In this article, the author wishes to emphasize two fundamental points related to theory that were significantly underplayed in Simon et al.'s "A Developing Approach to Studying Students' Learning through Their Mathematical Activity" (2010). The author believes these points are central to any study of children's mathematical learning. The first…

Several researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children…

This article describes a set of learning activities that use algebraic problems and written student work to help preservice and in-service teachers understand students' algebraic thinking. (Contains 4 figures.)

The sport of Ultimate has grown from parking lot fun to international competition in its 35 year existence. As in many sports, the team that scores is subsequently on defense. Thus the probability that a team will score next is dependent on which team has scored most recently. Unlike in many other sports, teams switch ends after each score. Thus…

Noting that effective teaching models that emphasize critical thinking in mathematics and science are used less often in early childhood classrooms than in those for older students, this book provides early childhood educators with an explanation of teaching models that promote 3- to 8-year-olds critical thinking, problem solving, decision making,…