16 resultados para The language of mathematics

em Brock University, Canada


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This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

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The strength and nature of the video game practice effect on tests of visual and perceptual skills were examined using high functioning Grades Four and Five students who had been tested with the WISC-R .for the purpose of gifted identification and placement. The control group, who did not own and .play video games on a sustained basis, and the experimental group, who did own a video game system and had some mastery of video games, including the -Nintendo game, "Tetris", were each composed of 18 juniorg:r;-ade students and were chosen from pre-existing conditions. The experimental group corresponded to the control group in terms of age, sex, and community. Data on the Verbal and Performance I.Q. Scores were· collected for both groups and the author was interested in the difference between the Verbal and Performance Scores within each group, anticipating a P > V outcome for the experimental group. The results showed a significant P > V difference in the experimental, video game playing group, as expected, but no significant difference between the Performance $cores of the control and experimental groups. The results, thus, indicated lower Verbal I.Q. Scores in the experimental group relat'ive to 'the control group.' The study conclu~ed that information about a sUbject's video game experience and "learhing style pref~rence is important for a clear interpretation of the Verbal and Performance I.Q. Scores of the WISC-R. Although the time spent on video game play may, 'indeed, increase P~rformance Scores relative to Verbal Scores for an individual, the possibilities exist that the time borrowed and spent away from language based activities may retard verbal growth and/or that the cognitive style associated with some Performance I.Q.subtests may have a negative effect on the approach to the tasks on the Verbal I.Q. Scale. The study also discussed the possibility that exposure to ,the video game experience, in pre-puberty, can provide spatial instruction which will result in improved spatial skills. strong spatial skills have been linked to improved performance and preference in mathematics, science, and engineering and it was suggested that appropriate video game play might be a way to involve girls more in the fields of mathematics and science.

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Forty-five 12- and 13-year-old females attending Grade 7 in North York, Ontario were randomly selected from a group of 100 females who had volunteered to participate in a oneday hands-on workshop called It's Your Choice at Seneca College. The goals of this intervention were to broaden the career horizons of these students and to help them realize the need to continue mathematics and science through high school in order to keep occupational options unlimited. The young women were given a pre- and post-attitude survey to provide background information. In the month following participation in the workshop the students were interviewed in small groups (S students per group) to discover their perceptions of the impact of the workshop. The interviews revealed that participants felt that after the workshop their feelings of self-confidence increased, specifically with respect to working with their hands. Participants felt more aware of the usefulness and importance of the study of mathematics, science and technology, They also felt that It's Your Choice increased their interest in careers in these domains and helped them to see that these careers are viable choices for females. The interviews also revealed that many of the participants felt that in this society their roles and their choices were influenced and probably limited by the fact that they are female.

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Through aggressive legislative and educational policies Indigenous languages globally have been shifted to the language of the dominant society. Globalization has brought previously geo-politically and/or geo-linguistically isolated people and language . groups into close proximity that necessitated interaction and at times intense power struggles. There are currently approximately 6,000 spoken languages in the world, more than half are either endangered, dying or disappearing altogether. Canadian statistics reveal an overall 3 % decline in the intergenerational transmission of language. Of the original 60 Indigenous languages spoken in Canada, 8 are extinct, 13 are nearly extinct, and 23 are critical. The remaining languages have a slim chance of survival. Within the next 100 years only 4 Indigenous languages will remain. The Hodenosaunee languages of Southern Ontario are not incl~ded among the list of languages that will survive the next 100 years. There are, without a doubt, complex challenges in the maintenance of Indigenous languages within a dominant-culture influenced environment. Given the increasing awareness of the social impact of linguistic integrity and preservation of languages on Indigenous people as a whole, this study considers how language is currently being used; the social, economic, and political implications of language shifting; the need to shift our social consciousness in order to understand the urgency in privileging our Hodenosaunee languages; as well as ways in which we might achieve those goals as individuals, as families, and as a community.

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The topic of this thesis is marginaVminority popular music and the question of identity; the term "marginaVminority" specifically refers to members of racial and cultural minorities who are socially and politically marginalized. The thesis argument is that popular music produced by members of cultural and racial minorities establishes cultural identity and resists racist discourse. Three marginaVminority popular music artists and their songs have been chosen for analysis in support of the argument: Gil Scott-Heron's "Gun," Tracy Chapman's "Fast Car" and Robbie Robertson's "Sacrifice." The thesis will draw from two fields of study; popular music and postcolonialism. Within the area of popular music, Theodor Adorno's "Standardization" theory is the focus. Within the area of postcolonialism, this thesis concentrates on two specific topics; 1) Stuart Hall's and Homi Bhabha's overlapping perspectives that identity is a process of cultural signification, and 2) Homi Bhabha's concept of the "Third Space." For Bhabha (1995a), the Third Space defines cultures in the moment of their use, at the moment of their exchange. The idea of identities arising out of cultural struggle suggests that identity is a process as opposed to a fixed center, an enclosed totality. Cultures arise from historical memory and memory has no center. Historical memory is de-centered and thus cultures are also de-centered, they are not enclosed totalities. This is what Bhabha means by "hybridity" of culture - that cultures are not unitary totalities, they are ways of knowing and speaking about a reality that is in constant flux. In this regard, the language of "Otherness" depends on suppressing or marginalizing the productive capacity of culture in the act of enunciation. The Third Space represents a strategy of enunciation that disrupts, interrupts and dislocates the dominant discursive construction of US and THEM, (a construction explained by Hall's concept of binary oppositions, detailed in Chapter 2). Bhabha uses the term "enunciation" as a linguistic metaphor for how cultural differences are articulated through discourse and thus how differences are discursively produced. Like Hall, Bhabha views culture as a process of understanding and of signification because Bhabha sees traditional cultures' struggle against colonizing cultures as transforming them. Adorno's theory of Standardization will be understood as a theoretical position of Western authority. The thesis will argue that Adorno's theory rests on the assumption that there is an "essence" to music, an essence that Adorno rationalizes as structure/form. The thesis will demonstrate that constructing music as possessing an essence is connected to ideology and power and in this regard, Adorno's Standardization theory is a discourse of White Western power. It will be argued that "essentialism" is at the root of Western "rationalization" of music, and that the definition of what constitutes music is an extension of Western racist "discourses" of the Other. The methodological framework of the thesis entails a) applying semiotics to each of the three songs examined and b) also applying Bhabha's model of the Third Space to each of the songs. In this thesis, semiotics specifically refers to Stuart Hall's retheorized semiotics, which recognizes the dual function of semiotics in the analysis of marginal racial/cultural identities, i.e., simultaneously represent embedded racial/cultural stereotypes, and the marginal raciaVcultural first person voice that disavows and thus reinscribes stereotyped identities. (Here, and throughout this thesis, "first person voice" is used not to denote the voice of the songwriter, but rather the collective voice of a marginal racial/cultural group). This dual function fits with Hall's and Bhabha's idea that cultural identity emerges out of cultural antagonism, cultural struggle. Bhabha's Third Space is also applied to each of the songs to show that cultural "struggle" between colonizers and colonized produces cultural hybridities, musically expressed as fusions of styles/sounds. The purpose of combining semiotics and postcolonialism in the three songs to be analyzed is to show that marginal popular music, produced by members of cultural and racial minorities, establishes cultural identity and resists racist discourse by overwriting identities of racial/cultural stereotypes with identities shaped by the first person voice enunciated in the Third Space, to produce identities of cultural hybridities. Semiotic codes of embedded "Black" and "Indian" stereotypes in each song's musical and lyrical text will be read and shown to be overwritten by the semiotic codes of the first person voice, which are decoded with the aid of postcolonial concepts such as "ambivalence," "hybridity" and "enunciation."

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The purpose of this study was to determine the effect that calculators have on the attitudes and numerical problem-solving skills of primary students. The sample used for this research was one of convenience. The sample consisted of two grade 3 classes within the York Region District School Board. The students in the experimental group used calculators for this problem-solving unit. The students in the control group completed the same numerical problem-solving unit without the use of calculators. The pretest-posttest control group design was used for this study. All students involved in this study completed a computational pretest and an attitude pretest. At the end of the study, the students completed a computational posttest. Five students from the experimental group and five students from the control group received their posttests in the form of a taped interview. At the end of the unit, all students completed the attitude scale that they had received before the numerical problem-solving unit once again. Data for qualitative analysis included anecdotal observations, journal entries, and transcribed interviews. The constant comparative method was used to analyze the qualitative data. A t test was also performed on the data to determine whether there were changes in test and attitude scores between the control and experimental group. Overall, the findings of this study support the hypothesis that calculators improve the attitudes of primary students toward mathematics. Also, there is some evidence to suggest that calculators improve the computational skills of grade 3 students.

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A cognitively based instructional program for narrative writing was developed. The effects of using cognitively based schematic planning organizers at the pre-writing stage were evaluated using subjects from the Primary, Junior and Intermediate divisions. Results indicate that the use of organizers based on problem solving significantly improved the organization and the overall quality of narrative writing for students in grades 3, 6 and 7. The magnitude of the improvement of the treatment group over the control group performance in Organization ranged from 10.7% to 22.9%. Statistical and observational data indicate many implications for further research into the cognitive basis for writing and reading; for the improvement and evaluation of school writing programs; for the design of school curricula; and for the inservice education for teachers of writing.

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Over the past decade, research has suggested that phonological and word awareness skills (i.e., the ability to reflect on and manipulate the components of language) are important for early reading acquisition. This study examined the phonological and word awareness skills of language-delayed kindergarten children at the beginning and end of a language intervention program using five tasks. The results were compared to the performances of average kindergarten children who did not participate in the language intervention program. There were significant performance differences for all tasks, favouring the average children, at the beginning of the intervention program. However, at the end of the training interval, the languagedelayed children performed as well as the average children.

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Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.

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A class of twenty-two grade one children was tested to determine their reading levels using the Stanford Diagnostic Reading Achievement Test. Based on these results and teacher input the students were paired according to reading ability. The students ages ranged from six years four months to seven years four months at the commencement of the study. Eleven children were assigned to the language experience group and their partners became the text group. Each member of the language experience group generated a list of eight to be learned words. The treatment consisted of exposing the student to a given word three times per session for ten sessions, over a period of five days. The dependent variables consisted of word identification speed, word identification accuracy, and word recognition accuracy. Each member of the text group followed the same procedure using his/her partner's list of words. Upon completion of this training, the entire process was repeated with members of the text group from the first part becoming members of the language experience group and vice versa. The results suggest that generally speaking language experience words are identified faster than text words but that there is no difference in the rate at which these words are learned. Language experience words may be identified faster because the auditory-semantic information is more readily available in them than in text words. The rate of learning in both types of words, however, may be dictated by the orthography of the to be learned word.

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The effects of a complexly worded counterattitudinal appeal on laypeople's attitudes toward a legal issue were examined, using the Elaboration Likelihood Model (ELM) of persuasion as a theoretical framework. This model states that persuasion can result from the elaboration and scrutiny of the message arguments (i.e., central route processing), or can result from less cognitively effortful strategies, such as relying on source characteristics as a cue to message validity (i.e., peripheral route processing). One hundred and sixty-seven undergraduates (85 men and 81 women) listened to eitller a low status or high status source deliver a counterattitudinal speech on a legal issue. The speech was designed to contain strong or weak arguments. These arguments were 'worded in a simple and, therefore, easy to comprehend manner, or in a complex and, therefore, difficult to comprehend manner. Thus, there were three experimental manipulations: argument comprehensibility (easy to comprehend vs. difficult to comprehend), argumel11 strength (weak vs. strong), and source status (low vs. high). After listening to tIle speec.J] participants completed a measure 'of their attitude toward the legal issue, a thought listil1g task, an argument recall task,manipulation checks, measures of motivation to process the message, and measures of mood. As a result of the failure of the argument strength manipulation, only the effects of the comprehel1sibility and source status manipulations were tested. There was, however, some evidence of more central route processing in the easy comprehension condition than in the difficult comprehension condition, as predicted. Significant correlations were found between attitude and favourable and unfavourable thoughts about the legal issue with easy to comprehend arguments; whereas, there was a correlation only between attitude and favourable thoughts 11 toward the issue with difficult to comprehend arguments, suggesting, perhaps, that central route processing, \vhich involves argument scrutiny and elaboration, occurred under conditions of easy comprehension to a greater extent than under conditions of difficult comprehension. The results also revealed, among other findings, several significant effects of gender. Men had more favourable attitudes toward the legal issue than did women, men recalled more arguments from the speech than did women, men were less frustrated while listening to the speech than were ,vomen, and men put more effort into thinking about the message arguments than did women. When the arguments were difficult to comprehend, men had more favourable thoughts and fewer unfavourable thoughts about the legal issue than did women. Men and women may have had different affective responses to the issue of plea bargaining (with women responding more negatively than men), especially in light of a local and controversial plea bargain that occurred around the time of this study. Such pre-existing gender differences may have led to tIle lower frustration, the greater effort, the greater recall, and more positive attitudes for men than for WOlnen. Results· from this study suggest that current cognitive models of persuasion may not be very applicable to controversial issues which elicit strong emotional responses. Finally, these data indicate that affective responses, the controversial and emotional nature ofthe issue, gender and other individual differences are important considerations when experts are attempting to persuade laypeople toward a counterattitudinal position.

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This research studioo the effect of integrated instruction in mathematics and~ science on student achievement in and attitude towards both mathematics and science. A group of grade 9 academic students received instruction in both science and mathematics in an integrated program specifically developed for the purposes of the research. This group was compared to a control group that had received science and mathematics instruction in a traditional, nonintegrated program. The findings showed that in all measures of attitude, there was no significant difference between the students who participated in the integrated science and mathematics program and those who participated in a traditional science and mathematics program. The findings also revealed that integration did improve achievement on some of the measures used. The performance on mathematics open-ended problem-solving tasks improved after participation in the integrated program, suggesting that the integrated students were better able to apply their understanding of mathematics in a real-life context. The performance on the final science exam was also improved for the integrated group. Improvement was not noted on the other measures, which included EQAO scores and laboratory practical tasks. These results raise the issue of the suitability of the instruments used to gauge both achievement and attitude. The accuracy and suitability of traditional measures of achievement are considered. It is argued that they should not necessarily be used as the measure of the value of integrated instruction in a science and mathematics classroom.

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Research points clearly to the need for all concerned stakeholders to adopt a preventative approach while intervening with children who are at-risk for future reading disabilities. Research has indicated also that a particular sub-group of children at-risk for reading impairments include preschool children with language impairments (Catts, 1993). Preschool children with language impairments may have difficulties with emergent literacy skills - important prerequisite skills necessary for successful formal reading. Only in the past decade have researchers begun to study the effects of emergent literacy intervention on preschool children with language impairments. As such, the current study continues this investigation of how to effectively implement an emergent literacy therapy aimed at supporting preschool children with language impairments. In addition to this, the current study explores emergent literacy intervention within an applied clinical setting. The setting, presents a host of methodological and theoretical challenges - challenges that will advance the field of understanding children within naturalistic settings. This exploratory study included thirty-eight participants who were recruited from Speech Services Niagara, a local preschool speech and language program. Using a between-group pre- and posttest design, this study compared two intervention approaches - an experimental emergent literacy intervention and a traditional language intervention. The experimental intervention was adopted from Read It Again! (Justice, McGinty, Beckman, & Kilday, 2006) and the traditional language intervention was based on the traditional models of language therapy typically used in preschool speech and language models across Ontario. 5 Results indicated that the emergent literacy intervention was superior to the ,t..3>~, ~\., ;./h traditional language therapy in improving the children's alphabet knowledge, print and word awareness and phonological awareness. Moreover, results revealed that children with more severe language impairments require greater support and more explicit instruction than children with moderate language impairments. Another important finding indicated that the effects of the preschool emergent literacy intervention used in this study may not be sustainable as children enter grade one. The implications of this study point to the need to support preschool children with language impairments with intensive emergent literacy intervention that extends beyond preschool into formal educational settings.

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Previous research has suggested that drama has positive effects on learners' oral communication and anxiety; however, it is unclear which dimensions, or to what extent, they are affected by drama. This research narrows the investigation by examining how a drama-based EFL program impacts three dimensions of oral communication: fluency, comprehensibility, and accentedness, and one anxiety factor - foreign language speaking anxiety (FLSA) -, over time. Speech samples were collected from EFL learners in a treatment and a control group, and subsequently assessed by untrained Canadian-born raters. FLSA levels were measured through questionnaires and interviews. Pre- and post-test analysis indicate that learners in the treatment group made significant gains in oral fluency while oral fluency among learners in the control group remained unchanged. There was a significant reduction in FLSA levels among learners in both groups. Finally, qualitative analyses suggest that drama activities, among others, enhance learners' comfort levels in speaking English.

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This thesis presents Zen experience as aesthetic in nature. This is done through an analysis of language, a central concern for Zen Buddhism. The thesis develops two modes of language at work in Zen: representational and indexical. What these modes of language entail, the kind of relations that are developed through their use, are explored with recourse to a variety of Zen platforms: poetry, the koan, zazen, music, and suizen. In doing so, a primacy of listening is found in Zen - a listening without a listener. Given this primacy of listening, silence comes to the forefront of the investigation. An analysis of John Cage's 4'33" provides this thesis with justification of the groundlessness of silence, and the groundlessness of subjectivity. Listening allows for the abyssal subject to emerges, which in tum allows for reality to present itself outside of the constitutive function of language.