The Development of Teacher Knowledge in Support of Student Mathematical Inquiry

Abstract

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities from multiple courses in the program, we offer general principles of instruction for supporting mathematical inquiry at all grade levels. We contend that an awareness and application of the multiple facets of mathematical knowledge for teaching can be critical to supporting mathematical inquiry across the K-16 spectrum.     

Response to the discipline review of teacher education in mathematics and science

This paper relates to a study commissioned by the Department of Employment, Education and Training to evaluate the impact of the Discipline Review of Teacher Education in Mathematics and Science. The major datagathering strategies employed in that study have been to visit every higher education institution in Australia involved in teacher education to interview relevant staff and to seek information by mail from other bodies to whom recommendations of the Review were addressed. This paper reports a supplementary activity, the analysis of citations of the Report of the Discipline Review in the journal of the Australasian Science Education Research Association,Research in Science Education. This research reveals that there has been relatively little critical analysis of the Review, somewhat surprising in the light of its significance for science teacher education. Further the citations in the journal suggest that the Review Report has struck a responsive chord with those involved in the science education of primary school teachers. Its impact on secondary teacher education would appear to be less significant. This difference is explored in the context of professional education. Specializations: science education, teacher education. Specializations: international education, educational measurement, science education.     

Participation and equity towards a sociology of policy language in education

The problem of making education policies explicit and context independent is addressed in this paper. As a vehicle for discussion the paper examines a contemporary policy that has major shortcomings in the explicitness of its language: Australia’s “Participation and Equity Program”, a policy directed at increasing access to education by post-compulsory level students. Problems in making policies explicit and context independent are discussed. Policies are seen as complex messages whose meanings can become scrambled for implementers remote from the language community of policy framers. The links between speech communities and the limited contexts of policies are examined. The paper suggests the inauguration of a sociology of policy language in education to assist in policy design and dissemination. Its concluding sections recommend the kinds of applied work that that sub-discipline might engage in and strategies for improving the explicitness of policy language generally.     

Metaphors and maps in evaluation

This paper considers efforts made in evaluating a distance‐learning course, which was intended to prepare students for working on an undergraduate dissertation in business and economic areas. Course delivery had stressed a tutorial approach with an emphasis on individual mentor–student exchanges. Given the nature of the learning approach and the backgrounds of the students, an attempt was made to open the evaluation process to participants and allow them to articulate their learning experiences. In seeking this end, the evaluation employed both metaphor and mapping techniques to chart the experiences that had been provoked by the learning encounters.     

Temperament, Emotion, and Cognition at Fourteen Months: The MacArthur Longitudinal Twin Study

200 pairs of twins were assessed at 14 months of age in the laboratory and home. Measures were obtained of temperament, emotion, and cognition/language. Comparisons between identical and fraternal twin correlations suggest that individual differences are due in part to heritable influences. For temperament, genetic influence was significant for behavioral observations of inhibition to the unfamiliar, tester ratings of activity, and parental ratings of temperament. For emotion, significant genetic influence was found for empathy and parental ratings of negative emotion. The estimate of heritability for parental report of expression of negative emotions was relatively high, whereas that for expression of positive emotions was low, a finding consistent with previous research. For cognition and language, genetic influence was significant for behavioral indices of spatial memory, categorization, and word comprehension. Shared rearing environment appears influential for parental reports of language and for positive emotions, but not for other measures of emotion or for temperament.     

Amnesia induced by hypothermia as a function of treatment-test interval and recooling in rats

In Experiment I, a repeated tests procedure was employed to assess hypothermia-induced amnesia of a footshock experience. Rats tested 4 h after training treatment showed no memory loss, but amnesia was present at 24 h. Although recovery of memory was obtained when the same animals were cooled 2 h prior to a 50-h test, repeated testing also tended to attenuate amnesia. In Experiment II, independent groups were tested at 6 or 50 h after training treatment. Again, memory of the footshock was present at the short, but not at the long, interval. Recooling shortly prior to the 50-h test eliminated amnesia. Experiment III indicated that the return of memory produced by recooling did not persist if testing was delayed. These findings suggested that hypothermia may function as an important contextual cue for memory retrieval.     

Gender bias in IQ-discrepancy and post-discrepancy definitions of reading disability

The present study investigated the hypothesis that the higher prevalence of reading disability (RD) often observed among boys is partly an artifact of gender bias in the prediction of reading from IQ. The relevant regression statistics derived from a sample of more than 900 children revealed a statistically significant intercept bias. Predicted reading scores for boys were systematically overestimated, thereby inflating IQ-reading discrepancies; the converse was found for girls. When defined separately for girls and boys, severe underachievement in reading was found to be equally prevalent in both genders and, furthermore, was associated with qualitatively and quantitatively similar patterns of deficits. Because the bias arose from general differences between boys and girls in reading score distributions (a lower mean and greater variance for boys) rather than from differences in IQ scores, gender bias poses a potential threat not only to traditional IQ-discrepancy definitions but also to post-discrepancy definitions that are based solely on reading score cutoffs. Future classification criteria for RD need to take heed of the possibility that when the distributions of reading scores for boys and girls are not identical, performance cutoffs designating low achievement that are based on data pooled from both genders are likely to result in the overidentification of boys with RD and the underidentification of girls with RD.