[Chapter 2 - Teaching Practices in Mathematics and Science]
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[Content Coverage and High Standards]
Designing Effective Development: Lessons from the Eisenhower Program - December 1999
Chapter 2
An understanding of good mathematics and science instruction begins with a vision for the classroom. This is a difficult vision to capture for two reasons. First, effective learning experiences differ; there is no single model of an ideal class. Second, educators and researchers do not know all there is to know about ideal instructional strategies. However, research has identified some common elements of "good instruction" in mathematics and science. In particular, certain elements of content and pedagogy improve student learning.
Overall, effective instruction can be characterized by content that is aligned with high standards and pedagogy focused on active learning. Content includes both the topics of instruction, such as fractions, and the teacher?s expectations for student performance, such as memorizing or understanding concepts. Pedagogy refers to the types of activities used in instruction and typically includes dimensions such as whole class versus individual instruction or project versus text-based instruction.
Content coverage matters for student learning. Student achievement improves when the content of instruction is consistent with national standards and assessments (Cohen & Hill, 1998; Gamoran et al., 1997). National standards for mathematics and science specify critical content areas that effective instruction should address: covering core topics, such as life science, and developing students? topic understanding in sophisticated ways, such as making connections to real-world situations.
The National Council of Teachers of Mathematics (NCTM) developed standards for mathematics curricula (NCTM, 1989) and instruction (NCTM, 1991).6 The key content areas differ by school level (i.e., K-4, 5-8, 9-12), but generally focus on the following:
The mathematics standards also identify standards for student performance that apply across all grades:
Reform in science education has emphasized real-world problems, investigations of natural phenomena, and linkages to other subjects rather than abstract knowledge (Raizen, 1998). In setting content standards for science, the National Research Council (NRC) identified certain content areas as central to teaching and learning science: 7
In addition, NRC identified some concepts and student performance standards that cross content areas, such as systems, order, and organization; evolution and equilibrium; and understanding of and ability to conduct scientific inquiry.
In setting standards for student performance, the NRC emphasized developing skills to do scientific inquiry, such as asking questions, collecting data, and developing explanations. An underlying premise of these standards is to focus less on "student acquisition of information" and more on "student understanding and use of scientific knowledge, ideas, and inquiry processes" (NRC, 1996: p. 52). Thus, the performance goal of memorizing material is less central than the goals of understanding concepts or making connections.
As the standards imply, the organization of the curriculum within the school also affects students? learning experiences. Past research has suggested that there is too much redundancy in content from one grade level to the next, at least for kindergarten through eighth grade. Compared to other countries, the curriculum in the U.S. covers more topics; each year the curriculum expands to incorporate new topics but, unlike the practice in other countries, topics are not phased out of the curriculum in successive grades (Schmidt, McNight, and Raizen, 1997). Effective instruction entails organizing the curriculum so that learning at each grade builds on prior learning, developing deeper and more complex understandings.
Pedagogy
Pedagogy--or the way content is presented--also matters for student learning. National mathematics and science standards emphasize the pedagogical approach of active instruction. For example, the science standards advocate inquiry-based learning, in which the teacher facilitates rather than informs (NRC, 1996). The mathematics standards stress instruction that builds on students? experience, in which students are actively engaged in wrestling with complex problems (NCTM, 1998).
The standards are based on research that indicates that active learning is especially effective. Students learn science best when they are active participants, engaged in activities, rather than passive recipients of lecture-style instruction (Raizen, 1998). Active learning calls for students to be involved in creating their own learning experiences. Pedagogical approaches that support active mathematics and science learning include using inquiry-based instruction, in which the teacher facilitates rather than informs, actively engaging students in complex problems for which there are no simple solutions, and incorporating multiple disciplines in activities (NCTM, 1998; NRC, 1996; Raizen, 1998).
National standards in mathematics and science, consistent with research on effective instruction, indicate that both content-especially core topics and complex performance goals-and pedagogy-especially active learning-are important to student learning. Clearly, content and pedagogy are interrelated. While active learning is especially student-driven, it is still coordinated around content-effective teachers set instructional goals and monitor activities, intervening when appropriate. Thus, while we examine content and pedagogy in turn in this chapter, the two together contribute to effective instruction.
7 The National Science Teachers Association (NSTA), the American Association for the Advancement of Science (AAAS), and the NRC each developed standards documents (see AAAS, 1993; AAAS, 1989; NSTA, 1992.) The three standards are the primary focus here (Raizen, 1998).
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[Chapter 2 - Teaching Practices in Mathematics and Science] |
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[Content Coverage and High Standards] |