Beyond the bars: Exploring pre-service teachers’ understanding of histograms

Aims: This study explored the ability of first-year pre-service mathematics teachers to interpret graphical representation, with an emphasis on histograms.

Study Design: The descriptive survey design was employed as the methodological framework for the investigation.

Place and Duration of Study: The study was carried out at the Department of Mathematics Education, University of Education, Winneba, Ghana, during the 2022/2023 academic year.

Methodology: The purposive and convenient sampling techniques were used to sample 342 first-year pre-service mathematics teachers. This sample included 31.3% (107) trained teachers who have taught mathematics at the basic school level. Females also formed 15.5% (53) of the sample. The test used as the instrument for collecting data was adapted from previous studies and classified into two skill types: statistical literacy (SL) and statistical reasoning (SR). Data was analysed by computing the success rates for the items as well as assessing participants’ valid justifications for their responses. This gave insight into the challenges participants encountered.

Results: Under statistical literacy items, findings revealed that for items which covered tasks like reading frequencies and identifying axes, success rates ranged from 45.6% (156) to 63.7% (218), whereas those which required identification of the median of a categorical dataset in a bar chart and comparing modes of two histograms presented a more complex situation with success rates around 26.0% (89). Under the statistical literacy items, only 12.1% (11) could provide valid justifications for their correct response on the item on identifying the median of a categorical dataset in a bar chart, and 28.1% (25) for the item on comparing modes of two histograms. On statistical reasoning items, moderate success rates were recorded for items requiring interpretation of information from histograms with success rates ranging from 33.0% (113) to 56.1% (192). Challenges were encountered with matching a given description to an appropriate histogram and comparing and contrasting distribution characteristics, with success rates of 24.0% (82) and 0.6% (2), respectively. Under these statistical reasoning items, participants’ lack of conceptual understanding was evident, as either zero conceptually sound justifications were recorded or an abysmally low one (5.3% (9) or 6.2% (7)), even for correct responses, with just a repetition of the choice of answer from the options.

Conclusion: Participants demonstrated moderate proficiency in basic statistical tasks; however, significant challenges were encountered with more complex tasks which required inferential reasoning. It was recommended that teachers integrate creative pedagogical approaches and interactive technologies that emphasise statistical reasoning into their teaching.