Flowery math: a case for heterodiscoursia in mathematics problems solving in recognition of students’ authorial agency

In an innovative, progressive school, students were asked to solve a fairly routine mathematical problem using real money in a “real-world” scenario. Even though the school values students’ ideas, the reaction of the teacher to one student’s alternative modelling of the problem suggests that he was expecting a particular answer to be provided using routine mathematical models and thinking while not being interested in exploring the student’s unexpected alternative. We place his reasoning for doing so within broad pedagogical discourses that we think define the “allowable” responses of teachers and students in ways that inhibit meaning-making for both. These broad discourses are defined as the progressive constructivist approach, the scaffolding discursive approach, the situation modelling approach and the dialogic approach. We consider the advantages and the potential consequences each might bring to the case. We suggest that extensive consideration of pedagogical discourses in mathematics classes must be reconsidered both for how we understand students’ mathematical meaning-making and how we construct student agency in relationship to culture, whether as apprentices or authors.     

A quantitative analysis of high school chemistry textbooks for scientific literacy themes and expository learning aids

The purpose of this study was to examine the content of seven high school chemistry textbooks for curriculum balance and emphasis on the following aspects of scientific literacy: (a) science as a body of knowledge, (b) science as a way of investigating, (c) science as a way of thinking, and (d) the interaction among science, technology, and society. In addition, the number of textbook pages, vocabulary terms, pictures, questions, and problems at the end of the chapter were determined. The textbook is an important teaching aid in high school chemistry courses, which conveys some of the information that students receive and influences how students perceive this subject. The majority of chemistry textbooks we analyzed stress science as a body of knowledge, place some emphasis on science as a way of investigating, have practically eliminated science as a way of thinking, and devote very little text to the interaction among science, technology, and society. Furthermore, these are voluminous books that range in length from 466 to 729 pages, with as many as 60 questions per chapter.     

A naturalistic study of children and their parents in family learning courses in science

During the 1960s and 1970s a number of family learning projects evolved, most of which focused on pre-schoolers and their parents. The goal of some of these programs was to provide enjoyable, structured experiences in which parents and their children learned together. Recently, a number of institutions have been sponsoring enrichment science classes or learning experiences for parents and older children. The study described here is based on a project funded by the National Science Foundation (DISE No. 07872) which was attempting to show that it was possible to increase scientific literacy of two different age groups by simultaneously exposing parents and their middle school children to short courses in science. The project is an outgrowth of a study previously reported (Gennaro, Bullock, & Alden, 1980) carried out at the Minnesota Zoological Gardens. The study is based on data obtained during the first two years of the project and used various data gathering procedures such as the use of questionnaires, interviews, observations, and cognitive testing. It was found that children register for the courses primarily because of interest in the subject matter of the courses and that parents register because of their desire to nurture the child and the child's interest in the subject matter of the course. Both parents and children made significant gains in learning as measured by subject matter tests. Participants reported that the experience was both enjoyable and valuable. Children's attitudes toward their parents and the course were significantly higher if the children perceived a highly cooperative learning environment with their parents. Parents who scored in the medium or high range on the pretest had significantly more interactions with their children concerning information about course tasks than those who scored low on the pretest.     

Literacy and Numeracy Events in Social Interactive Contexts

Experiences relevant to emergent literacy and numeracy in 2‐year‐ old and 3‐year‐old children were examined in 10public nurseries. The research was guided by three aims, ie. to describe the frequency and variety of such experiences and investigate the contexts in which they occur; to gauge the quality of the experiences in terms of the type of adult‐child interaction in which they are embedded: and to examine variation between nurseries with regard to the frequency of relevant experience. Observations showed numeracy experiences to be infrequent relative to literacy experiences; both were highly context‐ dependent and related to adult input. Variation between the nurseries on a number of measures was examined and showed consistent patterns between variables relating to staff background and nursery organisation on the one hand and the frequency of literacy and numeracy experiences provided for children on the other. In those nurseries with smaller groups, more effectively implemented staff‐child assignment systems and younger staff, the children were more frequently observed involved in some kind of literacy or numeracy experience, and more often seen having positive and less often negative interaction with adults around these experiences. The importance of the interactive basis of early learning is stressed by these findings.     

Effects of cross-modal transfer on direct and reversal learning in the rat

In the first experiment, using within- and between-sensory modality CSs, direct and reversal transfer of active avoidance learning was studied in 48 male and 48 female albino rats. Training in each of two sessions employed either a high- or low-intensity light or noise CS. The analyses of both raw score data and proportional or savings score data indicated significant cross-modal transfer in direct as well as reversal learning conditions. Although females learned faster than males, there were no sex differences in amount of transfer. A second experiment, which examined the potential of compound conditioning within the cross-modal learning procedures, replicated the cross-modal results of the first experiment without finding evidence for compound conditioning. These results are interpreted in terms of specific and nonspecific transfer effects during avoidance learning.