AMA calculus day 2013 Transition Powerpoint - Auckland

68 Pages·2013·1.99 MB·English

by  Mike Thomas

The Transition from School to
University: Implications for
School Mathematics Teaching
Mike Thomas
The University of Auckland
"
The Transition from School to University:
Implications for School Mathematics Teaching

 The two studies
 What are some transition issues?
 What we learn about calculus, algebra,
argumentation and proof and modelling
 Some implications
The Transition from School to University:
Implications for School Mathematics Teaching

 Study 1
 A 2 year NZ project supported by a grant from the
TLRI through NZCER; 178 teachers, 26 lecturers
and 77 students
 Study 2
 An ICME-12 survey team of 7 working for two
years on worldwide data
The Transition from School to University:

Implications for School Mathematics Teaching
 79 responses from 21 countries, 5 or more from
each of USA, New Zealand, South Africa
and Brazil
 45 A/Prof or Reader or Full Professor; 30
Lecturer, or SL or Assistant Professor; 3 Tutors
 Mean years university teaching 21.9
The Transition from School to University:
Implications for School Mathematics Teaching

 Claim of under-prepared university students
 Falling competency, although not universal, in:
  essential technical facility, analytical powers, and the
role of rigour and proof in mathematics
 Concern about the level of student enrolment and
retainment in undergraduate mathematics
programmes
The Transition from School to University:
Implications for School Mathematics Teaching

Some of the questions from Jennings with facility ≤ 35%
The Transition from School to University:
Implications for School Mathematics Teaching
The Transition from School to University:
Implications for School Mathematics Teaching

 Under-prepared university students
  The characteristics of students in Australian undergraduate
university mathematics courses have changed markedly in
recent years. Students are now entering university with weaker
mathematical backgrounds and changes have had to be made
to mathematics and engineering programmes to accommodate
these students…Students remember and understand little of
their senior secondary mathematics in comparison to their
junior secondary content, and this has serious implications for
university staff.

Jennings, M. (2011). The Transition From High School to University: The University
of Queensland Perspective. In J. Hannah & M. O. J. Thomas (Eds.) Proceedings of Volcanic Delta 2011
The Eighth Southern hemisphere Conference on Teaching and Learning Undergraduate Mathematics and
Statistics (pp. 139-149), Rotorua, NZ.
The Transition from School to University:
Implications for School Mathematics Teaching

  How would you rate first year students’ mathematical
understanding of each of the following on entry to university?
(Max score = 5)
  Algebra 3.0 Functions 2.8
  Real numbers 2.7 Differentiation 2.5
  Complex numbers 1.9 Sequences and series 1.9
  Definitions 1.9 Vectors 1.9
  Riemann integration 1.8 Limits 1.7
  Matrix algebra 1.7 Proof 1.6
The Transition from School to University:
Implications for School Mathematics Teaching

  How well does secondary school calculus prepare
students to study calculus at university?
  Where students did study calculus at school
preparation for calculus, rated at 2.4 out of 5
  How well does secondary school calculus prepare
students to study analysis at university?
  Rated at 1.5 out of 5