Reasoning about Representations: Effects of an Early Math Intervention

ABSTRACT

The outcomes of a longitudinal randomized number sense intervention including pre-, post- and follow-up tests are reported. The intervention was conducted in Grade 0 when children were six years old. Using Concrete-Representational-Abstract principles, a structured explicit 10-week program focusing on numbers and collective reasoning about representations was conducted by the classroom teachers. In addition to their regular mathematics teaching, a trained control group received an equally structured and explicit intervention program but without the critical mathematics component. The children in the experimental group outperformed the children in the control group on number sense growth between the pre- and the post-test. There was also a sustained effect of the intervention nine months later when children were assessed in Grade 1.     

Incommensurability and Multiple Models: Representations of the Structure of Matter in Undergraduate Chemistry Students

The notion of incommensurability has provided a rationality criterion for the development of scientific theories, as well as some insight into theories developed by students while learning science. However, the relationship between the multiple models held by students and incommensurability requires further discussion. We present the results of empirical work that investigated the multiple models of the structure of the matter held by university students and we analyze these results using the notion of incommensurability. We also point out implications in the construction of students’ scientific models as they move forward in their careers.     

A Case Study of Teacher Beliefs on Students' Beliefs about Multiple Representations

The mathematics education community, in its call for reform, underscores the importance of mathematics instruction emphasizing the use of multiple representations in the presentation of concepts. The focus of the study was how teacher beliefs affect their ability to implement a multiple representations curriculum. The novice instructor's attitude remained neutral while the experienced instructor's attitude remained somewhat positive. Of the eight students in the study, six of them showed a more positive attitude towards technology use and multiple representations by the end of the semester. The students increased their calculator use in both classes, particularly in the experienced teacher's class. Implications for further research were that teacher training is essential if reform curricula are to be properly implemented.     

Tracing Young Children's Scientific Reasoning

This paper explores the scientific reasoning of 14 children across their first two years of primary school. Children's view of experimentation, their approach to exploration, and their negotiation of competing knowledge claims, are interpreted in terms of categories of epistemological reasoning. Children's epistemological reasoning is distinguished from their ability to control variables. While individual children differ substantially, they show a relatively steady growth in their reasoning, with some contextual variation. A number of these children are reasoning at a level well in advance of curriculum expectations, and it is argued that current recommended practice in primary science needs to be rethought. The data is used to explore the relationship between reasoning and knowledge, and to argue that the generation and exploration of ideas must be the key driver of scientific activity in the primary school.     

概念设计中的产品建模及功能求解

In this paper, a product model in conceptual design, Domain Structure Template, is proposed, which combines the functional domain and the physical domain with the behaviour domain. Seven types of primary mappings units connecting functions, behaviours and carriers during conceptual design process are identified according to the characteristics of the conceptual design of mechanical products.Based on these seven primary mappings, a hierarchical functional reasoning framework characterizing the process of conceptual design is presented. A case study for the conceptual design of industry sewing machines with chain-stitch is described to demonstrate the product modelling and the scheme generation based on the presented model.     

非言语学习困难青少年空间和非空间关系推理策略分析

目的:探讨非言语学习困难青少年二维空间和非空间关系推理策略。方法:从初中二年级选取三组被试:非言语学习困难组(简称NLD)、言语学习困难组(简称VLD)和一般组(简称C)。结果:(1)NLD组空间关系推理成绩显著低于一般组;(2)在空间关系推理中,两类单模题推理成绩显著高于双模题。在非空间关系推理中,有无关前提的题推理成绩显著高于没有无关前提的题;(3)一般组正确运用模型建构策略显著高于NLD和VLD组。结论:NLD青少年通过建构模型解决空间关系推理,但不能有效运用该策略,非空间关系推理则采用逻辑规则策略。     

The Effect of External Representations on Compare Word Problems: Supporting Mental Model Construction

This study explored the effectiveness of external representations presented together with compare word problems, and whether such effectiveness was moderated by working memory. Participants were 49 secondary school students. Each participant solved 48 problems presented in 4 presentation types that included 2 difficulty treatments (number of steps and language consistency). Data from errors and response times indicated that adding a graph to compare word problems helped accuracy (d =.60) and response time (d =.44). This effect was larger for difficult and cognitively demanding problems. Findings suggest that external representations might help problem-solvers build a mental model of the described problem situation. In addition, working memory was not found to moderate the effectiveness of external representations.     

Reasoning across ontologically distinct levels: Students' understandings of molecular genetics

In this article we apply a novel analytical framework to explore students' difficulties in understanding molecular genetics—a domain that is particularly challenging to learn. Our analytical framework posits that reasoning in molecular genetics entails mapping across ontologically distinct levels—an information level containing the genetic information, and a physical level containing hierarchically organized biophysical entities such as proteins, cells, tissues, etc. This mapping requires an understanding of what the genetic information specifies, and how the physical entities in the system mediate the effects of this information. We therefore examined, through interview and written assessments, 10th grade students' understandings of molecular genetics phenomena to uncover the conceptual obstacles involved in reasoning across these ontologically distinct levels. We found that students' described the genetic instructions as containing information about both the structure and function of biological entities across multiple organization levels; a view that is far less constrained than the scientific understandings of the genetic information. In addition, students were often unaware of the different functions of proteins, their relationship to genes, and the role proteins have in mediating the effects of the genetic information. Students' ideas about genes and proteins hindered their ability to reason across the ontologically distinct levels of genetic phenomena, and to provide causal mechanistic explanations of how the genetic information brings about effects of a physical nature. © 2007 Wiley Periodicals, Inc. J Res Sci Teach 44: 938–959, 2007     

An Inquiry-Based Quantitative Reasoning Course for Business Students

Abstract

Quantitative Reasoning for Business is a two-semester sequence that serves as an alternative to elementary and intermediate algebra for first-year business students with weak mathematical preparation. Students who take the sequence have been retained at a higher rate and demonstrated a larger reduction in math anxiety than those who take the traditional developmental courses. We share the challenges that led to our choices in adopting and modifying inquiry-based instruction in order to serve our population.     

Representations as mediation between purposes as junior secondary science students learn about the human body

The aim of this article is to investigate students’ meaning-making processes of multiple representations during a teaching sequence about the human body in lower secondary school. Two main influences are brought together to accomplish the analysis: on the one hand, theories on signs and representations as scaffoldings for learning and, on the other hand, pragmatist theories on how continuity between the purposes of different inquiry activities can be sustained. Data consist of 10 videotaped and transcribed lessons with 14-year-old students (N?=?26) in Sweden. The analysis focused instances where meaning of representations was negotiated. Findings indicate that continuity is established in multiple ways, for example, as the use of metaphors articulated as an interlanguage expression that enables the students (and the teacher) to maintain the conversation and explain pressing issues in ways that support of the end-in-view of the immediate action. Continuity is also established between every day and scientific registers and between organisation levels as well as between the smaller parts and the whole system.     

以学生为主线的遗传学教学模式构建

遗传学是一门综合性学科,随着高等教育改革的深入,其课程体系和教学内容也不断深化改革。文章阐述了在生物技术、生物科学专业遗传学精品课程建设中的思路和实践,围绕在教学中始终树立“以学生为本”的教学理念,提出了兴趣教学法、利用现代教育技术以及实验教学等方面的改革,探讨了遗传学教学改革的一些新思路和具体实践。     

“三个代表”思想与高校党的建设

高校是中国先进社会生产力的重要源泉 ,是中国先进文化的生产者和推动器 ,与中国最广大人民群众的根本利益息息相关。因此 ,高校党委要把贯彻、落实江泽民同志“三个代表”重要思想作为加强高校党的建设 ,办好高等学校的关键来抓。要紧密结合高校实际 ,着眼大局 ,理解内涵 ,明确定位 ;遵守规范 ,把握导向 ;抓好基础 ,持之以恒 ;勇于校正 ,自觉防范。     

University Education and Deliberation: In Defence of Practical Reasoning

In this article I argue that the use of practical reasoning in university classrooms is necessary to establish conditions under which university teachers and students can move beyond the dominant “transmission mode” of education (teaching and learning). This mode of education had been, and in many cases remains to be prevalent in several (South African) university classrooms. I argue what it could mean for university teachers and students to reason together with one another in classroom practices. Central to reasoning together is the idea of deliberation which provides opportunities for teachers and students to experience “intelligent action” (Biesta 2004a) that could enhance educational problem solving in (and beyond) university classrooms.     

Refutational text and multiple external representations as a method to remediate the misinterpretation of box plots

The ability to interpret graphs is highly important in modern society, but has proven to be a challenge for many people. In this paper, two teaching methods were used to remediate one specific misinterpretation: the area misinterpretation of box plots. First, we used refutational text to explicitly state and invalidate the area misinterpretation of box plots. Second, we used multiple external representations (MERs): Histograms were used as an overlay on box plots in order to give students a better insight in the way box plots represent data distributions. Third, we combined refutational text and MERs. We found that refutational text was successful in improving students’ interpretation of box plots, but that the use of MERs did not improve students’ interpretation of box plots. The addition of MERs also did not increase the effect of refutational text.     

促进深度学习的教学推理:实践逻辑与策略选择

学生的深度学习是以学生的知识理解与运用为价值取向,以培养学生的高阶思维能力和问题解决能力为目标的一种学习。但知识论证不充足、知识点状分布、绝对真理知识观等表层知识教学已偏离了学习的本质及价值,产生了知识教学阻滞深度学习的困局。教学推理是教师根据已知教学条件及个体情境认知,确定问题并生成教学策略的连续性思维活动。它克服了以往僵化的教学方式,为促进深度学习提供可能逻辑。其中,学科知识逻辑能促进学习触及知识的意义世界,学生经验逻辑能促进学习进入学生的心灵世界,实践自为逻辑能促进学习关联自我的生活世界。最后,促进深度学习的教学推理策略应着力于以"批判与交融"为取向的教学理解,形成以"联结与转化"为纽带的教学逻辑,开展以"假设与证据"为核心的课堂论证教学,创设以"推断与评估"为特质的教学情境。     

External Visual Representations in Science Learning: The case of relations among system components

The present paper reports on a study that examined whether practical work can be said to have affective outcomes, and if so in what sense. The term ‘affective’ is used here to refer to the emotions, or feelings, engendered amongst pupils towards school science in general, or one of the sciences in particular. The study is based on 25 multi‐site case studies that employed a condensed fieldwork strategy. Data were collected, using tape‐recorded interviews and observational field notes, in a sample of practical lessons undertaken in English comprehensive (non‐selective) schools during Key Stages 3 and 4 (ages 11–14 years and 15–16 years, respectively). The findings suggest that whilst practical work generates short‐term engagement, it is relatively ineffective in generating motivation to study science post compulsion or longer‐term personal interest in the subject, although it is often claimed to do so. This suggests that those involved with science education need to develop a more realistic understanding of the limitations of practical work in the affective domain.     

多媒体学习的认知体系

本文对主要的认知体系进行了概述,据此可以形成多媒体教学设计的理论基础.这些认知体系包括对记忆存储、记忆编码以及认知操作的描述.与多媒体学习相关的认知体系有Paivio的双重编码理论、Baddeley的工作记忆模型、Engelkamp的多模块理论、Sweller的认知负荷理论、Mayer的多媒体学习理论以及Nathan的动画理论.本文重点讨论传统研究和教学应用之间的交互作用,教学应用主要涉及如何增加回忆率、减少干扰、降低认知负荷以及加强理解等方面.得出的初步结论是:虽然各自有所侧重,不同的理论之间仍有一些共性;这些模型中缺乏对学习者多元编码整合作用的研究;在心理模拟足够的情况下并不需要动画教学;动作必须有意义才能有效果;多模块教学比单个不同的特定模块更加有效.     

The impact of a classroom intervention on grade 10 students' argumentation skills,informal reasoning,and conceptual understanding of science

The literature provides confounding information with regard to questions about whether students in high school can engage in meaningful argumentation about socio‐scientific issues and whether this process improves their conceptual understanding of science. The purpose of this research was to explore the impact of classroom‐based argumentation on high school students' argumentation skills, informal reasoning, and conceptual understanding of genetics. The research was conducted as a case study in one school with an embedded quasi‐experimental design with two Grade 10 classes (n = 46) forming the argumentation group and two Grade 10 classes (n = 46) forming the comparison group. The teacher of the argumentation group participated in professional learning and explicitly taught argumentation skills to the students in his classes during one, 50‐minute lesson and involved them in whole‐class argumentation about socio‐scientific issues in a further two lessons. Data were generated through a detailed, written pre‐ and post‐instruction student survey. The findings showed that the argumentation group, but not the comparison group, improved significantly in the complexity and quality of their arguments and gave more explanations showing rational informal reasoning. Both groups improved significantly in their genetics understanding, but the improvement of the argumentation group was significantly better than the comparison group. The importance of the findings are that after only a short intervention of three lessons, improvements in the structure and complexity of students' arguments, the degree of rational informal reasoning, and students' conceptual understanding of science can occur. © 2010 Wiley Periodicals, Inc. J Res Sci Teach 47: 952–977, 2010