Developmental trajectories of children's spatial skills: Influencing variables and associations with later mathematical thinking

Few studies have examined the long-term relations between children's early spatial skills and their later mathematical abilities. In the current study, we investigated children's developmental trajectories of spatial skills across four waves from age 3–7 years and their association with children's later mathematical understanding. We assessed children's development in a large, heterogeneous sample of children (N = 586) from diverse cultural backgrounds and mostly low-income homes. Spatial and mathematical skills were measured using standardized assessments. Children's starting points and rate of growth in spatial skills were investigated using latent growth curve models. We explored the influence of various covariates on spatial skill development and found that socioeconomic status, language skills, and sex, but not migration background predicted children's spatial development. Furthermore, our findings showed that children's initial spatial skills––but not their rate of growth––predicted later mathematical understanding, indicating that early spatial reasoning may play a crucial role for learning mathematics.     

Young children's use of spatial coordinates

4-6-year-old children were given problems in which they had to decide which 1 of an array of points was in line with 2 coordinate markers. The simplest problems had 4 points to choose between and markers perpendicular to the horizontal and vertical axes. Children of all ages were able to extrapolate lines from both coordinates to solve these problems. The older children were also given more complex problems. In some of these, 1 marker was at 45 degrees to an axis, the other perpendicular: in others the array was increased to 16 points and presented sometimes in a regular, sometimes in an irregular pattern. There were developmental improvements in performance, and the complex problems were more difficult than the simpler ones. However, 5- and 6-year-olds did extremely well even on the complex problems. The results establish that young children's grasp of Euclidean spatial relationships is more adequate than has often been suggested.     

Maternal variables related to sexually abused children's functioning.

OBJECTIVE: The purpose of this study was to explore how mothers' developmental history and current functioning affects their sexually abused children's functioning and recovery. METHOD: A sample of 67 African-American mothers and their sexually abused children participated in this study. Interviews and a range of adult and child measures were administered in order to assess maternal developmental history and current functioning, and child functioning. RESULTS: Mothers' past experiences as children were associated with their children's behavior and general functioning following the sexual abuse. Mothers who experienced more discontinuity of childhood care, who were sexually abused as children, and/or had more problems in their family of origin had children who showed poorer functioning and more behavioral symptomatology. In addition, mothers who currently were experiencing more trauma symptomatology, reported substance abuse, and/or were less able to provide support to their children, had children with more behavior problems and poorer functioning. CONCLUSIONS: The findings from this study point to the impact of mothers' developmental history and current functioning upon the symptomatology of their sexually abused children.     

Some temporal factors affecting conditional discrimination

Pigeons acquired a serial conditional discrimination in which the onset of one of two colors (the instructional cue) on the center key preceded the onset of a white light (the trial cue) on one of two side keys. An autoshaping preparation was employed, in which food was delivered depending upon the color-side combination. Five groups of birds were studied at instructional cue durations of either 30 or 60 sec, and trial cue durations of 3, 6, or 12 sec. These temporal parameters allowed for different ratios of the instructional stimulus duration (I) to the trial stimulus duration (T), while keeping the absolute duration of the instructional stimulus constant, and for different absolute durations of the instructional stimulus, while keeping the I/T ratio constant. These manipulations were studied with either a 30 or a 60-sec cycle (the interval between the onset of the intertriai interval and the offset of the trial cue), thus permitting examination of the cycle duration to trial duration ratios as well. The results showed that the larger the value of I relative to that of T, the greater the final level of accuracy; this implicates the I/T ratio as a controlling variable. In contrast, the larger the cycle duration (C) relative to T, the greater the rate of responding to the trial stimulus, which is consistent with previous findings in autoshaping studies. These results suggest that whereas the C/T ratio directly influences response rate, the I/T ratio affects accuracy in a serial conditional discrimination.     

Some aspects of children's ability to solve mathematical problems

This survey presents the essentials of a study concerning problem solving ability in children aged 12–13. It forms part of a large project concerning the impact of calculators and computers in school mathematics and the consequences for certain basic abilities. The contents of the survey are in brief:

? definition of problem solving ability;

? test construction;

? interviews;

? supplementary investigations.

     

Parental perceptions of life context variables for involvement in their young children's education

The purpose of this study was to discover Turkish parents’ perceptions of life context variables, including personal knowledge and skills and personal time and energy for involvement activities in their young children's education. The scales used in this study were based on parents’ self-report, and included: (1) Parental Perceptions of Personal Knowledge and Skills for Involvement Activities and (2) Parental Perceptions of Personal Time and Energy for Involvement Activities. Moreover, a demographic survey was developed and used as the second instrument in this study. The results suggested that parents as a group tend to have positive perceptions of life context variables for involvement in their young children's education and their income is the strongest predictor of these perceptions.     

Biases in young children's communication about spatial relations: containment versus proximity

Four experiments examined 3- and 4-year-olds' ability to communicate about containment and proximity relations. One hundred twenty-eight children either described where a miniature mouse was hiding in a dollhouse or they searched for the mouse after the experimenter described where it was hiding. The mouse was always hidden with a small landmark that was either in or next to a large landmark. When describing where the mouse was hiding, children were more likely to successfully disambiguate the small landmark when it was in the large landmark (e.g., under the plant in the dresser) than when it was next to the large landmark (e.g., under the plant next to the dresser). When searching for the mouse, 3-year-olds were faster to initiate their searches when the small landmark was in the large landmark than when it was next to the large landmark. Together, these results suggest that there are informational biases in young children's spatial communication.     

Linguistic and pedagogical factors affecting children's understanding of arithmetic word problems: A comparative study

2493 children aged from 5 to 15 years in 114 classes in 25 primary schools were asked to do a similar set of 22 arithmetic word problems. 1195 of the children were in Grades K through 6 in Victorian schools (Australia) and 1298 were in Grades 4 through 6 in Papua New Guinea (PNG) schools. For both samples the questions were posed in English. This was the first language for most children in the Victorian sample but, for the PNG sample, English was usually the second, third, or even fourth language (even though it is the language of instruction in PNG schools). While the test instrument was based on widely accepted information processing models of how children solve arithmetic word problems, the data obtained were not so much in accord with these models as with psycholinguistic theories on children's acquisition of polarised comparative pairs (like more and less). The data also indicate that children from the two samples used similar strategies and made similar errors, with the order of relative difficulty being the same for both samples, the main factor determining difficulty being the semantic structure of the questions. Differences in performance between corresponding grades from the two samples can be attributed to differences in the degree of English language competence rather than to numerical facility.     

Structural variables affecting CAI performance on arithmetic word problems of disadvantaged and deaf students

Summary We have shown that it is possible to account for a substantial portion of variability in student responses to arithmetic word problems using variables that describe structural features of the problems. However, the results obtained at this stage in our investigations are situation-dependent. The greater variance in observed proportion correct compared with the variance in the predicted proportions, and the differing sets of variables contributing significantly to the regressions come as no surprise. First, the population for this study differed from that used in the pilot study. Second, it is clear that characteristics of the problem set, for example, the frequency of occurrence of exemplars for the range of values for each variable and the way variable values are combined in problem types, affect the weighting for each variable in the regression analysis. Thus, differences were expected because different problem sets were used for the pilot study and the present study.In the light of these differences, the similarity in performance of the two disadvantaged groups gains in significance, and deserves further study. We believe we can increase the generalizability of our results by redesigning the basic problem set to exemplify in a balanced fashion the full range of variables found to account for problem difficulty. Given, however, the difficulty of making accurate predictions about problem-solving results, the correctness of this belief needs to be explicitly tested.This research was supported by Office of Education Grant OEG-0-70-4797 (607) and NSF Basic Research Grant GJ-443X.     

对影响我国高职教育发展某些因素的分析及其对策

当前 ,我国高职教育呈现“三热三冷”现象。即“政府热、民众冷 ,院校热、考生冷 ,录取热、报到冷”。并由此干扰了我国总体招生计划的顺利完成 ,扰乱了高等教育的合理层次结构 ,对我国高等教育合理、快速、健康的发展带来了较大的影响。我国已将“积极发展高等职业教育”作为加快发展高等教育的重要战略举措。 2 0 0 0年教育部公布的具有招生资格的普通高等学校中独立设置称为高等职业 (技术 )学院的高校就有 1 1 8所 ,普通本科院校也纷纷设置二级职业 (技术 )学院。 1 999年曾单独拨出 1 0万指标用于普通高校招收“双新”高职生。 2 0 0 0…     

Counselling in the culturally diverse society: Some neglected variables in research

Cross-cultural research, especially in the area of counselling, has received considerable attention in the professional literature. Closer inspection of published research reveals that most often the variable of race is considered central. Some crucial cross-cultural variables have been ignored in favour of the racial factor. This paper discusses some of these conspicuous cultural factors which are relevant to the counselling process. In addition, some research-specific problems in the cultural arena of investigation are considered. The need of effective models for counselling in a culturally mosaic society such as Canada is stressed.Paper presented at the ninth IRTAC, Greece, April 1980.     

Young children's ability to infer spatial relationships: evidence from a large, familiar environment

Young (mean age = 3-9) and old (mean age = 5-0) nursery school children were tested on their ability to infer spatial relationships in a large, familiar environment. Each child in the younger group was matched to a child of the same sex in the older group who had been attending the nursery school for the same number of months. Subjects were taken to 3 different locations in their nursery school and were asked to point to 5 targets on the school grounds. Older children were more accurate than younger children on nursery school targets, but children's spatial representations were relatively nonintegrated at both age levels. Consistent sex differences in favor of males were discussed in the context of a new framework that could potentially explain the appearance of sex differences on spatial tasks conducted in large-scale environments. It was concluded that very young children have difficulty inferring spatial relationships, even in a large, familiar environment. This difficulty seems to be due to a relative lack of symbolic capacity.