A Tale of Two More Metaphors: Storylines About Mathematics Education in Canadian National Media

In this companion piece to the article “A Tale of Two Metaphors: Storylines About Mathematics Education in Canadian National Media” (this issue), we further explore constructed meanings through the use of positioning theory. In our examination of 71 articles in the two Canadian national newspapers (The Globe and Mail and The National Post), we focus primarily on communication acts and further our investigation into storylines and positionings concerned with mathematics education. Elaborating on aspects of two more metaphors, those of war and competition, we highlight the production of dichotomies and the shared aspect of taking sides. An investigation of the ramifications and effects that are brought to the fore in the articles we examined involves two general themes: the purpose of education and the point of mathematics education itself. We draw on David Labaree's framework identifying social efficiency and social mobility as different patterns of educational goals and highlight its parallels with the storylines in the articles we examined. The messages of the storylines feed the continued production of culturally shared narratives surrounding the purposes of mathematics education and education in general.     

Encouraging Citizenship in Science Education: Continuing Questions and Hopeful Possibilities

Abstract

This special issue of the Canadian Journal of Science, Mathematics and Technology Education invokes questions intended to further the discourse of citizenship in science and mathematics education, such as, How do we define citizen and democracy? Is our call for student action hypocritical? Does positioning school science through the work of Rancière present a “straw man” argument for change? To what extent does the ghost of John Dewey animate and inform a “wild pedagogy” in science education? Challenging the view of the science and mathematics curriculum as a barrier to overcome, this article argues that possibilities for developing citizenship and critical thinking can be found and developed in existing curriculum formations and practices of school science and mathematics education.     

Getting the whole story: an experience report on analyzing data elicited using the war stories procedure

When analyzing data elicited using the ??war stories?? technique, previously introduced by Lutters and Seaman (Inf Softw Technol 49(6):576?C587, 2007), we encountered unexpected challenges in applying standard qualitative analysis techniques. After reviewing the literature on stories and storytelling, we realized that a richer analysis would be possible if we accorded more respect to the data??s structure and nature as stories, rather than treating our participants?? utterances simply as textual data. We report on five lessons learned regarding how we can better analyze war stories as stories: 1) war stories tend to be about exceptional situations; 2) war stories tend to be diverse and resistant to being combined into a single grand narrative; 3) the humanities can be a valuable resource for analyzing war stories; 4) war stories are not just text, they are also performances; and 5) war stories are not just data, they are also instructive and evocative.     

Postsecondary Student Perceptions of Received Mathematical Proofs

Abstract: This article reports on a study investigating how postsecondary students interact with mathematical proofs with a focus on how they go about unpacking a “received proof,” how they make meaning from what they are given, and whether they believe that mathematical meaning can be drawn from such proofs. Case studies were conducted with seven non-mathematics majors of varying mathematical competence. Data sources included semistructured interviews aimed at exploring their knowledge, beliefs, and learning approach regarding received mathematical proofs. This included engaging them in “proof mapping.” The findings discussed here are based on two of the participants who had seen some basic mathematics proofs and their beliefs about received proofs. The study shows that though both students displayed a respect for proofs, their beliefs indicated that they had not received or understood their importance in mathematics education. Moreover, they believed that their efforts to engage with received proofs are largely self-created, based on modeling classroom discussions. Implications are discussed for teaching through received proofs.     

The big data of violent events: algorithms for association analysis using spatio-temporal storytelling

This paper proposes three methods of association analysis that address two challenges of Big Data: capturing relatedness among real-world events in high data volumes, and modeling similar events that are described disparately under high data variability. The proposed methods take as input a set of geotemporally-encoded text streams about violent events called “storylines”. These storylines are associated for two purposes: to investigate if an event could occur again, and to measure influence, i.e., how one event could help explain the occurrence of another. The first proposed method, Distance-based Bayesian Inference, uses spatial distance to relate similar events that are described differently, addressing the challenge of high variability. The second and third methods, Spatial Association Index and Spatio-logical Inference, measure the influence of storylines in different locations, dealing with the high-volume challenge. Extensive experiments on social unrest in Mexico and wars in the Middle East showed that these methods can achieve precision and recall as high as 80 % in retrieval tasks that use both keywords and geospatial information as search criteria. In addition, the experiments demonstrated high effectiveness in uncovering real-world storylines for exploratory analysis.     

Rethinking Technology-Enhanced Physics Teacher Education: From Theory to Practice

This article discusses how modern technology, such as electronic response systems, PeerWise system, data collection and analysis tools, computer simulations, and modeling software can be used in physics methods courses to promote teacher-candidates' professional competencies and their positive attitudes about mathematics and science education. We show how modeling technology-enhanced deliberate pedagogical thinking in physics methods courses can improve teacher-candidates' subject-specific pedagogical knowledge and their positive attitudes about science learning. We also discuss potential challenges that must be addressed in order to help teacher-candidates successfully implement these pedagogies during the practicum and in their early years of teaching.     

Visualizations for Mathematics Courses Based on a Computer Algebra System

This paper discusses the introduction of a computer-algebra system to perform visualizations in mathematics education.With theIllustrated Mathematicsproject, we provide a comprehensive collection of graphics and animations for various topics in mathematics, which can directly be used for teaching. Because the programs (written inMathematica) we used for the creation of this collection are included, it is easy to design new examples by modifying parameters in existing examples. Therefore,Illustrated Mathematicscan be used as a first step of the introduction of a computer-algebra system in mathematics education.In the second part, we report on the development of a workbench and learning environment, with which the students can discover the mathematical concepts by themselves. For that, the given examples have to be didactically enriched and processed. By creating their own visualizations of increasing complexity, the students improve their knowledge about the underlying computer-algebra system.     

基于Apriori 数据挖掘算法的应用与实践

精准教育从诞生之初就受限于技术发展缓慢,随着信息技术的大力发展,教学管理系统,学生自主学习APP系统,基于微信学习平台的广泛应用,促使数学课程教育方面数据快速增长,使得学生的学习的行为,过程,状态,练习结果,成绩等成为可以被信息技术自动抓取的数据存在,这样使得获取精准教学的测量数据更为便捷和有效。首先分析了数学课程教学活动中存在的问题,然后对信息化教学模型构建进行了分析。以大数据中Apriori算法为主要思想,设计了基于学生数学学习效果提示和老师教学效果预测功能的数据挖掘系统,实现了对可能学习效果不理想的学生和可能教学方向不精准的老师的及早提示,同时可避免学生教师过度重复已掌握很好的知识,精准定位每位学生薄弱环节并加以改进,既可减轻师生负担,又可提高教学效果。     

Virtual learning environments as sociomaterial agents in the network of teaching practice

This article presents findings related to the sociomaterial agency of educators and their practice in Norwegian education. Using actor-network theory, we ask how Virtual Learning Environments (VLEs) negotiate the agency of educators and how they shape their teaching practice. Since the same kinds of VLE tools have been widely implemented throughout Norwegian education, it is interesting to study how practices are formed in different parts of the educational system. This research is therefore designed as a case study of two different teaching contexts representing lecturers from a higher education institution and teachers from primary schools. Data are collected by means of interviews, online logging of VLE activities and self-reported personal logs. From the analysis of the data, three main networks of aligned interests can be identified. In each of those, the sociomaterial agency of the teaching practice with VLE is crucial in shaping and consolidating the network.     

Explanations in Mathematics Classrooms: A Discourse Analysis

Abstract

This article focuses on student explanations as a discourse practice central to mathematics teaching and learning. I discuss classrooms as hybrid discourse spaces and focus on how talk is used to accomplish social action. In doing so, I contrast several different social and sociomathematical norms for explanation and suggest that students’ choices of discourse practices position them within the classroom. Further, I caution educators against assuming that complete and detailed explanations are always best to support student learning. I discuss how explanations that are coconstructed by several students can actually support joint engagement in mathematical work and help peers stay “on the same page” while avoiding hierarchical positioning.     

The joy of formula manipulation

In mathematical circles, there is the overall opinion that formulae, in their capacity of syntactic units, are dead things, and that formula manipulation tears the heart out of mathematics. In these circles, formulae largely live by virtue of what they stand for, of what they mean, of how they feel and appeal to our intuition—our(?) intuition? And their meanings then tell which formulae to consider next. Poor Leibniz, poor Lagrange, poor Boole, poor Hilbert, and all others who shifted their attention towards uninterpreted formulae manipulation: they were all wrong, weren't they? Oh, and poor we, Edsger W. Dijkstra and all those programmers who converted themselves to formulae manipulators, because their profession demanded it. (This cultural gap in doing mathematics was once expressed quite aptly by Dijkstra when he remarked, “Ik hou van wiskunde, maar spaar me de mathematen”. [“I love mathematics, but it's the mathematicians I cannot stand”.])Well, our profession of programming demanded a conscious and active engagement in formula manipulation and therefore we entered that field of endeavour; and we learned how mighty and powerful, how prosperous and effective, and how indicative of designing this change in attitude turned out to be, not only for the benefit of programming, but for vast parts of mathematics as well. And moreover, we learned to enjoy the activity.In this note we try to convey the effectiveness and joy of formula manipulation through a small number of simple examples from both mathematics and programming.     

"问题解决"在计算机专业课教学中的应用

"问题解决"是数学教育教学中的一种较为先进的教学思想、教学手段和教学艺术.笔者在多年的计算机专业课的教学中,一直在探索适合计算机专业课特点且具有特色的教学方法、教学模式、教学思想.笔者认为既然计算机技术可以为其他学科课程教学服务,那么也可以借鉴其他学科课程教学中好的教学方法、教学模式、教学思想,为计算机专业课程教学服务,解决计算机专业课程教学中难题.笔者通过教学实践发现,借助于在数学教育教学中较为成功的、相对较为成熟的"问题解决"教学思想和教学手段应用于计算机专业课程的教学,并与计算机专业课程自身特点相结合,在教学中可以达到较好的效果,对计算机专业课程的教学优化起到很好的促进作用.     

“I Fall Asleep in Class … But Physics Is Fascinating”: The Use of Large-Scale Longitudinal Data to Explore the Educational Experiences of Aspiring Girls in Mathematics and Physics

This article explores how students' aspirations to study mathematics or physics in post-16 education are associated with their perceptions of their education, their motivations, and the support they feel they received. The analysis is based on the responses of around 10,000 students in England in Year 8 (age 12–13) and then in Year 10 (age 14–15). The students were first surveyed during 2008–2009 and then followed up in 2010–2011. t-tests revealed a decline in their perceptions of their mathematics and physics education. Factor analyses indicated subject-specific constructs that were associated with gender aspiration groups (i.e., high-aspiring girls, high-aspiring boys, low-aspiring girls, low-aspiring boys). High-aspiring girls were more likely than low-aspiring boys to be positive about mathematics/physics education, motivation in these subjects, and support received. However, high-aspiring girls were less likely than high-aspiring boys to be encouraged by their teachers and families to continue with these subjects post-16 and had lower self-concepts, intrinsic valuations, and perceptions of lessons. Low-aspiring girls reported the least favorable views of their mathematics/physics education of all four gender aspiration groups. Findings were generally similar for mathematics and physics, although students overall responded more favorably to mathematics than to physics. The quantitative findings are illustrated with extracts from longitudinal interviews (ages 15, 16, and 17) of two high-aspiring girls.     

Casting shadows in the science classroom

Abstract

Research in mathematics and science education frequently directs one's attention to the limited content knowledge of elementary pre‐service teachers. It is believed, however, that research of this nature leads to a deficit approach to understanding more about the teaching and learning of these subjects. In addition to focusing on the knowers of school mathematics and science, there is a call to acknowledge the problematic nature of knowing (in) mathematics and science. In this paper, the metaphor of shadows is used in a critical exploration of what it means to know and how the cultures of classrooms have shaped these images of knowing. Through the voices of pre‐service teachers, this paper directs one's attention to objects that cast shadows on the learning and knowing of mathematics and science. Three such shadow‐casting objects discussed in this paper are textbooks, teachers, and gendered ideology. The paper seeks to critically illuminate the problematic nature of what it means to know (in) mathematics and science by examining the shadowy texture of unquestioned ideologies.     

3D数学教学平台在立体几何图形探究与学习中的有效应用

现代信息技术的应用对教育教学手段的变革产生深刻影响,数字化学科工具的使用为教育教学注入了新得活力,熟练将各种信息技术辅助工具应用于教育教学成为信息时代每一个教师都应该具备的技能。本文从3D数学教学平台自身的功能特点,立体几何图形教学中的难点分析入手,结合3D数学教学平台在立体几何图形教学中的应用案例进行论述,使读者对3D数学教学平台及其在立体几何图形中的应用有一个整体认识,并能在本文的引导下将3D数学教学平台应用到自己的教育教学过程中。     

A framework for intelligence analysis using spatio-temporal storytelling

Social media have ushered in alternative modalities to propagate news and developments rapidly. Just as traditional IR matured to modeling storylines from search results, we are now at a point to study how stories organize and evolve in additional mediums such as Twitter, a new frontier for intelligence analysis. This study takes as input news articles as well as social media feeds and extracts and connects entities into interesting storylines not explicitly stated in the underlying data. First, it proposes a novel method of spatio-temporal analysis on induced concept graphs that models storylines propagating through spatial regions in a time sequence. Second, it describes a method to control search space complexity by providing regions of exploration. And third, it describes ConceptRank as a ranking strategy that differentiates strongly-typed connections from weakly-bound ones. Extensive experiments on the Boston Marathon Bombings of April 15, 2013 as well as socio-political and medical events in Latin America, the Middle East, and the United States demonstrate storytelling’s high application potential, showcasing its use in event summarization and association analysis that identifies events before they hit the newswire.     

Exploring the links between pre-service teachers’ beliefs and video-based reflection in wikis

In teacher education, video has been used frequently for the development of competencies for effective teaching. However, few empirical studies have investigated reciprocal relationships between pre-service teachers’ beliefs and video-based reflection activities. The present study investigated the influences of epistemological beliefs about mathematics on video-based reflection in wikis. Elementary school pre-service teachers had carried out reflective writing and questioning activities after watching a video clip about mathematics learning or instruction in wikis for six weeks. This study also explored the relationships between video-based reflection activities and the change of mathematical beliefs for teaching (MBT). Both quantitative and qualitative data were collected to examine the links between beliefs and reflection activities. This study found that epistemological beliefs partially influenced reflective writing and questioning activities in wikis. In addition, video-based reflection activities were beneficial for the beliefs of mathematical knowledge and students. This study also identified a few reflection and question categories that were closely related to the change of MBT. Lastly, implications of this study were discussed in regard to video-based reflection practices in teacher education.     

几何画板在中学数学教学中的应用

多媒体技术的应用为数学教学的更新创造了条件,也给学校教育带来了一场深刻的变革。数学作为一门独立的自然科学,有它自身的特点、体系和规律,而几何画板作为电子尺规,是研究几何图形的关系、动态地观察几何图形运动状态、探索数学信息的有力工具。从几何画板辅助中学数学教学的现状、目标及其意义入手,结合几何画板辅助中学数学教学的实例,就几何画板在中学数学教学中的应用及其在教学活动中的重要作用做了系统地阐述和说明。     

计算机技术在高等数学教学中的应用模式研究

本文旨在探讨计算机技术与传统数学教学的优化整合模式,研究如何充分利用现代教育资源,构思、设计出符合学生认知水平的计算机辅助教学,以达到充分调动学生学习积极性、提高高等数学课教学质量的目的。