Skip to main content

Currently Skimming:

4 Content Analysis
Pages 65-95

The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.


From page 65...
... An analysis of a curriculum's content should extend beyond a mere listing of content to include a comparison with a set of standards, other textual materials, or other countries' approaches or standards. For the purposes of this study -- reviewing the evaluations of the effectiveness of mathematics curricula -- content analyses will refer to studies that range from documenting the coverage of a curriculum in relation to standards to more extended examinations that also assess the quality of the content and presentation.
From page 66...
... Those classified as internal were undertaken directly by an author, project evaluator, or member of the staff of a publisher associated with the curricular program. Content analyses categorized as external
From page 67...
... CONTENT ANALYSIS 67 TABLE 4-2 Content Counts by Program Number of Reviews by Program Curriculum Name 0 1 2-5 >5 Everyday Mathematics 7 Investigations in Data, Number and Space 2 Math Trailblazers 1 Connected Mathematics Project 8 Mathematics in Context 7 Math Thematics 5 MathScape 1 MS Mathematics Through Applications Project 0 Interactive Mathematics Project 4 Mathematics: Modeling Our World (ARISE) 2 Contemporary Mathematics in Context (Core-Plus)
From page 68...
... LITERATURE REVIEW We identified four sources where systematic content analyses were conducted and applied across programs. They were (1)
From page 69...
... reflect what is known generally about student learning and effective teaching and, more important, the degree to which they support student learning of the specific knowledge and skills for which a content match has been found. · Summarize the relationship between the curriculum materials being evaluated and the selected learning goals.
From page 70...
... Mathematically Correct On the Mathematically Correct website, reviews of curricular materials are made available, often via links to other sites viewed as similarly aligned; we collected those pertaining to the relevant curricula. A set of reviews of 10 curricular programs for grades 2, 5, and 7 by Clopton and colleagues presented a systematic discussion of the methodology where the reviewers selected topics "designed to be sufficient to give a clear impression of the features of the presentation and an assessment of the mathematical depth and breadth supported by the program" (1999a, 1999b, 1999c)
From page 71...
... Although these reviews identified missing content strands and produced judgments of general levels of quality, we found them to be of limited rigor for use in our study; in particular, this was because of their lack of specificity on method. Other content analyses ranged from those by authors explaining the design and structure of the materials (Romberg et al., 1995)
From page 72...
... Each of these influences on the content analysis should be explicitly articulated to the degree possible as part of an evaluation report, a form of "full disclosure" of values and possible bias. Faced with the current status of "content analysis," we recognized that rather than specifying methods for the conduct of content analyses to produce identical conclusions, we needed to assist evaluators in providing decision makers with clearer delineation of the different dimensions and underlying theories they used to make their evaluations.
From page 73...
... . There was agreement among respondents that the expertise of mathematics educators is needed to ensure careful considerations of student learning and classroom practices (McCallum testimony at the September 2002 Workshop)
From page 74...
... Because the United States is at the forefront of scientific and technological advances, the Singapore comparison dimension cannot be ignored: content analysis studies that make comparisons across a variety of types of curricular material must be encouraged and supported. The Adams report demonstrated the importance of the selection of the standards and the comparative curricula in their reported results.
From page 75...
... Once the participants, standards, and comparison curricula are selected and identified, other factors remains that are useful in creating the necessary types of distinctions to conduct the content analyses. In the next section, we identify some of these additional considerations.
From page 76...
... Both are neces sary: topics that are mentioned in the table of contents but unaccompanied by a realistic plan for preparing teachers and reaching students cannot be said to add to the content of a curriculum, nor can activities that work well in the classroom but are mathematically ill conceived." -- William McCallum, University of Arizona "One very important [issue of vital importance to mathematics education that is not captured by broad measures of student achievement] is the maintenance of a challenging high-quality education for the best students.
From page 77...
... In developing a method to determine these factors, many content analyses found that determining comprehensiveness can be difficult if curricular programs offer too many disjointed and overlapping topics. This finding motivated a call for the clarity of objectives or the identification of the
From page 78...
... The pendulum has, apparently, swung to the other side, and we feel a return to some middle ground emphasizing both conceptual knowl edge and computational efficiency is warranted. As an example of the positive impact of content analyses, the authors have indicated that in response to criticisms and the changes advised by PSSM, plans are being made to strengthen these dimensions in subsequent versions (Adams et al., 2000)
From page 79...
... It appears that not all content analyses paid appropriate attention to the accuracy issue. For example, Richard Askey, University of Wisconsin, in commenting on the Department of Education reviews to the committee during his September 17, 2002, testimony, pointed out that "In these 48 reviews, no mention of any mathematical errors was made.
From page 80...
... Richard Askey (University of Wisconsin) , who has examined curricular adequacy, responded at the Workshop to our question as to whether the program's content reflects the nature of the field and the thinking that mathematicians use.
From page 81...
... CONTENT ANALYSIS 81 In the formula, B is the area of the cross-section at the base, M is the area of the cross-section at the "middle," T is the area of the cross-section at the top, and h is the height of the space shape. The authors of Core-Plus informally explain this formula as a form of a weighted average, then use it to derive the formula for the particular cases of a triangular prism, a cylinder, a sphere, and a cone.
From page 82...
... Intent matters. These differing views about content provide a valuable window into the challenges associated with the evaluation of content analyses.
From page 83...
... In reference to mathematics curricula, decisions on balance include: conceptual versus procedural, activities versus practice, applications versus exercises, and balance among selected representations such as the use of numerical data and tables, graphs, and equations. The level of use and reliance on technology is another consideration of balance, and many content analyses comment directly on this.
From page 84...
... Although the efficiency of doing some activities depends heavily on the teachers' comfort level with the technology, these firsthand experiences are efficient when compared to others that could be used." A discussion of the balance of the use of technology is a useful way for a reviewer to indicate his or her stance on the appropriate place of technology in the curriculum. In content analyses, we indicated that rather than making statements that indicated either complete rejection or unbridled acceptance of technological use, a more useful approach is to more clearly identify effects on particular mathematical ideas in terms of gains and losses.
From page 85...
... For some, mathematics curricula derive their coherence from their connection to a set of concepts ordered and sequenced logically, carefully scripted to draw on students' prior knowledge and prepare them for future study, with extensive examples for practice. For others, the coherence is derived from links to
From page 86...
... Clearly, all reviewers claim that their approach best serves the needs of the students, but differences in how this is evaluated emerge among content analyses. The first criterion we categorized in this dimension is student engagement.
From page 87...
... (Instructional Category II, Building on Student Ideas about Mathemat ics -- http://www.project2061.org/tools/textbook/matheval/13saxon/ instruct.htm) The next set of passages demonstrates that not all reviewers see the most important source of student engagement as being through the use of context or building on prior knowledge, but rather by the careful choice of student example, sequencing of topic, and adequate and incremental challenge.
From page 88...
... This is far too late, for students need time to develop algebra skills, and plenty of problems using algebra to develop the needed skills." Christian Hirsch, Western Michigan University and author of Core-Plus, responded in written testimony, "the topic is treated in CPMP Course 3, pages 212-214 for the beginning of the expansion/factorization development," and that "students study Course 3 in grade 11 or grade 10, if accelerated." Yet including timeliness raises the legitimate issue of whether such a delay in learning this material could put students at a disadvantage when compared with the growing number of students entering college with Advanced Placement calculus and more advanced training in mathematics. Although absent from some studies, this timeliness theme is consistent through those content analyses that focused on the challenge of the mathematics.
From page 89...
... . In the content analyses, support for diversity was typically addressed only in terms of performance levels, and even then, high performers were identified as needing the most attention (Howe testimony)
From page 90...
... The quality of attention to assessment in these content analyses is generally weak. In the Mathematically Correct Reviews (Clopton et al., 1998, 1999a, 1999b, and 1999c)
From page 91...
... For example, in reviewing the assessment practices for each of these three questions concerning the Interactive Mathematics Program (IMP) , the reviewers wrote: There is at least one assessment item or task that addresses the specific ideas in each of the idea sets, and these items and tasks require no other, more sophisticated ideas.
From page 92...
... Testimony indicates that even for more traditional curricula, professional development is needed. Deeper understanding is possible only through added support; if stipulated, such requirements should be reported in content analyses.
From page 93...
... . Differences in content analyses are inevitable and welcome, as they can contribute to providing decision makers with choices among curricula.
From page 94...
... It is possible, for example, that based on critical content analyses, subsequent versions of reform curricula could be revised to strengthen weak or incomplete areas, traditional curricular materials could be revised to provide more uses of innovative methods, and new hybrids of the approaches could be developed. At the same time, while the issue of content analysis is critical from philosophical, academic, and logical viewpoints, it is not clear what degree or type of impact current content changes have on student learning and
From page 95...
... Content analyses are also valuable to inform the conduct of comparative studies. A content analysis can help an evaluator to select appropriate outcome measures, to measure particularly important content strands, and to concentrate on the essential aspects of implementation and professional development.


This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More information on Chapter Skim is available.