Investigating Teachers' Mathematics Teaching Understanding: A Case for Coordinating Perspectives

This paper provides a microanalysis of one Algebra I teacher's instruction to explore the advantages that are afforded us by coordinating two perspectives to document and account for the teacher's mathematical understandings. We use constructs associated with Stein, Grover and Henningsen's domain of mathematical didactics and Realistic Mathematics Education's instructional design theory to infer what the teacher might understand to effectively implement her instructional goals and, more importantly, support student learning. By coordinating these perspectives, we developed a working framework for analyzing the teacher's classroom practice retrospectively. For example, we illustrate how the mathematical possibilities related to one student's question might inform the teacher's decisions as she initiates shifts in students' self-generated models. Additionally, we illustrate how the teacher's decision to capitalize on particular students' models contributes in part to the kinds of mathematical ideas that can be explored and the connections students can make among those ideas. More generally, we explore the utility of coordinating these two perspectives to understand the landscape of ideas that teachers might traverse to align their practices with reform recommendations in the United States.     

Approaches to Multicultural Education in Preservice Teacher Education: Philosophical Frameworks and Models for Teaching

The authors in this article connect teacher education to multiple theoretical frameworks around the ongoing debate and issues of multicultural education. Connecting conservative, liberal, and radical theories of multicultural education particularly to preservice teachers, the authors argue that a more eclectic theoretical avenue must be striven and struggled for if there exists any hope in transforming schools, particularly, as they note, in urban environments. Practical avenues are discussed that promote such a multilayered interpretive/analytical approach to social change.     

Joint determination of college student achievement and effort: Implications for college teaching

In this paper, a four-equation simultaneous equations model is developed with college student effort and achievement being jointly determined. The model is then tested using a sample of students from one comprehensive university. The empirical results provide evidence that student efforts with respect to faculty interaction, but not with respect to library usage or course effort, significantly affect achievement.You know, teachers sometimes think they are all that happen in class. But I have to take what a teacher is trying to teach me and translate it into something I learn, and that has little to do with the teacher. The learning is what I do.—A student named Susan, fromOn College Teaching, by Ohmer Milton and AssociatesAn earlier version of this paper was presented at the Lilly Conference on College Teaching at Miami University in November 1989.     

Effects of Concept and Vee Mappings Under Three Learning Modes on Students' Attitudes Towards the Mappings,Learning Modes,Ecology and Genetics

This study investigates the effects of concept and vee mappings under cooperative, cooperative-competitive and individualistic learning modes, ability levels and gender on students' attitudes towards concept and vee mappings, the three learning modes, ecology and genetics. A pre-test-post-test experiment, with control groups, involving 808 eleventh grade (fourth form) students, was used for data collection. Students taught the use of concept and vee mappings, under cooperative conditions, developed superior positive attitudes towards the two heuristics, ecology and genetics, compared with those taught under cooperative-competitive and individualistic conditions. Statistically significant differences in their attitudes were due mainly to treatment and ability. High ability students developed the most superior positive attitudes to concept and vee mappings, ecology and genetics. Students' attitudes towards cooperation were mostly positive but totally negative to individualisation and mostly negative to competition. Students' positive attitudes to ecology and genetics correlated negatively with their attitudes towards competition and individualisation. The implications of the study's findings for the teaching of science are addressed.     

Specific reading impairments--are they to be associated with emotional difficulties?

The assumption that specific learning disabilities are not causally related to emotional disturbances is crucial for the cognitive research approaches that endeavor to isolate specific malfunctioning cognitive-computational processes. Because there are conflicting data regarding the emotional status of subjects with learning difficulties, the purpose of this study was the evaluation of the emotional status of subjects with specific learning difficulties in comparison with that of subjects from several relevant control groups. The HSCL-90 profiles of 38 subjects suffering developmental dyslexia, 28 subjects with subjective complaints regarding general concentration and reading comprehension difficulties, and 23 psychiatric patients were compared with those of 44 skilled readers without any known emotional difficulties. All subjects were adolescents and young adults (age range = 15 to 23). A cluster analysis of subjects' HSCL-90 profiles did not reveal any significant differences between subjects with dyslexia and control subjects. Both groups, on the other hand, were easily differentiated from psychiatric patients. Subjects with severe deficits in their ability to remember details of a text, and with subjective complaints regarding concentration difficulties, tended to generate emotional profiles that testify to a high level of anxiety. Although these subjects, as well as individuals with dyslexia, may be regarded at the functional level as inefficient readers, the two groups seem to clearly differ regarding the failure factors that underlie their phenotypic difficulties.     

A Comparison of Three Variations on a Standard-Setting Method

The purpose of this study was to determine whether two variations on the typical Angoff group standard-setting process would produce sufficiently consistent results to recommend their use. Judgments obtained from a group of experts during a meeting were compared with judgments gathered from the same group before and after the meeting. The results indicate that differences between passing scores obtained with the three variations are relatively small, but those gathered before the meeting were less consistent than ratings gathered during and after the meeting. These results imply that judgments gathered after an initial traditional group-process session can provide an efficient alternative mechanism for setting cutting scores using the Angoff method.
This research was supported by The American Board of Internal Medicine, but does not necessarily reflect its opinions or policies.     

Obtaining more out of less text in CBI: Effects of varied text density levels as a function of learner characteristics and control strategy

Learning from expository text in computer-based instruction (CBI) was examined as a function of text density level (high, low, or learner-controlled) and learner characteristics in achievement, attitudes, and reading ability. Low-density text was found to be as effective for learning as high-density text, but was more popular among students and also reduced completion time. The highest achievement was obtained in the learner-control condition, with low-ability readers showing a greater tendency to select high-density text than did high-ability readers. Reading ability was also positively related to achievement in learning from high-density computer text and to preferences for learning from CBI relative to print. Based on the resulte, use of low-density text is suggested as a standard feature or learner-control option for CBI lessons.     

A stroll down Kármán street

The Kármán vortex street is an exquisite flow pattern that can be seen in a variety of flow situations. In this article, we present some of the main features of the phenomenon starting from its interesting history, and also show why it is important in a number of engineering situations. Raghuraman N Govardhan is in the Mechanical Engineering Department at the Indian Institute of Science. He works in the areas of separated flow, fluid-structure interaction and micro-flows. O N Ramesh is at the Department of Aerospace Engineering, Indian Institute of Science, Bangalore. His research interests include transitional and turbulent flows, vortex dynamics and separated flows.