What Do Elementary Textbooks Say about Estimation of Length?

1. Scott Foresman Addison Wesley Mathematics 1 366 Scott Foresman Addison Wesley Mathematics K 141B Scott Foresman Addison Wesley Mathematics 1 366 L H I A M C J B K What Do Elementary Textbooks Say about Estimation of Length? Division of Science & Mathematics Education and Teacher Education, Michigan State University Kuo-Liang Chang, Lorraine Males, Aaron Mosier, and Funda Gonulates Sample Coding of Length Estimation Background/Rationale Results The curricula appear homogeneous in their attendance to Start/End and Unit Indication. Since they are heterogenous with respect to the other categories, we could not combine the data to make solid, overarching claims about ambiguity. It appears that Start/End and Unit Indication are attended to the most. The curricula are, however, homogenous in the quantity of ambiguous categories per task (Chi-squared=1.38, df = 4). As a result, the curricula can be aggregated for this analysis. Of all instances of Visual Estimation that were identified, less than 2% lacked ambiguity and more than 25% were ambiguous in more than 2 categories. Research suggests that the teaching and learning of length estimation is often associated with vagueness and ambiguity (Forrester & Pike, 1998; Joram, Subrahmanyam, & Gelman, 1998). Some researchers have attributed ambiguity and vagueness of mathematical practice in classrooms to different interpretations of meaning between individuals (Bishop, 1988; Christiansen, 1997; Voigt, 1994). Based on Kasten and Newton’s (2008) literature review on measurement learning, four focusing questions which need to be addressed in order for a prompt involving estimation to be clear are identified as follows: 1. Which dimension should be estimated? 2. Where are the starting and ending points of the estimation? 3. What is the unit of the estimate (e.g. inches, cubes)? 4. How precise should the estimate be? We have chosen to analyze written curricula which have been identified as contributing generally to the poor teaching and learning of spatial measurement (Kamii & Kysh, 2006; Lehrer, 2003). Research Questions • We ask the following two research questions in this study: • Which of the focusing questions are attended to and to what extent in the instances of length estimation found in elementary school curricula? • What do the curricula provide teachers or students to do about the possible foci of attention? D E F Discussion Method G Given the results, it appears as though concern about the ambiguity of Visual Estimation tasks is justified. With more than 25% of the tasks ambiguous in several categories, there is a lot of room for improvement. A theme that appeared in the data was the lack of reference to precision. Simply attending to precision would have a positive impact on 75% of items. It is interesting to note that Saxon and Scott-Foresman appear to be quite homogeneous in the attention paid to different categories. This is surprising, because they were constructed with different design principles. It should be noted that there was some content that STEM1 identified as Visual Estimation that did not fit into our conception of the topic. This could have an impact on our results. Identify Estimation Texts Select Elementary Curricula Coding Generate Coding Scheme Compile Results 1 The analyses reported in this paper were carried out with support from the National Science Foundation (REC-0634043, John P. Smith III, PI) to analyze the content of written curricula in the area of spatial measurement. The opinions, findings, and conclusions or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of NSF.