# Chapter

• ### Introduction

This chapter outlines the challenges in teaching and learning probability and states the mission of this book. This book aims to review and analyze the research literature on the teaching and learning of probability in the K-12 curriculum.

• ### The nature of chance and probability.

In this chapter we will examine different interpretations of the nature of chance, randomness, and probability and will highlight how these multiple conceptions are complementary and can influence curriculum goals. Finally we include some implications for the teaching and learning of probability in schools.

• ### Towards "probability literacy" for all citizens: Building blocks and instructional dilemmas.

This chapter focuses on "probability literacy", the knowledge and dispositions that students may need to develop to be considered literate regarding real-world probability matters. Models of adult literacy, numeracy, and statistical literacy that define the terrain in which knowledge of probability is situated are reviewed. Then, the five basic elements of probability-related knowledge and points to some dispositions that are needed for adults to be able to effectively interpret and engage real-world probabilistic situations are discussed. Implications for instructional practice and research are examined.

• ### An overview of research into the teaching and learning of probability.

This is an historical overview of research on the learning and teaching of probability. Research will be classified chronologically as Phase 1, the Piagetian Period; Phase 2, the Post-Piagetian Period; and Phase 3, the Contemporary Period. The research of each of these phases will be analyzed and we will identify the theoretical developments and implications for teaching and learning that have been associated with each phase.

• ### Characteristics of elementary school students' probabilistic reasoning.

We examine probabilistic intuitions and concepts as they relate to children aged 5 to 11 from research over the past 50 years. In the first section, we review the research pertaining to specific concepts and skills associated with probabilistic reasoning. The other section presents a discussion of theoretical perspectives on instruction in probability.

• ### Combinatorics and the development of children's combinatorial reasoning.

Some elementary ideas of combinatorics and its role in supporting children's development of beginning probability ideas and problem-solving skills are explored. A review of studies that addressed children's combinatorial reasoning is then presented. To conclude, ways in which children's access to powerful ideas are considered.

• ### The probabilistic reasoning of middle school students.

This chapter covers a wide range of ideas associated with probabilistic thinking and provides some examples of the potential development in understanding that occurs in students in Grades 6 through 9. The first sections include intuitive ideas on luck and fairness, as well as chance language. Secondly, various types of probabilistic events, ranging from simple events to conjunction events are explored. Finally, appreciation of random behavior, sampling and variation in a probabilistic setting, the equiprobability bias, and the importance of dealing with probability in context, are considered in the last four sections.