ABSTRACT
The second half of this book focuses on the important issues of arithmetical instruction and arithmetical learning in special populations. The former represents an area of considerable debate in the United States, and the outcome of this debate could affect the mathematics education of millions of American children (Hirsch, 1996; Loveless, 2001). At one extreme in this debate are advocates of unguided discovery learning, whereby teachers provide materials and problems to solve and encourage students to discover for themselves the associated concepts and problem-solving procedures. At the other extreme are those who advocate direct instruction and drill, whereby teachers provide explicit instruction on basic skills (facts, definitions, and procedures) and children are required to practice these basic skills until memorized by rote. In the first section of my commentary, I briefly address this debate, as it relates to chapters 9, 10, and 11 (by Dowker; Fuson and Burghardt; and Ambrose, Baek, and Carpenter, respectively). Chapters 12 to 15 (by Donlan; Jordan, Hanich, and Uberti; Delazer; and Heavey, respectively) focus on the important issue of arithmetical learning in special populations, a topic that has been largely neglected, at least in relation to research on reading competencies in special populations. I discuss these chapters and related issues in the second section of my commentary. In the third, I briefly consider future directions.
