学习进阶视域下的初中数学教学评价模式及实践——以“因式分解”概念课为例

教师的课堂评价更指向对学生数学核心素养的培养,初中数学教学中如何引导学生对新概念进行自主建构,提升数学核心素养是当下亟须解决的问题.文章以七年级数学第四章第一节“因式分解”为例,阐述学习进阶视域下初中数学教学评价模式在教学中的实施过程,以学生学习目标进阶为主线,以任务为驱动,结合诊断性评价、过程性评价、总结性评价、个人评价、小组评价等多维度不同的评价方式,实现教学评价对教师的教和学生的学的促进作用,进而将该评价方式运用到整个数学教学过程中,引导学生对数学概念进行自主构建.     

学习进阶视域下电化学核心概念的认识功能分析

日常教学中核心概念的认识功能容易被忽视,电化学核心概念在高中的教学是分阶段进行的,每个阶段有不同的教学目标和认识思路,建构电化学核心概念的学习进阶,并分析每个进阶阶段的认识深度、认识思路和认识功能,为促进认识发展的电化学核心概念教学提供参考.     

为学生认知发展建模：学习进阶十年研究回顾及展望

为了改变科学课程学习内容零散且缺乏衔接的现状,学习进阶成为了国际科学教育研究的热点议题。对学习进阶的研究系统追踪学生的认知发展过程,为科学教育中标准设计、课程开发、学业评价和教师培训等多个系统的整合提供了统一框架。基于文献综述并结合自身研究经验,并从学习进阶的定义、进阶研究的基础、进阶研究的模式和研究成果的应用四个方面展开分析讨论后发现：科学教育界对学习进阶内涵理解上的差异逐渐消弭,进阶研究在描述学生认知发展过程上取得了阶段性的成果并在向着精细化发展,在学习进阶中融合知识学习与能力培养、学习进阶与教学实践的交互影响等将是后续研究的核心议题。     

数学知识观视角下学习进阶的再审视

数学学习进阶主要描述学生对数学知识或技能在一段时间内的发展历程,学习进阶的明确可以推动形成性评价、教学、学习的一致性,可以帮助教师承前启后地对照学习目标设计评价任务、分析评价结果、确定学习差距。对数学知识观的学科审视发现,数学知识兼备科学和人文的特点,数学知识具有发现性和发明性。建构数学学习进阶包括个体经验、朴素尝试,逐步内化、产生冲突,形成概念、内化运用,知识整合、拓展延伸。当然,数学学习进阶的建构过程,不是简单的从无到有的过程,也不是将现存的要素进行简单机械组合而必定实现的过程,其过程具有主体作用性、整合生成性、渐进性和未竟性、深度性和开放性等特点。     

论课堂教学时序——基于怀特海教育节奏思想的视角

怀特海在《教育的目的》中将教育的节奏划分为浪漫阶段、精确阶段和综合运用阶段,充分揭示了基于学习者智力发展特点的学习进阶规律,以及教育遵循智力发展的阶段性所应体现出的节奏性。这为分析课堂教学时序,促进课堂教学的有序运行提供了新的视角。具体而言,课堂教学时序包括学习主体之身心时序、课程知识之逻辑序、教学过程之运行序。这就要求教学遵循学习者的身心发展序,让“适合学生的教学”成为可能;课程知识的选择、组织与传递符合知识的内在逻辑,并联结主体经验,让课程富有活力;厘清教学关系,精心设计教学流程,合理创设教学情境,让教学过程富有诗意,让学习者在学习中充满体验和遐想。     

构建单元学习进阶 发展学生核心素养——以人教版初中“圆”为例

构建单元学习进阶是落实“以学生为中心”的有效路径,是进行单元整体教学设计的必由之路。文章基于学习进阶的教学理念,以初中“圆”单元为载体,以《义务教育阶段数学课程标准（2022年版）》为理论依据,探究如何通过学习进阶进行单元整体教学设计,填充单元学习进阶的组成要素,划分单元学习进阶的维度,构建学生单元学习进阶框架,促进学生数学核心素养的发展,实现“教—学—评”一致性。     

提升在职幼儿教师数学素养的培训研究

幼儿的数学学习是其数学认知的启蒙阶段,这一阶段数学思维习惯的养成对其后续的数学学习有着重要的影响。幼儿教师队伍的数学素养塑造他们的数学教学实践,教师的数学教学行为直接影响幼儿的数学言语习得,因此研究提升幼儿教师数学素养的培训模式具有重要的价值。本文构建了提升幼儿教师数学素养的培训方案,培训方案基于学习圈理论及数学学科知识反生发展视角。     

数学意识的培育:从直观感受到理性感悟

数学意识是数学核心素养在小学阶段的主要表现。然而,传统的培育方式长期停滞于“直观感受”的初级水平,不利于发挥数学学科的育人功能。呼应《义务教育数学课程标准(2022年版)》的增订内容和基本理念,当下数学课程应将“理性感悟”作为数学意识的新培育路向。数学意识的培育过程表现为:在知识维度上,从观察具体实例进阶至建构概念内涵;在方法维度上,从表述生活经验进阶至领悟数学思想;在信念维度上,从着意学习体验进阶至濡染理性精神。     

浅谈幼儿教师的语言技能

幼儿教师的语言是提高幼儿教学的重要手段。幼儿教师的语言技能是教师运用已有的知识经验,通过练习和自己多年的教学实践形成的,在幼儿园各种教育活动中能够运用自如,并在实际工作中充分发挥其作用的语言行为方式。幼儿教师语言技能直接关系到幼儿的活动、学习、情绪、情感的发展。因此至关重要。     

智适应学习系统支持的精准教学模式构建与应用研究

因材施教是精准教学所追求的价值取向,然而,如何知悉学生的知识点掌握程度、满足学生的个性化学习需求并引领学习者依循最佳学习路径则是教师面临的挑战。智适应学习系统支持的精准教学模式,包含“课前、课中、课后”三个阶段以及“测—设—学—练—析—辅”六个步骤的进阶路径。以小学五年级数学“平均数”这一内容为例进行教学实践,教师借助智适应学习系统的数据分析,监测调整教学策略,优化教学环节,提升教学效率,可将精准教学落到实处。模式应用案例表明,其对提升学业成绩、发展数学思维能力、改善学习效果具有显著作用。     

Exploring Teachers’ Meta-Cognitive Skills in Mathematics Classes in Selected Rural Primary Schools in Eastern Cape,South Africa

Undoubtedly the acquisition of mathematical skills for problem solving is critically important in today’s sophisticated technological world. There is growing evidence that meta-cognition application is an important component of academic success in general and impacts on mathematical achievement in particular. Teachers’ application of meta-cognition therefore directs and reflects their teaching-practice behaviour which influences their learners’ learning with understanding in problem-solving. The purpose of the study reported on in this article was to explore teachers’ available meta-cognitive skills in class with the intention of supporting learners’ development of mathematics in problem-solving in some selected rural primary schools in the Eastern Cape, South Africa. The participants were three teachers purposefully selected from three primary schools. Interviews were conducted with the three teachers and three lessons were observed. The interviews, as an extension of observation, focused on the teachers’ knowledge or understanding of available meta-cognitive skills and how they used these skills in helping their learners’ development of mathematics problem-solving. The findings included a detailed exploration of the teachers’ acquisition and use of specific metacognitive skills, either consciously or unconsciously, during teaching and learning processes in order to develop their mathematics learners’ meta-cognitive skills as well as in solving mathematical problems. The results of the observation showed that there was evidence of teachers applying meta-cognitive skills unconsciously in assisting their learners in problemsolving in class. The interviews confirmed this evidence of available meta-cognitive skills which the teachers usually applied in assisting their learners in problem-solving in class. Recommendations have been made regarding teachers’ methods of teaching to improve the development of such skills in the lives of their mathematics learners through problemsolving.     

A novice mathematics teacher educator–researcher’s evolution of tools designed for in-service mathematics teachers’ professional development

This study documented the process of evolution of the continuous design and revision of the tools of a novice mathematics teacher educator–researcher (MTE-R) as he planned and implemented design-based professional development workshops for in-service mathematics teachers in Taiwan. In order to effectively facilitate teachers designing and implementing their own conjecturing activities during the workshops, the MTE-R fostered their professional learning and growth through reflection upon students’ performance. From the perspective of activity theory, this study examined the evolution of the MTE-R’s mentoring activities and tools whose design gradually changed from being based on the literature content toward being learner-centered activities with teachers as learners. Such evolution not only enhanced teachers’ learning outcomes, but also facilitated the MTE-R’s own professional growth in different areas, including mathematics, mathematics learning, mathematics teaching, teacher education, and, in particular, the extrapolation of generic examples for understanding mathematical concepts.     

Professional noticing of coordinated mathematical thinking

Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture-oriented mathematics instruction to inquiry-based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision-making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi-dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms.     

基于MQI评估系统的大班数学集体活动质量分析及其启示

数学是学前儿童学习和入学准备的重要领域,也是学前教育质量监测的重要方面。MQI评估系统作为一种评估数学课堂教学质量的框架,体现了最新数学教育观念,突出了数学的学科特性和认知要求,强调儿童的主动参与和生成性的教学过程,可同时对教师的教和儿童的学进行评估。本研究使用MQI评估系统对我国幼儿园大班数学集体活动的质量进行考察,结果表明除数学意义建构和数学语言之外,数学丰富度领域各维度表现水平不高;教师对儿童行为进行处理和反馈的水平较低;大多数活动片段中不存在数学表达和语言上的错误及不严密性问题;儿童参与有意义的解释或者提问和推理较少,参与活动的认知要求不高。幼儿园大班数学集体活动质量受到集体教学中"教"与"学"的关系、教师对数学领域知识和儿童数学发展目标的认知、教师评价儿童数学思维的能力及师幼互动技巧、教师培训与考核的侧重点等因素的影响。我国学前教育界应重视数学教育活动的过程性质量,关注儿童数学学习过程性能力的发展,并应在借鉴MQI评估系统的基础上开发适合我国幼儿园数学教育实践的质量评估系统。     

Under-threes’ mathematical learning – teachers’ perspectives

This project highlights preschool teachers’ views of toddlers’ learning in mathematics. The Swedish national curriculum covers even the youngest children who are 1–3?years old. Interesting questions are thus: what should mathematics be for this age group and how should preschool teachers work with maths to achieve the curriculum objectives? Data were collected through interviews with six preschool teachers working in four different preschools. The data show that the teachers emphasize the body as very important for the learning process, which means that for these children, it is not a matter of simply talking about mathematical concepts, but experiencing them bodily. The teachers also report that they now pay more attention than previously to what material the children use and how they interact with it. They are more aware of how they organize and offer the various materials in the preschool and how this influences the way children use them and, consequently, their learning processes.     

Teachers’ beliefs and practices related to mathematics instruction

Beliefs and practices related to mathematics were assessed for 21 fourth- through sixth-grade teachers. At the beginning and the end of the school year teachers’ beliefs about (1) the nature of mathematics (i.e., procedures to solve problems versus a tool for thought), (2) mathematics learning (i.e., focusing on getting correct solutions versus understanding mathematical concepts), (3) who should control students’ mathematical activity, (4) the nature of mathematical ability (i.e., fixed versus malleable), and (5) the value of extrinsic rewards for getting students to engage in mathematics activities were assessed. (6) Teachers self-confidence and enjoyment of mathematics and mathematics teaching were also assessed. Analyses were conducted to assess the coherence among these beliefs and associations between teachers’ beliefs and their observed classroom practices and self-reported evaluation criteria. Findings showed substantial coherence among teachers’ beliefs and consistent associations between their beliefs and their practices. Teachers’ self-confidence as mathematics teachers was also significantly associated with their students’ self-confidence as mathematical learners.     

Interesting and difficult mathematical problems: changing teachers’ views by employing multiple-solution tasks

The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers’ knowledge. It is aimed at exploring the development of teachers’ mathematical and pedagogical conceptions associated with systematic employment of multiple-solution tasks (MSTs) in a “problem-solving” course for prospective mathematics teachers (PMTs). Our attention to teachers’ mathematical conceptions focused on the development of PMTs’ problem-solving competences. Our attention to teachers’ meta-mathematical and pedagogical conceptions focused on changes in teachers’ views concerning the level of interest and level of difficulty of the mathematical tasks. We differentiated between the systematic and craft modes of professional development integrated in the course. Systematic mode involved problem-solving sessions and reflective discussions on collective solution spaces. Craft mode involved interviewing school students. The study demonstrates the effectiveness of MSTs for PMTs’ professional development.     

Building preschool teachers’ capacity for teaching Chinese to ethnic minority children in Hong Kong: A qualitative study

ABSTRACT

Teaching Chinese to second language learners is a challenge for preschool teachers in Hong Kong so effective teacher professional development programmes are urgently needed to enhance their knowledge and skills. An Integrative Model Teacher Professional Development Programme which incorporates three theoretical underpinnings (i.e., culturally responsive teaching, meaningful and pleasurable learning, and effective teaching of Chinese as a second language) is designed to equip preschool teachers with knowledge, skills, and awareness in teaching Chinese to ethnic minority students. Through qualitative interviews with 15 in-service preschool teachers who joined the Programme, teachers’ perceptions and changes in three theoretical areas of teaching Chinese to ethnic minority students were explored. Particularly, teachers increased their awareness of ethnic minority cultures, developed empathy with ethnic minority children and their families, gained knowledge of implementing culturally responsive teaching and meaningful and pleasurable learning of Chinese. The role of teacher sharing in effective professional development was highlighted.     

构建“适境”课堂提高数学教学质量探究

所谓"适境"课堂,就是指在数学教学过程中,教师要创设一定的问题情境,激发学生学习兴趣,培养学生探究意识,调动学生学习的积极性和主动性,提高教学效率,提升学生数学核心素养。文章从创设猜测问题情境、生活问题情境、创设趣味问题情境、创设开放问题情境等方面,对构建"适境"课堂提高数学教学质量进行探究。     

Development of Arithmetical Thinking: Evaluation of Subject Matter Knowledge of Pre-Service Teachers in Order to Design the Appropriate Course

One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs.