The effect of epistemic fidelity and accessibility on teaching with physical materials: A comparison of two models for teaching decimal numeration

Multi-base arithmetic blocks (MAB) are the most frequently used physical materials for teaching about decimal numbers, despite published reservations about their appropriateness. This paper presents an alternative, LAB (linear arithmetic blocks) and compares the two materials on the basis of epistemic fidelity and accessibility for students. Two teaching experiments involving 30 matched students indicated that LAB is considerably more accessible for students, and identify three contributing factors (LAB modeling number with length rather than volume, MAB incorporating an apparent dimensional shift and having prior use). Use of LAB was associated with more active engagement by students and deeper discussion. Epistemic fidelity is critical to facilitate teaching with the models, but we attribute the enhanced classroom environment to the greater accessibility of the LAB material. Further research is warranted, so that teaching of mathematics with physical materials can be improved. This revised version was published online in July 2006 with corrections to the Cover Date.     

葡萄牙经济游

A spring visit to Portugal Can be a tranquil respite in theseturbulent times.It can also provide a holiday that iS easy on one’s budget.April on the Lisbon coast,when the weather is balmy and before the summer tourists arrive,is perfect. Instead of staying at a hotel,live it up,rent a villa!The magazine“In Britain”is an excellent source for villas and holi-day flats to“let”.Another resource is the Internet where you     

Predicting reading performance using the slingerland procedures

The purpose in this study was to examine predictive relationships between the Slingerland Pre- Reading Screening Procedures and performance on measures of word recognition and reading comprehension. Longitudinal data were collected on 104 children administered the Slingerland Procedures in kindergarten and the Stanford Achievement Test at first, third, and fifth grades. Outcome measures included achievement subtests, Word Study Skills, Reading Comprehension, Reading and Listening Total. Significant relationships were found between Slingerland measures and reading outcomes. However, prediction varied across grades and according to the measure of reading used. Listening contributed to reading comprehension but not to word recognition, and visual skills influenced early but not later reading performance. Gender and socioeconomic status influenced the strength of associations.     

The Relation between Critical Thinking Abilities and Student Study Strategies

This paper describes an investigation of the relationship between students' critical thinking abilities and their study strategies. The 54 students involved in the investigation were first year engineering students at a university in New South Wales who had completed their Higher School Certificate in 1991. Their critical thinking abilities were assessed with the Cornell Critical Thinking Test Level X and information about their study strategies was obtained from their responses to the General Study Processes Survey, a 21 item Likert scale questionnaire which is a component of Biggs' Study Processes Questionnaire. The survey of study processes provided information about students' study strategies on three dimensions: surface study strategy, deep study strategy and achieving study strategy. The achieving dimension was the only study strategy which correlated significantly with scores on the test of critical thinking. There was a negative correlation between this dimension and critical thinking ability. The implications of the results of this study for promoting the development of critical thinking abilities are discussed.     

Teaching with new technology: four ‘early majority’ teachers

This paper explores how four good teachers, who do not have a special interest in technology, meet the challenge of introducing the rapidly developing mathematics analysis software (e.g. spreadsheets, function graphers, symbolic algebra manipulation and dynamic geometry) into their classrooms. These teachers’ practice is viewed through the lens of Roger’s framework for the diffusion of innovation and Pierce and Stacey’s pedagogical opportunities map. Data on teachers, views and practices were collected over 2 years. ‘Pedagogical Maps’ give a picture of the teachers’ perception and uptake of pedagogical opportunities. New practices have been added slowly to each teacher’s repertoire and their increasing fluency in practical ability to teach with the technology resulted in some changes to the classroom didactic contract. Overall, new technology seemed to have been absorbed into current practice, more than changing practice. At this stage of their development, these teachers do not identify the distinctive new mathematical capabilities as contributing to the major relative advantage of the innovation. Instead, they see the relative advantage mostly in the incremental improvements to capabilities of earlier calculators, and meeting the need for students to be up to date. One of the current challenges is that significant changes in both software and hardware design have been happening so rapidly that these early majority teachers felt almost constantly hampered by the need to learn and teach new technical skills and so continue to make limited progress in taking advantage of opportunities to approach mathematics concepts in new ways.