enriched students tend to choose more challenging subjects when they leave school.

Outline of enrichment case study:

Selected a small group of first year students

Five activities to look at sibling curves in an inquiry-based learning environment

Qualitative and quantitative research to capture student’s perspectives on the enrichment project.

5 activities with 22 first semester students

worked at their own pace on:

  • Non-routine problems: can you find a quartic polynomial with a local minimum at P(1;0)?
  • Open problems: Is it possible for the sibling curves to meet twice or more?

Students could consult Dr Higgins or on a Facebook group with fellow students.

Feedback from the questionnaire:

  • 89.5% enjoyed solving the new problems
  • 84.2% would do another enrichment project over the holiday
  • 78.9% indicated this project changed their view of mathematics

“I enjoy the project because it was challenging and I get to know how hard research is”

Interviewed four of the students:

  • “I didn’t know what type of maths this was”
  • “I don’t see the point of you coming to study if you don’t want to challenge yourself to become better”
  • “You don’t always rely on a lecturer, just do your own stuff…”
  • “I feel very honoured if they [lecturers] share their passion with students. It makes me enjoy the subject and classes more”
  • “New problems exposes me to different knowledge”

Can the study be duplicated?

  • Yes, but it takes a lot of work. Needs:
  • Designer with a goal
  • Willing participants who want to learn
  • Suitable content that is interesting and has educational value to the students

This project allows students to scratch deeper.

More engaging than in a classroom setting

Academically strong students have a desire to be challenged

Personal growth for all the participants.

Hopes:

  • Puts the spotlight on student enrichment
  • Educators take note of this when teaching, creating worksheets, tests and exams
  • Educators provide extra reading, recommended books or weblinks to interested students
  • We must feed our students intellectually. Sometimes need to throw the students in the deep end.
  • Lecturers will find a way to challenge students, expose them to interesting problems and to tap into their problem solving potential

Come up with a problem of the week:

Second year calculus:

Calculate:

\int_0^1\int_0^1 max(x^3,y)dx dy

Find the volume of the points inside:

x^2+y^2=2 y^2+z^2=2 and z^2+x^2=2

Conclusions:

We should have high expectations for all students!

It is a miracle that curiosity survives formal education – Einstein

 

How clear is this post?