Multiple representations as sites for teacher reflection about mathematics learning

This documentary account situates teacher educator, prospective teacher, and elementary students’ mathematical thinking in relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning skill—creating and analyzing representations. The author examines responses of prospective teachers to a visual representation task and, in turn, their examination of school children’s responses to mathematical tasks. The analysis revealed the initial tendency of prospective teachers to create pictorial representations and highlights the importance of looking beyond the pictures created to how prospective teachers use mathematical models. In addition, the challenges prospective teachers face in moving beyond a ruled-based conception of mathematics and a right/wrong framework for assessing student work are documented. Findings suggest that analyzing representations helps prospective teachers (and teacher educators) rethink their teaching practices by engaging with a culture of teaching focused on reading for multiple meanings and posing questions about student thinking and curriculum materials.     

Inquiry learning for gifted children

The aim of the study was to investigate the effects of support on knowledge acquisition of gifted learners and their flow and mood during inquiry learning. Sixty-four gifted primary school children were randomly assigned to one of three conditions differing in support given in an inquiry task. Results showed that learners who were allowed to experiment themselves learned more, experienced more flow, and felt more positive toward the task than those who were not given this opportunity, but only when they were guided through the inquiry cycle by prompts to generate hypotheses, perform experiments, and draw conclusions. The overall conclusion is that gifted children benefit more from open, complex tasks when their learning process is externally regulated.     

Overcoming the positive-capture strategy in young children: learning about indeterminacy

Two experiments were conducted to examine whether and how 4- and 5-year-olds learn to distinguish determinate from indeterminate evidence. Children were asked to decide whether various patterns of evidence were sufficient to reach unambiguous conclusions. This study replicated the finding that young children tend to use a strategy that, although generally successful, fails on evidence patterns in which a single positive instance co-occurs with an unexplored source of evidence. Experiment 1 demonstrated that this positive-capture strategy is deeply entrenched, even in a meaningful, pragmatic context. With a microgenetic design, Experiment 2 revealed that young children are capable of replacing the positive-capture strategy with a correct strategy when they are exposed to various analogous tasks in several training sessions.     

Learning about learning

The aim of this study has been to explore possible developmental differences in conceptions of learning amongst a group of people with very different learning experiences. The data consist of interviews with 90 people concerning their approach to learning. The sample was selected according to two criteria: age (which ranged from 15 years 7 months up to 73 years 3 months) and level of formal education (with a minimum of 6 years and a maximum of 16/17 years).Analysis of the interviews revealed that there are distinctive differences between people in terms of their subjective conceptions of learning, the nature of which has been described elsewhere. In the present article, the focus is on describing what seems to be an important developmental process: for some people the phenomenon of learning has become thematized — it has been made an object of reflection — while for others it represents an activity the nature of which is taken for granted.     

Consequences of learning about historical racism among European American and African American children

Knowledge about racism is a critical component of educational curricula and contemporary race relations. To examine children's responses to learning about racism, European American (Study 1; N= 48) and African American (Study 2; N= 69) elementary-aged children (ages 6-11) received history lessons that included information about racism experienced by African Americans (racism condition), or otherwise identical lessons that omitted this information (control condition). Children's racial attitudes and cognitive and affective responses to the lessons were assessed. Among European American children, racism condition participants showed less biased attitudes toward African Americans than control condition participants. Among African American children, attitudes did not vary by condition. Children in the two conditions showed several different cognitive and affective responses to the lessons.     

A Comparison of the Nontraditional Students' Experience on Traditional Versus Nontraditional College Campuses

The majority of research on nontraditional students has been conducted in environments where they constitute a significant portion of the college population. For the most part, this research found few problems and indicated that nontraditional students' college experiences are positive. This article compares the experience of nontraditional students at two types of campuses—a traditional campus where older students constitute a small percentage of the student population and two branch campuses where there is a substantial number of older students. The findings indicate areas in which a lack of age diversity may have an impact on the nontraditional students' experience.     

Analysis of cognitive abilities for learning disabled children

The study investigated WISC-R subtest pattern scores of 58 learning disabled children (42 boys and 16 girls) ranging in age from 6 years to 15 years, 10 months. The variation in subtest scores was analyzed by a 1 X 10 analysis of variance with repeated measures on the single factor. Differences between individual subtest means were analyzed by the Newman-Keuls test for simple effects. The evidence indicates that the low subtest scores on Arithmetic, Coding and Information were characteristic of this group. The study did not support the verbal-Performance discrepancies as useful in the diagnosis of learning disabilities.     

A potential for learning probability in young children

Sixty-one children, from 4 to 11 years old, were presented with two sets, each containing blue and yellow elements. Each time, one colour was pointed out as the payoff colour (POC). The child had to choose the set from which he or she would draw at random a POC element in order to be rewarded. The sets were of varying sizes with different proportions of the two colours. The problem was to select the higher of the two probabilities. Three kinds of materials were used: Pairs of urns with blue and yellow beads, pairs of roulettes divided into blue and yellow sectors, and pairs of spinning tops, likewise divided into two colours.Roughly around the age of six, children started to select the greater of the two probabilities systematically. The dominant error was selecting the set with the greater number of POC elements. Verbal concepts of probability and chance were explored and some egocentric thought processes were described. The study indicates that probability concepts could be introduced into school teaching even in the first grades. The deterministic orientation in the instruction for young ages should be attenuated, permitting concepts of uncertainty right from the beginning.     

Nontraditional degree options for nurses: A model program

The Institute for Personal and Career Development of Central Michigan University offers external degree programs for adult learners utilizing nontraditional study. The competency-based programs described in this paper include credit given for the educational background and relevant career-life experiences of registered nurses in Michigan. The curriculum options most often chosen by nurses culminate in a BS degree in Community Development with a concentration either in school health or in public health and a BS degree in Management and Supervision with a concentration in health care administration.     

Pedagogical and technological augmentation of mobile learning for young children interactive learning environments

The ubiquity and educational potential of mobile applications are well acknowledged. This paper proposes six theory-based, pedagogical strategies to guide interaction design of mobile apps for young children. Also, to augment the capabilities of mobile devices, we used a humanoid robot integrated with a smartphone and developed an English-learning app that applied the design strategies to this environment. Our observations of children's one-on-one use support the promise of the strategies and the combined use of robots and mobile devices to be a viable option to help optimize mobile learning.     

关于教会学生学会认知的若干问题

学会认知是国际21世纪教育委员会提出的未来教育所必须形成的四种学习能力的首要能力,它侧重于学生对发现问题和解决问题的手段和方法的掌握。教会学生学会认知要求在教学中做到“三个结合”“两种学习”“一种训练”。同时,教师和学生在教学中要有正确的角色定位。     

关于"研究性学习"的几个问题

剖析研究性学习的几个典型定义,区别"研究"与"探索"、"探究"的不同,从人类研究活动的四个基本特征出发,揭示研究性学习的本质特征和内涵及其对教学实践的要求,提出不宜把所有探索性学习都纳入研究性学习范围,最后得出几个初步结论.