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.

2002

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.

2007

Various terms in the field of Statistical Inference and their presentation in secondary school text books are examined. A comparison of these terms in secondary school textbooks is carried out against their meanings in everyday use as well as in the mathematical context from two standard university textbooks from the field. We offer evidence that the meanings are not necessarily the same and that in some cases the definition which appears in the secondary school textbook is closer to its everyday use than to its mathematical one. Some implications for school textbook writers are derived. THEORETICAL FRAMEWORK Changes in mathematics secondary school curriculum, including statistics, have taken place in several Western European countries, such The Netherlands and Spain, since the late 70´s. Some statistical concepts which were previously introduced during the early years at the university level are now being taught at the secondary level, i.e. confidence intervals and hypothesis testing based on the normal distribution. Some recommendations have even been made to introduce basic concepts of statistical inference during earlier schooling (NCTM, 2000), but of course without the required sophistication and formalization seen at the university levels. Ample research into the difficulties and obstacles that students encounter when facing statistical inference have also appeared lately. Vallecillos and Batanero (1997) identified difficulties in the learning and understanding of statistical inference in the university context, especially with respect to the concepts of significance levels, parameters, and a statistic, among others, in addition to a general understanding of the logic involved in hypothesis testing. Moreno and Vallecillos (2002), researched the secondary school setting. Their study of 15 and 16 year-old students showed that students had misconceptions about statistical and carried incorrect inferences. They identify Representativeness as the key concept which presents the most difficulty (Kahnemann et al., 1982). Specifically, they point out that Representativeness is characterized by the belief that small samples must reproduce the essential characteristics of the population from which it has been taken. Students also find Hypothesis Testing to be difficult. Vallecillos (1999) indicates that students possess different ideas about exactly what a hypothesis test is. García-Alonso and García-Cruz (2003) carried out a study using a sample of (n=50) students who sat for the University Entrance Examination. They concluded that most students (86%) were unable to completely carry out those problems in the exam which dealt with Statistical Inference, even though these exercises were no different than the typical

Canadian Journal of Science, Mathematics and Technology Education, 2022

This study investigates the support provided using technology for learning the notion of normal distribution in high school students through the implementation of a teaching experiment. A strategy was designed and implemented using Fathom software as the main teaching resource. Data analysis focused on the role of the use of technology in student learning and the simulation process, considering the initial session. The conceptual framework was based on the documentational approach to didactics, whose perspective is to study the teacher’s use and design of resources in his teaching practice. Likewise, the results of the teaching experiment, whose objective was to introduce high school students to the notion of normal distribution by taking advantage of the repeated sampling resource using the Fathom software, are presented. The results show that the collaborative aspect of the lesson study methodology allowed professors to reflect and become aware of how they usually use the resource...

International Journal of Mathematical Education in Science and Technology, 1994

This paper presents a survey of the reported research about students' errors, difficulties and conceptions concerning elementary statistical concepts. Information related to the learning processes is essential to curricular design in this branch of mathematics. In particular, the identification of errors and difficulties which students display is needed in order to organize statistical training programmes and to prepare didactical situations which allow the students to overcome their cognitive obstacles. This paper does not attempt to report on probability concepts, an area which has received much attention, but concentrates on other statistical concepts, which have received little attention hitherto.

1994

This paper presents a survey of the reported research about students' errors, difficulties and conceptions concerning elementary statistical concepts. Information related to the learning processes is essential to curricular design in this branch of mathematics. In particular, the identification of errors and difficulties which students display is needed in order to organize statistical training programmes and to prepare didactical situations which allow the students to overcome their cognitive obstacles. This paper does not attempt to report on probability concepts, an area which has received much attention, but concentrates on other statistical concepts, which have received little attention hitherto.

2006

Data and chance are the two related topics that deal with uncertainty. On the discussions of probability and statistics in both research and instruction, the existing literature depicts an artificial separation, to which other researchers have already called attention in recognition of the inseparable nature of data and chance. Hence, this paper addresses how to integrate the discussions of distributions and probability, starting from the elementary grades. We report on a study that examines fourth-grade students' informal and intuitive conceptions of probability and distribution through a sequence of tasks for developing their understandings about probability distributions. These tasks include various random situations that students explore with a set of physical chance mechanisms and that can be modeled by a binomial probability distribution.

This paper presents a report of people's errors, difficulties and conceptions concerning elementary statistical concepts. Information related to the learning processes is essential to curricular design in this branch of mathematics. In particular, the identification of errors and difficulties which people display is needed in order to organize statistical training programmes and to prepare didactical situations which allow the people to overcome their cognitive obstacles. This paper concentrates on other statistical concepts, which have received little attention hitherto.

stat.auckland.ac.nz

This research focuses on fourth-grade (9-year-old) students' informal and intuitive conceptions of probability and distribution revealed as they worked through a sequence of tasks. These tasks were designed to study students' spontaneous reasoning about distributions in different settings and their understanding of probability of various binomial random events that they explored with a set of physical chance mechanisms. The data were gathered from a pilot study with four students. We analyzed the interplay of reasoning about distribution and understanding of probability. The findings suggest that students' qualitative descriptions of distributions could be developed into the quantification of probabilities through reasoning about data in chance situations.