Investigating the nature of teacher knowledge needed and used in teaching statistics : a thesis presented in partial fulfilment of the requirements for the degree of Doctorate in Education (Ed.D.) at Massey University, Palmerston North, New Zealand
This thesis explores the knowledge needed for teaching statistics through
investigations at the primary (elementary) school level. Statistics has a relatively
short history in the primary school curriculum, compared with mathematics. Recent
research in statistics education has prompted a worldwide move away from the
teaching of statistical skills, towards a broader underpinning of statistical thinking
and reasoning. New Zealand’s nationally mandated curriculum reflects this move.
Consequently, little is known about the types of knowledge needed to teach statistics
effectively. Ideas from two contemporary areas of research, namely teacher content
knowledge in relation to mathematics, and statistical thinking, are incorporated into a
new framework, for exploring knowledge for teaching statistics.
The study’s methodological approach is based on Popper’s philosophy of realism,
and the associated logic of learning approach for classroom research. Four primary
teachers (in their second year of teaching) planned and taught a sequence of four or
five lessons, which were videotaped. Following each lesson, a stimulated recall
interview, using an edited video of the lesson, was conducted with the teacher.
The video and interview recordings were analysed in relation to the teacher
knowledge and statistical thinking framework. The results provide detailed
descriptions of the components of teacher knowledge in relation to statistical
thinking that are needed and used in the classroom. Included in the results are
profiles of each teacher’s knowledge. These profiles describe ‘missed
opportunities’, which were defined as classroom incidents in which teacher
knowledge was needed but not used, and consequently resulted in the teachers not
taking advantage of chances to enhance students’ learning.
A number of significant themes were revealed, linked to knowledge for teaching
statistics. The themes include: problems associated with teacher listening; the need
for the teacher to be familiar with the data; students’ difficulties with various
components of the statistical investigation cycle; and understanding variation and the
development of inference.
The study concludes that for effective teaching of statistics through investigations, it
is necessary for teachers to have knowledge in each of four categories as related to
each component of statistical thinking. If any aspect of knowledge is not available
or not used, teachers will not enhance, and could disadvantage, students’ learning.
Implications from the findings are considered for initial and on-going teacher