Teachers’ perceptions of assessments of their mathematical knowledge in a professional development course

The purpose of the project reported in this article was to evaluate how assessing teachers’ mathematical knowledge within a professional development course impacted from the teachers’ perspective their learning and their experience with the course. The professional development course consisted of a 2-week summer institute and the content focus was geometry. We had decided to assess the mathematical learning of the teachers during this professional development course for various accountability reasons, but were concerned about possible negative by-products of this decision on the teachers and their participation. Thus, we worked to design assessment in ways that we hoped would minimize negative impacts and maintain a supportive learning environment. In addition, we undertook this evaluation to examine the impacts of the assessment, which included homework, quizzes, various projects, and an examination for program evaluation. Seventeen grade 5–9 teachers enrolled in the course participated in the study by completing written reflections and by describing their experiences in interviews. We learned that while our original intent was “to do no harm,” the teachers reported that their learning was enhanced by the assessment. The article concludes by describing the various properties of the assessments that the teachers identified as contributing to their learning of the geometry content, many of which align with current recommendations for assessing and evaluating grade K-16 mathematics students.

Roadkill on the electronic highway? The threat to the mathematical literature

This article begins with an analysis of reliability and usability in the mathematical literature. Mathematical practice is seen to be adapted to very high standards in these respects, and quite sensitive to even modest declines in quality. Unfortunately most scenarios for the transition to electronic publication suggest serious loss of quality. This is a problem special to mathematics: other sciences are adapted to lower standards, and should be much less sensitive to changes. Some ways to prevent this decline are suggested. A condensed version of this article appeared inNotices of the American Mathematical Society, 42, 1, January 1995. Published with permission of the American Mathematical Society.     

The Developmental Sequence and Relations Between Gesture and Spoken Language in Toddlers With Autism Spectrum Disorder

In typical development, gestures precede and predict language development. This study examines the developmental sequence of expressive communication and relations between specific gestural and language milestones in toddlers with autism spectrum disorder (ASD), who demonstrate marked difficulty with gesture production and language. Communication skills across five stages (gestures, word approximations, first words, gesture-word combinations, and two-word combinations) were assessed monthly by blind raters for toddlers with ASD participating in an randomized control trial of parent-mediated treatment (N = 42, 12–30 months). Findings revealed that toddlers acquired skills following a reliable (vs. idiosyncratic) sequence and the majority of toddlers combined gestures with words before combining words in speech, but in contrast to the pattern observed in typical development, a significant subset acquired pointing after first words.     

Assessing Marital Conflict from the Child''s Perspective: The Children''s Perception of Interparental Conflict Scale

Guided by Grych and Fincham's theoretical framework for investigating the relation between interparental conflict and child adjustment, a questionnaire was developed to assess children's views of several aspects of marital conflict. The Children's Perception of Interparental Conflict Scale (CPIC) was initially examined in a sample of 222 9-12-year-old children, and results were cross-validated in a second sample of 144 similarly aged children. 3 factor analytically derived subscales (Conflict Properties, Threat, Self-Blame) demonstrated acceptable levels of internal consistency and test-retest reliability. The validity of the Conflict Properties scale was supported by significant relations with parent reports of conflict and indices of child adjustment; the Threat and Self-Blame scales correlated with children's responses to specific conflict vignettes. The CPIC thus appears to be a promising instrument for assessing perceived marital conflict, and several issues regarding its interpretation are discussed.     

Mathematical images in advertising: constructing difference and shaping identity, in global consumer culture

Mathematics educators have long emphasised the importance of attitudes, beliefs, and feelings towards mathematics, as crucial in motivating (or not) its learning and use, and as influenced in turn by its social images. This paper is about images of mathematics. Our search for advertisements containing such images in UK daily newspapers, during 2006–2008, found that 4.7 % of editions included a “mathematical” advert, compared with 1.7 % in pilot work for 1994–2003. The incidence varied across type of newspaper, being correlated with class and gender profiles of the readership. Three quarters of advertisements were classified as containing only very simple mathematics. ‘Semiotic discursive’ analysis of selected advertisements suggests that they draw on mathematics not to inform, but to connote qualities like precision, certainty, and authority. We discuss the discourse on mathematics in advertising as ‘quasi-pedagogic’ discourse, and argue that its oversimplified forms, being empty of mathematical content, become powerful means for regulating and ‘pedagogising’ today's global consumers.     

Correspondence Training as a Means of Improving Study Skills

This study was an attempt to encourage middle school pupils to use time spent on topic (project) work to better effect. They were taught some elements of correspondence training which required them to think ahead, to plan carefully what they were going to do in a certain time period and to make a forecast. At the end of each working session, they were required to look back at what they had achieved and to discuss the outcomes with a partner in terms of their success at forecasting and in achievement. Especially among the more able pupils, there were marked improvements in both quantity and quality of work produced     

Mentoring interdisciplinary undergraduate students via a team effort

We describe how a team approach that we developed as a mentoring strategy can be used to recruit, advance, and guide students to be more interested in the interdisciplinary field of mathematical biology, and lead to success in undergraduate research in this field. Students are introduced to research in their first semester via lab rotations. Their participation in the research of four faculty members-two from biology and two from mathematics-gives them a first-hand overview of research in quantitative biology and also some initial experience in research itself. However, one of the primary goals of the lab rotation experience is that of developing teams of students and faculty that combine mathematics and statistics with biology and the life sciences, teams that subsequently mentor undergraduate research in genuine interdisciplinary environments. Thus, the team concept serves not only as a means of establishing interdisciplinary research, but also as a means of incorporating new students into existing research efforts that will then track those students into meaningful research of their own. We report how the team concept is used to support undergraduate research in mathematical biology and what types of team-building strategies have worked for us.     

Worked examples with errors: when self-explanation prompts hinder learning of teachers diagnostic competences on problem-based learning

To diagnose classroom situations is crucial for teachers’ everyday practice. The approach of worked examples with errors seems promising to support the diagnosis of classroom situations in student teachers (Stark et al. in Learn Instr 21(1):22–33, 2011). To enhance that approach, error-explanation prompts and an adaptable feedback method to help the learner realize why an error happened and how to prevent a recurrence might be beneficial. In this empirical study, we investigated whether error-explanation prompts and adaptable feedback can facilitate diagnostic competences. N = 108 student teachers took part in a 2 × 2 factorial design (with and without error-explanation prompts as well as with and without adaptable feedback). Error-explanation prompts had a positive effect on declarative-conceptual knowledge if combined with adaptable feedback. Student teachers might have realized a lack of basic concepts and focused their attention on the declarative-conceptual knowledge in the feedback. Contrary to our expectations, however, error-explanation prompts hindered rather than facilitated learning of practical diagnostic knowledge.