In this chapter, we provide brief concluding remarks which focus on summarizing key frameworks discussed throughout the first six chapters. We argue that by developing a testable model of statistics cognition we can make specific predictions about learning and errors which can help provide educators with the guidance needed to curb the influence errors can have on learning. Additionally, by developing a cognitive curriculum, which is designed to assess student affect and make use of meaningful individual differences, we can enhance the quality of statistics education in online environments. We conclude this chapter by outlining several future directions that can help facilitate our understanding of statistics cognition.
Technology has led to numerous changes in statistical practice... These changes in statistical practice have a direct impact on the content that should be taught, even in introductory material. - Chance, Ben-Zvi, Garfield, & Medina, 2007, p. 2
Top1. Developing A Cognitive Oriented Statistics Course
This text has taken the view that the purpose of statistics education is to enhance statistics cognition (Chapter 1). We have argued that to enhance statistics cognition we must have a clear model that allows us to make specific predictions about the type of content statistics classes should offer and how they are designed, based on evidence supported methods to enhance cognitive development (Chapter 2). With a specific model of statistics cognition it is not only possible to understand how students learn statistics, but can also provide insight into the types of errors students make, allowing the learning process to become more efficient (Chapter 3). Taken together, the information afforded by a specific model of statistics cognition allows educators to develop a curriculum oriented on those cognitions (Chapter 4). However, in addition to teaching statistics content, educators must be aware of the role affect plays in learning, and develop procedures to test and correct harmful affective states (Chapter 5). To do this, educators and scholars must develop meaningful frameworks for exploring individual differences (Chapter 6).
Collectively, we propose an integrative framework for understanding the relationship of course features with learning processes when using a cognitive curriculum (Figure 1). In particular, this framework dictates that evidence is collected at each stage of the learning process that is used to inform specific hypotheses about student learning.
Figure 1. Model of a cognitive statistics educational course in an online environment
As depicted in Figure 1, any one unit has types of literacy, reasoning, and thinking objectives that are specific to material categorized within a unit. Before the course even begins, the educator needs to ensure that these cognitive learning objectives are aligned with appropriate assessments, and remain in the same relative proportion throughout each stage (i.e., if 30% of all learning objectives in a unit are based on literacy, then roughly 30% of all questions on the summative exam should measure literacy outcomes).
During the course the educator must monitor and evaluate student success. For instance, the educator must ensure students are following the correct procedures, such as mastering literacy before tackling thinking objectives. By giving learning a specific progression, students may begin to realize what to expect on exams (potentially reducing negative affective states) and better understand how they can succeed on assessments. For example, if students know that the majority of questions on an exam are based on recall, a strategy such as making flash cards could be effective. However, if most questions are on reasoning, then students may realize elaborative rehearsal works better (see Dunlosky, Rawson, Marsh, Nathan, & Willingham, 2013). Further, the educator must collect baseline information about student cognitive ability and affective responses to materials so that curriculum may be adjusted in real time. As outlined throughout this book, there are a variety of ways to improve student affect (Chapter 5) and potentially enhance motivation (Chapter 6). We argue that by collecting baseline information educators can adjust the tone, pace, or even content depending upon the cognitive ability of students that term. Once the student has taken the summative exam for the unit, their progress can be assessed, and a decision about the student's ability to progress toward the next unit can be made.