1. Textual Expression of Knowledge in Curricula: Illuminating Opportunities to Learn Area Measurement Lorraine Males & Funda Gönülateş* Michigan State University Research Questions How is knowledge presented to students through textual elements in curricula for area measurement in grades K-4? Framework & Analysis Results Implications Rationale Students were asked to do, rather than know (little conceptual content) Students did not have direct access to conceptual content (mostly in Teacher materials) Stephan & Clements (2003) Covering and Counting recommendation expressed more than their other three recommendations (mostly expressed by procedural Queries) Poor performance in measurement including area (Blume, Galindo, & Walcott, 2007; Lehrer, 2003; Stephan & Clement, 2003; Kamii & Kysh, 2006). Instructional approaches become crucial in developing a strong understanding of area measurement With the reliance on curriculum materials by many teachers (Remillard, 2005) it is important to know: what area measurement content is provided in materials how area measurement is treated in these materials Important Points Curriculum materials provide: A Procedural focus, Mostly Queries (Q + P) As grades increase more content appears in Student materials Conceptual Knowledge is provided mostly by Statements in Teacher materials Data Sources Michigan Mathematics (Foresman-Addison Wesley, 2008) Everyday Mathematics (The University of Chicago School Mathematics Project, 2007) Saxon Math (Larson, 2004) Percentage of Knowledge Types in Each Curricula ConceptualProceduralConventional Total SFAW K2.197.90.0292 10.299.80.0492 23.496.60.0298 310.388.11.7477 44.694.11.31039 Saxon K0.0100.00.0233 11.398.70.0240 21.098.50.5391 32.593.63.9514 41.789.98.6888 EM K0.0100.00.020 12.897.20.0144 26.587.65.9185 36.091.82.2730 48.189.22.7732 Conceptual Statements S Statements T Queries S Queries T SFAW K0004 10100 22422 3471220 46141513 EM K0000 10310 20930 3816612 41011248 Saxon K0000 10003 20202 30661 40506 Taking a closer look at Conceptual Knowledge Area Coding Scheme Examples StatementsQuestionsProblemsDemosWEs STSTSTTS Conceptual Knowledge Unit Measure Compensation 1 (C) Definition of Area 1 (D) Meaning of Area Measure 1 (D) Order/Equality 1 (S) Procedural Knowledge Measure Area on a Grid, counting whole 2 (F) 1 (L) Measure Area on a Grid, counting whole and fractional 1 (J) Measure Area of a Rectangle on Grid, row and columns 1 (M) Measure General with support 11 (N, O, P, R) Measure by Covering with Sufficient Non- Standard Units 2 (B, C) Visual Estimation of Area 2 (G, I) Read an array 2 (A) Draw region X standard units with Support 1 (H) Conventional Knowledge Definition of non-standard area units 4 (D, E, K) Stephan & Clements(2003) provide the following recommendations: a)construct the idea of measurement units (including measurement sense for standard units) b)have many experiences covering quantities with appropriate measurement units and counting those units c)structure spatially the object they are to measure d)construct the inverse relationship between the size of a unit and the number of units used in the measurement (p.13-14) Building an Understanding of Area Michigan Mathematics, Scott Foresman Addison Wesley, Grade 3, p. 468 * This work is based on the work of the STEM Project, Principal Investigator: Dr. Jack Smith, Michigan State University Project Team: Rachel Ayieko, Kuo-Liang Chang, Yi-Ling Cheng, Dan Clark, Leslie Dietiker, Hanna Figueras, Funda Gönülateş, Pat Greeley, Jia He, Danny Johns, KoSze Lee, Lorraine Males, Aaron Mosier, Matt Pahl, Gulcin Tan Sisman (Middle East Technical University), Ashley Taglauer, Alexandria Theakston