What Mathematical Knowledge Do Prospective Teachers Reveal When Creating and Solving a Probability Problem?

The teaching of probability is conditioned by teachers’ mathematical knowledge. In this paper, an exploratory study is carried out with prospective teachers. A training task was designed requiring them to create and solve a probability problem using the values of euro coins, which was adapted to students aged 11 to 12. The study aimed at determining what mathematical knowledge prospective teachers show when dealing with the task. The data were collected through the Moodle online Campus. We framed the data analysis in the Mathematical Knowledge for Teaching model and we used content analysis as the methodological approach. The results indicate that, despite finding evidence of adequate common and specialised mathematical knowledge, in approximately half of the prospective teachers participating in the study, too many of them still show a lack of knowledge in both subdomains. There was also little evidence of knowledge of the curriculum. The main finding of the research is that, when prospective teachers get involved in complex creative tasks, they mobilised together specialised and common mathematical knowledge, working into different mathematical processes such as problem posing and solving, communication, and argumentation, which reinforces the need to continue working on these types of complex tasks.

Disentangling hand and tool processing: distal effects of neuromodulation

The neural processing within a brain region that responds to more than one object category can be separated by looking at the horizontal modulations established by that region, which suggests that local representations can be affected by connections to distal areas, in a category-specific way. Here we first wanted to test whether by applying transcranial direct current stimulation (tDCS) to a region that responds both to hands and tools (posterior middle temporal gyrus; pMTG), while participants performed either a hand- or tool-related training task, we would be able to specifically target the trained category, and thereby dissociate the overlapping neural processing. Second, we wanted to see if these effects were limited to the target area or extended to distal but functionally connected brain areas. After each combined tDCS and training session, participants therefore viewed images of tools, hands, and animals, in an fMRI scanner. Using multivoxel pattern analysis, we found that tDCS stimulation to pMTG indeed improved the classification accuracy between tools vs. animals, but only when combined with a tool training task (not a hand training task). However, surprisingly, tDCS stimulation to pMTG also improved the classification accuracy between hands vs. animals when combined with a tool training task (not a hand training task). Our findings suggest that overlapping but functionally-specific networks can be separated by using a category-specific training task together with tDCS - a strategy that can be applied more broadly to other cognitive domains using tDCS - and demonstrates the importance of horizontal modulations in object-category representations.

Effects of Counter-Stereotypes Cognitive Training on Aging Stereotypes in 12– to 13-Year Olds

The purpose of this study was to investigate the effect of counter-stereotypes cognitive training on adolescents’ aging stereotypes and to further investigate the best training method to intervene in aging stereotypes by comparing the effect of single and multiple intervention training methods on aging stereotypes and their retention effects. Three experiments examined the different intervention outcomes of different counter-stereotypes cognitive training on adolescent aging stereotypes. The study used a randomized block group experimental design and recruited a total of 183 middle school students for testing. Experiment 1 verified the effect of counter-stereotypes cognitive training by taking a single training task (evaluative conditioning technique), randomly assigning subjects to different conditions (training task or unrelated drawing task), and administering a follow-up test 24h after the posttest. Experiment 2a compared the effects of multiple versus single cognitive training, where we took multiple (adding the counter-stereotypes situational storytelling method) versus single training tasks and administered a follow-up test 72h after the posttest. Experiment 2b increased the number of training sessions based on Experiment 2a, with a second intervention training 72h after the end of the posttest and a follow-up test 72h after the second training. Experimental results suggest that evaluative conditioning techniques are effective in weakening subjects’ aging stereotypes, but are less effective in maintaining them. Compared to a single training task, multi-tasking is more effective and the effects of the intervention are maintained for up to a week by increasing the number of training sessions.

A method for evaluating the results of the educational process:

The article addresses the problem of evaluating the results of specialists as they graduate from their training. There are difficulties, not only with the decreasing number of students in training courses, but also with inadequate methods for educational management. There is a growing need for managers and subject lecturers to obtain information on the results of specialists’ training and graduation. This article sets out a method for evaluating the results of the educational management using the probability multiplication theorem for dependent events. The study shows that the results of the educational process can - and should - be managed if the results of training and graduation are periodically evaluated. At the same time, the evaluation results are of great value to the university and improve the educational management. They show the scale of the specialists’ training and graduation in relation to their training task and create a data base for subjects enabling appropriate managerial decisions aimed at maximizing approaching the results of the specialists’ graduation to their training task. It is of practical and scientific importance for the permanent staff of vocational educational institutions when developing managerial decisions for qualified specialists’ training, as well as for graduate students and researchers involved in the study of the effectiveness of educational management.

Learning to Call Bullsh*t via Induction: Categorization Training Improves Critical Thinking Performance

Participants performed a categorization training task, where each trial presented an example scenario in which an individual makes a claim based on an observation, and participants marked which fallacy or bias, if any, the individual in the scenario was committing. In two studies, we measure the effect of this training task on critical thinking, measured using an open-ended critical thinking assessment, both pre- and post-training. In Study 1, we pilot these materials in an online college course across a full academic semester and observe credible improvements in critical thinking performance. In Study 2, we conduct a pre-registered randomized controlled experiment using online research participants and observe credible improvements in critical thinking relative to no training, and relative to comparable learning activities focused on conventional curricular content. We infer that the categorization training task facilitated inductive learning of patterns of biased and flawed reasoning, which improved participants’ ability to detect and identify such patterns in the delayed open-ended critical thinking assessment. Such categorization training shows promise as an effective and practical method for improving learners’ resistance to online disinformation.

EXPRESS: Working memory training does not improve executive functioning or fluid intelligence

Several studies have reported that cognitive training can lead to improvements of complex mental skills such as intelligence. However, attempts to replicate these findings have not been very successful with many studies reporting lack of transferable effects on cognitive processes unrelated to the training task. On the other hand, transfer effects on cognitive processes closely related to the training task have been more commonly reported. In this study, we investigated the effects of a frequently used working-memory training programme on fluid intelligence and specific executive functions (updating, inhibition, switching, the focus of attention, and sustained attention). We remedied common issues with previous training studies by using an active control group, using more than one instrument to assess each function, and including a larger sample size. The experimental group showed significant improvement in the training task, indicating strong practice effects. However, no evidence of training-specific transfer was found in any of the variables investigated, and we could not find any of the previous improvements reported. Participants in both the training and control group showed post-training improvements in most of the outcome variables, suggesting that practice effects can be found even when a task is only performed twice. We conclude by discussing possible explanations for the differences between our results and those reported in prior studies, and recommend that any claims of improvement should be supported by studies capable of replicating them.

Improving Context-Aware Neural Machine Translation with Source-side Monolingual Documents

Document context-aware machine translation remains challenging due to the lack of large-scale document parallel corpora. To make full use of source-side monolingual documents for context-aware NMT, we propose a Pre-training approach with Global Context (PGC). In particular, we first propose a novel self-supervised pre-training task, which contains two training objectives: (1) reconstructing the original sentence from a corrupted version; (2) generating a gap sentence from its left and right neighbouring sentences. Then we design a universal model for PGC which consists of a global context encoder, a sentence encoder and a decoder, with similar architecture to typical context-aware NMT models. We evaluate the effectiveness and generality of our pre-trained PGC model by adapting it to various downstream context-aware NMT models. Detailed experimentation on four different translation tasks demonstrates that our PGC approach significantly improves the translation performance of context-aware NMT. For example, based on the state-of-the-art SAN model, we achieve an averaged improvement of 1.85 BLEU scores and 1.59 Meteor scores on the four translation tasks.