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This study examines the capabilities of in-service secondary school teachers to provide financial education. Data were gathered from online surveys, which were spread among 300 teachers in the Flemish region of Belgium. We distinguish between perceived and actual capabilities. Our results reveal that only one third of teachers consider themselves sufficiently competent to provide financial education. Actual capabilities are assessed using a broad measure of financial literacy, which takes into account teachers' financial knowledge, financial behaviour and financial attitudes. Our results indicate that only approximately half of teachers score sufficiently on financial knowledge and only a third attains the preferred minimum score for financial attitudes. In addition, our heterogeneity analysis shows differences in scores related to teacher characteristics such as gender, teaching discipline and teaching experience. The large share of teachers not reaching the threshold indicating adequate capabilities for providing financial education raises concern, as teacher quality is an important factor contributing to the effectiveness of financial education. Teacher professional development can play a crucial role here.

Symbolic circuit analysis is a cornerstone of electrical engineering education. Solving a suitable set of selected problems is essential to developing professional skills in the field. A new method is presented for automatic validation of circuit equations representing a student's intermediate steps in the solving process. Providing this immediate feedback may strongly enhance the training effects. The new method was embedded in a Web-based e-learning system and has proved to be useful in circuit analysis training, both at an introductory level and for more advanced problems in analog electronics. (Contains 1 table and 5 figures.)

Upper primary school children often routinely apply proportional methods to missing-value problems, even when it is inappropriate. We tested whether this tendency could be weakened if children were not required to produce computational answers to such problems. A total of 75 sixth graders were asked to classify 9 word problems of three types (3 for which proportionality is an appropriate model, 3 implying an invariant additive relationship, and 3 for which the result is constant) and to solve a parallel version of this set of problems. Half of the children first found the solution and then did the classification task (SC-condition), while for the others the order was the opposite (CS-condition). On the word problem test, children often overused proportional methods, but those in the CS-condition performed better than those in the SC-condition, suggesting a positive impact of the classification task. On the classification task, most pupils took into account the underlying mathematical models, but they did not always distinguish proportional from non-proportional problems. Students in the SC-condition performed worse than those in the CS-condition, suggesting that solving the word problems first negatively affects later classifications. (Contains 4 tables and 4 figures.)

Background: From upper elementary education on, children develop a tendency to over-use linearity. Particularly, it is found that many pupils assume that if a figure enlarges "k" times, the area enlarges "k" times too. However, most research was conducted with traditional, school-like word problems. Aims: This study examines whether pupils also over-use linearity if non-linear problems are embedded in meaningful, authentic performance tasks instead of traditional, school-like word problems, and whether this experience influences later behaviour. Sample: Ninety-three sixth graders from two primary schools in Flanders, Belgium. Method: Pupils received a pre-test with traditional word problems. Those who made a linear error on the non-linear area problem were subjected to individual interviews. They received one new non-linear problem, in the S-condition (again a traditional, scholastic word problem), D-condition (the same word problem with a drawing) or P-condition (a meaningful performance-based task). Shortly afterwards, pupils received a post-test, containing again a non-linear word problem. Results: Most pupils from the S-condition displayed linear reasoning during the interview. Offering drawings (D-condition) had a positive effect, but presenting the problem as a performance task (P-condition) was more beneficial. Linear reasoning was nearly absent in the P-condition. Remarkably, at the post-test, most pupils from all three groups again applied linear strategies. Conclusions: Pupils' over-reliance on linearity seems partly elicited by the school-like word problem format of test items. Pupils perform much better if non-linear problems are offered as performance tasks. However, a single experience does not change performances on a comparable word problem test afterwards.

In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules. Two major intuitive rules are manifested in comparison tasks: "More A--more B" and "Same A--same B". In this paper, we address two important questions for which the existing literature on intuitive rules does not provide a convincing research-based answer: (1) are the reasoning processes of students who respond in line with a given intuitive rule actually affected by that rule or by essentially other misconceptions (leading to the same answer), and (2) are individual students consistent in their choice of one of the intuitive rules when confronted with different, conceptually unrelated tasks? A test consisting of five comparison problems from different mathematical subdomains was administered collectively to 172 Flemish students from Grades 10 to 12. An analysis of students' written calculations and justifications suggested that the students were considerably less affected by the intuitive rules than their multiple-choice answers actually suggested. Instead, essentially different misconceptions and errors were found. With respect to the issue of individual consistency, we found that students who made many errors did not answer systematically in line with one of the two intuitive rules.

Studied the influence of authentic contexts and self-made graphical representations on students' well-documented tendency to apply the linear model improperly in representing and solving nonproportional word problems. Findings for 152 Flemish 8th graders and 161 10th graders do not show the expected effects; in fact, these forms of help had negative effects as discussed. (SLD)

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Copyright of Biotechnologie, Agronomie, Societe et Environnement is the property of Les Presses Agronomiques de Gembloux and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Biotechnologie, Agronomie, Societe et Environnement is the property of Les Presses Agronomiques de Gembloux and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Biotechnologie, Agronomie, Societe et Environnement is the property of Les Presses Agronomiques de Gembloux and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)