The relationship between early childhood teachers' instructional quality and children's mathematics development

This study examined how early childhood (EC) teachers' instructional quality predicted children's development in mathematics across two measurement occasions. Therefore, EC teachers' (n = 25) instructional quality was assessed using one standardized observation instrument covering both domain-specific and general aspects of instructional quality. Additionally, data on children's (n = 208) outcome in early number skills was collected applying a standardized test. Multilevel structural equation modeling was used accounting for nested data. Children's age and the average size of preschool groups were controlled for. Results revealed that EC teachers' instructional quality predicted children's development but was not associated with their initial achievement. The findings suggest that instruments covering domain-specific and general aspects might be helpful in order to measure EC teachers' instructional quality in mathematics and predict children's learning growth. Understanding the mechanisms between instructional quality and children's development may help EC teachers to enhance their math teaching in practice.     

Motivation coaching training for instructional coaches: a pilot study of motivational interviewing skills training

In our paper we describe a newly developed teacher coaching model that provides training on motivational interviewing (MI) to improve instructional coaches’ effectiveness with classroom teachers. Participants were 38 coaches who completed a three-day coaching training. At pre- and post-test, the participants completed role plays with an actor who played the role of a new teacher. Then, these sessions were coded for MI-consistent behavior. The results of our study revealed that the majority of the coaching conversations were inconsistent with effective MI. At baseline, conversations were primarily characterized by questions (60%) followed by attempts to persuade without permission (20%). Following training, coaches did not change their conversational style. Because an MI-inconsistent conversation style is associated with decreased self-efficacy and motivation for change, the findings suggest a need to help coaches develop interactions that are more consistent with best practices of MI.     

Expanding the instructional triangle: conceptualizing mathematics teacher development

As mathematics educators think about teaching that promotes students’ opportunities to learn, attention must be given to the conceptualization of the professional development of teachers and those who teach teachers. In this article, we generalize and expand the instructional triangle to consider different interactions in a variety of teacher development contexts. We have done so by addressing issues of language for models of teachers’ professional development at different levels and by providing examples of situations in which these models can be applied. Through the expansion of our understanding and use of the instructional triangle we can further develop the concept of mathematics teacher development.     

Novice and experienced instructional software developers: effects on materials created with instructional software templates

The development of instructional software is a complex process, posing high demands to the technical and didactical expertise of developers. Domain specialists rather than professional developers are often responsible for it, but authoring tools with pre-structured templates claim to compensate for this limited experience. This study compares instructional software products made by developers with low production experience (n = 6) and high production experience (n = 8), working with a template-based authoring tool. It is hypothesized that those with high production experience will be more productive and create software with a higher didactical quality than those with low production experience, whereas no differences with regard to technical and authoring quality are expected. The results show that the didactical quality was unsatisfactory and did not differ between groups. Nevertheless the templates compensated for differences in experience because the technical and authoring quality was equal for both groups, indicating that templates enable domain specialists to participate successfully in the production process.     

Effects of coaching on teacher use of sociocultural instructional practices

This study evaluates a performance-based instructional coaching model intended to improve teacher pedagogy and classroom organization for educating diverse student populations. Elementary teachers (N = 21) participated in a 30-h workshop and seven individual coaching sessions across an academic year. The coaching model promoted use of the Standards for Effective Pedagogy, five research-based practices known to increase student achievement. Findings demonstrate performance-based instructional coaching led to statistically significant (a) improvements in teacher pedagogy, (b) patterns of teacher growth, and (c) changes in classroom organization. Implications for improving teachers’ ultimate achievement, the coaching protocol, and research are addressed.     

数学教育中的认知心理初探

文章针对如何提高数学教学质量这一研究课题,从心理学角度,结合数学学科教育的特殊性与实践结果,分析了如何实现有效的数学教育,提倡知情意合一的数学教育模式.     

Examining focus,duration, and classroom impact of literacy and mathematics professional development

Over $18 billion is spent annually on professional development for in-service teachers. This study examined the focus, duration, and impact of professional development activities in which elementary (students ages 5–11) and middle school (students ages 11–14) teachers participated. Ninety-eight teacher-participants completed an online survey about their professional development experiences. In the analysis of literacy survey items and mathematics survey items, there were similarities in focus areas that received greater participation and areas that received less. There were also noticeable differences in frequency of participation in literacy and mathematics professional development. Comparisons between literacy and mathematics professional development indicated that more teachers reported participating in literacy experiences. This included workshops as well as ongoing support through planning meetings and mentorship. Overall, the consensus from teachers was that professional development was effective and has a beneficial impact on their classroom. Researchers share implications for the design and research of future professional development programs.     

"假性理解"原因浅析

“假性理解”是中学生数学学习中比较普遍的现象，也是老师们一时难以找到真正原因而无法很好解决的问题，它严重地影响了中学数学的教学质量。本以现代认知理论中数学学习过程理论为主要依据，探讨分析了中学生在数学学习中可能造成假性理解的几点因素：感知因素、数学思维因素、原数学认知结构因素等。     

Rethinking classroom-oriented instructional development models to mediate instructional planning in technology-enhanced learning environments

Although classroom-oriented instructional development (ID) models have the potential to help teachers think and plan for effective instruction with technology, research studies have shown that they are not widely employed. Many of these models have not factored in the complexities that teachers faced when planning for instruction in technology-enhanced learning environments (TELE). They also fail to facilitate teachers’ critical re-examination of their existing practices and exploration of other practices to take up the affordances of technologies for effective instruction. Adopting an activity theoretical perspective towards instructional planning in the TELE, this paper examines two existing ID models: Reiser and Dick [1996. Instructional planning: A guide for teachers. Boston: Allen and Bacon] and Morrison, Ross, and Kemp [2004. Designing effective instruction (4th ed.) New York: Wiley]. It then constructs a classroom-oriented expansive and reflective ID model that: (1) facilitates the teacher's re-examination of their existing practices to identify contradictions in his/her instructional planning process in the TELE; (2) treats the ID elements in a nonlinear and non-sequential way; (3) accounts for the decisions made by other participants in the TELE, especially students and other teachers; (4) supports teachers’ formulation of solutions to the contradictions and transforms practices to take up the affordances of technology in the TELE; and (5) recognizes the need for teachers to move beyond the current activity by reflecting upon it so as to enable the emergence of new norms of practice.     

Teacher education through the history of mathematics

In this paper I consider the problem of designing strategies for teacher education programs that may promote an aware style of teaching. Among the various elements to be considered I focus on the need to address prospective teachers’ belief that they must reproduce the style of mathematics teaching seen in their school days. Towards this aim, I argue that the prospective teachers need a context allowing them to look at the topics they will teach in a different manner. This context may be provided by the history of mathematics. In this paper I shall discuss how history affected the construction of teaching sequences on algebra during the activities of the ‘laboratory of mathematics education’ carried out in a 2 year education program for prospective teachers. The conditions of the experiment, notably the fact that our prospective teachers had not had specific preparation in the history of mathematics, allow us to outline opportunities and caveats of the use of history in teacher education.     

Effects of metacognitive instruction on mathematics achievement and attitude towards mathematics of low mathematics achievers

An experiment was conducted to examine the effects of metacognitive instruction on mathematics achievement and attitude towards mathematics of low mathematics achievers at a middle school in the North‐West Province of South Africa. Forty standard (std) 7 pupils were identified whose non‐verbal general ability and previous mathematics achievements were significantly lower than those of other std 7 pupils. These subjects were randomly assigned to an experimental group and a control group. Metacognitive strategies in solving mathematical problems related to four mathematics topics were individually taught to the members of the experimental group, while the pupils in the control group were taught the four mathematics topics through the conventional method of teaching mathematics. The comparisons of pretest and posttest measures of general ability, metacognitive awareness, attitude towards mathematics, and mathematics achievement revealed that the posttest scores of all the four variables for the experimental group were significantly higher than those for the control group.     

高职院校中高等数学课程的实验教学探析

数学实验教学的开展使计算机在数学学习中得到应用,由此激发学生的学习兴趣和积极性,让他们知道如何应用数学知识解决实际问题。将数学知识学习与计算机实验操作相结合,充实和发展了高等数学课程的内容及其作用,强化了对学生数学素质、计算机应用能力、创新意识和工程意识的培养。     

研究性数学、教育数学与数学教育

数学可分为研究性数学和教育性数学。研究性数学主要注重科学逻辑的序,而教育性数学则注重科学逻辑的序与认知心理的序之间的完美结合,后者即“教育数学”。教育数学是在研究性数学基础上的再创造、再提高,教育数学对数学教育改革具有深远的意义。     

System-wide improvement of early-grade mathematics: New evidence from the Gauteng Primary Language and Mathematics Strategy

This article reports on a two-year evaluation of the Gauteng Primary Language and Mathematics Strategy (GPLMS), an innovative system-wide reform intervention designed to improve learning outcomes in Gauteng Province, South Africa. Using data from universal testing of all learners in 2008 on a provincial systemic evaluation, as well as data from the 2011, 2012 and 2013 Annual National Assessment tests, this article investigates whether or not the GPLMS improves the numeracy skills of learners in early-grade mathematics in underperforming schools. Using as identification strategy, the natural experiment that resulted from a miscalculation of the provincial systemic evaluation test scores in 2008, which had been used to assign schools to the GPLMS intervention, the study shows that the GPLMS intervention is positively associated with improvements in early-grade mathematics performance of schools in the neighbourhood around the assignment threshold. The findings of the study contribute to the growing body of knowledge that shows the effectiveness of combining lesson plans, learner resources, and quality teacher capacity building.     

The role of teacher instructional practices in student collaboration

Prior research on collaborative learning identifies student behaviors that significantly predict student achievement, such as giving explanations of one’s thinking. Less often studied is the role of teachers’ instructional practices in collaboration among students. This article investigates the extent to which teachers engage in practices that support students’ explanations of their thinking, and how these teacher practices might be related to the nature of explanations that students give when asked by the teacher to collaborate with each other. The teachers observed here, all of whom received specific instruction in eliciting the details of student thinking, varied significantly in the extent to which they asked students to elaborate on their suggestions. This variation corresponded to variation across classrooms in the nature and extent of student explanations during collaborative conversations and to differences in student achievement.     

Teacher support,instructional practices,student motivation,and mathematics achievement in high school

The authors examined the relationships among teacher classroom practices, student motivation, and mathematics achievement in high school. The data for this study was drawn from the base-year data of High School Longitudinal Study of 2009. Structural equation modeling method was used to estimate the relationships among variables. The results indicate that conceptual teaching positively affected student mathematics achievement, whereas procedural emphasis in mathematics instruction had a negative effect. Teacher support influenced student mathematics achievement indirectly through students' mathematics self-efficacy, and also influenced students' interest in mathematics courses. Finally, students with higher levels of family socioeconomic status and prior achievement were more likely to have teachers who use conceptual teaching strategies. Students with higher prior achievement were also more likely to perceive higher levels of teacher support. The findings have theoretical and practical implications.     

Student learning emotions in middle school mathematics classrooms: investigating associations with dialogic instructional practices

Emotions are central to how students experience mathematics, yet we know little about how specific instructional practices relate to students’ emotions in mathematics learning. We examined how dialogic instruction, a socially dynamic form of instruction, was associated with four learning emotions in mathematics: enjoyment, pride, anger, and boredom. We also examined whether these associations differed by student gender and prior mathematics achievement. The sample consisted of 1307 sixth through eighth grade students (51.6% female, 59.0% White, 30.8% African American, and 10.3% other race; 42.3% receive free/reduced price lunch) from 70 mathematics classrooms. Results indicated that teachers who used more dialogic mathematics instruction had students who reported more enjoyment and pride, and less anger and boredom. Males and low-achieving students reported more positive and fewer negative emotions with greater dialogic instruction compared to their female and high-achieving counterparts.     

关于数学教师教育的若干思考（续）

剖析了当前我国数学教师教育中存在的若干问题,并提出了一些改进的思路与方法．