The role of numerical and non-numerical ordering abilities in mathematics and reading in middle childhood

This study investigated whether different types of ordering skills were related to mathematics achievement in children (n = 100) in middle childhood, after the effects of age, socio-economic status, IQ, and processing speed were taken into account. The relations between ordering skills and magnitude processing were also investigated, as well as the possibility that some of the shared variance between math and reading is explained by ordering abilities. The ordering tasks included the ordering of familiar numerical and non-numerical sequences, a parental report of children’s everyday ordering skills, and an order working memory task. Three magnitude processing tasks (symbolic and non-symbolic comparison and number line estimation), were also administered, as well as measures of inhibition and spatial working memory. From this set of measures, number ordering, order working memory and number line estimation emerged as the most important predictors of mathematics skills. We found that number ordering mediated the effect of both symbolic and non-symbolic comparison skills on mathematics, further confirming that this task captures some essential skills related to mathematics. Additionally, order working memory mediated the effect of both number comparison and reading skills on math. Finally, whereas non-symbolic comparison and number line estimation are considered important indicators of magnitude processing skills, there was no relationship between these abilities, but there was a correlation between each of these abilities and reading skills, with number line estimation also mediating the effect of reading skills on math. These novel findings could contribute to a better understanding of the basic processes underlying math ability, and why math and reading are strongly related in typical populations and in children with learning difficulties.     

Explaining common variance shared by early numeracy and literacy

How can be explained that early literacy and numeracy share variance? We specifically tested whether the correlation between four early literacy skills (rhyming, letter knowledge, emergent writing, and orthographic knowledge) and simple sums (non-symbolic and story condition) reduced after taking into account preschool attention control, short-term memory, speed of processing, visual-spatial skills, vocabulary, and shared book reading. 228 Dutch native preschoolers (mean age 54.25; SD = 2.12 months) participated. The results revealed that 1) all literacy skills were related to sums (non-symbolic and story condition), 2) rhyming was the strongest predictor of non-symbolic sums, and letter knowledge of sums in story context, 3) visual-spatial skills explained part of the shared variance in the non-symbolic condition and visualspatial skills, vocabulary and short-term memory explained part of the shared variance in sums in story context. Implications for the preschool curriculum and early interventions are discussed.     

Using kindergarten number sense to predict calculation fluency in second grade

Children's number sense in kindergarten was used to predict their calculation fluency in second grade (N = 198). Using block entry regression, usual predictors of age, reading, memory, and verbal and spatial cognition were entered in the first block and number sense measures were added in the second block. Number sense measures contributed a significant amount of variance over and above the more general predictors (26%-42%). Uniquely predictive subareas were active memory for numbers, number knowledge, and number combinations, with number combinations standing out as the strongest single predictor. Number sense screening in kindergarten, using "at-risk" versus "not-at-risk" criteria, successfully ruled out 84% of the children who did not go on to have calculation fluency difficulties and positively identified 52% of the children who later showed fluency difficulties. The relation of early number skills to later calculation fluency has important implications for math screening and intervention.     

边疆安全视阈中公民意识的建构

新疆少数民族地区多元文化背景下,"民族意识"的专一性和"宗教意识"的排他性是影响区域稳定的重要因素。培育和增强新疆各族群众的公民意识,并以"公民意识"统摄民族宗教意识,对于提高和强化新疆各族群众的国家认同意识,正确定位个人、民族、国家之间的关系,夯实中国共产党在西北边疆少数民族地区的执政基础意义重大。     

教师的课程意识及其生成

新一轮基础教育课程改革强烈呼唤教师的课程意识。课程意识是教师对课程系统的基本反映和“课程哲学”,而课程观是课程意识的核心。课程意识支配着教师在教育中的行为方式、存在方式乃至生活方式。教师的课程意识内在地包含着教师的主体意识、生成意识和资源意识。教师课程意识的形成要求教师转变课程观念 ,具有反思性实践能力 ,学校应重建学校课程制度     

Strategies of Number Sense in Pre-service Secondary Mathematics Teachers

This paper presents some results of an investigation on the number sense of a group of pre-service secondary teachers from Spain. The objective of this research was to analyze students’ use of strategies associated to number sense and compare them with those obtained in a previous study with pre-service primary teachers in Taiwan, (Yang, Reys & Reys, International Journal of Science and Mathematics Education, 7, 383–403, 2009). Pre-service secondary teachers showed lower success than pre-service primary teachers in a number sense test. Nevertheless, these last based their reasoning mainly on rules and algorithms, while pre-service secondary teachers used more strategies of number sense. In an attempt to delve into the low success shown by of Spanish pre-service secondary teachers, some students were interviewed. Those interviews showed that a deeper work on number sense in the training of these students is needed.     

"数感""符号感"与其它——《课程标准》大家谈

《课程标准》作为课程改革的指导性文件应加强科学性和严谨性.应对“(数、符号)感”、“观念”、“能力”、“意识”等词的涵义和用法做出更为深入的研究.“数感”的提法有一定合理性;“帮助学生掌握数学的符号语言”则要比“发展学生的符号感”这一提法更为恰当.     

大学生公民责任意识的养成——基于公民身份视角

公民身份外在表现为公民责任,公民身份的真正实现需要有自觉的公民责任意识.目前,我国大学生公民责任意识不稳定、不全面,是由于没有形成良好的公民身份认同.对公民身份认同的高低,直接表现为公民责任意识的强弱.具备较强公民身份认同感的大学生,公民责任意识就较强,反之亦然.大学生公民责任意识的提高,有赖于其对自身公民身份认同感的增强.大学生公民责任意识的培养需要“内在自修”和“外在培养”相结合.     

大学生失业的心理学阐释及对策

大学生“新失业群体”的形成不仅仅是简单的制度和市场机制等发挥的作用,心理因素更是其不可忽视的影响因素,主要包括“温室效应”“精英情结”“归属无着”“目标焦虑”等四方面,与此对应,可以从自我适应能力、职业心理辅导、人文环境等方面提出对策。     

A model for nurturing and assessing multidigit number sense among first grade children

Based on a synthesis of the literature and on the results of a two-year teaching program working with young primary children, a framework was developed, refined and validated for nurturing and assessing multidigit number sense. The major constructs incorporated in this framework were counting, partitioning, grouping, and number relationships. For each of these constructs, four different levels of thinking were established which, in essence, reflected a learning apprenticeship for multidigit number sense. At each level, and across all four constructs, learning indicators were developed and matched to distinctive problem tasks that went beyond the four basic operations.The framework was validated through data obtained from six case studies of grade 1 children. The thinking of these children was assessed and analyzed on the problem tasks for the four constructs and four levels. While the students were at different levels, all but one showed striking consistencies across the four constructs. Moreover, no student was able to solve a problem at a higher level when they had not solved a lower-level problem in the same category. The present framework for multidigit number sense covers only the lower primary grades, but research and instruction would benefit from an extended framework across the elementary grades.     

A Study of Teaching and Learning Number Sense for Sixth Grade Students in Taiwan

Two public schools (A and B) from two cities in southern Taiwan were selected to participate in this study. In each school, two sixth grade classes (an experimental and a control class) were studied. Number sense activities were conducted in the experimental classes through process-oriented teaching model to help children develop number sense, while the control classes followed the standard teaching method. Quantitative analyses showed that there were statistically significant differences on group tests in experimental classes for post-test and retention-test as compared with the pre-test at =0.01 level. However, there was no statistically significant difference between pre-test and post-test (pre-test and retention-test) for control classes at =0.01 level. Qualitative data indicated that the changes made by students in the experimental classes were apparent after the instruction and compared with the students in the control classes. There was little change found by students in the control classes after the instructions. These data demonstrated that the teaching of number sense activities is effective and helpful in developing childrens number sense in the experimental classes. Furthermore, the results of retention demonstrated that the students learning is meaningful and significant. Der-Ching Yang: Author for correspondence.     

低年级学生数感培养的实践与思考

《义务教育数学课程标准(2011版)》提出了十个核心词,“数感”是其中一个,且位列第一,是教师在备课、研课、评课时常用的关键词。关于数感及学生数感的培养,许多专家、学者、一线教师已有了丰硕的理论及实践研究结果。相比之下,小学低年级的研究较之中高年级则单薄得多。然而数感作为一种自觉的行为,更应该从学生起步阶段加以培养,应渗透到数学学习的整个过程。     

Investigating the improvement of prospective elementary teachers’ number sense in reasoning about fraction magnitude

We report on interview results from a classroom teaching experiment in a Number and Operations course for prospective elementary teachers. Improving the number sense of this population is an important goal for mathematics teacher education, and researchers have found this goal to be difficult to accomplish. In earlier work, we devised a local instruction theory for the development of number sense, which focused on whole-number mental computation. In this study, the local instruction theory was applied to the rational-number domain, with the help of a framework for reasoning about fraction magnitude, and it guided instruction in the content course. We interviewed seven participants pre- and post-instruction, and we found that their reasoning on fraction comparison tasks improved. The participants made more correct comparisons, reasoned more flexibly, and came to favor less conventional and more sophisticated strategies. These improvements in number sense parallel those that we found previously in mental computation. In addition to the overall results, we highlight two cases of improvement that illustrate ways in which prospective elementary teachers’ reasoning about fraction magnitude can change.     

Public versus private schools in developing countries: Evidence from Colombia and Tanzania

The paper presents evidence on differences between public and private schools in Colombia and Tanzania on a number of indicators like cognitive achievement, unit cost and labor market outcomes. The findings are mixed, in the sense that in both countries, statistically controlling for student ability and socioeconomic background, private school students outperform their public school counterparts on academic achievement, whereas the reverse is true regarding achievement on specialized subject-matter. One possible explanation of this finding is that parental pressure (social demand) on private schools makes them tacitly emphasize academic subjects which are viewed by their customers as leading to a higher level of opportunities after graduation.     

谈化学教学对学生记忆能力的培养

人的记忆能力是发展其它智力结构的基础,是智力活动的“仓库”。充分发挥各种感官的功能,深刻理解识记内容,并通过思维想象,抓其规律,掌握本质及简化记忆内容,均是提高记忆力的有效手段。     

Features in children's counting books that lead dyads to both count and label sets during shared book reading

This study examined how book features influence talk during shared book reading. We used data from a study in which parent–child dyads (n = 157; child's M_age = 43.99 months; 88 girls, 69 boys; 91.72% of parents self-reported as white) were randomly assigned to read two number books. The focus was comparison talk (i.e., talk in which dyads count a set and also label its total), as this type of talk has been shown to promote children's understanding of cardinality. Replicating previous findings, dyads produced relatively low levels of comparison talk. However, book features influenced the talk. Books containing a greater number of numerical representations (e.g., number word, numeral, and non-symbolic set) and a greater word count elicited more comparison talk.     

‘Uni has a different language … to the real world’: demystifying academic culture and discourse for students from low socioeconomic backgrounds

The Australian government has set ambitious targets for increased higher-education participation of people from low socioeconomic backgrounds. There is, thus, a pressing need to explore how best to empower these students with what they require to progress and succeed at university. The paper draws on a literature review and qualitative data from a national study in which 89 students from low socioeconomic backgrounds and 26 staff were interviewed. The paper argues that demystifying academic culture and discourses for these students is a key step institutions and staff can take in assisting students from low socioeconomic backgrounds to progress and succeed at university. A recurring theme to emerge from both the literature and interviews with students and staff was that teaching the discourse empowers and enables students to learn, has a positive impact on their sense of belonging and ultimately helps them succeed in higher education.     

The role of socioeconomic background and prior achievement for students’ perception of teacher support

Abstract

Building on the sociological work by Lareau, this study examined the association between students’ socioeconomic background, prior achievement and the perception of teacher support within the classroom. We expected that students from higher socioeconomic backgrounds would be more critical about the support they receive in the classroom and rate their teachers more negatively, while those with higher prior achievement would perceive teacher support more positively. Multilevel models confirmed that there is a negative association between wealth and students’ perception of two dimensions of teacher support, and a negative association between parental educational attainment and one dimension of teacher support. Our findings were in line with the ‘sense of entitlement’ theory by Lareau. Having higher prior achievement was associated with a more positive perception of teacher support, but did not seem to interact with socioeconomic background.     

高考加分违背公平原则

在高考分数面前,人人应该平等。高考加分政策的实行,则使一小部分考生获得了某种特权;对其他考生来说,这就意味着不公平。高考加分是滋生考试腐败的“温床”,只有铲除这个“温床”,才能确保高考的公平与公正。     

图书馆工作研究与"精品意识"

研究是客观事物在人们观念中的反映,因图书馆工作中待改进之处较多,研究者群体近年也在持续扩大与变更,这都对研究的方式、路向有一定影响.变革时期的图书馆工作研究要深入发展,宜加大科研导向力度,倡导严肃质朴的学风;引导研究者树立正确的荣誉观;自觉地培养"精品意识".