To Define Or Not To Define: The Case Of (-8)1/3

This paper discusses two possible approaches to (-8)^1/3. The first is that (-8)^1/3 = ³(-8) = -2. The second is that (-8)^1/3 is undefined. The pros and cons of each of these approaches are considered and some implications to teacher education are specified.This revised version was published online in September 2005 with corrections to the Cover Date.     

The Role of Intuitive Rules in Science and Mathematics Education

During the last two decades many researchers in mathematics and science education have studied students’ conceptions and ways of reasoning in mathematics and science. Most of this research is content‐specific. It was found that students hold alternative ideas that are not always compatible with those accepted in science. It was suggested that in the process of learning science or mathematics, students should restructure their specific conceptions to make them conform to currently accepted scientific ideas. In our work in mathematics and science education it became apparent that some of the alternative conceptions in science and mathematics are based on the same intuitive rules. We have so far identified two such rules: “More of A, more of B”, and “Subdivision processes can always be repeated”. The first rule is reflected in subjects’ responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, volume, matter, etc.) in all tasks related to intensive quantities (density, temperature, concentration, etc.) and in all tasks related to infinite quantities. The second rule is observed in students’, preservice and inservice teachers’ responses to tasks related to successive division of material and geometrical objects and in seriation tasks. In this paper, we describe and discuss these rules and their relevance to science and mathematics education.     

Oxidative injury and antioxidant vitamins E and C in Schizophrenia

Susceptibility of Schizophrenic patients to lipid peroxidation relative to healthy control subjects was investigated by measuring the malondialdehyde (MDA) levels in plasma. The main finding was that Schizophrenic patients were more susceptible than control subjects to oxidative damage as evident from increased MDA levels in plasma. Antioxidant levels are also depleted in Schizophrenic patients when compared to normal subjects as evident from decreased levels of vitamins E and C in the plasma. Impaired antioxidant defense and increased lipid peroxidation suggests that treatment with antioxidants (Vitamin E, Vitamin C, beta carotene) at the initial stages of illness may prevent further oxidative injury and deterioration of associated neurological deficits in Schizophrenia.     

Attitudes toward Family Obligations among American Adolescents with Asian, Latin American, and European Backgrounds

This study was designed to examine the attitudes toward family obligations among over 800 American tenth ( M age = 15.7 years) and twelfth ( M age = 17.7 years) grade students from Filipino, Chinese, Mexican, Central and South American, and European backgrounds. Asian and Latin American adolescents possessed stronger values and greater expectations regarding their duty to assist, respect, and support their families than their peers with European backgrounds. These differences tended to be large and were consistent across the youths' generation, gender, family composition, and socioeconomic background. Whereas an emphasis on family obligations tended to be associated with more positive family and peer relationships and academic motivation, adolescents who indicated the strongest endorsement of their obligations tended to receive school grades just as low as or even lower than those with the weakest endorsement. There was no evidence, however, that the ethnic variations in attitudes produced meaningful group differences in the adolescents' development. These findings suggest that even within a society that emphasizes adolescent autonomy and independence, youths from families with collectivistic traditions retain their parents' familistic values and that these values do not have a negative impact upon their development.     

Simplifying Algebraic Expressions: Teacher Awareness and Teaching Approaches

This study investigates four seventh-grade teachers' awareness of students' tendency to conjoin or 'finish' open expressions. It also investigates teachers' ways of coping with this tendency. Three types of data were collected: 1) lesson plans, 2) lesson observations, and 3) post-lesson interviews. The analysis showed that the two experienced teachers were aware of this tendency and some of its possible sources, while the novices were unaware of either. Teaching approaches related to this tendency also differed considerably. In conclusion we analyze these teaching methods in light of the existing literature and discuss possible short- and long-term implications of the use of each approach.     

Exploring cultural differences in critical thinking: Is it about my thinking style or the language I speak?

Critical thinking is deemed as an ideal in academic settings, but cultural differences in critical thinking performance between Asian and Western students have been reported in the international education literature. We examined explanations for the observed differences in critical thinking between Asian and New Zealand (NZ) European students, and tested hypotheses derived from research in international education and cultural psychology. The results showed that NZ European students performed better on two objective measures of critical thinking skills than Asian students. English proficiency, but not dialectical thinking style, could at least partially if not fully explain these differences. This finding holds with both self-report (Study 1) and objectively measured (Study 2a) English proficiency. The results also indicated that Asian students tended to rely more on dialectical thinking to solve critical thinking problems than their Western counterparts. In a follow-up data analysis, students' critical thinking was found to predict their academic performance after controlling for the effects of English proficiency and general intellectual ability, but the relationship does not vary as a function of students' cultural backgrounds or cultural adoption (Study 2b). Altogether, these findings contribute to our understanding of the influence of culture on critical thinking in international education.     

Effect of carbohydrate ingestion during cycling exercise on affective valence and activation in recreational exercisers

Carbohydrate (CHO) ingestion enhances “feel-good” responses during acute exercise but no study has examined the effect of regular ingestion of CHO on affective valence. We investigated the effect of CHO ingestion on perceptual responses and perceived work intensity of individual exercise sessions throughout a 10-week cycling (“spin”) exercise intervention. We also assessed whether any changes in affect and/or perceived work intensity would influence health and fitness parameters. Twelve recreational exercisers (46 ± 9 years; nine females and three males) were randomly allocated to either CHO (7.5% CHO; 5 mL · kg^?1 per exercise session; n = 6; CHO) or placebo (0% CHO, taste- and volume-matched solution; n = 6; PLA) groups. Participants exercised 2 × 45-min per week, over a 10-week intervention period. Perceptual measures of exertion (RPE), affect (feeling scale, FS) and activation (felt arousal scale, FAS) were assessed after each exercise session. The FAS ratings increased over time in CHO but decreased throughout the intervention in PLA (P = 0.03). There were no differences in heart rate (P = 0.70), RPE (P = 0.05) and FS (P = 0.84) between trials. Furthermore, no changes in health and fitness parameters were observed over time or between groups. CHO ingestion enhanced ratings of activation in recreational exercisers throughout a 10-week cycling intervention.     

Toy safety and selection

Toys can be used to promote children's cognitive, physical, motor, language, social, and emotional development. Safety and developmental appropriateness are of the utmost importance when selecting children's toys. Parents and teachers and other helping professionals need to teach children the safe use of toys to prevent toy-related accidents. Obtain additional information regarding toy safety by calling the U.S. Consumer Product Safety Commission at 1(800)638-CPSC.