Elementary statistics laboratory

A "Reverse Order" Elementary Statistics Course

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.

One of the main themes of statistics courses is to teach about variability, as well as location. This is especially important for non-statistics students, who often overlook variability. We consider particularly the problem of comparing variability among k samples (k > 2) that are not necessarily drawn from Gaussian populations. This can also be viewed as testing for homoskedasticity of samples. We examine tools for this problem from the perspective of their suitability for inclusion in elementary statistics courses for students of non-mathematical subjects. The ideas are illustrated by an example that arose in a student project.Supplemental data for this article can be accessed on the publisher's website.

A collaborative, statistics education research project (Lovett, 2001) is discussed. Some results of the project were applied in the computer lab sessions of my elementary statistics course. I detail the process of applying these research results, as well as the use of knowledge surveys. Furthermore, I give general suggestions to teachers who want to put educational research results into effective use in their own classes.

The Statistics Anxiety Rating Scale has 51 items, each scored on a 5-point rating scale to measure statistics anxiety with six subscales, Worth of Statistics, Interpretation Anxiety, Test and Class Anxiety, Computational Self-concept, Fear of Asking for Help, and Fear of Statistics Teachers. Psychometric properties included analyses of construct and concurrent validities an internal consistency and test-retest reliability. 221 college students (74% women; M age=28 yr.) in elementary statistics courses at several southwestern state universities participated. The findings are consistent with previous reports and indicate adequate concurrent validity, internal consistency, and split-half reliability, but for construct validity confirmatory factor analysis yielded marginal support.

This month, we bring you some “Technology Tips” that are related to probability and statistics. We begin with a contribution by Bishnu Naraine and Peiyi Zhao: an exploration that uses The Geometer's Sketchpad to discuss the broken-stick problem, which is also known as the spaghetti problem. This totally geometric solution nicely complements the analytic solution of the same problem, given in “The Spaghetti Problem Problem,” by Dennis Ippolito, which appeared on pages 422–26 of the May 2000 issue of the Mathematics Teacher. Next is a feature by Allen Holmes that discusses obtaining an explicit definition for a recursively defined sequence by using the built-in statistics regression ability of graphing calculators to model the equation of the sequence. Then a short program by John Jose for the TI-83 and TI-83 Plus graphing calculator helps investigate the law of large numbers by simulating the results of a simple two-dice experiment. Finally our “Surfing note” features a Web site that is devoted to statistics. It contains many resources for an elementary statistics course.

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to regression and correlation analysis to increase student understanding of the concepts and methods in elementary statistics courses and in courses at the college algebra/precalculus level that stress ideas on curve fitting techniques.

This study qualitatively investigates the nature of the challenges that a student who is highly successful in mathematics faces in learning college-level elementary statistics. The study draws on the constructs of eagerness, flexibility and willingness to characterize the necessary disposition for critical thinking that is essential in learning statistics. The case study is based on data collected through a survey assessment and a follow-up interview with a mathematics major enrolled in an elementary college statistics course at the time of the study. The qualitative analysis relies on the student's verbal descriptions of the challenges he was experiencing in the course. The findings suggest that while his strong inclination towards inquisitive learning and strong understanding of mathematical concepts supported this student's mathematics learning, the same characteristics might have been causing him difficulties in learning college-level elementary statistics.

The introduction of microtechniques in elementary science courses: I. Blood glucose determination

The introduction of microtechniques in elementary science courses: II. Serum cholesterol and cholesterol ester determination

Students in many elementary science courses are taught a little neurophysiology. This may be the only knowledge of working neurones and of the nervous system such students will encounter as their education progresses in social science and humanities. In teaching the spinal motoneurone as a model nerve cell and the frog myoneural junction as a model synapse we offer such students an overly simplistic and misleading view of functioning nerves. This picture leads to a stimulus-response or Pavlovian mechanistic view of behavior, even of human behavior. A better teaching method, beginning with a description of an endogenously active neurone is suggested. Such neurones are commonly encountered in all animals. In vertebrates endogenously active cells give rise to the electroencephalogram, a phenomenon clinically associated with a functioning central nervous system. Somewhat more elaborate views of synapses based on electron micrographs, patch clamping studies of channels and studies of calcium flux at endings is recommended even for elementary students. Nerve endings which contain and release more than one transmitter should be offered as a physiological example of how the brain works. Only thus can the flexible behavior of both the nerve cells and the organism they contain be understood. Development of nerve cells and their migration and possible destiny should be discussed, particularly for the student for whom this may be a last course in biological science. An appreciation of the process and timing of the development of the human nervous system may help such students in later life in making personal and political decisions about human reproduction.

This study reports on the measured change in the attitude of students toward teaching science as a result of their experiences in an elementary activity-based science course for preservice elementary teachers. Overall, the students in this study showed a positive shift in attitude as measured by the Revised Science Attitude Scale instrument that was administered at the beginning and the end of the semester. When the researchers looked at specific subscales within the instrument, one of the four subscales did not show a statistically significant change in attitude. The course is required for all elementary preservice teachers.

In conventional classroom driven instructor training, disabled student achieved low personality & motivation, more mental load due to lack of practical learning and unsuitable usage of learning material through different simulated contexts. Therefore, intent of proposed study is to integrate microworld game-based learning to different learning styles of special needs students which enhance their learning performance and encourage them to discover and solve problems they faced during classroom teaching. A quasi experimental design was implemented in the proposed SmartLearn system in natural science behavioral course to examine the effectiveness of the proposed approach. The experimental results showed that students who adopted microworld gaming-based system was able to reduce their cognitive load, enhance learning motivation skills to gain understanding on novel concepts, improve personality to foster interpersonal skills, self-efficacy and improvements in learning achievements in comparison to the conventional learning technology driven approach. The findings of this study provide good evidence for special needs children where association of practically applied learning scenarios with gaming contexts improve their performance which encourages development of such systems for learners suffered from Autism, Dyslexia, Dysgraphia. Alzheimer etc.

Since the entrance of the graduates of technical high schools to engineering programs is hindered, in application, the graduates of general or science high schools only are accepted to engineering education. For these students, four years are not sufficient to teach the basic and the related application courses of the profession. Looking at the existing curriculum of mechanical engineering, it can be seen that in the 1st Year, the physics and chemistry courses repeat the content of the ones given in high school education. The current approach considers the students as they come to university with inadequate and incomplete knowledge and therefore not ready to follow the engineering science courses. This approach underestimates and denies the high school education contrary to the main objective of its curriculum. The main objective of high schools (secondary schools) is expressed in the Laws and Regulations with such a statement: “General high schools do not prepare students for a specific profession but rather for higher education”. Today, the existing curriculum of Mechanical Engineering is to be renewed by some new science and application courses to satisfy the demands of labor market. However, the total course credit limit prevents such a renewal. In the face of this dilemma, the answer to this question becomes important: Should the university really repeat high school physics and chemistry? In science high schools and in science branch of general high schools the science and mathematics courses have the major importance. The students are well educated on physics, chemistry, biology and mathematics. They are provided with the necessary science and mathematics background that is required in engineering education. Although only the well-educated graduates of science and general high schools are admitted to engineering programs and the students are already ready to follow the engineering science courses thanks to their high school background, unfortunately in some universities (in Turkey in all) science courses part of engineering curricula is filled by physics and chemistry courses with the same content of the ones taught in high school.

In this project, a method that had been developed using a single setup was employed to correctly measure the tilt of the Earth’s axis on 21 June 2015. The method is an easily comprehensible and applicable technique that can be used in elementary science and astronomy courses and understood by students of every age group.