疫情背景下初中数学“线上教学”效度提升的策略研究

在新冠肺炎疫情影响下,教育部提出了“停课不停学”的教学指导方针.如何在疫情防控期间,提升线上教学的效度是各年级各科教师密切关注的问题.本文基于这一现实背景,在结合个人多年初中数学教学经验的基础上,对疫情背景下初中数学开展“线上教学”的必要性、原则及策略展开了详细探讨.     

“求锐角的三角比”类问题的教学设计与策略探索

笔者执教了“求锐角的三角比”初三专项在线复习课,通过优化教学设计,探索此类问题的教学策略,提升课堂教学的实效,进一步发展学生的数学思维品质.     

“以学生为中心、以知识为吸引”的雨课堂线上教学设计

面对新冠疫情的突然袭击,运用现代信息化手段,创造性地开展教学改革.对信息与计算科学专业数学分析课程进行“以学生为中心、以知识为吸引”的雨课堂线上教学设计,包括:“以知识为吸引”的课前预习环节,“以学生为中心”的线上教学直播环节,“学生必做和自选”的课后复习环节,运用雨课堂回放功能进行习题讲解的补充环节,实现对知识熟练掌握和运用的教学目标.实现了疫情期间“停课不停学,保障教学质量”的目的.     

高中数学“翻转课堂”到底要“翻转”什么?

近年来,“翻转课堂”作为一种创新型的教学模式风靡全球,引发了国内外教育教学领域研究者的广泛关注.所谓“翻转课堂(Flipped Classroom或Inve Rted Classroom)”,就是由教师创建视频,学生在家中或课外观看视频中教师的讲解,回到课堂上师生面对面交流和完成作业的这样一种教学形态.简单地说,“翻转课堂”就是“将原本在课上进行的教学活动放在课下,课上的时间则用来解决小组和个人的问题或是讨论、做实验”.“翻     

单元整体视角下的初中数学章起始课教学探究——以“代数式”为例

章起始课是开启整章学习的统领课,为学生明确学习方向,搭建学习框架,指导学习方法,起着“先行组织者”的作用.本文从单元整体的视角阐释章起始课的内涵和价值,以初中数学“代数式”为例,探究如何进行单元整体视角下的章起始课教学,提出教学建议：发挥好章起始课的“吸引力”;把握好章起始课的“内容尺度”;渗透好章起始课中的“数学思想”.     

明确目标 精选例题 高效备考——数列综合复习课的实践与思考北大核心

在我校组织的一次跨省校际高考数学复习研讨会上,笔者以一节“高三数列综合复习课”为载体,就“如何加强高考复习有效性”展开研究,期间经历了教学目标的确定、例题的选择、备课与磨课、教学实践与评课、教学反思与总结等一系列活动．在此过程中,与专家、同行的交流使我获益良多,解决了高考复习教学中的一些困惑与问题.     

基于“一题一课”的初三数学主题复习设计与思考——以“等腰直角三角形手拉手模型”复习为例

本文呈现“等腰直角三角形手拉手模型”主题复习的教学过程,教师立足“一题,一类,一课”的新课标主题活动设计思路和理念,基于一道题,借助变式教学,将一类题“串珠成线”,设计了一节高质量、高效率的初三主题复习课,很好地在主题活动中落实了学科素养.     

概念教学,因自然生长而美好——对《角》一课的教学赏析与感悟

在老子的《道德经》中,“自然”一词意即“万物”,佛教称为“法尔如是”,意即“本来” .现在一般认为“自然”有两重含义,一是指自然界、大自然;另一是口语上的自然、当然、自然而然,它是一种无为而自成、自由发展的境界.数学是自然的,其概念、方法、思想的形成与发展都是自然的,展现出不竭的生命力.因此,数学课堂呼唤自然、有人情味.近期,无锡市金桥双语实验学校开展“同课异构”教学研讨活动,滨湖区教学能手洪高峰老师为大家展示了一堂精彩的七年级概念课《6.2.1角》,笔者有幸聆听、学习这节课,收获颇丰.现呈现本课的一些教学片段,谈一些自己的思考与感受.     

"再创造""发现法"与"启发式"

一位青年教师在学习《数学课程标准》（高中）后向作者提出一个问题：《课标》中为什么不提“启发式”教学了？这个问题促使作者对《课标》中有关教学过程的提法进行思考。作者认为《课标》中有关教学过程的基本理念是“倡导自主探索，动手实践，合作交流，阅读自学等学习数学的方式。使学生的学习过程成为在教师引导下的‘再创造’过程。”（[1]P2）“教师要以鼓励学生发现数学的规律和问题解决的途径，使他们经历知识形成的过程。”（[1]P111）总之，《课标》中提倡的是弗赖登塔尔的“再创造”，“发现法”的教学过程。于是有人就问“再创造”，“发现法”与传统的“启发式”教学有什么异同？下面来探讨一下这个问题。     

数式同性,追求教学的"本心"--以"分式的加减"为例

2020年的一场疫情,让我们的学习有了诸多变化.在此期间,笔者受邀录制“分式的加减”教学微课,供学生网络学习.对于录制的微课,在授课前笔者精心设计、授课后反复思考,其间的收获颇丰,故撰文与读者交流.一、“分式的加减”教学分析“分式的加减”这节课是苏科版教材八年级下册第十章“分式”的第三节“分式的加减”的内容分式是代数式的重要组成部分.     

《高等代数》“线上教学”随笔

本文回顾了疫情期间《高等代数》课程“线上教学”的教学过程,具体剖析了“教师指导下的学生自主学习与教师线上直播课相结合的教学方法”的环节和要素,总结了提高各环节的效率和实现各环节、各要素间完美对接的经验,并提出了适用于常态性教学的“线下课堂教学与线上教学相结合”的教学改革探索新方向.     

Periodic stopping games

Stopping games (without simultaneous stopping) are sequential games in which at every stage one of the players is chosen, who decides whether to continue the interaction or stop it, whereby a terminal payoff vector is obtained. Periodic stopping games are stopping games in which both of the processes that define it, the payoff process as well as the process by which players are chosen, are periodic and do not depend on the past choices. We prove that every periodic stopping game without simultaneous stopping, has either periodic subgame perfect ϵ-equilibrium or a subgame perfect 0-equilibrium in pure strategies. This work is part of the master thesis of the author done under the supervision of Prof. Eilon Solan. I am thankful to Prof. Solan for his inspiring guidance. I also thank two anonymous referees of the International Journal of Game Theory for their comments.     

Teaching mathematics using Steplets

This article evaluates online mathematical content used for teaching mathematics in engineering classes and in distance education for teacher training students. In the EU projects Xmath and dMath online computer algebra modules (Steplets) for undergraduate students assembled in the Xmath eBook have been designed. Two questionnaires, a compulsory student project and teaching in front of class show that using Steplets turn mathematics teaching from drill to understanding. The Steplets use algorithms developed for the Mathematica programming language.     

基于模糊理论的教师教学质量评价的研究

为克服课堂教学质量评价工作中的主观随意性,根据不同课程类型及全员、全方位评教的原则设计了评价教师教学质量的指标.由模糊层次分析法(FAHP)确立了评价指标权重,建立了教师教学质量的模糊综合评价的数学模型.系统试用结果表明,该模型能科学、客观、公正、准确地定出被评价者的教学质量优劣.同时,开发了教师教学质量的网上模糊评价系统.     

The design of tasks that address applications to teaching secondary mathematics for use in undergraduate mathematics courses

This paper describes theoretical design principles emerging from the development of tasks for standard undergraduate mathematics courses that address applications to teaching secondary mathematics. While researchers recognize that mathematical knowledge for teaching is a form of applied mathematics, applications to teaching remain largely absent from curriculum resources for courses for mathematics majors. We developed various materials that contain applications to teaching that have been integrated into four standard undergraduate mathematics courses. Three primary principles influenced the design of the tasks that prepare future teachers to learn and apply mathematics in a manner central to their future work. Additionally, this paper provides guidance for instructors desiring to develop or implement similar applications. The process of developing these tasks underscores the importance of key features regarding the roles of human beings in the tasks, the intentional focus on advanced content connected to school mathematics, and the integration of active engagement strategies.     

Martingale convergence and the stopped branching random walk

We discuss the construction of stopping lines in the branching random walk and thus the existence of a class of supermartingales indexed by sequences of stopping lines. Applying a method of Lyons (1997) and Lyons, Pemantle and Peres (1995) concerning size biased branching trees, we establish a relationship between stopping lines and certain stopping times. Consequently we develop conditions under which these supermartingales are also martingales. Further we prove a generalization of Biggins' Martingale Convergence Theorem, Biggins (1977a) within this context. Received: 21 December 1998 / Revised version: 28 June 1999 / Published online: 7 February 2000     

Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times

In this paper we demonstrate how to develop analytic closed form solutions to optimal multiple stopping time problems arising in the setting in which the value function acts on a compound process that is modified by the actions taken at the stopping times. This class of problem is particularly relevant in insurance and risk management settings and we demonstrate this on an important application domain based on insurance strategies in Operational Risk management for financial institutions. In this area of risk management the most prevalent class of loss process models is the Loss Distribution Approach (LDA) framework which involves modelling annual losses via a compound process. Given an LDA model framework, we consider Operational Risk insurance products that mitigate the risk for such loss processes and may reduce capital requirements. In particular, we consider insurance products that grant the policy holder the right to insure k of its annual Operational losses in a horizon of T years. We consider two insurance product structures and two general model settings, the first are families of relevant LDA loss models that we can obtain closed form optimal stopping rules for under each generic insurance mitigation structure and then secondly classes of LDA models for which we can develop closed form approximations of the optimal stopping rules. In particular, for losses following a compound Poisson process with jump size given by an Inverse-Gaussian distribution and two generic types of insurance mitigation, we are able to derive analytic expressions for the loss process modified by the insurance application, as well as closed form solutions for the optimal multiple stopping rules in discrete time (annually). When the combination of insurance mitigation and jump size distribution does not lead to tractable stopping rules we develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.     

高等数学多媒体课堂教学浅议

从使用多媒体讲授高等数学的经验出发,分析高等数学教学中应用多媒体教学手段的优势,同时给出在多媒体教学条件下进一步提高教学效果的几点建议,指出教师必须用现代化的教学思想为指导,综合运用各种教学手段提高高等数学教学效果,适应现代化教学的发展.     

教师课堂教学质量的对应分析

教师课堂教学质量的优劣,直接影响着学生的学习效果和人才培养的质量,关系到学校的办学水平.科学分析研究教师的课堂教学质量,优化教学过程,实现教师和学生的全面发展,对提高整个高等教育的质量意义重大.以重庆第二师范学院经济与工商管理系为例,运用对应分析方法,分析了不同教师课堂教学的现状和特点,找出了影响课堂教学质量的因素,并针对各个不同类型的教师组提出分类引导,及时改进教学工作,提高课堂教学质量的建议.     

Mobile-phone-based classroom response systems: Students’ perceptions of engagement and learning in a large undergraduate course

Using a Classroom Response System (CRS) has been associated with positive educational outcomes, by fostering student engagement and by allowing immediate feedback to both students and instructors. This study examined a low-cost CRS (VotApedia) in a large first-year class, where students responded to questions using their mobile phones. This study explored whether the use of VotApedia retained the advantages of other CRS, overcame some of the challenges of other CRS, and whether new challenges were introduced by using VotApedia. These issues were studied within three themes: students’ perceptions of using VotApedia; the impact of VotApedia on their engagement; and the impact of VotApedia on their learning. Data were collected from an online survey, focus groups and student feedback on teaching and course content. The results indicated that using VotApedia retains the pedagogical advantages of other CRS, while overcoming some of the challenges presented by using other CRS, without introducing any new challenges.