Grading the Nation's Report Card Evaluating NAEP and Transforming the Assessment of Educational Progress (1999) / Chapter Skim
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Appendix C: A Sample Family of Items Based on Number Patterns at Grade 4
Appendix C: A Sample Family of Items Based on Number Patterns at Grade 4
Pages 237-255
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From page 237... ...
In fact, the NCTM Algebra Working Group realized that children can develop algebraic concepts at an early age and suggested that working with patterns of shapes and numbers helps to build the foundation for algebraic thinking needed in the later grades. RELEASED NAEP PATTERN ITEMS AS THE BASIS FOR AN ITEM FAMILY Not only did numerical pattern items appear on recent NAEP mathematics assessments, but also some of those items were released to the public.
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From page 238... ...
Also, the family could be created with minimal time spent on developing original items. However, a potentially serious limitation of this method is that taking items developed individually and putting them together as a set post hoc carries with it a degree of artificiality.
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From page 239... ...
For example, performance results could show that most fourth graders can work with patterns involving constant increases between the terms (Items 1, 2, and 3) , but performance levels could be lower for items involving patterns based on nonconstant increases (Items 4 and 5)
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From page 240... ...
ITEM 6 Nonconstant increase in a complex, problem solving setting FIGURE C-1 Progression of concepts within the number pattern family of items. SOURCE: Kenney (1999~.
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From page 241... ...
However, as illustrated in the example, it is possible to use existing NAEP materials as the foundation for building families. We recommend that future assessment developers build item families that better reflect the intentions for families of items described in the 1996 NAEP mathematics framework document.
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From page 243... ...
would best serve this purpose. The other versions are presented here as additional examples of simple pattern items based on single-digit, constant differences between consecutive numbers.
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From page 245... ...
The NAEP version, however, should be modified so that more information can be obtained from student responses. In particular, the original NAEP item asked for three numbers in the pattern based on a given constant increase of 50 students.
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From page 248... ...
The original NAEP item was discussed in an earlier section of this paper, and it had some flaws from the lack of analysis of performance results on both parts of the item pair together. In particular, the results did not completely reveal the degree of consistency between the rule selected by students and whether they used that rule to answer the second question.
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From page 249... ...
As noted earlier in the paper, this item and the ones that follow could provide evidence about an important misunderstanding about patterns; that is, the notion that all patterns (even those that are based on nonconstant differences) contain pairs of numbers that have a constant difference.
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From page 252... ...
It is scaffolded so that students must identify the first two nonconstant differences between the weights, in the hope that students will more easily recognize that the weight gains are decreasing between consecutive months. The final question involves a transition from the nonconstant differences to the actual weight of the puppy.
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From page 254... ...
As the culminating item, it has characteristics based on work done on the previous items. For example, Marcy's Dot Pattern involves a pattern of nonconstant differences between the number of dots in each step and requires students to identify the rule that underlies the pattern.
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From page 255... ...
:268-274. National Council of Teachers of Mathematics 1992 Curriculum and Evaluation Standards for School Mathematics Addenda Series, Grades K-6: Fourth-Grade Book.
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