In keeping with the Equity Principle of the Principles and Standards for School Mathematics (NCTM 2000), educators must maintain high expectations for all children and continually examine their practices to ensure that all children learn mathematics with understanding. The instructional practice of using manipulatives for problem solving merits closer examination because it may send the wrong message to some children. Recent research indicates that some girls' understanding seems to be limited by their overreliance on manipulatives. Before presenting the research findings, I will outline the role of manipulatives in supporting the development of children's understanding, then examine how this promising practice can be detrimental when used too often.
Cathleen M. Alexander and Rebecca C. Ambrose
When students are asked to write original story problems about fractional amounts, it can illustrate their misunderstandings about fractions. Think about the situations your students would describe to model 1/2 + 2/3.
Marta Molina and Rebecca C. Ambrose
How third-grade students developed an understanding of the equals sign and began to use relational thinking as they discussed true/false and open-number sentences. The sequence of instructional activities and children's responses to them are provided.
Rebecca C. Ambrose and Karen Falkner
What kind of spatial understanding do first and second graders have? What do they see when they look at three-dimensional objects? What words do they use to describe what they see? How might their visualization skills be sharpened by building and describing threedimensional structures? These questions emerged as we, a teacher educator and a classroom teacher, considered infusing spatial tasks into the primary school mathematics curriculum.
Victoria R. Jacobs and Rebecca C. Ambrose
Honoring students' solution approaches helps teachers capitalize on the power of story problems. No more elusive train scenarios!
Victoria R. Jacobs, Rebecca C. Ambrose, Lisa Clement and Dinah Brown
Victoria R. Jacobs, Heather A. Martin, Rebecca C. Ambrose and Randolph A. Philipp
Avoid three common instructional moves that are generally followed by taking over children's thinking.
Randolph A. Philipp, Rebecca Ambrose, Lisa L.C. Lamb, Judith T. Sowder, Bonnie P. Schappelle, Larry Sowder, Eva Thanheiser and Jennifer Chauvot
In this experimental study, prospective elementary school teachers enrolled in a mathematics course were randomly assigned to (a) concurrently learn about children's mathematical thinking by watching children on video or working directly with chil-dren, (b) concurrently visit elementary school classrooms of conveniently located or specially selected teachers, or (c) a control group. Those who studied children's mathematical thinking while learning mathematics developed more sophisticated beliefs about mathematics, teaching, and learning and improved their mathematical content knowledge more than those who did not. Furthermore, beliefs of those who observed in conveniently located classrooms underwent less change than the beliefs of those in the other groups, including those in the control group. Implications for assessing teachers' beliefs and for providing appropriate experiences for prospective teachers are discussed.