Data analysis or how high school students “read” statistics
Bibliographic record
Abstract
In most countries, statistics are included in the mathematics curriculum and taught by mathematics teachers. This leads to students learning the elements of statistical concepts as mathematical and to more emphasis placed on being able to compute different measures (e.g. mean, median, standard deviation) rather than their meaning and use. Moreover, in Quebec, the high school curriculum favours a scattered presentation of statistical concepts: tables and simple graphical representations are seen in the first year; averages, medians and histograms in the third; position measures in the fourth and some aspects of correlation and standard deviation are seen in the fifth. Some elements of probability are seen in the second year. But “statistics requires a different kind of thinking” (Cobb & Moore, 1997). Is it possible by making students compute statistical measures to foster the development of statistical thinking and prepare to draw conclusions from different data sets - all important abilities for “reading” statistics, an essential part of communication. This study attempts to determine if high school graduates develop the ability to effectively interpret the use and meaning of statistics (i.e. develop a “statistical way of thinking”). To this purpose we investigated (a) if a mode of data representation (1) list of data, (2) graphical, (3) principal location and dispersion parameters (mean, median, quartiles, standard deviation, etc), influences the students’ answers, (b) if students take into account the context of the data in their analysis, and (3) if students’ reasoning reveals “statistical thinking” as described in McGatha, Cobb and McClain (1998). A multiplicative argument combined with the use of the context in which the data are presented is preferable to an argument using only one point or only one measure (usually the mean) or only an arithmetic reasoning. To do so, a questionnaire with seven items asking students to choose from two or three samples and to justify the choice was presented to 141 fifth year high school students in the three different modes of presentation mentioned above. The results show that almost one third of the students revealed correct statistical thinking and another 41 % take the whole sample into account. The majority of the explanations are linked to the context. However, for some students more difficult tasks seemed to trigger a more global interpretation.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.009 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".