Teaching probabilities to preschoolers is a very important task as daily decision making is based on probabilities. Although all children are well acquainted with probabilistic terms very few discussions are held in their classrooms because most of the preschool teachers are not prepared to teach probabilities. This study presents a way of teaching probabilities using Internet games and the constructivism theory.
Our approach to teaching statistics to economics students is presented in our 2-volume book. Though written as a textbook for economics students, a broad population who seem to recognize the universalism of the approach is using it. We discuss here the dilemmas encountered in deciding course content and level of mathematical sophistication. The course at Tel Aviv University has undergone several changes, reflecting the changing viewpoints of the "consumer" (Dept. of Economics) and the "supplier" (Dept. of Statistics and OR). Presently, the course is almost as rigorous as the courses offered to statistics majors. Students appreciate the challenges arising in statistical theory, even if they lack sophisticated mathematical reasoning. We illustrate by examples how we teach relatively high-level mathematical concepts in statistical inference, such as maximum likelihood estimation and the Neyman-Pearson Lemma.
Taught modules on sample survey methods provide a useful means of integrating and extending a range of statistical ideas. Knowledge and expertise gained in basic Statistics modules at Levels 1 and 2 can be brought together and applied in sample surveys, and provide the platform for the development and application of more advanced concepts. This paper mainly concerns Level 3 modules in the programme of Statistics learning in the undergraduate degree(s) at The Nottingham Business School, but the principle has been applied elsewhere.
In this work, we describe the elements of meaning related to normal distribution, which appear in a data analysis course based on the use of computers. The course was directed to students in their first year of university studies. We study the elements implemented in a teaching unit for the normal distribution in which computers were introduced as a didactic tool. We pay special attention to the specific meaning conveyed by the use of computers as well as to the meaning attributed by the students throughout the teaching sequence.
Statistics has become an integral part of individuals' formal and everyday lives. Experiences that help learners make sense of statistical information are needed so that they can make informed decisions. The view of statistics as a decision-making tool can be emphasized in project-based environments, where students investigate problems that require formulating questions and collecting, analyzing, and representing data to address these questions. Producing investigations in collaboration with peers and presenting results to classmates require that students articulate the understanding that formed the basis of particular design decisions. We found that decisions in this context can be mitigated by factors (e.g., efficiency and social influences) that circumvent the appropriate application of principles (e.g., sampling) in the discipline or practices established in the classroom (e.g., use of criteria to assess peer projects) even though students understand them.
This paper proposes a first approach with random situations by using a modeling process within the model of Bernoulli's Urn. This way of learning is accessible to 14-15 years old pupils. The software Cabri-géomètre II is used as an empirical computation environment for simulation of the game of "Franc-Carreau", principal activity proposed to pupils in our didactical engineering.
Paradoxes have played an important role in the development of mathematics, as they brought about clarification of basic concepts and the introduction of new approaches. Probability theory offers a large variety of Paradoxes. Some of them are (nowadays) interesting mainly from a historical point of view, as the theory has already been adapted to resolve them. Others actually hide common misconceptions in a very subtle and tricky way. Introducing Paradoxes in class carries potential danger: it may result in a feeling of insecurity when the conflict between the mathematical solution and the intuition (or between two seemingly correct mathematical solutions) seems unresolvable. On the other hand, properly introduced, Paradoxes can play a very useful role in the classroom as they serve as leverage to fruitful discussions, and provoke deeper thinking about the (not always intuitive) probabilistic ideas.
Here is the description of a presentation of probability-statistics science to 10 years old children. This pedagogical experiment is based on a reasoning with images rather than direct simulations and can be divided into 7 parts:<br><br>1. Demonstrating continuity with what they already knew in math.<br>2. Showing with easy graph theory that a drawing can be math.<br>3. Presenting the basis of Boolean algebra thanks to our Boolean Bingo.<br>4. Introducing measurement theory on areas, using generalized Venn diagrams.<br>5. Throwing 3 coins and analysing the results.<br>6. Throwing 2 dice and analysing the results.<br>7. Using their great new ability to win chewing gums, images, sweets, or cookies while playing simple dice or coins games with other children.
Marasinghe, Meeker, Cook, and Shin (1996) used graphical and simulation techniques to construct a system of computer-based modules for teaching statistical concepts. The software component of these modules consisted of a computer program written in LISP-STAT incorporating a highly interactive user interface. The instructional component is set of a prototype lessons providing information to instructors such as a description of concepts that may be illustrated with the program and possible exercises. Since then, the addition of several new modules have enhanced the usefulness of the system. In this paper we illustrate several of these modules useful for teaching concepts as different from how sample size and confidence level affects the width and coverage of confidence intervals to how variability affects precision of experimental results.
In survey research, sub optimal sampling methods or formats of the questions asked can result in biased data, and so in poor results. Teaching this topic is hard because students can only "believe" the teacher and try to understand why and how biases can occur and contaminate the data. This paper introduces a new generic electronic learning environment that gives students hands-on experience with how their methodological choices affect the data. The learning environment consists of three modules. In the population module, the teacher defines a population. In the sampling module, the student can apply different sampling plans. In the survey module, the student can design a questionnaire and actually execute the survey. The resulting data file can be analyzed and compared to the population data. It is concluded that hands-on experience in a problem-based approach can support a deep understanding of several types of sampling errors and response biases.