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1.
A bottlenose dolphin was trained to discriminate two simultaneously presented stimuli differing in numerosity (defined by
the number of constituent elements). After responding correctly to stimuli consisting of three-dimensional objects, the dolphin
transferred to two-dimensional stimuli. Initially, a variety of stimulus parameters covaried with the numerosity feature.
By systematically controlling for these stimulus parameters, it was demonstrated that some of these attributes, such as element
configuration and overall brightness, affected the animal’s discrimination performance. However, after all the confounding
parameters were under control, the dolphin was able to discriminate the stimuli exclusively on the basis of the numerosity
feature. The animal then achieved a successful transfer to novel numerosities, both intervening numerosities and numerosities
outside the former range. These findings provide substantial evidence that the dolphin could base his behavior on the numerosity
of a set independently of its other attributes and that he represented ordinal relations among numerosities. 相似文献
2.
Pigeons were trained in a conditional discrimination paradigm to differentiate successively presented visual arrays according to the relative number of their elements. Transfer tests with novel stimuli demonstrated that they discriminated the categories of “many” (6 or 7) from “few” (1 or 2) items. In further tests, other new stimuli were introduced that consisted not only of these training numerosities, but also of the intervening ones (3, 4, and 5). Variations in the birds’ discrimination performance corresponded to the order of stimuli on a numerosity dimension. This serial ordering was maintained when other factors such as brightness, size, shape, area, and contour of the elements were systematically controlled across tests. Smaller numerosities were somewhat better discriminated than those at the higher end of this test range. 相似文献
3.
Koen Luwel Joke Torbeyns Lieven Verschaffel 《European Journal of Psychology of Education - EJPE》2003,18(4):425-447
In the research literature several positions concerning the role played by metacognition in adaptive strategy choice can be
distinguished. While many authors adhere so-called metacognitive models of strategy choice and strategy change, others have
questioned the extent to which metacognitive factors are associated with strategy choice and task performance and have proposed
alternative theoretical frameworks wherein strategy choices are described in terms of associative models. In the present article
we report data coming from a larger research project on the development of children’s numerosity judgement strategies and
skills. The experimental task involved judging numerosities of colored blocks presented in a rectangular grid. Participants
were 59 second grade and 50 sixth grade children, whose strategic performance data — obtained by means of a systematic analysis
of their response-time patterns — were compared with interview data collected at the end of the experiment. The major result
of this comparison is that not only the children from the oldest age group, but also the children from the youngest age group
showed clear evidence of metacognitive awareness and understanding of different aspects of their strategic performance. 相似文献
4.
Five-year-old children categorized as skilled versus unskilled counters were given verbal estimation and number word comprehension tasks with numerosities 20-120. Skilled counters showed a linear relation between number words and nonsymbolic numerosities. Unskilled counters showed the same linear relation for smaller numbers to which they could count, but not for larger number words. Further tasks indicated that unskilled counters failed even to correctly order large number words differing by a 2 : 1 ratio, whereas they performed well on this task with smaller numbers, and performed well on a nonsymbolic ordering task with the same numerosities. These findings provide evidence that large, approximate numerosity representations become linked to number words around the time that children learn to count to those words reliably. 相似文献
5.
Jacky Emmerton 《Learning & behavior》1998,26(3):243-256
Two experiments are described in which pigeons were trained in a simultaneous conditioning procedure to discriminate small arrays of dots that differed in numerosity. The birds successfully learned to choose the array of each pair that contained fewer dots when these choices were reinforced and choices of the array with more dots led to timeout. For the majority of numerosity values tested, discrimination performance for a fixed S+ value was better when the numerical difference between S+ and S-values was larger rather than smaller. This effect was seen in the first experiment when the numerical difference value was shifted between training trials and novel test trials. In the second experiment, too, performance level depended on the size of the numerosity difference when the birds were concurrently trained with two difference values that varied across trials within sessions. However, discrimination accuracy was influenced secondarily by variations in the density, or interdot spacing, of the stimulus arrays. In order to explain the latter finding, it is suggested that a tendency to “scan” a lowdensity array incompletely might alter the probability of accepting it as the smaller numerosity (S+) stimulus. This would increase error rates with S? arrays in which the dots are more widely spaced. 相似文献
6.
Koen Luwel Lieven Verschaffel Patrick Onghena Erik De Corte 《European Journal of Psychology of Education - EJPE》2001,16(2):233-255
A previous study (Luwel, Verschaffel, Onghena, & De Corte, 2000) revealed that 2nd and 6th graders use at least 3 different kinds of strategies for determining different numerosities of blocks presented in square grids: (a) an addition strategy by means of which (groups of) blocks are counted (and added), (b) a subtraction strategy in which the number of empty squares is subtracted from the total number of blocks in the grid (i.e. the anchor), and (c) an estimation strategy, whereby the number of blocks is determined in a quick but imprecise way. Although 6th as well as 2nd graders used the clever subtraction strategy, the majority of 2nd graders had serious trouble with the correct determination of the anchor, resulting in huge numerosity judgement errors. Since this finding seriously complicated the testing of a number of hypotheses in that study, we replicated the above study but presented the children information about the grid size. This manipulation led to a substantial increase in the proportion of appropriate subtraction strategy users and made it possible to investigate the effect of several subject and task variables on the frequency, accuracy, and adaptiveness with which the different strategies were applied. Results are discussed in terms of the conceptual framework of Lemaire and Siegler (1995) regarding strategic change. 相似文献
7.
The array representation and primary children’s understanding and reasoning in multiplication 总被引：1，自引：0，他引：1
Patrick Barmby Tony Harries Steve Higgins Jennifer Suggate 《Educational Studies in Mathematics》2009,70(3):217-241
We examine whether the array representation can support children’s understanding and reasoning in multiplication. To begin,
we define what we mean by understanding and reasoning. We adopt a ‘representational-reasoning’ model of understanding, where
understanding is seen as connections being made between mental representations of concepts, with reasoning linking together
the different parts of the understanding. We examine in detail the implications of this model, drawing upon the wider literature
on assessing understanding, multiple representations, self explanations and key developmental understandings. Having also
established theoretically why the array representation might support children’s understanding and reasoning, we describe the
results of a study which looked at children using the array for multiplication calculations. Children worked in pairs on laptop
computers, using Flash Macromedia programs with the array representation to carry out multiplication calculations. In using
this approach, we were able to record all the actions carried out by children on the computer, using a recording program called
Camtasia. The analysis of the obtained audiovisual data identified ways in which the array representation helped children,
and also problems that children had with using the array. Based on these results, implications for using the array in the
classroom are considered. 相似文献
8.
Researchers debate whether one represents the magnitude of a fraction according to its real numerical value or just the discrete numerosity of its numerator or denominator. The present study examined three effects based on the notion that people possess a mental number line to explore how children represent fractions when they compare fractions with common numerators. Specifically, the effect of the spatial numerical association of response codes (SNARC), the distance effect and the size effect in representing fractions were examined in a sample of 72 sixth graders, who successfully solved the fraction comparison task with a real number (.2) or a fraction (1/5) as the reference. Results showed that in the fraction-reference group (1/5 as the reference), there was a significant reverse SNARC effect and a distance effect between the denominators of the target fractions and the reference fraction; in the real number-reference group, the three effects were also observed. These results revealed that both groups used the mental number line to represent fractions and did not represent their real numerical values but rather the discrete numerosities of denominators when comparing fractions with common numerators. It seems that the way people represent fractions may depend on their strategy choices. 相似文献
9.
Koen Luwel Lieven Verschaffel 《European Journal of Psychology of Education - EJPE》2008,23(3):319-338
Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities
smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts
were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third had a clear structure
(e.g., a 16x4 rectangular parking lot completely filled with 64 cars), and a last third had a “semi-structure” (e.g., the
same 16x4 parking lot but with a number of cars missing). Besides analyzing the effects of different task and subject variables
on pupils’ accuracy and response-time data, the study involved and analysis of their estimation strategies, with an emphasis
on multiplicative strategies that profited by some of the tasks’ geometrical (semi-)structure. It was found that many children
actually made use of such strategies, that using these strategies did however not always led to accurate estimations, and
that their frequency and efficiency increased with age. 相似文献
10.
We trained 4 pigeons in a numerical bisection task to discriminate between pairs of keylight flashes with a ratio of 1∶3 (2
vs. 6, 4 vs. 12, and 8 vs. 24) that were presented in a sample phase. Responses to the blue key were reinforced after a sequence
of a larger number of flashes, and responses to the white key were reinforced after a sequence of a smaller number of flashes.
The intervals between flashes in the sample phase were randomized to attenuate the covariation of temporal cues with flash
number. Pigeons responded accurately in each of the discriminations, with typically 85%–90% correct responses. Transfer tests
showed that the proportion of large responses increased with number and performance generalized to larger values outside the training ranges. Psychometric functions
superposed when plotted on a relative scale, and estimates of Weber fractions were approximately constant, suggesting that
variability was scalar. However, contrary to previous research in nonhumans, bisection points were located at the arithmetic,
not geometric, mean. Hierarchical logistic regressions confirmed significant control over responding by number beyond that
attributable to temporal cues. These results show that pigeons are able to respond accurately in a relative numerosity discrimination
with successively presented visual stimuli, although the nature of the numerical representation and response rule remains
unclear. 相似文献
11.
This article presents a Vygotsky-inspired analysis of how a teacher mediated a “thinking aloud” whole-group discussion in
a 6th grade mathematics classroom. This discussion centered on finding patterns in a triangular array of consecutive numbers
as a phase towards building recursive and direct algebraic formulas. By a “thinking aloud” discussion we mean a conversation
wherein students exchange and further develop ideas-in-the-making with their peers under the teacher’s guidance. Drawing upon
Halliday’s systemic functional linguistics (SFL), we treated the selected discussion as a text. We then analyzed how the teacher
mediated the conjoined making of this text so that it served as an interpersonal gateway for students to practice searching
for patterns and signifying these patterns in propositional form. This analysis was guided by the following questions: How
did the discussion as a text-in-the-making mean what it did? What was the role of the teacher in the conjoined making of this
text? Our study illustrates the power of SFL for capturing the inner grammar of instructional conversations thus illuminating
the complexities and subtleties of the teacher’s role in mediating semiotic mediation in mathematics classrooms. 相似文献
12.
Tracy Linderholm Qin Zhao David J. Therriault Kristi Cordell-McNulty 《Metacognition and Learning》2008,3(3):175-188
Low accuracy levels are often obtained when readers are asked to predict test performance over reading materials. Three investigations
further explore the information readers use to make predictions during metacomprehension. Our results show that readers’ estimates
are influenced by factors such as their initial impression of the reading task, based in part on their perceptions surrounding
text genre and test item type. To explain these and other published results, a new framework for investigating metacomprehension
using Tversky and Kahneman’s (Science, 185:1124–1131, 1974) anchoring and adjustment heuristic as a guide is proposed. We argue that readers anchor comprehension test performance on
factors such as self-perceptions of reading ability and/or perceptions of the reading task and then insufficiently adjust
their predictions to reflect the demands of the specific reading task at hand such as text difficulty. 相似文献
13.
This study examined the unique and joint contributions of engineering students’ classroom and out-of-class experiences on
the development of two sets of skills central to students’ successful performance as engineers: analytical and group skills.
Although the study focuses on engineering, the conceptual underpinnings and criterion measures are relevant to studies of
teaching and learning in other fields. Multiple regression analyses using data from 4198 graduating engineering students on
39 campuses nationwide indicate that, after controlling an array of students’ precollege characteristics, both students’ classroom and out-of-class experiences make statistically significant and independent contributions to student
learning in both skill areas.
An earlier version of this paper was presented at the meeting of the Association for Institutional Research, June 2005, San
Diego, CA.
This study was supported by a grant from the Accrediting Board of Engineering and Technology (ABET, Inc.). The opinions expressed
here do not necessarily reflect the opinions or policies of ABET, and no official endorsement should be inferred. 相似文献
14.
A survey exploring the views of scientists, chemists and chemical engineers, on current trends in Chemistry Education was
conducted in Greece. Their opinions were investigated using a questionnaire focusing on curricula (the content and process
of chemistry teaching and learning), as well as on the respondents’ general educational beliefs and their underlying epistemological
views. The aim of this work was to investigate the respondents’ opinions and, if possible, to identify the areas where convergence
or even consensus occurred. The results showed that some of the items on the research questionnaire produced a high degree
of agreement with the respondents’ views, while a few others were exactly the opposite. These items are considered to be representative
of more widespread views. In order to explore the diverging opinions, the items on the research questionnaire that showed
great variance were analyzed to determine, whether or not there were significant inter-item correlations among subgroups of
participants with different demographic characteristics. Postgraduate studies, professional occupation, age/experience, and
career within or outside the wide educational sector were among the main factors that significantly influenced the research
results. The study did not reveal any single belief framework underlying the opinions of the respondents. Nevertheless, three
specific approach frameworks—ACADEMIC, CONSTRUCTIVIST and SCIENTIFIC REALISM—were analyzed to determine which had the highest
degree of agreement. It was found that the SCIENTIFIC REALISM framework and the curriculum emphasis characteristic of the
context-based CTSE (Chemistry, Technology, Society and Environment) prevailed, as they produced a significantly higher mean
score. The ACADEMIC framework followed with a moderate mean score and the CONSTRUCTIVIST framework had a lower mean score. 相似文献
15.
Two groups of pigeons were trained with a go/no-go procedure to discriminate video images of conspecifics based on the individuals or else on their actions. Both groups showed rapid acquisition, and the discrimination transferred to new scenes in Experiment 1 and to static scenes in Experiment 2. In Experiment 3, experimentally naive pigeons were trained to discriminate video images of particular birds showing different actions. Transfer to novel scenes, including a new bird and a new motion, revealed the dominance of motion as a cue to discriminate video images. In Experiment 4, the pigeons trained to discriminate video scenes of 2 pigeons showing a variety of activities successfully recognized these stimuli regardless of whether the video was played forward or backward, and transferred the discrimination to still scenes. The findings suggest that pigeons’ discrimination of video images is primarily based on information that is invariant across static and dynamic conditions. 相似文献
16.
Keith R. Leatham 《Journal of Mathematics Teacher Education》2006,9(1):91-102
This article discusses theoretical assumptions either explicitly stated or implied in research on teachers’ beliefs. Such
research often assumes teachers can easily articulate their beliefs and that there is a one-to-one correspondence between
what teachers state and what researchers think those statements mean. Research conducted under this paradigm often reports
inconsistencies between teachers’ beliefs and their actions. This article describes an alternative framework for conceptualizing
teachers’ beliefs that views teachers as inherently sensible rather than inconsistent beings. Instead of viewing teachers’
beliefs as inconsistent, teachers’ abilities to articulate their beliefs as well as researchers’ interpretations of those
beliefs are seen as problematic. Implications of such a view for research on teacher beliefs as well as for the practice of
mathematics teacher education are discussed.
This article is based on the author’s doctoral dissertation completed at the University of Georgia under the direction of
Thomas J. Cooney. Parts of this article were presented at the 2004 meeting of the North American Chapter of the International
Group for the Psychology of Mathematics Education (Toronto, Canada). 相似文献
17.
In three experiments, pigeons were trained to discriminate between uniform arrays of two elements that differed in color, form, or size. They were then tested with arrays that contained different proportions of the two elements on these dimensions. In all cases, orderly discrimination gradients reflected these proportions. The discrimination readily transferred to new arrays with similar stimuli, but with different total numbers of elements. In Experiment 4, the pigeons were taught to discriminate between two groups of categorical stimuli: pictures of birds and pictures of flowers. A test with different proportions of each again produced a gradient based on relative numerosity. Experiment 5 demonstrated transfer of stimulus control on the numerosity dimension when pigeons were trained with one set of instances from two categories, and then were tested with new instances from the same categories. 相似文献
18.
We previously reported that chimpanzees were unable to optimally select the smaller of two candy arrays in order to receive a larger reward. When Arabic numerals were substituted for the candy arrays, animals who had had prior training with numerical symbols showed an immediate and significant improvement in performance and were able to select reliably the smaller numeric representation in order to obtain a larger reward. Poor performance with candy arrays was interpreted as reflecting a response bias toward the intrinsic incentive and/or perceptual features of the larger array. In contrast, the Arabic numerals represent numerosity symbolically and appear to promote response choice on the basis of abstract processing of numerosity, with minimal interference from the inherent properties of the choice stimuli. The present study tested the hypothesis that, for mixed symbol-candy choice pairs, the requisite processing of the abstract numeral may foster a mode of numerical judgment that diminishes the interfering incentive/perceptual effects of the candy stimuli. The results were consistent with this hypothesis. Whereas performance on candy-candy arrays was significantly below chance levels, performance on numeral-candy choice pairs was significantly above chance and comparable with performance on numeral-numeral pairs. 相似文献
19.
MS Ruth Coulson 《Research in Science Education》1992,22(1):101-105
The attitude towards science of first year early childhood education students was explored using an instrument developed for
the purpose. The instrument comprises four Likert-type scales, biographical items and two open-ended attitude items. The four
scales, characterised as ‘confidence’, ‘enjoyment’, ‘usefulness’ and ‘appropriateness of science for young children’, were
supported by varimax factor analysis and had reliabilities from 0.83 to 0.88. Use of the combined scales as a general ‘attitude
towards science’ scale was supported by principal components analysis; reliability for the combined scale was 0.94. Comments
made in response to the open-ended items supported the validity of the scales. For the student group as a whole, mean scores
on all scales were slightly to moderately positive, with the highest mean being for the ‘science for young children’ scale.
Students who had studied at least one science subject at Year 12 level had significantly higher scores on all scales than
students who had not studied science at senior level.
Australia.Specializations: early childhood science education, biological aspects of child development, conservation biology of gulls. 相似文献
20.
Guolin Lai Brendan Calandra 《Educational technology research and development : ETR & D》2010,58(4):421-437
This study employed an explanatory mixed methods design to examine the effects of two computer-based scaffolds on novice teachers’
reflective journal writing. The context for the study was an attempt to refine the reflective writing component of a large
scale electronic portfolio system. Quantitative results indicated that the computer-based scaffolds significantly enhanced
the participants’ reflective journal writing as well as the length of their written artifacts. Moreover, correlation analysis
revealed that there was a positive relationship between the highest level of reflection and the length of journal writing.
Three factors gleaned from qualitative data helped explain how and why the scaffolds enhanced participants’ reflective thinking,
including (a) the specific requirements conveyed in the scaffolds; (b) the structure of the scaffolds; and (c) the use of
the critical incidents to anchor reflective journal writing. It is hoped that the analyses and results of the current study
can help inform others on how to leverage the affordances of computer-based scaffolds to augment reflective practice in technology-enhanced
educational systems. 相似文献