Instructions and recipes in mathematical proofs

Educational Studies in Mathematics - In mathematics education research, proofs are often conceptualized as sequences of mathematical assertions. We argue that this ignores proofs that contain...     

The application of artificial intelligence principles to teaching and training*

This paper compares and contrasts the use of AI principles in industrial training with more normal computer‐based training (CBT) approaches. A number of applications of CBT are illustrated (for example simulations, tutorial presentations, fault diagnosis, management games, industrial relations exercises) and compared with an alternative approach using AI. An evaluation of the relative merits of the two approaches will be given. Existing CBT packages are used to illustrate the points raised and the emphasis of the arguments will be on the effectiveness of AI and CBT in terms of both cost and learning. The position of AI applications within CBT is discussed, as is the task of getting started in applying these techniques.     

EVALUATING THE EFFECTS OF ON‐TASK IN A BOX AS A CLASS‐WIDE INTERVENTION

The present study evaluated the effects of the On‐Task in a Box intervention on student on‐task behavior when used as a class‐wide intervention. The intervention package includes self‐monitoring, video modeling, and reinforcement contingency components. A multiple baseline design across three elementary classrooms was used to determine the effects of the intervention on student behavior. Results indicated immediate increases in on‐task behavior in all classrooms. Calculation of nonoverlap of all pairs’ effect sizes indicated strong intervention and maintenance effects on on‐task behavior of students in all classrooms. Social validity data were also collected, which indicated adequate validity of the intervention. Results of the study suggest that the intervention package may be effective for improving class‐wide levels of on‐task behavior.     

Qualitative Outcomes of a Homestay Immersion With Critical Reflection

The authors explore the impact of a 3‐week homestay cultural immersion on 10 counselor trainees by analyzing their 210 structured journals using consensual qualitative research. Findings suggest that establishing meaningful relationships and engaging in critical reflection are central to increasing multicultural awareness. Implications for multicultural counseling training and research are provided.     

The multi-stage fitness test as a predictor of endurance fitness in wheelchair athletes

Abstract

The aims of this study were two-fold: (1) to consider the criterion-related validity of the multi-stage fitness test (MSFT) by comparing the predicted maximal oxygen uptake ([Vdot]O_2max) and distance travelled with peak oxygen uptake ([Vdot]O_2peak) measured using a wheelchair ergometer (n = 24); and (2) to assess the reliability of the MSFT in a sub-sample of wheelchair athletes (n = 10) measured on two occasions. Twenty-four trained male wheelchair basketball players (mean age 29 years, s = 6) took part in the study. All participants performed a continuous incremental wheelchair ergometer test to volitional exhaustion to determine [Vdot]O_2peak, and the MSFT on an indoor wooden basketball court. Mean ergometer [Vdot]O_2peak was 2.66 litres · min^?1 (s = 0.49) and peak heart rate was 188 beats · min^?1 (s = 10). The group mean MSFT distance travelled was 2056 m (s = 272) and mean peak heart rate was 186 beats · min^?1 (s = 11). Low to moderate correlations (ρ = 0.39 to 0.58; 95% confidence interval [CI]: ?0.02 to 0.69 and 0.23 to 0.80) were found between distance travelled in the MSFT and different expressions of wheelchair ergometer [Vdot]O_2peak. There was a mean bias of ?1.9 beats · min^?1 (95% CI: ?5.9 to 2.0) and standard error of measurement of 6.6 beats · min^?1 (95% CI: 5.4 to 8.8) between the ergometer and MSFT peak heart rates. A similar comparison of ergometer and predicted MSFT [Vdot]O_2peak values revealed a large mean systematic bias of 15.3 ml · kg^?1 · min^?1 (95% CI: 13.2 to 17.4) and standard error of measurement of 3.5 ml · kg^?1 · min^?1 (95% CI: 2.8 to 4.6). Small standard errors of measurement for MSFT distance travelled (86 m; 95% CI: 59 to 157) and MSFT peak heart rate (2.4 beats · min^?1; 95% CI: 1.7 to 4.5) suggest that these variables can be measured reliably. The results suggest that the multi-stage fitness test provides reliable data with this population, but does not fully reflect the aerobic capacity of wheelchair athletes directly.