The psychology of number and its applications to methods of teaching arithmetic.

Abstract

In this article, Kurt Stemhagen reconstructs mathematics education in light of Dewey's democratic theory and his ideas about mathematics and mathematics education. The resulting democratic philosophy and pedagogy of mathematics education emphasizes agency and the connections between mathematics and students' social experiences. Stemhagen considers questions about the disconnect between constructivist reformers and critical mathematics educators, and he positions Dewey's ideas as a way to draw on the best of both to create an active and more democratic school math experience.

Teacher and students’ joint production of a reversible fraction conception

“…In this domain, research-based, content-specific explanations are crucial because "The teaching and learning of fractions is not only very hard, it is, in the broader scheme of things, a dismal failure" (Davis, Hunting, & Pearn, 1993, p. 63). Such view is consistent with numerous works about children's difficulties in learning fractions (Behr, Post, Harel, & Lesh, 1993;Behr, Harel, Post, & Lesh, 1992;Davydov & Tsvetkovich, 1991;Hiebert & Behr, 1991;Kieren, 1976;Mack, 1990;McLellan & Dewey, 1908;Smith, 2002). Besides pointing to possible difficulties involved in learning concepts related to the reversible fraction conception, this vast body of studies neither addressed the particular process in which this conception might be constructed, nor how the teacher might support its construction.…”

Development of Mathematical Understanding

“…The constructivist approach to children's learning and understanding of mathematics also has a long history (McLellan & Dewey, 1895), and continues to be influential (Ginsburg, Klein, & Starkey, 1998). There is variation in the details of this approach from one theorist to the next, but the common theme is that children's learning should be self-directed and emerge from their interactions with the physical world.…”

The Story of a South Korean Elementary Teacher's Knowledge of Mathematics Curriculum

“…According to the Common Core State Standards for Mathematics (2010), elementary teachers' should help students develop conceptual understanding of mathematics as well as procedural fluency. In order to develop conceptual understating, students should make connections among mathematics concepts (Hiebert, & Carpenter 1992;Mclellan, & Dewey 1895;Polya 1957;Wertheimer 1950). In this case, it is important that elementary teachers know the relationship among mathematical concepts in order to support their students, because there are direct parallels between the ways teachers connect their mathematical knowledge and the instruction they implement in their classrooms as a result (Carpenter, Fennema, Peterson, Chiang, & Loef 1989;Peterson, Fennema, & Carpenter 1991).…”