Transformational Geometry in New Middle Grades Textbooks: What do teachers need to know?
College of Liberal Arts and Sciences
Physical Sciences and Mathematics
Teachers plan tasks for students to engage with mathematical content and thus play a significant role in determining what students have the opportunity to learn. As teachers work to enact the Common Core State Standards in Mathematics (CCSSM), they are turning to new textbooks to implement these standards. Therefore, teachers understanding of the mathematical content with respect to the CCSSM becomes ever more vital. With this in mind, we pose the following research question: How are new middle grades textbooks (published since 2010) organizing and presenting transformational geometry concepts aligned to the CCSSM? Research has determined that the textbooks teachers use in their classrooms impact the learning outcomes of their students (Grouws, Smith, & Sztajn, 2004; Tarr et al., 2006). What happens when there is a mismatch between the mathematical content presented in the textbooks and the CCSSM teachers are held accountable to teach? Most mathematics teachers use textbooks as the authority in their classroom, meaning the textbook becomes a script rather than a resource (Roth McDuffie & Mather, 2009). Teachers' decisions about what lessons to teach and how to present the mathematical concepts depend on a number of factors, one being the characteristics of the curriculum materials and how they interpret the materials in order to deliver instruction (Davis & Krajcik, 2005). Roth McDuffie and Mather (2009) state, curricular goals and materials [should] remain a primary focus for activities throughout the reasoning process (p. 306). These decisions and goals rely heavily on a teachers curricular reasoning, which is a specific form of pedagogical reasoning that teachers employ while working with curriculum materials to plan, implement, and reflect on instruction (Roth McDuffie & Mather, 2009, p. 302, italics added). As mathematics teacher educators prepare pre-service teachers to teach mathematics are we providing opportunities for them to build their curricular reasoning? Are pre-service teachers able to decide how textbook materials provide (or do not provide) opportunities for students to learn the specified mathematical content addressed in the CCSSM? The development of pre-service teachers curricular reasoning is necessary to effectively analyze curriculum and make decisions about planning, implementation, and reflecting on instruction. In this session we will provide participants an opportunity to examine textbooks and participate in a curriculum analysis activity that we have used with our pre-service teachers. We will then share results from our curriculum analysis of transformational geometry in new middle grades textbooks and how this can be applied at any grade level and in any mathematical content area. Curricular reasoning will be highlighted as we discuss transformational geometry concepts presented among textbooks relative the CCSSM. This is critical for mathematics teacher educators as they prepare pre-service teachers to understand and be knowledgeable of the treatment of topics and the characteristics of textbooks they will be asked to use and evaluate as classroom teachers. In particular the presentation of transformational geometry concepts are important to highlight, as the treatment of this aspect in the geometry domain is vastly different than in previous standards documents and in middle grades textbooks.
Association of Mathematics Teacher Educators 2015
Kasmer, Lisa; Dingman, Shannon Dr.; Teuscher, Dawn Dr.; and Olson, Travis Dr., "Transformational Geometry in New Middle Grades Textbooks: What do teachers need to know?" (2015). Faculty Scholarly Dissemination Grants. 553.