Transition from Textbook to Classroom Instruction in Mathematics: The Case of an Expert Chinese Teacher

This study reports how an expert Chinese teacher implements mathematics textbook lessons in enacted instruction. Our video analysis indicates that both textbook and enacted teaching included only one worked example; however, the teacher engaged students in unpacking the example in great depth. Both the textbook and the enacted teaching showed “concreteness fading” in students’ use of representations. However, the Chinese teacher incorporated students’ self-generated representations and facilitated students’ active modeling of quantitative relationships. Finally, the Chinese teacher asked a greater number of deep questions than were suggested by the textbook. These deep questions often occurred as clusters of follow-up questions that were either concept-specific or promoted comparisons which facilitated connection-making between multiple representations and solutions.     

北京师范大学新世纪义务教育课程标准实验教科书小学语文教材简介

北京师范大学新世纪义务教育课程标准小学语文实验教科书是首批进入国家课程改革实验区的三套语文教材之一。在本套教材的编写和实验中 ,我们力图解决三个问题 ,一是学习语文的兴趣问题 ,让学生喜欢语文 ;二是学习语文的方法问题 ,让学生会学语文 ;三是人文性和工具性的统一 ,让语文学习的过程 ,既是学习语言文字的过程 ,又是学习现代文化知识的过程 ,还是接受现代文明熏陶、感染的过程。我们以“兴趣先导 ,学会学习、整体推进、文化积累”作为本套教材总的指导思想     

Coordinating principles and examples through analogy and self-explanation

Research on expertise suggests that a critical aspect of expert understanding is knowledge of the relations between domain principles and problem features. We investigated two instructional pathways hypothesized to facilitate students’ learning of these relations when studying worked examples. The first path is through self-explaining how worked examples instantiate domain principles and the second is through analogical comparison of worked examples. We compared both of these pathways to a third instructional path where students read worked examples and solved practice problems. Students in an introductory physics class were randomly assigned to one of three worked example conditions (reading, self-explanation, or analogy) when learning about rotational kinematics and then completed a set of problem solving and conceptual tests that measured near, intermediate, and far transfer. Students in the reading and self-explanation groups performed better than the analogy group on near transfer problems solved during the learning activities. However, this problem solving advantage was short lived as all three groups performed similarly on two intermediate transfer problems given at test. On the far transfer test, the self-explanation and analogy groups performed better than the reading group. These results are consistent with the idea that self-explanation and analogical comparison can facilitate conceptual learning without decrements to problem solving skills relative to a more traditional type of instruction in a classroom setting.     

The Relations Between Number Property Strategies,Working Memory,and Multiplication in Elementary Students

This study aimed to examine the relations among property strategies, working memory, and multiplication tasks with 101 Chinese fourth-grade students. Two multiplication property strategies (associative and distributive) were compared with no strategy and demonstrated differentiated effects on students’ accuracy and reaction time. Associative property strategy outperformed the distributive strategy and no strategy on the measures of accuracy and reaction time. The findings support the problem difficulty effect. The findings indicate that if a strategy does not necessarily simplify a problem, it might not help to enhance accuracy, suggesting that multiplication property strategies should be used with respect to the structural features of the problems. Among more difficult problems, visuospatial sketchpad consistently explained unique variances in problem accuracy.     

从练习活动编制走向学习活动设计——语文教科书的价值转型

语文教科书从"教本"转向"学本"编制的最大价值,在于引导教师和学生真正从基于教科书的教与学走向基于教科书中活动设计的教与学。当语文教科书由"教本"转向"学本",语文教科书中的练习活动的功能就由复制转向沟通、由巩固转向整合、由引导转向拓展,其内涵与价值已超出"练习"范畴,需用"学习活动"涵盖"练习活动"。语文教科书的学习价值体现在学习活动的设计,基于学习价值的语文教科书中的活动设计强调在组织与衔接教科书文本时,把学生的需求建构与规划进去。     

基于知识转换模型的科学写作探析

科学写作是将学生的科学理解和科学思维过程具体化为外在表征的过程,对学生的科学学习具有重要价值。知识转换模型作为解释学生科学写作心理过程的理论框架,有效揭示了写作促进学生学习的认知过程。与知识陈述模型相比,基于知识转换模型的科学写作更有助于促进学生生成与建构新知识,凸显学生的科学思维和科学理解。基于知识转换模型的科学写作需要教师明确科学写作目的,以合作者身份参与学生写作;引导学生设定科学写作目标,形成任务的心理表征;指导学生在科学写作的体裁与功能之间建立联系,激活问题空间;为学生设计多样化的作品读者,推动知识转换的进程;重视对学生科学写作过程的评价。     

MATLAB仿真在通信原理课程中的应用

针对通信原理课程中的二进制振幅键控、二进制频移键控调控和二进制相移键控技术的原理和频谱公式推导过于繁杂、枯燥等问题,提出借助于MATLAB仿真,把抽象的问题具体化,增强学生的感性认识,激发学生的学习兴趣,取得了良好的教学效果．     

DISTRIBUTIVE PARTITIONING OPERATION IN MATHEMATICAL SITUATIONS INVOLVING FRACTIONAL QUANTITIES

In the present study, we describe a participating student’s (Carol’s) distributive partitioning scheme and operations along with Steffe’s and his colleagues’ studies about children’s constructions of fraction knowledge as a particular model of mathematical learning. Analysis of Carol’s mathematical behaviors indicates that an operationally common mathematical behavior (distributive partitioning operation) was revealed in various mathematical problem situations such as fraction multiplication, fraction division, and multiplicative transformation between fractional quantities. It both provides a rationale for why becoming versed in one mathematical subject could facilitate working with another mathematical subject and also implies the necessity of describing and defining students’ mathematical behaviors from an operational view of knowledge, which might lead to building foundations of a substantial cognitive map for students’ mathematical development.     

DISTRIBUTIVE PARTITIONING OPERATION IN MATHEMATICAL SITUATIONS INVOLVING FRACTIONAL QUANTITIES

In the present study, we describe a participating student’s (Carol’s) distributive partitioning scheme and operations along with Steffe’s and his colleagues’ studies about children’s constructions of fraction knowledge as a particular model of mathematical learning. Analysis of Carol’s mathematical behaviors indicates that an operationally common mathematical behavior (distributive partitioning operation) was revealed in various mathematical problem situations such as fraction multiplication, fraction division, and multiplicative transformation between fractional quantities. It both provides a rationale for why becoming versed in one mathematical subject could facilitate working with another mathematical subject and also implies the necessity of describing and defining students’ mathematical behaviors from an operational view of knowledge, which might lead to building foundations of a substantial cognitive map for students’ mathematical development.

     

Making the invisible visible: enhancing students’ conceptual understanding by introducing representations of abstract objects in a simulation

This study aimed to identify if complementing representations of concrete objects with representations of abstract objects improves students’ conceptual understanding as they use a simulation to experiment in the domain of Light and Color. Moreover, we investigated whether students’ prior knowledge is a factor that must be considered in deciding when to use representations of abstract objects. A pre-post comparison study design was used, involving 69 participants assigned to two conditions. The first condition consisted of 36 students who had access to a simulation with representations of concrete objects, whereas the second condition consisted of 33 students who had access to a simulation with representations of both concrete and abstract objects. Both conditions used the same inquiry-oriented curriculum materials, consisting of three sections that included physical phenomena with increasingly complex underlying mechanisms, so that the third section’s mechanisms were more complex in nature than those in the first two sections. Tests were administered to assess students’ conceptual understanding before and after the presentation of the curricular material as a whole, as well as before and after each of its three sections. Results revealed that the presence of representations of abstract objects was helpful for the first two sections, but only for students with low prior knowledge. On the third, most complex section, also the students with higher prior knowledge profited from the presence of abstract objects. From these findings, we conjecture that for physical phenomena with a lower level of complexity, students with high prior knowledge are able to mentally construct the necessary abstract concepts on their own, whereas for higher levels of complexity they need an explicit representation of the abstract objects in the learning environment.     

Using structured examples and prompting reflective questions to correct misconceptions about thermodynamic concepts

This paper explores the effectiveness of using ‘structured examples in concert with prompting reflective questions’ to address misconceptions held by mechanical engineering students about thermodynamic principles by employing pre-test and post-test design, a structured questionnaire, lecture room observation, and participants’ interviews. Students’ misconceptions were identified through pre-tests that evaluated students’ understanding of the chosen concepts, while conceptual change was assessed in pre-test–post-test design that revealed students’ ability to apply the concepts and transfer skills from a worked example to satisfactorily undertake a fairly complex similar problem. The use of worked examples in concert with prompting reflective questions is effective for inducing correct conceptual change and effective problem-solving skills. However, it is recommended that engineering tutors should incorporate inquiry-based learning approach and computer simulations alongside the use of worked examples with prompting reflective questions in order to enhance students’ conceptual understanding of thermodynamic concepts.     

泥沙淘尽始见金——小学语文深度学习的有效策略探讨

语文是小学众多学科中最重要的一门学科,因为它是学习其他所有学科的重要基础。在小学语文教学中,教师要与时俱进对自己的教学方式进行创新和改革,以加深学生对语文知识的掌握和理解,并且还能培养学生的核心素养,最终达到深度学习小学语文的目的。本文立足相关理论和实践对统编版教科书的课堂深度学习中出现的问题以及有效策略进行了分析。     

Teachers’ views of mathematics textbook series in Flanders: Does it (not) matter which mathematics textbook series schools choose?

The debate on the differential effects of mathematics textbook series is a recurrent topic in the research literature. Research results remain inconclusive, pointing to a lack of evidence to decide on the relevance of the selection by schools of a mathematics textbook series. Studies also point to difficulties in comparing textbooks. Recently, in order to examine the influence of mathematics textbook series on student learning, the need to take into account mediating variables between the mathematics textbook series and the enacted curriculum is stressed. This paper focuses on one such mediating variable: teachers’ views of mathematics textbook series. Views of a mathematics textbook series of 814 teachers and mathematics performance results of 1579 students were analysed. The results point out that, with regard to teachers’ views of mathematics textbook series, the question ‘Does it really matter which mathematics textbook series schools choose’ has to be answered positively. Implications of the findings are discussed.     

About cooperative engineering: theory and emblematic examples

In this article we focus on ‘cooperative engineering’, in which teachers and researchers co-design didactic sequences. In the first part of the article, we present cooperative engineering by describing some of the main principles on which it is grounded. The second part is dedicated to a case study, which enables us to illustrate some elements of the collective work in a specific cooperative design in kindergarten. The designed learning game, the ‘Treasure Game’, aimed to assist kindergarten students to build a system of graphical representations, which was implemented in a series of phases in which students were asked to memorise a series of items with increasing levels of difficulty. The game demonstrated the students’ growing competence in recalling items using strategies such as making lists and working collaboratively to collectively recall items through a ‘treasure box’. In the third part of the article, we show how this case study embodies some of the main principles put forward in the first part.     

An Analysis of Problem-Posing Tasks in Chinese and US Elementary Mathematics Textbooks

This paper reports on 2 studies that examine how mathematical problem posing is integrated in Chinese and US elementary mathematics textbooks. Study 1 involved a historical analysis of the problem-posing (PP) tasks in 3 editions of the most widely used elementary mathematics textbook series published by People’s Education Press in China over 3 decades. Study 2 compared the PP tasks in Chinese and US elementary mathematics textbooks. This allows for the examination of PP tasks from an international comparative perspective, which provides one point of view about the kinds of learning opportunities that are available to students in China and the USA. We found evidence that the inclusion of PP tasks in the Chinese textbook series reflected, to some degree, changes in the curricular frameworks in China. However, the distribution of PP tasks across grade levels and content areas, as well as the variety of types of PP tasks included, suggest a need for greater intentionality in the design and placement of PP tasks in both the Chinese and US textbook series. Findings from the 2 studies reported in this paper not only contribute to our understanding about the inclusion of PP tasks in curriculum both historically and internationally, but also suggest a great need to systematically integrate PP activities into curriculum and instruction. The fact that both Chinese and US curriculum standards have heavily emphasized PP in school mathematics, despite there being only a small proportion of PP activities in both Chinese and US elementary mathematics curricula, suggests the existence of challenges that are delaying the implementation of reform ideas such as problem posing in school mathematics.     

Understanding Linear Function: a Comparison of Selected Textbooks from England and Shanghai

This study describes a comparison of how worked examples in selected textbooks from England and Shanghai presented possible learning trajectories towards understanding linear function. Six selected English textbooks and one Shanghai compulsory textbook were analysed with regards to the understanding required for pure mathematics knowledge in linear function. Understanding was defined as being at five levels: Dependent Relationship, Connecting Representations, Local Properties Noticing, Object Analysis and Inventising. These levels were developed by examining the most prominent theories from the existing literature on understanding function. Findings suggested that the English textbooks constrained the structural aspect of understanding linear function due to a point-to-point view of function, while the Shanghai textbook which focussed on a variable view of function overemphasised the algebraic approach. The discussion explored the drawbacks to each approach and what teachers or textbook writers could do to balance these two approaches in order to facilitate students’ understanding towards a structural view of linear function.     

高中语文教材文本中的人文精神探究——以人教社2006年第2版（必修）为例

当下高中语文教材文本的人文精神,主要体现在：胸怀天下,以人类或民族大业为己任;关爱人生,感慨命运离愁、人生失意和情爱难舍;坚定信念,追求人的价值存在;利于教学,对语文的教与学给予充分关注。     

The Importance of Multiple Representations of Mathematical Problems: Evidence from Chinese Preservice Elementary Teachers’ Analysis of a Learning Goal

This article describes a study of how Chinese preservice teachers unpacked a learning goal pertaining to adding fractions and understanding the concepts underlying the operation. Based on work in the USA by Morris, Hiebert, and Spizter (Journal for Research in Mathematics Education, 40(5), 491–529, 2009), 50 Chinese preservice teachers completed a task, anticipating an ideal student response, in the context of four representations: (1) fraction pieces, (2) graph paper, (3) common denominator algorithm, and (4) pennies. Like the US-based study, this study shows that Chinese preservice teachers’ ability to unpack a learning goal was highly influenced by how the problem was represented. The pennies and graph paper problems provided more supportive contexts for unpacking the learning goal; the algorithm problem provided the least supportive context. The main difference between the preservice teachers from these two countries was the US preservice teachers chose the pennies and graph paper problems as having the most potential for revealing students’ understanding of the learning goal; while the Chinese preservice teachers chose the algorithm problem despite the problem’s unsupportive context. Chinese preservice teachers’ preference suggests that they privileged algorithmic/symbolic representations over pictorial/concrete representations. Based on our results, we argue that it is time for cross-cultural comparative research to refocus on the common barriers, challenges, and benefits as related to mathematics teacher preparation and professional development. A cooperative instead of competitive orientation will lead to richer and deeper dialogues among mathematics educators.