Disruption of the representativeness heuristic: Can we be perturbed into using correct probabilistic reasoning?

Some misconceptions in learning and understanding statistical or probabilistic concepts stem from the use of what is called the representativeness heuristic for solving such problems. Incorrect solutions to problems is the result. This study provided graduate students enrolled in beginning inferential statistics with a series of experiences which seemed to disrupt such faulty logic by having them experience logical inconsistencies. Such direct experimental involvement with applied probability problems was recommended as a means to enhance the use of more appropriate probabilistic reasoning in subsequent statistical or probability problems.     

Teaching probability: a socio‐constructivist perspective

There is a considerable and rich literature on students' misconceptions in probability. However, less attention has been paid to the development of students' probabilistic thinking in the classroom. This paper offers a sequence, grounded in socio‐constructivist perspective for teaching probability.     

Using camels to teach probability and expected value

There is much debate about the place of probability in an introductory statistics course. While students may or may not use probability distributions in their post‐collegiate lives, they will likely be faced with day‐to‐day decisions that require a probabilistic assessment of risk and reward. This paper describes an innovative way to teach students in an introductory statistics course how to reason about probability and expected value through the board game Camel Up. The in‐class activities described here can be scaled to fit the needs and abilities of the students in a wide range of introductory statistics courses at a variety of levels.     

Does the teaching of probability improve probabilistic intuitions?

The paper analyzes the effects of a teaching programme in probability devised for junior high school pupils (grades 5, 6 and 7). It was found that most of the notions were too difficult for the fifth grade pupils. In contrast, about 60–70% of the sixth graders and about 80–90% of the seventh graders were able to understand and use correctly most of the concepts contained in the programme. It was also found that, as an indirect effect the course on probability had a beneficial effect on some intuitively based misconceptions of the subjects, like: the representiveness effect; the positive recency effect; the notion of a lucky choice; the superstitious belief in the possibility of influencing the course of events by some particular behaviour.     

The effects and side-effects of statistics education: Psychology students’ (mis-)conceptions of probability

In three studies we looked at two typical misconceptions of probability: the representativeness heuristic, and the equiprobability bias. The literature on statistics education predicts that some typical errors and biases (e.g., the equiprobability bias) increase with education, whereas others decrease. This is in contrast with reasoning theorists’ prediction who propose that education reduces misconceptions in general. They also predict that students with higher cognitive ability and higher need for cognition are less susceptible to biases. In Experiments 1 and 2 we found that the equiprobability bias increased with statistics education, and it was negatively correlated with students’ cognitive abilities. The representativeness heuristic was mostly unaffected by education, and it was also unrelated to cognitive abilities. In Experiment 3 we demonstrated through an instruction manipulation (by asking participants to think logically vs. rely on their intuitions) that the reason for these differences was that these biases originated in different cognitive processes.     

高校概率统计课程教学方法的研究

长期以来,在高校的概率统计课程教学中,一直存在着教学方法及考试模式等方面的问题。文章通过结合教学实践与理论思考,阐述了概率统计课程教学改革的几点看法,以期对高校概率统计课程的教学工作的完善提供参考。     

The effects of different oral directions as to disposition of results on student ratings of college instruction

A review of the literature is presented with particular reference to design flaws in previous studies of the effect of stated purpose of evaluation upon student ratings of instruction. Special attention in this study is paid to insuring the salience of the manipulated purpose-of-evaluation variable through using different oral instructions given to college students concerning the purposes of course evaluation. Students (N=516) within each of 18 classes were divided randomly into faculty use and administrative use conditions. Data were analyzed using global course and global instructor items as dependent variables on a standard short-form rating instrument. No statistically significant effect of the independent variable on either dependent variable was found. Recommendations regarding the design of this type of investigation are discussed as well as the implications of misconceptions about student ratings held by many college faculty.     

浅谈比较法在概率论教学中的作用

比较法是一种常用的数学思维方法,它能使学生在识同辨异的过程,加深对概念和定理的理解,还有助于发现问题,活跃思维,达到对事物的本质的认识。在概率论教学中,恰当的运用比较法教学,可以帮助学生加深对该课程的理解,并激发他们思考的积极性,从而提高教学质量。     

独立学院概率统计课程教学方法初探

笔者基于教学实践,分析独立学院在数学公共课课程教学中存在的问题,并从独立学院学生的学习特点和目前概率统计课程教学现状入手,探讨独立学院概率统计课程教学内容、方法等方面的教学改革,以期为做好独立学院概率统计课程教学方法改革实践提供一些借鉴。     

ANNOUNCEMENTS

Most college professors want their students to grow personally as well as intellectually. They want their students to become more reflective and self-aware as a result of taking their courses. This goal is typically consistent with, and even serves to advance, the stated missions of the institutions in which they teach. But there is a problem: not only do these "ineffable" objectives seem difficult or impossible to assess within the context of a course, but it is also often unclear how the course itself will help students work toward these objectives. Critical thinking about one's experiences, attitudes, and values goes hand-in-hand with personal growth and development. This essay explores how conventional assignments can be modified and expanded to include such critical thinking and writing vis-a ¤ -vis the main concepts of the course. Also presented are grading rubrics that can serve as formative assessments of the student's abilities in these areas.     

The effects of instruction on college nonmajors' conceptions of respiration and photosynthesis

Students in a college nonscience majors' biology course took tests designed to reveal their conceptions of respiration and photosynthesis before and after course instruction. Even though most students had taken at least a full year of biology, serious misconceptions persisted. Most students gave definitions of respiration, photosynthesis, and food which were markedly different from those generally accepted by biologists. These incorrect definitions were associated with more fundamental misunderstandings about how plants and animals function. Most students could not explain how animal cells use either food or oxygen. They understood plants as vaguely analogous to animals, taking in food through their roots instead of mouths. Previous biology instruction seemed neither to improve student performance on the pretest nor to prepare them to master these conceptions during the course. Course instruction did improve student's understanding, but misconceptions persisted for many students. These results raise fundamental questions about the effectiveness of curriculum and instruction in current high school and college biology courses.     

Overcoming challenges in learning probability vocabulary

Students can struggle to understand and use terms that describe probabilities. Such struggles lead to difficulties comprehending classroom conversations. In this article, we describe some specific misunderstandings a group of students (ages 11–12) held in regard to vocabulary such as certain, likely and unlikely. We discuss our efforts to help the students use such terms appropriately. In particular, we show how engaging students in a game requiring the use of the terms helped them begin to develop their vocabulary more fully. We also explain how a probability ladder visual organizer helped students begin to organize their thinking about the meanings of terms relative to one another.     

Negative Thought Patterns of Undecided Community College Students: Implications for Counselors and Advisors

The purpose of this study was to explore the negative thinking patterns of incoming community college freshmen who were undecided about choosing a major and to suggest an approach for addressing these issues on a community college campus. Sixty community college freshmen attending their freshman orientation (FO) were surveyed using the Career Thoughts Inventory (CTI). Results indicated that the students who participated in the study scored higher on all CTI scales than high school or college students in the normative sample. There were no differences in scores in terms of ages, gender, or ethnicity. These results suggest that community colleges should design programming that can help new students, particularly freshmen; to identify and to address their unconstructive thoughts with the aim of helping these students learn how to manage their anxiety upon entering college. Counselors and advisors should work more collaboratively by shifting from an individual model of delivering services to a more holistic learning approach in order to help students to become more decisive about an educational career path.     

Slow thinking and deep learning: Tversky and Kahneman's taxi cabs

This article is based on classroom application of a problem story constructed by Amos Tversky in the 1970s. His intention was to evaluate human beings' intuitions about statistical inference. The problem was revisited by his colleague, the Nobel Prize winner Daniel Kahneman. The aim of this article is to show how popular science textbooks can serve as a source for rich classroom activity, with a little care in the implementation by teachers. Kahneman describes the problem as ‘standard’ and answers using a fixed point number. I describe how I have encouraged my students to challenge the certainty of this assertion by identifying ambiguities that are left unexplained in the story. This way, I claim to stimulate individuals to indeed move towards Thinking, Fast and Slow, the title of Kahneman's book.     

Providing ability to probability: Reducing cognitive load through worked‐out examples

Undergraduate students tend to struggle with probability in their introductory statistics course. Probability problem solving requires several steps. First, students must make sense of the probability scenario, then determine the appropriate probability rules, and finally, execute the procedures to solve the problem. With no previous exposure to probability, this presents too great a cognitive load for many students. Using worked‐out problems then transitioning to partially worked‐out problems in an introductory statistics course at a large university helped students succeed at solving probability problems. The worked‐out problems included writing prompts to encourage self‐explanation of students' thinking through studying the worked‐out examples. This paper explains the use of these instructional principles and their implementation in an introductory statistics course for non‐STEM majors, resulting in higher student achievement and understanding.     

Understanding probabilistic thinking: The legacy of Efraim Fischbein

The study and analysis of probabilistic thinking, in particular its development in children, is a key element in our attempts to uncover the workings of the human mind and an essential foundation for the development of effective instruction in concepts central to modern models of scientific and social phenomena. This paper honours the contribution of Efraim Fischbein, who died in July 1998, to these endeavours. The first section summarises Fischbein's early work, culminating in his 1975 book The Intuitive Sources of Probabilistic Thinking in Children. The second focusses on three major themes prominent in that book, and elaborated in later work by Fischbein and his colleagues, namely: (a) The role of intuition in mathematical and scientific thinking, (b) The development of probabilistic thinking, and (c) The influence of instruction on that development. In the final section, suggestions are made as to how Fischbein's pioneering work can be built upon, in particular for improving the teaching of probability in schools.This revised version was published online in October 2005 with corrections to the Cover Date.     

高职院校学生自卑心理案例分析

自卑属于性格的一种缺陷,表现为对自己的能力和品质评价过低。自卑心理是高职学生中常见的一种不良心理状态,他们通常表现为自我态度消极、情绪状态不佳、行为方式异常等。自卑心理容易导致学生不思进取、自甘堕落,甚至自毁前程。根据多年的班主任工作经验,结合自卑心理的案例分析,探讨了高职学生自卑心理的成因,提出了帮助学生克服自卑心理,建立自信的有效措施。     

Critical Race Theory Meets the NYPD: An Assessment of Anti-Racist Pedagogy for Police in New York City

This research describes and assesses Critical Race Theory (CRT) pedagogy in a higher education ethnic studies course for police officers. CRT pedagogy aims to help students overcome “color-blind” thinking, which minimizes awareness of racism, by raising their critical understanding of racism and framing it as a pervasive and institutionalized reality that everyone has a responsibility to change. Using the Color Blind Racial Awareness (COBRA) Scale, critical awareness in three cluster areas, white privilege, institutional discrimination, and blatant racism, is measured among those completing the ethnic studies course and a comparison group of officers completing a different college course for police. Conclusions reflect on the impact of the course on students’ awareness of racism, the correlation of identity and awareness of racism, the hypothetical impact of such awareness in policing and possibilities for future research.     

The Interrelation of First-Year College Students’ Critical Thinking Disposition, Perceived Academic Control, and Academic Achievement

While a great deal of research has examined students’ critical thinking skills, less is known about students’ tendencies to use these skills. Specifically, little is known about what factors contribute to students developing a disposition to think critically or what impact this disposition has on college students’ academic achievement. Perceived control, which has been found to be an important factor in college students’ academic success, may be an important factor in developing this disposition. The current longitudinal study examined the reciprocal-effects between critical thinking disposition and perceived academic control, and their comparative influences on academic achievement in 1196 first-year college students. Using a two-wave, two-variable cross-lag structural equation model, a reciprocal-effect was found whereby students’ perceived academic control predicted their subsequent critical thinking disposition, and students’ critical thinking disposition predicted their subsequent perceived academic control. Furthermore, after controlling for high school academic performance, perceived academic control was found to have a stronger impact on students’ GPAs than critical thinking disposition. Implications of fostering a critical thinking disposition and perceived academic control among college students are discussed.