SECONDARY SCHOOL STUDENTS’ UNDERSTANDING OF MATHEMATICAL INDUCTION: STRUCTURAL CHARACTERISTICS AND THE PROCESS OF PROOF CONSTRUCTION

In this study, we investigate the meaning students attribute to the structure of mathematical induction (MI) and the process of proof construction using mathematical induction in the context of a geometric recursion problem. Two hundred and thirteen 17-year-old students of an upper secondary school in Greece participated in the study. Students’ responses in 3 written tasks and the interviews with 18 of them are analyzed. Though MI is treated operationally in school, the students, when challenged, started to recognize the structural characteristics of MI. In the case of proof construction, we identified 2 types of transition from argumentation to proof, interwoven in the structure of the geometrical pattern. In the first type, MI was applied to the algebraic statement that derived from the direct translation of the geometrical situation. In the second type, MI was embedded functionally in the geometrical structure of the pattern.     

Correction to: Teaching and learning in a multilingual Europe: findings from a cross-European study

European Journal of Psychology of Education - A Correction to this paper has been published: https://doi.org/10.1007/s10212-021-00539-z     

Does speed-reading training work,and if so,why? Effects of speed-reading training and metacognitive training on reading speed,comprehension and eye movements

Background

Commercial speed-reading training programs are typically marketed with the promise to dramatically increase reading speed without impairing comprehension. From the perspective of reading psychology, it seems quite unlikely that speed-reading training can indeed have such effects. However, research on the effectiveness of modern speed-reading training programs on reading performance in typical readers is sparse. The present study had two goals. First, we sought to extend prior research on speed-reading by assessing the effects of a speed-reading application on reading performance in a pre-training and post-training design with a control group. Second, we aimed to identify the mechanism underlying speed-reading training programs.

Methods

We assessed reading speed, comprehension and eye movements of 30 German-speaking undergraduates (M_age = 22.77 years, SD_age = 3.41 years) before and after they received a commercial, app-based speed-reading training, a metacognitive training or no training.

Results

Results revealed higher reading speed in the speed-reading condition and metacognitive condition compared with the control condition, although not to the extent claimed in the application. Eye-movement data indicated that the increase in reading speed was due to fewer and shorter fixations in measures reflecting late but not early lexical processing. No differences in comprehension performance were observed between the three conditions.

Conclusions

We discuss our findings in support of the idea that the increase in reading speed was not caused by a change in basic characteristics of participants' reading behaviour, but rather by an increase in their awareness of their own reading process. Further research is needed to investigate whether the observed effects are maintained over time.