This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Investigating and mitigating implicit bias in questions are discussed in this article, which is another installment in the series.
Beth Herbel-Eisenmann and Niral Shah
Beth A. Herbel-Eisenmann
In this article, I used a discourse analytic framework to examine the “voice” of a middle school mathematics unit. I attended to the text's voice, which helped to illuminate the construction of the roles of the authors and readers and the expected relationships between them. The discursive framework I used focused my attention on particular language forms. The aim of the analysis was to see whether the authors of the unit achieved the ideological goal (i.e., the intended curriculum) put forth by the NCTM's Standards (1991) to shift the locus of authority away from the teacher and the textbook and toward student mathematical reasoning and justification. The findings indicate that achieving this goal is more difficult than the authors of the Standards documents may have realized and that there may be a mismatch between this goal and conventional textbook forms.
Beth A. Herbel-Eisenmann
A way to introduce and use mathematical language in mathematics classrooms that draws on multiple representations and student language.
Michelle Cirillo, Beth Herbel-Eisenmann and Corey Drake
Michelle Cirillo, Corey Drake and Beth Herbel-Eisenmann
Samuel Otten, Beth Herbel-Eisenmann and Lorraine Males
A vignette from an early algebra class reveals a rich opportunity for generating proof before geometry.
Corey Drake, Michelle Cirillo and Beth Herbel-Eisenmann
“Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well” (The Teaching Principle, NCTM 2000, p. 16).
Samuel Otten, Michelle Cirillo and Beth A. Herbel-Eisenmann
Reconsider typical discourse strategies when discussing homework and move toward a system that promotes the Standards for Mathematical Practice.
Beth A. Herbel-Eisenmann and M. Lynn Breyfogle
Teachers pose a variety of questions to their students every day. As teachers, we recognize that some questions promote deeper mathematical thinking than others (for more information about levels of questions, see Martens 1999, Rowan and Robles 1998, and Vacc 1993). For example, when asking, “Is there another way to represent or explain what you are saying?” students are given the chance to justify their thinking in multiple ways. The question “What did you do next?” focuses only on the procedures that students followed to obtain an answer. Thinking about the questions we ask is important, but equally important is thinking about the patterns of questions that are asked.
Beth A. Herbel-Eisenmann and Elizabeth Difanis Phillips
Recent literature has shown that having teachers examine student work can enhance teachers' thinking about what constitutes mathematical understanding (Crespo 2000; Crockett 2001). There is also evidence that teachers need to experience unconventional mathematics problems to see the value of using them in their own classrooms (Ball 1988; Crespo 2003).