From preschool teachers’ professional development to children’s knowledge: comparing sets

Recently, there have been increased calls for enhancing preschool children’s mathematics knowledge along with increasing calls for preparing preschool teachers to meet the demands of new preschool mathematics curricula. This article describes the professional development program Starting Right: Mathematics in Preschools. Focusing on four episodes that revolve around the topic of equivalent sets, it demonstrates how engaging preschool teachers with challenging tasks may promote their subject matter knowledge as well as their pedagogical content knowledge, leading to an interweaving of knowledge and practice. Assessment of the program included assessing the children’s knowledge. Results indicated that students of participating teachers learned to be more flexible and to give more possible answers than students of non-participating teachers.     

Stressful Effects of a University Faculty Strike on Students: Implications for Coping

This study examines university students' psychological reactions to a two-month faculty strike at a large Canadian university. Of particular interest were relationships between students' experience of angry feelings (state anger) about the strike and perceptions of the extent to which the strike had affected their plans involving important planned life experiences such as graduation, travel, and employment. The role of social support from the internet during the strike in alleviating the intensity of angry feelings was also investigated. Data were collected using an anonymous self-report questionnaire administered a few days after the labour dispute was settled. A total of 289 college students completed the questionnaire. Hierarchical multiple regressions were conducted with variables entered as blocks and with state anger and anxiety as dependent variables. The first block of variables entered were individual variables such as age and year of study. The second block included average ratings of the extent to which plans were affected by the strike and how fairly students felt they had been treated. The third block of variables included social support from the internet and self-efficacy. The fourth block was the interaction between internet support and sex. With anger as the dependent variable, results showed that the more unfairly students felt they were treated during the strike and the more their plans had been affected by the strike, the greater their anger. Support provided to students from the internet predicted to lower anger. Further regression results indicated that the more students' plans had been affected by the strike, the greater their anxiety. Higher self-efficacy in students contributed to lower anxiety. Implications of the results are discussed within a social context, particularly the importance of studying how individual and social resources can reduce distress resulting from an interruption of students' academic plans due to a strike.     

The Relative Merits of Explicit and Implicit Learning of Contrasted Algebra Principles

Knowledge representations that result from practicing problem solving can be expected to differ from knowledge representations that emerge from explicit verbalizing of principles and rules. We examined the degree to which the two types of learning improve problem-solving knowledge and verbal explanation knowledge in classroom instruction. We presented algebraic addition and multiplication problems to 153 sixth graders randomly assigned to two conditions. Students in the explicit learning condition had to verbally compare contrasted algebra problems. Students in the implicit learning condition had to generate and solve new problems. On three follow-up tests over 10 weeks, students in the explicit learning condition exhibited better problem-solving knowledge than students in the implicit learning condition, as well as some advantages in verbal concept knowledge. Implicit learning showed some advantages on not directly taught but incidentally learned aspects. Overall, this outcome favors the explicit learning of concepts. Explicit comparison fostered student performance on non-verbal and verbal measures, indicating that verbalization facilitates effective comparison.     

Asymmetries in Infant Cross-Modal Transfer

3 groups of 12-month-olds were tested for cross-modal and intramodal transfer of information about shape. Infants were given either visual (V) or tactual (T) familiarization and then tested for visual recognition (V-V, T-V) or tactual recognition (T-T, V-T). Transfer was tested after either 15, 30, or 60 sec familiarization. Overall, intramodal transfer was superior to cross-modal transfer. Whereas the V-V condition was easiest of all, the T-T condition proved easier than V-T cross-modal transfer, although it was no more difficult than T-V transfer; cross-modal asymmetries appeared, with T-V easier than V-T. The asymmetry in cross-modal transfer could not be explained by intramodal factors. Possible bases for cross-modal asymmetries were discussed.     

Improving the reading of bisyllabic words that involve context-sensitive spelling rules: focus on successes or on failures?

The effect of two training procedures on the improvement of reading accuracy in poor readers was examined in relation to their initial reading level. A randomized controlled trial was conducted with 60 poor readers. Poor readers were assigned to a control group that received no training, or one of two training conditions. One training concentrated on the words the children read correctly (successes), the other on the words they read incorrectly (failures). They repeatedly read bisyllabic Dutch words, half of the training words involving context-sensitive spelling rules (vowel degemination or consonant gemination). Some children repeatedly read their successes, others their failures. The training used a computerized flashcards format. The exposure duration of the words was varied to maintain the accuracy rate at a constant level. In general, children who received training improved their reading accuracy and reading speed of trained words, and reading accuracy of untrained words, more than the control group. Which training focus is superior, depends on the reading level of the child and the type of words used. For children with a low initial reading level, to improve reading accuracy of bisyllabic words that follow context-sensitive spelling rules, a training focus on failures was superior over a training focus on successes. For children with a high initial reading level, improvement of reading speed was largest in a training on successes. Evidently, the improvement of word reading skills depends both on the children’s level of reading competence and on the type of training.     

Temperament Characteristics and Science Achievement: A longitudinal study of elementary students in Taiwan

Based on data collected from 211 elementary school children in central Taiwan over four years, the role of temperament in science achievement was examined with multivariate analysis of covariance (MANCOVA) with repeated measures design. The results revealed that the students’ science achievement is stable over time. The task orientation characteristics (i.e., distractibility, hyperactivity, and persistence) identified by previous research as important in mathematics and reading achievement are not consistent with the findings of this study that although the impacts of distractibility and persistence are significant, the simple effect of activity level on science achievement was not significant. However, the interaction effect of activity level and persistence is significant. Further break down analyses conducted to pursuit the interaction effect revealed that: (1) persistence has a consistent significant positive effects on all children over the years, except for the ones with high activity level (the upper 25th percentile); and (2) activity level has significant negative effects on high persistence (the upper 25th percentile) children only, and the interaction effect of activity level increases over time—the older the child the more significant the influence. Also, the tendency of approach/withdraw has significant impact on science achievement The educational implications of the findings include: (1) teachers of high activity students with high persistence may need to consider the match between children’s interests and contents of instruction; (2) a good match between children’s individual differences in distractibility, persistence, and approach need to be considered in contents, expectations, and interactions of the instruction.     

Exploring one student’s explanations at different ages: the case of Sharon

This study describes the types of explanations one student, Sharon, gives and prefers at different ages. Sharon is interviewed in the second grade regarding multiplication of one-digit numbers, in the fifth grade regarding even and odd numbers, and in the sixth grade regarding equivalent fractions. In the tenth grade, she revisits each of these concepts again. The study investigates the different forms Sharon’s explanations take at different ages as well as how she perceives the nature of mathematical explanations at different ages. Sharon’s explanations are also used to investigate her conceptualization of the number zero, a concept which runs across the curriculum at different ages. Finally, the study explores a method for investigating the long-term mathematical development of one student. Implications for future research are discussed.     

Educational/Instructional Media

ERIC Clearinghouse on Information Resources, review of six recent items

Audiovisual Market Place 1980 (New York: Bowker, 1980---$29.95, paper)

Don Kaplan's Video in the Classroom: A Guide to Creative Television (White Plains, N.Y.: Knowledge Industry Publications, 1980---price not given, paper)

Anne Howe, ed. International Yearbook of Educational and Instructional Technology 1980/81 (London: Kogan Page/New York: Nichols Publishing Co., 1980---$32.50)

Esther R. Dyer, comp. “Cultural Pluralism and Children's Media” (Chicago: American Library Association, 1978 ---price not given, paper)