Source: Journal of Mathematics Teacher Education, Vol. 16, No. 6, p. 427-449, December 2013
(Reviewed by the Portal Team)
This study explored prospective secondary mathematics teachers’ conceptual understanding of statistics, attitudes towards statistics and the relationship between attitudes and conceptual understanding.
Participants in the study were 134 prospective mathematics teachers, the majority of whom were undergraduates on a 4-year physical education degree programme.
All of the students in this study had chosen mathematics as their elective option.
Conceptual understanding was measured using a standard assessment instrument comprehensive assessment of outcomes in a first statistics course, which allows comparison across other disciplines.
The findings reveal that prospective mathematics teachers in this study had all taken modules in linear algebra and calculus at university and higher-level mathematics at secondary school. Despite being very mathematically able and confident, these self-selecting prospective mathematics teachers do no better in the assessment than the students from other disciplines. The prospective teachers performed poorly on items relating to data production, in particular randomization, sampling and populations, and extrapolating from a regression model.
This finding, perhaps, gives further evidence that statistical thinking is different from mathematical thinking and that a strong background in mathematics does not necessarily translate to statistical thinking.
Furthermore, conceptual knowledge was poor in some fundamental areas of statistics such as being able to properly describe the distribution of a quantitative variable and data production.
The students also need to be exposed to the practice of statistics through activities like project work where they design data collection procedures themselves to answer a question of interest, summarize data graphically and numerically and draw inferences from the data. Almost four-fifths of prospective teachers in this study demonstrated considerable difficulty reasoning about fundamental concepts relating to the meaning and representation of quartiles and medians on box plots. Box plots are important representations that are core components of many secondary school curricula internationally.
In general, the prospective mathematics teachers in this study had positive attitudes towards statistics. The students placed a value on statistics and were interested in it. They were confident about their intellectual knowledge and skills when applied to statistics. The prospective teachers rated their ability to master introductory statistics material lower than their confidence in mathematics.
The results indicate generally positive attitudes but an acknowledgement that statistics is not a subject quickly learned by everyone and requires discipline to learn, but these positive attitudes are not strongly correlated with their conceptual understanding of statistics, as measured by CAOS. The most positive attitudes were held by the more mature postgraduate students yet these students performed no better on the test of conceptual understanding than the first-year students.
The prospective teachers in this study had little, if any, exposure to statistics in secondary school and in turn may have had little understanding of what experiences constituted as statistics. The positive attitudes towards statistics for the participants may actually reflect positive attitudes towards mathematics, particularly confidence about their intellectual knowledge and skills when applied to mathematics.
Teachers need robust conceptual understanding of the subject matter knowledge they will end up teaching, and the poor conceptual understanding of statistics of these prospective teachers has direct implications for classroom instruction and student outcomes. As future teachers, the participants in this study will be responsible for delivering a substantial statistics component of secondary school mathematics courses and given that they will not take additional courses in statistics in university, we would not expect their content knowledge to improve much further.
As teachers of statistics, a negative attitude to statistics may potentially impact on the teaching of statistics, on a teachers’ willingness to engage with statistics in the future in the classroom and in their own professional development. It may also impact on their future students’ performance in statistics by unconsciously transferring this negative attitude to their students while teaching.
Conceptual knowledge of the prospective teachers in this study was poor in some fundamental areas in statistics. In particular, the prospective teachers were not able to correctly identify which graphical representation best represented all the features of a distribution, why randomization was used in context, or the interpretation of centrality and variability in box plots. Despite being mathematically able and confident, the prospective mathematics teachers did no better on the assessment than students from non-quantitative disciplines, giving evidence that statistical thinking is different from mathematical thinking and that a strong background in mathematics does not necessarily translate to statistical thinking.
The generally positive attitudes reported in this study were not strongly correlated with conceptual understanding. It is clear that developing positive attitudes is not enough and the focus needs to be on teacher knowledge. Programmes must include tailored modules in statistics and highlight the differences between mathematical and statistical thinking.
There also needs to be a focus on pedagogical content knowledge which encompasses methodologies for teaching important statistical concepts and skills, the effective use of various statistical software packages and a rich knowledge that allows teachers to pre-empt typical statistical misconceptions that occur in the classroom.