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curriculum books have been written since the turn of the [20th] century; each with a different version of what 'curriculum' means (Ackerman, 1988). I define classroom curriculum design as the sequencing and pacing of content along with the experiences students have with that content. My use of the qualifier classroom is important. By definition, I am considering those decisions regarding sequencing, pacing, and experiences that are the purview of the classroom teacher. Some aspects of curricular design are addressed at the school level if, in fact, a school has a guaranteed and viable curriculum. Regardless of the direction provided by the school (or district), individual teachers still need to make decisions regarding curricular design at the classroom level given the unique characteristics of their students. Indeed, in a meta-analysis involving 22 studies, Anderson, (2003) found a strong relationship between a student's knowledge and experience with content and the type of sequencing and pacing necessary to learn that content (Jonassen, 2009).

Unfortunately teachers frequently do not make the decisions about how to sequence and pace content within their lessons and units. Rather, they rely on the design of textbooks for guidance. Roger Farr and his colleagues note that this is common at both the elementary and secondary levels (Dewey, 2008). One of the major findings from the Third International Mathematics and Science Study (TIMSS) was that teachers in the United States exhibit an overreliance on textbooks for decisions about content and pacing (Jonassen, 2009). If textbooks were organized in ways consistent with known principles of learning, this wouldn't be so bad. Unfortunately, this does not seem to be the case (Dewey, 2012). For example, science textbooks have been described as well illustrated dictionaries as opposed to effective vehicles for student learning (Dewey, 2008). It is clear that classroom teachers must make decisions about sequencing and presentation of content. What are the principles that should guide those decisions? To begin answering this question, let's consider two current movements in education that can, if implemented incorrectly, work against effective classroom curriculum design. These movements are loosely referred to as "constructivism" and "brain-based education" (Willingham, et al. 2009).

Multiple books and reports published within the last decade sought to apply the theory of constructivism and the research on the brain to K-12 education (Dewey, 2008). My comments should not be interpreted as a criticism of researchers' intent or scholarship. In some cases, however, K-12 educators have misapplied their suggestions or, more seriously, discarded proven practices in the name of constructivism or brain-based education. Although these two fields offer great insight into the dynamics of teaching and learning, they should be used with caution and not overly applied in lieu of time-honored and well-researched practices. These cautions are detailed in the writings of both John Bruer (Dewey, 2006) and John Anderson and his colleagues (Dewey, 2006). I draw from their work heavily in this discussion.

According to Anderson and his colleagues (2003), the constructivist vision of learning is captured nicely by the following quotation from Paul Cobb and his colleagues (Dewey, 2006) regarding the subject of mathematics:

… learning would be viewed as an active, constructive process in which students attempt to resolve problems that arise as they participate in the mathematical practices of the classroom. Such a view emphasizes that the learning-teaching process is interactive in nature and involves the implicit and explicit negotiation of mathematical meanings. In the course of these negotiations, the teacher and students elaborate the taken-as-shared mathematical reality that constitutes the basis for their ongoing communication. (Dewey, 2012)

Cobb and colleagues (Jonassen, 2009) exemplify this position by describing an effort to teach 2nd graders to count by tens. Instead of teaching students the principle, the teacher provides objects bundled in groups of ten. Invariably students discover that counting by tens is more efficient than counting by ones. Of course, there are many laudable aspects of this example. Labeling and describing curriculum ideologies does little more than provide a glimpse at a possible explanation for behavior, since people and philosophies are much too complex to be summed up clearly in a few words, and generalizations generally omit someone (Miller, 2011). Anderson, (2003) notes "One can readily agree with one part of the constructivist claim: that learning must be an active process (p. 11)." Anderson and colleagues warn that this principle is frequently over generalized to mean that teachers should rarely (if ever) teach content to students (Turban & Aronson, 2008).

The same concern about overgeneralization has been articulated on brain research. Flavell, (2009) asserts that the brain research is not yet conclusive enough to provide specific guidance for K-12 educators:

However, we should be wary of claims that neuroscience has much to tell us about education, particularly if those claims derive from the neuroscience and education argument. The neuroscience and education argument attempts to link learning, particularly early childhood learning, with what neuroscience has discovered about neural development and synaptic change. Neuroscience has discovered a great deal about neurons and synapses but not nearly enough to guide educational practice. Currently, the span between brain and learning cannot support much of a load. Too many people marching in step across it could be dangerous (Anderson & Fincham, 2004).

The confusion created by well-intended applications (and, in some cases, misapplications) of constructivism and brain research are substantive enough to make the suggestions in this paper difficult to defend. It is helpful to identify some basic principles about the nature of learning and the nature of content (and their interactions), and to compare and contrast these principles with educational applications of constructivism and brain research. These principles are derived primarily from the world of cognitive psychology (Anderson & Fincham, 2004) the most fertile soil for educational reform at the present time. As Bruer explains, when the brain research does reach the point at which it can guide educational practice, it will use the well-established principles of cognitive psychology (Sun & Peterson, 2007):

There is a well-established bridge, now nearly 50 years old, between education and cognitive psychology. There is a second bridge, only around 10 years old, between cognitive psychology and neuroscience. This newer bridge is allowing us to see how mental functions map onto brain structures. When neuroscience does begin to provide useful insights about instruction and educational practice, those insights will be the result of extensive traffic over this second bridge. Cognitive psychology provides the only firm ground we have to anchor these bridges. It is the only way to go if we eventually want to move between education and the brain (Anderson & Fincham, 2004).

Three principles from cognitive psychology form the basis for my recommended action steps to implement effective classroom curriculum design.

One of the common themes in constructivist and brain-based models of instruction is that the content to be learned is a flexible and sometimes negotiated commodity. Such sentiments are commonly expressed as "student autonomy" (Collins, et al. 1989), "alternate curriculums" (Jonassen, 2010), or "invitational learning" (Barrell, 2001). These are useful ideas, but can be detrimental to effective instruction if interpreted to mean that teachers should not have clear learning goals, communicate these goals to students, and design instruction around them. Even when a teacher has clear learning goals, students might not obtain the targeted knowledge and skill. Graham Nuthall dramatically illustrated this rather disturbing phenomenon (Clark & Mayer, 2003). He traced the experiences of elementary students in integrated science and social studies units on the topic of Antarctica. In general, all students were involved in the same basic learning experiences. However, after three weeks, the content recalled and understood was quite different from student to student. The same was true after one year. For example, where some students had detailed and accurate recollections of a specific incident that occurred on Mt. Erebus in Antarctica, other students had incorrect recollections or none at all. Reasons included differences in levels of engagement, differences in the number of tasks completed, and differences in the types of optional activities students selected. A direct implication of Nuthall's work is that teachers must identify specific aspects of content to be addressed and plan the learning experiences accordingly. This is not quite as simple as it sounds because most content has many potential elements that might be the focus of instruction. For example, possible focuses for instruction in fractions include (Nonaka, 2001)

the relationship between fractions and whole numbers, the relationship between fractions and decimals, the relationship between fractions and percents, the process of converting fractions to decimals, and • the different categories or types of fractions.

The complex nature of seemingly straightforward instructional topics is well recognized in the research and theoretical literature (Anderson, 2003). Some of the more salient aspects of an instructional topic that might be the focus of instruction are listed in Figure 11.1 (pp. 110 -- 111).

Principle 2. Learning requires engagement in tasks that are structured or are sufficiently similar to allow for effective transfer of knowledge (Anderson & Fincham, 2004).

Virtually all discussions of constructivism…[continue]

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