Mathematics Teaching in Italy: A Cross-Cultural Video Analysis

This study investigates the cultural nature of teaching. It compares a sample of 39 videotaped Italian mathematics lessons to German, Japanese, and U.S. lessons videotaped in TIMSS. This study expands on earlier work that was based on a smaller sample; analysis is also extended to the nature of the mathematical content presented. The results confirm the existence of an Italian cultural pattern for mathematics teaching, whose features we outline here. Italian teachers prefer whole-class instruction to individual seatwork; they engage in teacher talk/demonstration to transmit information; and they often call on students to solve problems at the board before the rest of the class. Italian lessons are characterized by the inclusion of a large number of mathematical principles and properties. These are explained 50% of the time, and simply stated the rest of the time. This study adds yet another perspective from which mathematics teaching can be studied, and, by acknowledging the difficulty to change cultural practices, it offers practical implications for teacher learning.     

从一道数学竞赛题谈起

第四届 ( 1 992年 )北京市大学生数学竞赛 (非数学专业 )有这样一道试题 :若函数 f ( x)对一切 u≠ v均有f( u) - f( v)u- v =αf′( u) + βf′( v) , ( 1 )其中 α,β>0且 α+ β=1 ,试求 f( x)的表达式 .本题有多种解法 ,现介绍两种不同于 [1 ]的解法 .解法一　 1°若 f′( x)≡ k( k为常数 ) ,则 f( x)为一次函数 ,问题已经解决 .2°若 f′( x)不恒为常数 ,则至少存在两点 x1与 x2 使 f′( x1)≠ f′( x2 ) ,在 ( 1 )式中分别令 u=x1,v=x2 及 u=x2 ,v=x1,可得f ( x1) - f ( x2 )x1- x2=αf′( x1) + βf′( x2 ) , ( 2 )f ( x2 ) - f ( …     

Factors Associated With Mathematics Achievement and Participation in Advanced Mathematics Courses: An Examination of Gender Differences From an International Perspective

This paper reports results of an exploratory study examining factors that might be associated with achievement in mathematics and participation in advanced mathematics courses in Canada, Norway, and the United States of America (USA). These factors, which were not directly related to schooling accounted for large degrees of variability, 24% to 39%, in mathematics achievement scores. Confidence in mathematics was the strongest predictor of achievement for students from Canada and Norway, whereas for the students from the USA, parents' highest education level was the highest predictor of achievement. Student home environment related variables were stronger predictors of achievement for females than for males in all three countries. The participation in advanced mathematics courses could be predicted with 72% to 76% accuracy by the same variables. In all of the three countries, the strongest predictors of participation in advanced mathematics courses were students' attitudes toward mathematics. Parents' education level, a socioeconomic related variable, was one of the strongest predictors of participation for Canadian female students and all students from the USA.     

Subtraction From a Historical Perspective

The algorithms used for subtraction vary. In the United States, three different algorithms were used almost equally until the 1940s: the equal additions, the decomposition, and the Austrian method. After William Brownell modified the decomposition algorithm, the use of other algorithms was practically eliminated in mathematics textbooks. Today, some texts introduce the equal additions algorithm, but the decomposition is still the predominant algorithm. This article reviews the historical use of each of the three algorithms in the United States, discusses the modification to the decomposition algorithm, and gives a brief overview of the current status of subtraction algorithms.     

浅谈高等数学习题课教学

探讨习题课教学应注意的问题．首先明确指出习题课的目的和意义,之后从重视对数学概念的理解运用、习题的选择、课堂互动等方面阐述如何提高课堂教学效率,以达到不断渗透数学思想、数学方法的目的,从而培养学生良好的思维品质．     

Teachers’ Activities in Technology-Based Mathematics Lessons

This paper focuses on high school mathematics teachers and what they do when they use digital technology in their lessons. It is essentially a discursive paper but it uses data from a project on teachers using technology to illustrate points. The main aim of the paper is to present an holistic account of factors influencing teachers’ practice. A secondary aim is to present the integration of technology into lessons as a complex issue. Saxe’s four parameter model of goal-linked practice is employed to show how different dimensions of teachers’ activities interrelate in this complex undertaking. The paper ends with a consideration of approaches related to Saxe’s model.     

Collegical Entrepreneurialism In Proactive Universities: Lessons From Europe

Abstract

Twenty years ago, when Change published the first survey on leadership in higher education, Clark Kerr was identified as the single most influential voice in higher education. He has remained a precise, creative thinker and writer on intellectual issues, on leadership, and otherwise. Virtually everyone who serves as a leader in higher education today owes something to Clark Kerr, to what he did and what he wrote. It was not only that he was ever on the cutting edge, that he fought the good fight in so many critical battles; unlike most other university presidents, he had the skill, the energy, and the desire to articulate what he was doing and reflect upon what it meant.

Clark Kerr lives the life of leadership. He took the risks, he fought good fights, he made mistakes (by his own admission), and writes about what he learned from them and would have done differently. It is with his words that we start this issue of Change, focused as it is on leadership. In our search for leadership, we've turned first to Clark Kerr to state its challenges.     

刍议大学数学教学活动的问题与对策

当前各高校的大学数学教学或多或少存在一些不协调的地方,如理科类学生课程深度过大,文科类学生数学能力弱,考核试卷的难度控制不好等等.针对大学数学的教学法及大众化教育的分析研究,结合教学实践,提出大学数学教学改革的一些对策.