TURKISH PRESERVICE ELEMENTARY TEACHERS’ SELF-EFFICACY BELIEFS REGARDING MATHEMATICS AND SCIENCE TEACHING

This study investigated Turkish preservice, elementary teachers’ personal mathematics teaching efficacy (PMTE), and science teaching efficacy (PSTE) beliefs at the end of their teacher education program. A majority of the participants believed they were well prepared to teach both elementary mathematics and science, but their PSTE scores were significantly lower than their PMTE scores. However, a significant correlation was found between the PMTE and PSTE scores. No significant gender effect on PMTE and PSTE scores was observed, but unlike the results from other countries, Turkish female preservice elementary teachers were found to have slightly higher PMTE and PSTE scores than their male peers. High school major area was found to be a significant predictor of participants’ PMTE and PSTE scores. Participants with mathematics/science high school majors were found to have significantly higher PMTE and PSTE scores than those with other high school majors.     

Collaborative Group Versus Individual Assessment in Mathematics: Processes and Outcomes

Large-scale assessment programs are beginning to design group assessment tasks in which small groups of students collaborate to solve problems or complete projects. Little is known, however, about the validity of data from group assessment for making inferences about the competence of individual students. This study compared performance in small-group and individual assessment contexts to determine how well achievement scores from the group setting represented the mathematics skills of individual students and to determine what additional information about students' skills was provided by data on their behavior in the group setting. All students performed at high levels in the group setting; the profile of group interaction was a better predictor of individual achievement than was individual performance in the group setting.     

The mental manipulation of 2-D representations of knots as deformable structures

Knowledge of the difficulties involved in processing deformable objects is necessary if learning activities are to be devised which develop visualisation skills in spatial aspects of mathematics. The research reported here attempts to determine an ordering in terms of complexity of tasks involving the mental manipulation of deformable objects, tasks which require the same skills as those employed in mathematical imagery.Subjects performed a series of spatial tests involving the comparison of diagrams of interlaced ropes, or knots at varying orientations. Knots were chosen not only because there is a mathematical structure to describe their properties but also, since they are deformable, the tasks differ from those in earlier work based upon the rotation of rigid objects.Results indicated that certain knot shapes are processed faster than others and, as with rigid objects, greater relative rotation of one of the deformable shapes increases the decision time. Tasks with more crossings were predicted to be of higher complexity, and to require longer decision times. However, this was found not to be the case, particularly where strong bilateral symmetry existed which significantly reduced decision time.     

RECALL OF BRIEF TELEVISION NEWS ITEMS: EFFECTS OF PRESENTATION MODE,PICTURE CONTENT AND SERIAL POSITION

An experiment was conducted to examine the effects of presentation mode, picture content and serial position upon the recall of brief television news items. Fifteen items were presented in either video or audio‐only mode to 40 subjects. Within the video mode, five items contained film footage, five contained still pictures and five consisted of the newscaster only.

Recall of the items was significantly better following video presentation than after audio‐only presentation; and in the video mode, film items were recalled significantly more often than still picture items, which were in turn recalled significantly more often than no‐picture items. Significant serial position effects occurred across all items in the audio mode, and over still picture and no‐picture items, but not film items in the video mode.

The results are discussed in terms of various imagery hypotheses.     

Prediction of the Probability of Graduation of Engineering Transfer Students

This study examined how retention of prose is affected by (1) outlines as advanced organizers, (2) preexperimentai familiarity with the material, and (3) text genre (i.e., narrative vs. expository prose). College students studied either a two-level outline, a one-level outline, or no outline before listening to 400 to 500 word passages that varied in familiarity and narrativity. Subjects were subsequently given a cued recall test or a 3-Alternative, Forced Choice test on the passages. Whereas outline condition and familiarity had no significant effects on retention, narrativity ratings on the passages predicted between 38% and 84% of the variance of retention scores. Stories were recalled much better than expository passages. These findings were discussed in the context of current theories in cognitive psychology, particularly those that have explored the structure, organization, and representation of knowledge and prose.     

The role of first person perspective and vivid imagery in memory for written narratives

The use of visualisation techniques in teaching has enabled students to improve their memory and comprehension of written narratives. Psychological research reveals how various factors can influence visualisation and learning, including; adopting a character’s perspective; constructing self-related images; multi-sensory text representing episodic events; and imagery ability. These factors were explored using narratives that represented real events, which contained subjective and objective information. University students (age range 18–25 years) recalled the narratives in a first person, third person and neutral perspective. In the first person perspective, information was connected to their sense of ‘self’, which improved memory. Additionally, the first person perspective improved memory for subjective and objective information for high imagery ability individuals and subjective information for low imagery ability individuals. Overall, the findings suggest that visualisation, first person perspective and narratives representing real experiences improve memory and comprehension. Implications for practice are also discussed.     

Cerebral laterality effects in the dual processing of prose

The degree to which the concreteness of prose material presented in an auditory fashion would interact with learners' lateral preference under different right hemispheric presentation conditions was investigated with 96 normal adults. Forty-eight subjects with consistent right preference patterns and a like number of bilateral individuals were either instructed to image, given a visual-spatial interference task, or given no instructions before listening to passages which differed in abstractness. As predicted across conditions, learners recalled a significantly greater number of ideas when the passage was concrete. Importantly, the abstractness was found to interact with subjects' inferred cerebral dominance. Whereas instructions to image and visual interference had little significant effect on mixed dominant subjects, for more consistently lateralized subjects imagery instructions increased and right-hemispheric interference decreased concrete recall. The results were interpreted in terms of visual and verbal encoding concomitant with cerebral lateralization.     

Evaluation of patterning instruction for kindergartners

Abstract

To determine whether patterning instruction was as useful or more useful than other forms of instruction, kindergarten children (age five) were taught either patterning or early literacy or mathematics or social studies in matched sessions. Instruction was conducted in 15-minute sessions from November through mid-April. Posttests on patterning, mathematics, early literacy, and three executive functions showed that the children taught patterning became significantly better at patterning than those in the other instructional conditions. No differences were found between the children taught mathematics, early literacy, or social studies. Correlational analyses indicated that the relations of patterning ability, working memory, and inhibitory control to mathematics achievement were similar. Cognitive flexibility was not very strongly related to any other measure and the executive functions were relatively independent of each other for the children who were age five.     

Effortful Control and Academic Achievement in Rural China

Research Findings: This study investigated the relationships between effortful control and early literacy and mathematics achievement. A total of 181 children (85 girls and 96 boys) from rural China were assessed when they were in Grades 1 and 2. Path analyses controlling for maternal education indicated that effortful control at the beginning of Grade 1 predicted incremental achievement in literacy and mathematics at the end of Grade 1 and mathematics achievement at the end of Grade 2. Growth in effortful control during Grade 1 also contributed significantly to the prediction of both literacy and mathematics achievement at the end of Grade 2. Although girls performed significantly better than boys in literacy achievement, gender did not moderate the relationships between effortful control and literacy and mathematics achievement. Practice or Policy: Children’s effortful control appears to be an important predictor of early literacy and mathematics achievement. Findings suggest that children’s effortful control should be fostered during the preschool and early years of formal schooling, and this can be done in both home and school contexts.     

The effect of vocabulary knowledge on novel word identification

The study investigated the relationship between vocabulary knowledge and novel word reading. Fourth-grade students were assessed on standardized measures of word identification, decoding, and receptive vocabulary, as well as on an experimental word identification measure using words that students in the fourth grade are unlikely to have seen before in print. In the experimental measure, pairs of words were matched on printed frequency and orthographic pattern (with a variety of spelling patterns represented), but differed in terms of the frequency of expected oral exposure for children (i.e., higher vs. lower). Results showed that students’ receptive vocabulary knowledge was significantly related to performance on both the standardized and experimental measures of word identification, even after accounting for the substantial amount of variance explained by decoding ability. Students performed better reading the words with higher expected oral frequencies on the experimental task than on those items with lower expected oral frequencies. The results point to the benefits, albeit modest, of oral word familiarity for reading words when they are first encountered in print and suggest that this top-down effect is not limited to exception words, as has been suggested, but has a wider scope.     

Connecting Science and Mathematics: The Nature of Proof and Disproof in Science and Mathematics

Disagreements exist among textbook authors, curriculum developers, and even among science and mathematics educators/researchers regarding the meanings and roles of several key nature-of-science (NOS) and nature-of-mathematics (NOM) terms such as proof, disproof, hypotheses, predictions, theories, laws, conjectures, axioms, theorems, and postulates. To assess the extent to which these disagreements may exist among high school science and mathematics teachers, a 14-item survey of the meanings and roles of the above terms was constructed and administered to a sample of science and mathematics teachers. As expected, the science teachers performed better than the mathematics teachers on the NOS items (44.1 versus 24.7%, respectively) and the mathematics teachers performed better than the science teachers on the NOM items (59.0 versus 26.1%, respectively). Nevertheless, responses indicated considerable disagreement and/or lack of understanding among both groups of teachers concerning the meanings/roles of proof and disproof and several other key terms. Therefore it appears that these teachers are poorly equipped to help students gain understanding of these key terms. Classroom use of the If/and/then/Therefore pattern of argumentation, which is employed in this paper to explicate the hypothesis/conjecture testing process, might be a first step toward rectifying this situation.     

中小学数学教师感知的创造性课堂环境的结构与特点

运用程黎和郑昊（2017）设计的中小学创造性课堂环境评估表（教师版）,调查发现中小学数学教师感受到的创造性课堂环境因素分为六个维度:（1）教师给予学生的支持;（2）教师对课堂的领导掌控力;（3）教师放权;（4）学生之间的关系;（5）促进学生间的交流;（6）提高学生的凝聚力。中小学数学教师对课堂的领导掌控力和促进学生间的交流在学历、职称、学段、学校类型和教师所获得的荣誉上都有显著性差异。初中数学教师在给予学生的支持、促进学生间的交流、提高学生的凝聚力及教师对课堂的领导掌控力等维度上都优于高中与小学数学教师。小学数学教师更重视放权让学生在课堂上的创造性表现,而高中数学教师则相对较少放权让学生在课堂上表现。获得省级及以上荣誉的教师对于课堂掌控及放权让学生表现上优于其他类型的教师,未获得荣誉的教师在课堂上的各方面都略差于获得过荣誉的教师。研究生学历的教师对课堂的领导掌控力、放权让学生在课堂上表现、与学生间的关系、促进学生间的交流以及提高学生的凝聚力这些维度上都比其他学历的数学教师更好。高级教师放权让学生在课堂上表现、对课堂的掌控力以及给予学生的支持和促进学生间的交流上都比其他级别的教师更好。重点学校的数学教师在创造性课堂环境的各个维度上都优于普通学校的数学教师。女教师给予学生的支持以及促进学生间的关系与交流上要优于男教师,男教师在对课堂的掌控力、放权让学生在课堂上表现及提高学生的凝聚力上比女教师稍有优势。这些结论对引导和干预中小学数学教师积极营造创造性的课堂环境有借鉴意义。     

Uncontrollable Mental Imagery: Graphical Connections Between A Function And Its Derivative

The view that imagery might be a disadvantage on certain tasks might surprise some mathematics educators who contend that a learner's conceptual understanding is increased whenever visual imagery is used. One of the limitations of imagery found in the literature comes to bear on a unique aspect of mathematics teaching and learning. This is the notion of an uncontrollable image, which may persist, thereby preventing the opening up of more fruitful avenues of thought, a difficulty which is particularly acute if the image is vivid. Although one calculus student's images supported high levels of mathematical functioning, occasionally his vivid images became uncontrollable, and the power of these images did more to obscure than to explain. This type of imagery can be a major hindrance in constructing meaning for mathematical concepts — contrary to the panacea view of imagery which is sometimes expressed.This revised version was published online in September 2005 with corrections to the Cover Date.     

ONE'S OWN TEACHER AND THE CHOICE OF THE TEACHING PROFESSION

Gustafsson, J.‐E. Differential Effects of Imagery Instructions on Pupils with Different Abilities. Scandinavian Journal of Educational Research, 21, 157‐179. A study investigating interactions between imagery instructions and aptitude variables is presented. A group of seven fifth‐grade classes was given imagery instructions in the reading of a short text, while another group read the text in a regular way. Three different outcomes covering different types of learning were registered. Tests of verbal ability and spatial (or imagery) ability were used as aptitude variables. The data analysis indicated that there were differences for the girls between the treatment groups among the aptitude variables; the results for the girls thus had to be excluded. A positive effect of imagery instructions was found for boys high in verbal and imagery ability with respect to the acquisition of simple terms. For other outcomes and groups of subjects either no effect or a negative effect was found.     

Mathematics Attribution Differences by Ethnicity and Socioeconomics Status

The differences in attributions for success and failure in mathematics between African American and White students and between students from low and higher socioeconomic status (SES) were examined. Two hundred sixty-four 7th-grade students from 5 schools in a midsize urban school district were surveyed to analyze attribution differences. Then, a stratified purposeful sample of 12 focus students, representing different ethnicity and economic combinations, were selected for follow-up interviews. Results indicated that students from all groups provided similar ratings on 5 attributions related to mathematics success-with effort rated more highly than ability, luck, task difficulty, or rapport with teacher. Notwithstanding this high rating for effort, other differences were found. Ability was rated significantly higher by Whites than by African Americans in relation to mathematics success. African Americans attributed their mathematics success significantly more to rapport with teachers than did Whites. Similar results were found for low versus higher SES students. Further, higher SES students attributed success significantly more to effort than did low SES students. Failure in mathematics was most commonly attributed to a lack of effort.     

Mathematics achievement and gender: A longitudinal study of selected cognitive and affective variables [grades 6–12]

This study examined the relationship of selected cognitive and affective variables to mathematics achievement for a random sample of 60 students as they progressed through 6th, 8th,10th and 12th grades. A consistent gender difference was found for stereotyping mathematics as a male domain. No consistent significant gender difference between means was found for spatial skills, verbal skill or mathematics achievement. Confidence, verbal skill and spatial visualization were each consistently positively correlated with mathematics achievement for both males and females. No gender difference was found for these correlations. However, spatial skills alone were found to be consistent significant predictors of mathematics achievement for females each year of the study, but not for males. Verbal skill was a consistent significant predictor of mathematics achievement for males, but not for females. The results of this study could lead to a reevaluation of the hypothesis that spatial skills help boys achieve in mathematics.     

Bilingual education for majority english-speaking children

A variety of second-language program options are available to anglophone children in Montreal’s public schools: French-as-a second-language (FSL), delayed and early French immersion, and full French-medium schooling. In this research, the achievement in French, English, and mathematics of two cohorts of anglophone students in each of these program options was evaluated longitudinally through grade 6 (12 years of age). The performance of these students was compared to that of comparable anglophone and francophone control groups who were attending conventional all-English and all-French schools, respectively. In terms of approximations to native-like command of French, the French-medium option was the most effective followed by the early immersion option: students in these programs were generally indistinguishable from the French Controls on all written French language tests and in mathematics. On tests of French oral skills, however, they scored below the French Controls, the extent of disparity depending on the opportunities available for social interaction with francophones. As well, no retardation in English language development was found for any of the options, even those that provided little instruction time in English. To the contrary, anglophone students scored significantly higher than English Controls on tests of English and mathematics, and in general the more concentrated the second language component, the better they performed relative to the controls on first language skills and mathematics. The apparent transfer of competence from second language to first and the bilingual advantages involved in these results are discussed in terms of time spent on the target language, the mode of instruction, and the opportunities provided for interaction with native-speaking peers.     

Structural pattern differences in course enrollment rates among community college students

This study tested a structural equation model of enrollment patterns of white and Hispanic males and females in two-year institutions and the invariance of parameter estimates among the different subgroups in the study. The model represented a multiequation model with three latent endogenous variables, high school academic preparation in mathematics and science, mathematics and science attitudes, and the dependent variable, enrollment patterns in mathematics and science courses. Exogenous variables included parents' education, levels of encouragement by others, and high school grades. Structural equation modeling was used to examine the structural and measurement coefficients of the hypothesized causal model for all subgroups in the study. In summary, an examination of the direct and total effect coefficients revealed different underlying patterns of factors for white and Hispanic females. No convergence on the model was found for white and Hispanic males. Equality constraints on all structural coefficients for both white and Hispanic females were tested and results indicated that all parameter estimates in the structural models for both subgroups were significantly different from each other.     

Reducing misinformation effects in children with cognitive interviews: dissociating recollection and familiarity

Two experiments examined the effect of a cognitive interview on 4- and 8-year-old children's correct recall and subsequent reporting of misinformation. Children viewed an event followed by misinformation that was read or self-generated either before or after a cognitive interview. Children were then given a recognition test under inclusion and exclusion instructions. A cognitive interview elicited more correct details than a control interview. Age-related changes were found such that the 8-year-old children's reports were more complete and they recalled more correct person, action, object, and location details than the 4-year-old children. A cognitive interview given after postevent misinformation reduced children's reporting of misinformation at interview and reduced reporting of self-generated misinformation at test. Process dissociation analyses revealed that recollection increased but familiarity decreased with age.     

Sources of self-efficacy of community college students enrolled in developmental mathematics

The need to improve student success in community colleges has resulted in a growing interest in developmental mathematics. Yet there remains a need to understand the motivations and beliefs of developmental mathematics students in order to cultivate their success. Self-efficacy has been identified to be a predictor of student success. Little is known about the antecedents or sources of self-efficacy of students enrolled in remedial courses at community colleges and how their self-efficacy can be bolstered through such courses. An instrument was developed to measure sources of mathematics self-efficacy and was originally tested with middle school students. Using a sample of 439 students, it was found that a scale which measures sources of self-efficacy is psychometrically acceptable for adults completing mathematics remediation. Our results indicated that the four theorised sources of self-efficacy explained a large percentage of the variance in mathematics skill self-efficacy for our sample. As hypothesised by others, mastery experiences was the best predictor of self-efficacy but all sources influenced mathematics skills self-efficacy.