Statistics education is the practice of teaching and learning statistics, along with related scientific research.
Statistics are both a formal science and a practical theory of scientific inquiry, and both aspects are considered in statistical education. Education in statistics has the same worries as education in other mathematical sciences, such as logic, mathematics, and computer science. At the same time, statistics relate to evidence-based reasoning, especially with data analysis. Therefore, education in statistics has a strong similarity to education in empirical disciplines such as psychology and chemistry, in which education is closely related to "direct" experiments.
Mathematicians and statisticians often work in the mathematics department (especially in colleges and small universities). Statistical courses are sometimes taught by non-statistics, against the recommendations of some professional organizations of statisticians and mathematicians.
The study of statistical education is an emerging field that grew out of various disciplines and is presently establishing itself as a unique field devoted to the improvement of teaching and learning statistics at all levels of education.
Video Statistics education
Destination education statistics
Statistical educators have cognitive and noncognitive goals for students. For example, former President of the American Association Association (ASA) Katherine Wallman defines statistical literacy as including the cognitive ability of understanding and critically evaluating statistical results as well as appreciating the contribution of thinking statistics can make.
Cognitive goal
In the text increased from the 2008 joint conference of the International Commission on Mathematical Instruction and the International Association of Teachers of Statistics, editors Carmen Batanero, Gail Burrill, and Chris Reading (Universidad de Granada, Spain, Michigan State University, USA and the University of New England, Australia, respectively ) records world trends in the curriculum reflecting data-oriented goals. In particular, educators today seek to have students: "investigative design, formulate research questions, collect data using observations, surveys, and experiments; describe and compare data sets; and propose and justify conclusions and predictions based on data." The authors noted the importance of developing thought and reasoning statistics in addition to statistical knowledge.
Despite the fact that cognitive goals for statistical education increasingly focus on statistical literacy, statistical reasoning, and statistical thinking rather than on skills, calculations and procedures alone, there is no agreement on what these terms mean or how to assess these results. The first attempt to determine and differentiate between these three terms appears on the ARTIST website created by Garfield, delMas and Chance and has since been included in several publications. A brief definition of these terms is as follows:
- Statistical literacy is able to read and use basic statistical language and graphical representations to understand statistical information in the media and in everyday life.
- Statistical reasoning is able to explain and relate different statistical concepts and ideas, such as knowing how and why imaging affects central statistical measurements and variability.
- Thinking statistics is the type of thinking used by statisticians when they encounter statistical problems. It involves thinking about the nature and quality of the data and, from where the data comes from, choosing the right analysis and model, and interpreting the results in the context of the problem and limiting the data.
Further cognitive goals of statistical education vary across educational levels of students and the contexts in which they expect to deal with statistics.
Statisticians have proposed what they consider to be the most important statistical concept for educated citizens. For example, Utts (2003) publishes seven areas that every educated citizen should know, including understanding that "variability is normal" and how "accidental... unusual because there are so many possibilities." Gal (2002) suggests adults in industrial societies are expected to train statistical literacy, "the ability to interpret and critically evaluate statistical information... in diverse contexts, and the ability to... communicate understanding and concerns about... conclusions. "
Non-cognitive goal
Non-cognitive outcomes include affective constructs such as attitudes, beliefs, emotions, dispositions, and motivations. According to leading researcher Gal & amp; Ginsburg, the statistics teacher should make it a priority to be aware of students' ideas, reactions, and feelings about statistics and how this affects their learning.
Confidence
Beliefs are defined as the individual ideas one holds about statistics, about oneself as a student of statistics, and about the social context of learning statistics. Beliefs differ from attitudes in the sense that attitudes are a relatively stable and intense feeling that develops over time in the context of a statistical learning experience. Web beliefs provide students context for their approach to their classroom experience in statistics. Many students enter statistics courses with an understanding of subject learning, which works against the learning environment that the instructor wants to achieve. Therefore, it is important for the instructor to have access to assessment instruments that can provide an initial diagnosis of student belief and monitor confidence during the course. Often, assessment instruments have monitored shared beliefs and attitudes. For an example of the instrument, see the attitude section below.
Disposition
Disposition deals with the way students question data and approach statistical problems. The disposition is one of four dimensions within the Wild and Pfannkuch framework for statistical thinking, and contains the following elements:
- Curiosity and Awareness: These characteristics are part of the process of generating questions and generating ideas for exploring and analyzing data.
- Involvement: Students will be very observant and aware in areas they find most attractive.
- Imagination: It is important to look at the problem from different perspectives and produce possible explanations.
- Skepticism: Critical thinking is important to receive new ideas and information and to evaluate the feasibility of research design and analysis.
- Be logical: The ability to detect when one idea follows from another is important to reach a valid conclusion.
- The tendency to seek deeper meaning: This means not taking everything at face value and being open to consider new ideas and digging deeper for information.
Scheaffer states that the goal of statistical education is to make students look at statistics extensively. He developed a list of statistical views that could lead to this broad view, and described it as follows:
- Statistics as a plausible number: Do I understand the meaning of the numbers? (View data as numbers in context, read charts, graphs and tables, understand summary of numbers and data graphs, etc.)
- Statistics as a way of understanding the world: Can I use existing data to help make decisions? (using census data, birth and death rates, disease level, CPI, rank, rank, etc., to describe, decide and defend)
- Statistics as an organized problem solving: Can I design and conduct research to answer specific questions? (causing problems, collecting data according to plan, analyzing data, and drawing conclusions from data)
Attitude
Because students often experience math anxiety and negative opinions about statistical courses, various researchers have discussed attitudes and anxieties about statistics. Several instruments have been developed to measure students' attitudes toward statistics, and have been shown to possess appropriate psychometric properties. Examples of such instruments include:
- Statistics Attitude Survey (SATS), developed by Schau, Stevens, Dauphinee, and Del Vecchio
- Attitude to the Statistics Scale, developed by Wise
- The Statistics Attitude Survey (SAS), developed by Roberts and Bilderback
The use of such a careful instrument can help statistical instructors to learn about students' perceptions of statistics, including their anxieties about learning statistics, perceived difficulties of study statistics, and perceived usefulness of the subject. Several studies have shown modest success in improving students' attitudes in individual courses, but no generalizable studies have shown an improvement in student attitudes have been seen.
Nevertheless, one of the goals of statistical education is to make a study of positive experience statistics for students and to bring examples and interesting and interesting data that will motivate students. According to a fairly recent literature review, increasing student attitudes toward statistics can lead to better motivation and engagement, which also improves cognitive learning outcomes.
Maps Statistics education
Primary-secondary level education
New Zealand
In New Zealand, a new curriculum for statistics has been developed by Chris Wild and his colleagues at Auckland University. Rejecting made, and now unnecessary because of computer power, under-zero reasoning approaches and normal theory restrictions, they use a comparative and bootstrap box plot to introduce the concept of sample variability and inference. The developing curriculum also contains aspects of statistical literacy.
United Kingdom
In the UK, at least some statistics have been taught in schools since the 1930s. Currently, A-level qualifications (usually taken by age 17-18 years) are being developed in "Statistics" and "Advanced Statistics". The first coverage includes: Probability; Data collection; Descriptive statistics; Discrete Probability Distribution; Binomial Distribution; Poisson Distribution; Continuous Probability Distribution; Normal Distribution; Estimates; Hypothesis testing; Chi-Squared; Correlation and Regression. Coverage of "Advanced Statistics" includes: Sustainable Probability Distribution; Estimates; Hypothesis testing; One Sample Test; Hypothesis testing; Two Sample Test; Goodness of Fit Tests; Experimental design; Analysis of Variance (Anova); Statistical Process Control; Sampling Reception. The Center for Innovation in Mathematics Teaching (CIMT) has an online course note for this series of topics. Revision records for existing qualifications show the same coverage. At an earlier age (usually 15-16 years old) GCSE qualifications in mathematics contain the topic "Statistics and Probability" on: Probability; Average; Standard Deviation; Example; Cumulative Frequency Graphics (including median and quantitative); Representing Data; Histogram. The UK Office for National Statistics has a web page that leads to materials suitable for teachers and students at the school level. In 2004, Smith's investigation made the following statement:
"There is much attention and debate about the position of Statistics and Data Handling in the current GCSE mathematics, where it occupies about 25 percent of the allocation of the schedule.On the one hand, there is widespread agreement that the Key Stage 4 curriculum is over-collected and that the introduction of Statistics and Handling The data may have sacrificed the time it takes to practice and gain fluency in the manipulation of core mathematics.Many in the departments of mathematics and engineering of higher education take this view.On the other hand, there is much recognition, shared by the Inquiry, on the importance of Statistics and Data Handling expertise either for a number of other academic disciplines and in the workplace. The investigation recommends that there be a radical review of this issue and much more from teaching and learning Statistics and Data Handling would be better removed from mathematical schedules and integrated with other disciplinary teaching and learning ( eg biol ogi or geography). Time restored to a mathematical schedule should be used to gain greater mastery of concepts and core mathematical operations . "
United States
In the United States, schools have increased the use of probability and statistics, especially since the 1990s. Summary statistics and charts are taught in elementary schools in many states. Topics in probability and statistical reasoning are taught in high school algebra (or mathematics) lessons; statistical reasoning has been tested in SAT tests since 1994. The College Board has developed an Advanced Placement course in statistics, which has provided college-level courses in statistics for hundreds of thousands of high school students, with the first test taking place in May. 1997. In 2007, ASA endorsed the Guidelines for Assessment and Guide in Statistics Education (GAISE), a two-dimensional framework for conceptual understanding of statistics in Pre-K-12 students. This framework contains learning objectives for students at every conceptual level and provides a pedagogical example consistent with the conceptual level.
Estonian
Estonia is driving a new statistical curriculum developed by the Computer Based Mathematics foundation based on computer usage principles as the primary tool of education. in collaboration with Tartu University.
College level
General
Statistics are often taught in the mathematics department or in the mathematics department. At the undergraduate level, statistics are often taught as a service course.
United Kingdom
Based on tradition in the UK, most professional statisticians are trained at Masters level. The difficulty of recruiting strong students has been noted: "Very few students are positively choosing to study statistics degrees, mostly choosing multiple statistical options in mathematics programs, often to avoid pure and advanced applied mathematics courses.Our view is that statistics as a theoretical discipline are more well taught late than early, while statistics as part of a scientific methodology should be taught as part of science. "
In the UK, university-level statistics teaching was initially conducted in the science department that needed topics to accompany the teaching of their own subjects, and the mathematics department had limited coverage before the 1930s. Over the next twenty years, while the mathematics department began teaching statistics, there was little realization that essentially the same basic statistical methodology was being applied in various sciences. The statistics department had difficulties when they had been separated from the mathematics department.
Psychologist Andy Field (Teaching and Book Award Psychology UK) creates a new concept of teaching statistics and textbooks that go beyond the printed pages.
United States
Registration in statistics has increased in colleges, in colleges and universities four years in the United States. In college in the United States, mathematics has increased enrollment since 1990. In college, the ratio of students enrolled in statistics for those enrolled in calculus increased from 56% in 1990 to 82% in 1995. One ASA- supported GAISE reports focuses on statistical education at the preliminary college level. The report covers a brief history of introductory statistics courses and recommendations how they should be taught.
In many colleges, basic courses in "statistics for non-statisticians" only require algebra (and not calculus); for future statisticians, on the contrary, the exposure of scholars to statistics is very mathematical. As a student, future statisticians must complete courses in multivariate calculus, linear algebra, computer programming, and years of calculus-based probabilities and statistics. Students seeking a doctorate in statistics from "one of the better graduate programs in statistics" should also take "real analysis". Laboratory courses in physics, chemistry and psychology also provide useful experiences with planning and conducting experiments and by analyzing data. ASA recommends that undergraduate students consider obtaining a bachelor's degree in applied mathematics as preparation for entering the master's program in statistics.
Historically, professional degrees in statistics have been at the Masters level, although some students may be eligible to work with a bachelor's degree and work-related experience or further self-study. Professional competence requires a background in mathematics --- including at least a multivariate calculus, linear algebra, and years of probability and calculus-based statistics. In the United States, the master's program in statistics requires courses in probability, mathematical statistics, and applied statistics (eg, experimental design, survey sampling, etc.).
For a doctorate in statistics, it has become a tradition that students complete coursework in probability-probability theory as well as courses in mathematical statistics. Such courses require good training in real analysis, which includes evidence of calculus theory and topics such as uniform convergence functions. In the last few decades, several departments have discussed allowing doctoral students to set aside courses in probability-theoretical probabilities by demonstrating advanced skills in computer programming or scientific computing.
Who should teach statistics?
The question of what qualities are required to teach statistics has been much discussed, and sometimes this discussion is concentrated on the qualifications required for those who do such teaching. Questions appear separately for teaching at the school and university levels, in part because of the need for a greater number of teachers numerically at the school level and partly because of the need for the teacher to cover various other topics in their overall task. Given that "statistics" are often taught to non-scientists, opinions can range from "statistics should be taught by statisticians", through "too mathematical statistical teaching" to the extreme that "statistics should not be taught by statisticians".
Teaching at university level
In the United States in particular, statisticians have long complained that many mathematics departments have assigned mathematicians (without statistical competency) to teach statistics courses, which effectively provide "double blind" courses. The principle that college instructors must have qualifications and engagement with their academic disciplines has long been violated in US colleges and universities, according to generations of statisticians. For example, Statistical Science journal re-publishes a "classic" article on non-statistical teaching by Harold Hotelling; The Hotelling articles are followed by comments from Kenneth J. Arrow, W. Edwards Deming, Ingram Olkin, David S. Moore, James V. Sidek, Shanti S. Gupta, Robert V. Hogg, Ralph A. Bradley, and by Harold Hotelling, Jr. (an economist and Harold Hotelling's son).
Data on teaching statistics in the United States have been collected on behalf of the Conference Board of the Mathematical Sciences (CBMS). Examining data from 2000, Schaeffer and Stasny report
So far the majority of instructors in the statistics department have at least a master's degree in statistics or biostatistics (about 89% for the doctoral department and about 79% for the master department). In the department of doctoral mathematics, however, only about 58% of statistics course instructors have at least a master's degree in statistics or biostatistics as the highest degree they get. In the master's math department, the corresponding percentage is close to 44%, and in the undergraduate department only 19% of the statistics course instructors have at least a master's degree in statistics or biostatistics as the highest degree they get. As we expected, most instructors in the statistics department (83% for the doctoral department and 62% for the master's department) have a doctoral degree in statistics or biostatistics. The comparable percentages for statistical instructors in the mathematics department are about 52% and 38%.
The principle that statistical instructors should have statistical competence has been confirmed by the guidelines of the American Mathematical Association, which have been endorsed by ASA. Unprofessional statistical teaching by mathematicians (without qualification in statistics) has been discussed in many articles.
Teaching Method
The literature on statistical methods of teaching is closely related to the literature on the teaching of mathematics for two reasons. First, statistics are often taught as part of the mathematics curriculum, by instructors who are trained in mathematics and work in the mathematics department. Second, statistical theory has often been taught as a mathematical theory rather than as a practical logic of science-as a science that "places the opportunity to work" in the phrase Rao --- and this requires an emphasis on formal and manipulative training. , such as solving combinatorial problems involving red and green jelly beans. Statisticians have complained that mathematicians tend to overemphasize mathematical manipulation and probability theory and less emphasize experimental questions, survey methodologies, analysis of exploratory data, and statistical inference.
In the last few decades, there has been an increasing emphasis on data analysis and scientific inquiry in statistical education. In the UK, Smith's investigation of Making Mathematical Counts suggests teaching basic statistical concepts as part of the science curriculum, rather than as a part of mathematics. In the United States, ASA guidelines for undergraduate statistics dictate that introductory statistics should emphasize the scientific method of data collection, especially random experiments and random samples: furthermore, the first course should review this topic when the theory of "statistical inference" is studied. Similar recommendations apply to the Advanced Placement (AP) course in Statistics. ASA and AP guidelines are followed by contemporary textbooks in the US, such as those by Freedman, Purvis & amp; Pisani ( Statistics ) and by David S. Moore ( Introduction to Statistical Practice with McCabe and Statistics: Concepts and Controversy with Notz) and by Watkins, Schaeffer & amp; Cobb ( Statistics: From Data to Decision and Statistics in Action ).
In addition to the emphasis on scientific inquiry in the initial content of statistics, there is also an increase in active learning in the execution of statistical classes.
Professional community
Association
The International Statistical Institute (ISI) now has a section dedicated to education, the International Association for Education of Statistics (IASE), which runs the International Conference on Teaching Statistics every four years as well as the IASE satellite conference around the ISI and ICMI meetings. The UK established the Royal Statistical Society Center for Statistics Education and the ASA now also has a Statistics Education Department, mostly focused on teaching statistics at the primary and secondary levels.
Conference
In addition to the international meeting of statistical teachers at ICOTS every four years, the US hosts the US Conference on Teaching Statistics (USCOTS) every two years and has recently started Electronic Conference on Teaching Statistics (eCOTS) to alternate with USCOTS. Sessions in the field of statistical education are also offered at many conferences in mathematics education such as the International Congress on Mathematics Education, the National Council of Mathematics Teachers, the International Group Conference for Mathematical Education Psychology, and the Mathematics Education Research Group of Australasia. The annual Joint Statistics Meeting (offered by ASA and Statistics Canada) offers many round sessions and tables on statistical education. The International Research Forum on Reasoning, Thinking and Literacy Statistics offers scientific meetings every two years and related publications in journals, CD-ROMs and research books in statistical education.
Graduated from college and program
Only three universities currently offer postgraduate programs in statistical education: the University of Granada, University of Minnesota, and the University of Florida. However, postgraduate students in various disciplines (eg, Mathematics education, psychology, educational psychology) have found a way to complete a dissertation on topics related to teaching and learning statistics. This dissertation is archived on the IASE website.
The two main courses in statistical education that have been taught in various settings and departments are courses on statistics teaching and courses on statistical education research. An ASA-sponsored workshop has set recommendations for additional graduate programs and courses.
Software to learn
- Fathom: Dynamic Data Software
- TinkerPlots
- StatCrunch
Trends in Statistics Education
Statistical teachers have been encouraged to explore new directions in curriculum content, pedagogy, and assessment. In an influential conversation at USCOTS, researcher George Cobb presented an innovative approach to teaching statistics that put simulation, randomization, and bootstrapping techniques at the core of a college level introductory course, where traditional content such as probability theory and
Another new direction is to tackle large data sets that are increasingly affecting or contributing to our daily lives. Statistical genius Rob Gould, the maker of the spectacular Dinner and theater, outlines many of these data types and encourages teachers to find ways to use data and solve problems around large data. According to Gould, a curriculum that focuses on large data will address the problem of sampling, prediction, visualization, data cleaning, and the underlying process that generates data, rather than methods traditionally emphasized to make statistical inferences such as hypothesis testing.
Source of the article : Wikipedia
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