Two-Year College Mathematics Journal最新文献

Additional Perspectives on Fractals 关于分形的其他观点

Two-Year College Mathematics Journal Pub Date : 2018-01-30 DOI: 10.2307/2686515

B. Mandelbrot

引用次数: 0

Computers and Calculators 电脑及计算器

Two-Year College Mathematics Journal Pub Date : 2018-01-30 DOI: 10.1090/spec/024/04

S. Gordon

引用次数: 0

What Makes Mathematics Lessons Easy to Follow, Understand, and Remember?. 是什么让数学课容易跟随、理解和记忆?

Two-Year College Mathematics Journal Pub Date : 1983-11-01 DOI: 10.2307/3026762

Nira Hativa

{"title":"What Makes Mathematics Lessons Easy to Follow, Understand, and Remember?.","authors":"Nira Hativa","doi":"10.2307/3026762","DOIUrl":"https://doi.org/10.2307/3026762","url":null,"abstract":"As a mathematics teacher at the high-school and college level for many years, I was always intrigued with the question of what makes an effective mathematics teacher. Thus, when I was to decide upon a topic for dissertation research in the domain of mathematics education, I chose to concentrate on a major component of teacher effectiveness: on lesson organization and clarity. A well-organized and clear presentation was defined in that study as a presentation that is easy to follow, understand, and remember. The following is a short description of the method and some findings of that study. The study was conducted at Stanford University. During the three quarters of the academic year 1978-1979, I visited all 49 sections of a five-course sequence of calculus and analytic geometry taught by 38 teaching assistants. A questionnaire was administered in each class asking students to rate their teacher on lesson organization and clarity. All scores per teacher were averaged. Five teachers who rated very high and four teachers who rated very low were chosen to form two groups for the study. Two lessons of each of these nine teachers were tape-recorded and transcribed. After analyzing the transcripts, about fifty teaching techniques were identified as contributing to lesson organization and clarity. These teaching techniques were sorted into three groups (not mutually exclusive), reflecting their contribution to making the presentation easy to follow, understand, or remember. Some strategies that belong to more than one group are listed under the group to which they are considered to contribute the most. Table 1 lists the teaching strategies as sorted into the three groups. Thirty-nine teaching strategies which were related to teacher discourse were chosen to be scored for each transcribed lesson. Analyzing these scores, it was found that on 18 of these techniques, the differences between the two groups of teachers-those rated low and those rated high by their students-were statistically significant. These variables are also recorded in Table 1. In a second analysis, several single variables that seemed to be closely related were combined into groups. In addition all variables belonging to the same major category were combined. Then, the differences between the two groups of teachers on these combined variables were examined. Results are summarized in Table 2.","PeriodicalId":448750,"journal":{"name":"Two-Year College Mathematics Journal","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1983-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115764902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 14

A Tiling of the Plane with Triangles 用三角形平铺平面

Two-Year College Mathematics Journal Pub Date : 1983-11-01 DOI: 10.2307/3026759

P. Mielke

引用次数: 0

Another Way to Introduce Natural Logarithms and e. 另一种引入自然对数和e的方法。

Two-Year College Mathematics Journal Pub Date : 1983-11-01 DOI: 10.2307/3026767

R. Christian

引用次数: 0

Computer Simulations to Clarify Key Ideas of Statistics. 计算机模拟澄清统计的关键思想。

Two-Year College Mathematics Journal Pub Date : 1983-11-01 DOI: 10.2307/3026765

T. Kersten

{"title":"Computer Simulations to Clarify Key Ideas of Statistics.","authors":"T. Kersten","doi":"10.2307/3026765","DOIUrl":"https://doi.org/10.2307/3026765","url":null,"abstract":"Hand calculators have come into common use for performing calculations in high school and undergraduate courses in elementary statistics. Computers have also been used to do standard statistical computations and tests. However, computers can be used in elementary statistics courses not only to do standard statistical tests, but to perform simulations which clarify concepts and theorems of statistics. These simulations allow the nonmathematically oriented student in elementary statistics to have inductive experiences with statistical concepts in a time-efficient manner. A basic concept in statistics is that of a sample distribution. The sampling distribution of a sample statistic is defined to be the theoretical probability distribution of values for that sample statistic obtained from all possible samples of a certain fixed size from the population. Typically elementary texts illustrate this concept by using a very small finite population which has a small number of possible samples of a given size. Although large or infinite populations are of interest since they have a large or infinite number of samples of a certain size it is difficult to develop a sample distribution. Computer simulation, however, makes this easy to explore. The computer can simulate taking many samples of a certain size from a population. By taking many samples the law of large numbers guarantees that the observed frequency distribution of the sample statistic is close to the theoretical sample distribution. The sample distribution of the mean is the most important sample distribution. The computer simulations in Figure 1 explore a sample distribution of the mean. These simulations employ an elementary statistical package called MINITAB developed at Pennsylvania State University. The MINITAB command URANDOM simulates random observations from a population where numbers between 0 and 1 all have an equal probability of occurring. The first simulation consists of drawing 200 samples of size 2 and computing the means of the samples. A histogram of the results is given. Continuing with samples of size 2, drawing 750 samples is simulated and then 1500 samples. As the number of samples increases the student can see the isosceles triangle-shaped theoretical sample distribution emerging. Note that, because of the small sample size and the nonnormal population, the sample distribution should not be expected to be normal.","PeriodicalId":448750,"journal":{"name":"Two-Year College Mathematics Journal","volume":"165 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1983-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115754022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 9

Ellipses From a Circular and Spherical Point of View 从圆形和球形的角度看椭圆

Two-Year College Mathematics Journal Pub Date : 1983-11-01 DOI: 10.2307/3026771

Alden R. Partridge

引用次数: 4

Integrating Writing into the Mathematics Curriculum 将写作融入数学课程

Two-Year College Mathematics Journal Pub Date : 1983-11-01 DOI: 10.2307/3026766

Dorothy Goldberg

引用次数: 11

The Address Problem 地址问题

Two-Year College Mathematics Journal Pub Date : 1983-11-01 DOI: 10.2307/3026763

Michael Tennor

引用次数: 0

Antisubmarine Warfare: Passive vs. Active Sonar 反潜战:被动声呐与主动声呐

Two-Year College Mathematics Journal Pub Date : 1983-11-01 DOI: 10.2307/3026770

L. Whitt, K. Wilk, D. H. Wagner

引用次数: 2