ABSTRACT
Bob Siegler drew many researchers' attention to the potential of the number line as a way to tap children's growing numerical knowledge. This chapter discusses questions related to the research. In addition to Bob's inspiration to pay careful attention to children's thinking and ways to empirically measure changes in their thinking, he has also taught us the importance of reviewing research critically and writing concisely. The chapter focuses on magnitude comparison and number line estimation as correlates and predictors of mathematical competence. Mathematical competence includes modeling situations mathematically, employing concepts, facts, and procedures to solve problems, and interpreting, applying, and evaluating mathematical outcomes in broad ranges of mathematical content areas and application contexts. However, two brief and easy-to-administer tasks, the magnitude comparison task and the number line estimation task, correlate with a wide range of assessments of mathematical competence, even though these assessments differ in their content areas, application contexts, notational systems, appropriate age groups, and required solution processes.
