Young Children’s Actions on Length Measurement Tasks: Strategies and Cognitive Attributes

• In Event: 1-134 - Development, Refinement, and Evaluation of Learning Trajectories for Geometric Measurement

Integrative Statement

Hypotheses


The Comprehensive Research-based Early Math Ability Test (CREMAT) project is designing a cognitively diagnostic, adaptive assessment yielding more useful and detailed information about children’s knowledge of mathematics in less time than previously possible using a combination of Q-matrix Theory, Rule Space Method (RSM), and poset models (for computer-adaptive testing, CAT).

Our hypothesis is that the items we adapted represented veridical measures of the levels of thinking they were posited to measure and that the attributes linked to them in the Q-matrix were those used by children to solve each item.

Study Population

We conducted interviews of 833 pre-K to Grade 3 children in a large, school district.

Method

Previous research and conceptual analyses established, and RSM statistical analyses refined, the Q-matrix that connected 70 length items and these strategies to attributes. To evaluate and refine these connections, we performed individual interviews, recording both correctness and strategy use. We examined these data to ascertain whether the coded attributes in the Q-matrix matched children observed behaviors, or whether fewer, additional, or alternate attributes were warranted.

Results

We will organize findings into categories: (a) items retained whose attribute assignments were confirmed, (b) items retained after minor task modification, (c) items removed from the CAT assessment, and (d) items retained after their attribute assignments were revised. We will report the number of items in each category and then describe several items that serve as exemplars, emphasizing those that suggested refinements in some attributes or in the item. Categorizations and refinements were determined with a combination of theory, frequency of strategy use and the relationship to correctness, detailed analyses of whether the attributes assumed to underlie each strategy were observed, and considerations of correctness and frequency of strategy.

We found that 61% of the original items were validated to show the use of and need for the attributes that were initially assigned to them; 14% of the items were removed from use in the CAT assessment because we determined that the correctness of children’s responses did not reliably reflect the attributes the items were intended to assess. That is, some children often used the attributes, but others did not and found other ways to generate correct answers, such as visual estimation. These items were retained only in the (original) non-CAT assessment version because the one-on-one interview format allows direct observations of the strategy. Without such observations, these items would reliably indicate children’s possession of the attributes assigned to them in a CAT environment. Finally, about 24% of the items were retained for the CAT, but only after adjustment of their attribute assignments. Such changes were considered carefully and will be re-checked using Q-matrix and RSM’s statistical techniques (Author et al., 2016).

In summary, at least for the domain of length measurement, we produced a satisfactory CAT that researchers and teachers will be able to administer easily, thus enabling efficient, timely, targeted, and effective formative assessment—one of the most effective but under-utilized pedagogical strategies (National Mathematics Advisory Panel, 2008). We will continue to work on other mathematical topics.
 

Authors

• Holland Banse, University of Denver
  Presenting Author

• Douglas H. Clements, University of Denver
  Non-Presenting Author

• Julie Sarama, University of Denver
  Non-Presenting Author

• Curtis Tatsuoka, Case Western Reserve
  Non-Presenting Author

• Candace Joswick, University of Denver
  Non-Presenting Author

• Aaron Hudyma, University of Denver
  Non-Presenting Author

• Douglas Van Dine, Metropolitan State University of Denver
  Non-Presenting Author