Data Handling and Statistics Teaching and Learning
KeywordsStatistics Data handling Exploratory data analysis Teaching and learning statistics Research on teaching and learning statistics Statistical reasoning Statistical literacy Technological tools in statistics learning
Over the past several decades, changes in perspective as to what constitute statistics and how statistics should be taught have occurred, which resulted in new content, pedagogy and technology, and extension of teaching to school level. At the same time, statistics education has emerged as a distinct discipline with its own research base, professional publications, and conferences (Ben-Zvi et al. 2018b). There seems to be a large measure of agreement on what content to emphasize in statistics education: exploring data (describing patterns and departures from patterns), sampling and experimentation (planning and conducting a study), anticipating patterns (exploring random phenomena using models, probability and simulation), and statistical inference (estimating population parameters and testing hypotheses) (Scheaffer 2001). Teaching and learning statistics can differ widely across countries due to cultural, pedagogical, and curricular differences and the availability of skilled teachers, resources, and technology.
Changing Views on Teaching Statistics Over the Years
By the 1960s statistics began to make its way from being a subject taught for a narrow group of future scientists into the broader tertiary and school curriculum but still with a heavy reliance on probability. In the 1970s, the reinterpretation of statistics into separate practices comprising exploratory data analysis (EDA) and confirmatory data analysis (CDA, inferential statistics) (Tukey 1977) freed certain kinds of data analysis from ties to probability-based models, so that the analysis of data could begin to acquire status as an independent intellectual activity. The introduction of simple data tools, such as stem and leaf plots and boxplots, paved the way for students at all levels to analyze real data interactively without having to spend hours on the underlying theory, calculations, and complicated procedures. Computers and new pedagogies would later complete the “data revolution” in statistics education.
In the 1990s, there was an increasingly strong call for statistics education to focus more on statistical literacy, reasoning, and thinking. Wild and Pfannkuch (1999) provided an empirically based comprehensive description of the processes involved in the statisticians’ practice of data-based inquiry from problem formulation to conclusions. One of the main arguments presented is that traditional approaches to teaching statistics focus on skills, procedures, and computations, which do not lead students to reason or think statistically.
These changes are implicated in a process of democratization that has broadened and diversified the backgrounds and motivations of those who learn statistics at many levels with very diverse interests and goals. There is a growing recognition that the teaching of statistics is an essential part of sound education since the use of data is increasingly common in science, society, media, everyday life, and almost any profession.
A Focus on Statistical Literacy and Reasoning
The goal of teaching statistics is to produce statistically educated students who develop statistical literacy and the ability to reason statistically. Statistical literacy is the ability to interpret, critically evaluate, and communicate about statistical information and messages. Statistically literate behavior is predicated on the joint activation of five interrelated knowledge bases – literacy, statistical, mathematical, context, and critical – together with a cluster of supporting dispositions and enabling beliefs (Gal 2002). Statistical reasoning is the way people reason with the “big statistical ideas” and make sense of statistical information during a data-based activity. Statistical reasoning may involve connecting one concept to another (e.g., center and spread) or may combine ideas about data and chance. Statistical reasoning also means understanding and being able to explain statistical processes and being able to interpret statistical results.
The “big ideas” of statistics that are most important for students to understand and use are data, statistical models and modeling, distribution, center, variability, comparing groups, samples, sampling and sampling distributions, statistical inference, and covariation. Additional important underlying concepts are uncertainty, randomness, evidence strength, significance, and data production (e.g., experiment design). In the past few years, researchers have been developing ideas of informal statistical reasoning in students as a way to build their conceptual understanding of the foundations of more formal ideas of statistics (Garfield and Ben-Zvi 2008).
What Does Research Tell Us About Teaching and Learning Statistics?
Research on teaching and learning statistics has been conducted by researchers from different disciplines and focused on students at all levels. Common faulty heuristics, biases, and misconceptions were found in adults when they make judgments and decisions under uncertainty, e.g., the representativeness heuristic, law of small numbers, and gambler’s fallacy (Kahneman et al. 1982). Recognizing these persistent errors, researchers have explored ways to help people correctly use statistical reasoning, sometimes using specific methods to overcome or correct these types of problems.
Another line of inquiry has focused on how to develop good statistical reasoning and understanding, as part of instruction in elementary and secondary mathematics classes. These studies revealed many difficulties students have with concepts that were believed to be fairly elementary such as data, distribution, center, and variability. The focus of these studies was to investigate how students begin to understand these ideas and how their reasoning develops when using carefully designed activities assisted by technological tools (Shaughnessy 2007).
A newer line of research is the study of preservice or practicing teachers’ knowledge of statistics and probability and how that understanding develops in different contexts. The research related to teachers’ statistical pedagogical content knowledge suggests that this knowledge is in many cases weak. Many teachers do not consider themselves well prepared to teach statistics nor face their students’ difficulties (Batanero et al. 2011).
The studies that focus on teaching and learning statistics at the college level continue to point out the many difficulties tertiary students have in learning, remembering, and using statistics and point to some modest successes. These studies also serve to illustrate the many practical problems faced by college statistics instructors such as how to incorporate active or collaborative learning in a large class, whether or not to use an online or “hybrid” course, or how to select one type of software tool as more effective than another. While teachers would like research studies to convince them that a particular teaching method or instructional tool leads to significantly improved student outcomes, that kind of evidence is not actually available in the research literature. However, recent classroom research studies suggest some practical implications for teachers. For example, developing a deep understanding of statistics concepts is quite challenging and should not be underestimated; it takes time, a well thought-out learning trajectory, and appropriate technological tools, activities, and discussion questions.
Teaching and Learning
As more and more students study statistics, teachers are faced with many challenges in helping these students succeed in learning and appreciating statistics. The main sources of students’ difficulties were identified as: facing statistical ideas and rules that are complex, difficult, and/or counterintuitive, difficulty with the underlying mathematics, the context in many statistical problems may mislead the students, and being uncomfortable with the messiness of data, the different possible interpretations based on different assumptions, and the extensive use of writing and communication skills (Ben-Zvi and Garfield 2004).
The study of statistics should provide students with tools and ideas to use in order to react intelligently to quantitative information in the world around them. Reflecting this need to improve students’ ability to reason statistically, teachers of statistics are urged to emphasize statistical reasoning by providing explicit attention to the basic ideas of statistics (such as the need for data, the importance of data production, the omnipresence of variability); focus more on data and concepts, less on theory, and fewer recipes; and foster active learning (Cobb 1992). These recommendations require changes of teaching statistics in content (more data analysis, less probability), pedagogy (fewer lectures, more active learning), and technology (for data analysis and simulations) (Moore 1997).
Statistics at school is usually part of the mathematics curriculum. New K–12 curricular programs set ambitious goals for statistics education, including promoting students’ statistical literacy, reasoning, and understanding (e.g., NCTM 2000). These reform curricula weave a strand of data handling into the traditional school mathematical strands (number and operations, geometry, algebra). Detailed guidelines for teaching and assessing statistics at different age levels complement these standards. However, school mathematics teachers, which are often not versed in statistics, find it challenging to teach data handling in accordance with these recommendations.
In order to face this challenge and promote statistical reasoning, good instructional practice consists of implementing inquiry or project-based learning environments that stimulate students to construct meaningful knowledge. Ben-Zvi et al. (2018a) suggest several design principles to develop students’ statistical reasoning: focus on developing central statistical ideas rather than on presenting set of tools and procedures; use real and motivating data sets to engage students in making and testing conjectures; use classroom activities to support the development of students’ reasoning; integrate the use of appropriate technological tools that allow students to test their conjectures, explore and analyze data, and develop their statistical reasoning; promote classroom discourse that includes statistical arguments and sustained exchanges that focus on significant statistical ideas; and use assessment to learn what students know and to monitor the development of their statistical learning, as well as to evaluate instructional plans and progress.
Technology has changed the way statisticians work and has therefore been changing what and how statistics is taught. Interactive data visualizations allow for the creation of novel representations of data. It opens up innovative possibilities for students to make sense of data but also place new demands on teachers to assess the validity of the arguments that students are making with these representations and to facilitate conversations in productive ways. Several types of technological tools are currently used in statistics education to help students understand and reason about important statistical ideas. However, using technological tools and how to avoid common pitfalls are challenging open issues (Biehler et al. 2013).
These changes in the learning goals of statistics have led to a corresponding rethinking of how to assess students. It is becoming more common to use alternative assessments such as student projects, reports, and oral presentations than in the past. Much attention has been paid to assess student learning, examine outcomes of courses, align assessment with learning goals, and alternative methods of assessment.
For Further Research
Research in statistics education has made significant progress in understanding students’ difficulties in learning statistics and in offering and evaluating a variety of useful instructional strategies, learning environments, and tools (Ben-Zvi et al. 2018b). However, many challenges are still ahead of statistics education, mostly in transforming research results to practice, evaluating new programs, planning and disseminating high-quality assessments, and providing attractive and effective professional development to mathematics teachers (Garfield and Ben-Zvi 2007). The ongoing efforts to reform statistics instruction and content have the potential to both make the learning of statistics more engaging and prepare a generation of future citizens that deeply understand the rationale, perspective, and key ideas of statistics. These are skills and knowledge that are crucial in the current information age of data, big data and data science.
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