Exploring the NATURE OF MATHEMATICAL activity: USING theory, research and `working hypotheses' to broaden conceptions of mathematics knowing

What proficiencies are brought tobear when students work on mathematicsproblems? And to what extent may these becaptured by knowledge categories? These arequestions that I consider in this article,as I explore notions of competency, that gobeyond knowledge to include themathematical `dispositions' that studentsbring to problems and the `practices' withwhich they engage. This exploration willdraw from two frameworks that have recentlybeen introduced in the US. In addition, Iconsider the ways in which researchknowledge is conceived and developed,reflecting upon the important role oftheory and the potential of `workinghypotheses' for connecting with practice innew ways.     

Native american related materials in elementary science instruction

The low achievement of Native American students, as measured by standardized tests, results from a number of factors, including the lack of cultural relevance of curriculum materials used in their instruction. Using a pretest–posttest control group design, Native American students in Bureau of Indian Affairs schools in Grades 4–8 who were taught science using culturally relevant materials achieved significantly higher and displayed a significantly more positive attitude toward Native Americans and science than comparable students who were taught science without the culturally relevant materials. It is suggested that when educators of Native Americans teach science, they should use materials that incorporate frequent reference to Native Americans and science.     

Temporal processing and reading disability

The present investigation examined thehypothesis that early auditory temporalprocessing deficits cause later specificreading disability by impairing phonologicalprocessing (Farmer & Klein 1995; Tallal1980, 1984). Temporal processing ability atschool entry was examined using Tallal'sRepetition Test in a large unselected sample ofover 500 children followed over subsequentyears. Although our data confirmed the presenceof certain non-speech auditory processingdeficits in children later classified asspecific reading-disabled, many findings wereclearly at odds with a causal interpretation ofthis relationship. (1) Reading-disabled (RD)children were impaired at school entry on thesubtest with long interstimulus intervals(ISIs) but not the critical short-ISIsubtest. (2) RD children were not inferior toreading-age (RA) controls. (3) A subgroup of RDchildren with evidence of temporal deficitswere no less proficient on later phonologicalor reading measures than RD children with noevidence of early temporal impairment. (4)Although there was a reliable concurrentcorrelation between temporal deficits andphonological awareness at school entry(suggesting a possible common causeexplanation), early temporal deficits did notpredict later phonological impairment,pseudoword processing difficulties, or specificreading disability. On the other hand, earlytemporal deficits did predict later oralreceptive vocabulary and reading comprehensionweaknesses. These findings suggest thatauditory temporal deficits in dyslexics may beassociated with the same dysphasic-typesymptoms observed by Tallal and her colleaguesin specific language-impaired populations, butdo not cause the core phonological deficitsthat characterize dyslexic groups.     

Motivational mechanisms and schedule-induced behavioral stereotypy

In two experiments, behavioral stereotypies elicited by scheduled presentations of food and water were compared. In Experiment 1, pigeons were exposed to a fixed-time 30-sec (FT 30-sec) schedule of food or water deliveries with a brightening keylight stimulus signaling time to the unconditioned stimulus (UCS) on each trial. Food and water presentations both produced terminal autoshaped keypecking that was similarly distributed in the trial but differed in response topography and persistence. Locomotor interim behavior was different in the two motivational conditions: With food presentations, it consisted of a “retreat” to the rear of the chamber after UCS termination, followed by “pacing” in the midportion of trials. The water schedule produced very little locomotor activity with no regular distribution in the trial. Experiment 2, using a random-time 30-sec (RT 30-sec) schedule, showed that the differences in interim locomotor behavior persisted in the absence of temporal predictability of the UCS and the keypecking terminal response. The results are taken to support Timberlake’s (1983a) behavior-system theory.     

Preschool children's exposure to story grammar elements during parent–child book reading

Twenty‐three preschool‐age children, 3;6 (years; months) to 4;1, were videotaped separately with their mothers and fathers while each mother and father read a different unfamiliar storybook to them. The text from the unfamiliar storybooks was parsed and coded into story grammar elements and all parental extratextual utterances were transcribed and coded for (1) their relationship to the story grammar elements found within the storybook, and (2) the natural strategies parents used to direct their children's attention to these elements. Children's overall exposure to story grammar elements during book reading was also explored for its relationship to their language abilities. Results indicated that parents focused significantly more on the resolution, attempt, and consequence compared to the initiating event and plan, and most frequently used the text and pictures as strategies for recruiting their children's attention to the story grammar elements within the book. In addition, the frequency of parental utterances related to story grammar elements was negatively correlated with children's language abilities. This study did not examine the complexity or depth of parental utterances related to story grammar elements. These findings provide initial evidence that children may derive their understanding of story grammar at least in part through their parents' extratextual discussions during parent–child book reading.     

Teacher educators as gatekeepers: Preparing the next generation of teachers for technology integration in education

This study aims at investigating the profiles of teacher educators in order to explore their ability to prepare preservice teachers for technology integration in education. Specifically, the current study examines whether teacher educators can be grouped on the basis of their attitudes toward ICT (in education), their ICT self-efficacy to design ICT-rich learning environments, their competencies to use ICT in their teaching practice and the strategies they use to prepare preservice teachers for technology integration. These strategies are included in the SQD (Synthesis of Qualitative Data) model and comprise: (1) teacher educators as role models, (2) reflecting on the role of technology in education, (3) learning how to use technology by design, (4) collaboration with peers, (5) scaffolding authentic technology experiences and (6) providing continuous feedback. Data were collected from a sample of 284 teacher educators in Flanders, the Dutch-speaking part of Belgium, and submitted to latent profile analysis. The added value of the current study lies in the account of how SQD strategies and a typical set of determinants of ICT integration can be associated within teacher educators’ profile. Based on the profiles emerging from this study, teacher training institutions should consider their teacher educators to be gatekeepers when preparing future generations of teachers for the learning environments of the twenty-first century. In the discussion section, the implications for practice and future research are discussed.     

Strengthening ‘the foundations’ of the primary school curriculum

The low status of the foundation subjects (e.g. Music and Physical Education (PE)) in English primary schools is well documented. Using PE as an illustrative example, a thematic analysis of 51 PE trainee students’ assignments, based on their perceptions of a two-week experience in a primary school, highlighted a number of areas of concern (e.g. limited/inadequate preparation; insufficient teacher knowledge/confidence; variable/limited subject leadership and non-qualified teachers delivering the curriculum). The possibility of teachers, coaches and other external specialists learning collaboratively with and from each other within a community of practice/learning is proposed as one way of strengthening the foundation subjects within the primary school curriculum.