1. TEXTUAL EXPRESSION OF AREA MEASUREMENT IN ELEMENTARY CURRICULA: ILLUMINATING OPPORTUNITIES TO LEARN Funda Gonulates, Lorraine Males ©STEM @ MSU 2011 – PME Ankara, Turkey Strengthening Tomorrow’s Education in Measurement (STEM) Project

2. Session Overview 2 Introductions STEM Project Overview STEM Project Methodology Background Results Discussion [last 20 minutes] ©STEM @ MSU 2011 – PME Ankara, Turkey

3. Introductions Lorraine - 4 th yr doctoral student at MSU currently working on my dissertation that investigates teachers opportunities to learn from middle school curriculum materials teachers’ guides and working for the STEM project (all four years). At MSU I have taught secondary methods and supervised student teaching interns and before graduate school I taught middle/high school (6 – 12) for 8 years in the US in New York, Hawaii, Massachusetts, and New Jersey. 3 ©STEM @ MSU 2011 – PME Ankara, Turkey Funda – 3 rd yr doctoral student at MSU, part of STEM project for three years, taught elementary content courses, history of mathematics. Interested in Curriculum and Instruction focus on algebra and geometry. Previously taught middle school (Grades 5-8) for 4 years in Istanbul. BS, MS Secondary School Mathematics Education –BU, Istanbul

4. STEM I (Fall 2007- Fall 2009) – Examine the curricular contribution to the problem Research Question: What “opportunity to learn” (OTL) spatial measurement do current US elementary mathematics curricula provide? Meeting with curriculum authors STEM II (August 2009 – July 2012) – Continuing curricular analysis – Teacher education (prospective and practicing teachers) – International comparisons (Singapore) 4 The STEM Project ©STEM @ MSU 2011 – PME Ankara, Turkey

5. The STEM Project Initial situation – Problem in measurement (NAEP, TIMSS) – We identified possible factors. 5 ©STEM @ MSU 2011 – PME Ankara, Turkey

6. ‘ Possible Contributing Factors 6 The Problem of Learning Spatial Measurement The Problem of Learning Spatial Measurement Time & Timing of Instruction Time & Timing of Instruction “procedural” “calculational” Discourse Challenges Teachers’ Understandings Limitations of Written Curricula Limitations of Written Curricula State Standards & Assessments Static Representations ambiguous terms ambiguous reference (2D, 3D) essential content student challenges content presentation in text Focus of instruction ©STEM @ MSU 2011 – PME Ankara, Turkey

7. STEM – Three United States Curricula The three carefully chosen curricula are:  Scott Foresman- Addison Wesley Mathematics  UCSMP’s Everyday Mathematics  Saxon Math 7 ©STEM @ MSU 2011 – PME Ankara, Turkey

8. STEM – Our Analysis In our analysis we are looking at every lesson, problem, and activity of teaching curricula for two important aspects:  Knowledge elements - Spatial measurement knowledge (conceptual, procedural, conventional) [What content is in the textbook]  Textual elements - The ways in which this knowledge is expressed (statements, demonstrations, worked examples, questions, problems, games) [How the content is presented in the textbook] 8 STEM @ MSU 2011 – PME Ankara, Turkey

9. Curriculum Coding Scheme (Simplified Version) 9 Textual ElementsDefinition Problems (Teacher/Student) Query requiring conceptual, procedural, or conventional knowledge and two of the following are true: a) not under teacher direction; b) all students expected to respond; c) high cognitive demand Questions (Teacher/Student) Query requiring conceptual, procedural, or conventional knowledge and two of the following: a) under teacher direction; b) limited number of students expected to respond; c) low cognitive demand Statements (Teacher/Student) Assertions of basic principles, a set of directions to complete a procedure or an assertion about tools, notations, and systems Demonstrations A measurement principle is exemplified, a set of steps/actions for a measurement process is performed, or the application of a convention is presented Worked ExamplesA completely worked out solution that expresses some conceptual, procedural, or conventional knowledge ©STEM @ MSU 2011 – PME Ankara, Turkey

10. Sample Curriculum Page STEM 2010 - MCTM Conference10

11. Sample Curriculum Page 11 ©STEM @ MSU 2011 – PME Ankara, Turkey (SFAW, Grade 3, p. 468) Problem Statement

12. Research Questions – How is area content expressed in written curriculum materials? Textual expression – What does this type of analysis illuminate? STEM 2010 - MCTM Conference12

13. Background Why area? – Area needed attention because is often perceived as a computational activity (Length x Width ) rather than as a measurement activity in its own right (Lehrer, 2003). Why written curriculum? – Written curriculum is a potential factor contributing to student poor performance in measurement – Features of written curriculum, such as textual elements, have received little attention in curriculum analysis (Stein, Remillard & Smith, 2007) and we hypothesize that these elements provide different Opportunities to Learn (OTL). 13 ©STEM @ MSU 2011 – PME Ankara, Turkey

14. Opportunity to Learn For students to have adequate opportunities to learn (OTL) area measurement they must be positioned in ways that allow them to identify as both “knowers” and “doers” of mathematics (Esmonde, 2009; Gresalfi & Cobb, 2006) 14 ©STEM @ MSU 2011 – PME Ankara, Turkey

15. 15 Results-Textual Expression by Curriculum and Grade ©STEM @ MSU 2011 – PME Ankara, Turkey

16. Results- Distribution of Content in terms of C, P, V ConceptualProcedural Conventional Total a EM K0.0100.0 0.0 20 12.897.2 0.0 144 26.587.6 5.9 185 36.091.8 2.2 730 48.189.2 2.7 732 SFAW K2.197.9 0.0 292 10.299.8 0.0 492 23.496.6 0.0 298 310.388.1 1.7 477 44.694.1 1.3 1039 Saxon K0.0100.0 0.0 233 11.398.7 0.0 240 21.098.5 0.5 391 32.593.6 3.9 514 41.789.7 8.6 888 16 ©STEM @ MSU 2011 – PME Ankara, Turkey

17. 17 Textual Expression of Conceptual Knowledge by Curriculum and Grade ©STEM @ MSU 2011 – PME Ankara, Turkey

18. Curricular Voice for Statements Expressing Conceptual Knowledge 18 ©STEM @ MSU 2011 – PME Ankara, Turkey

19. Selective Analysis of Area Measurement 19 Stephan and Clements Instructional Recommendations (2003, P. 13-14) [Conception of Area Measurement (a) construct the idea of measurement units (including measurement sense for standard units) [Conception of Area Measurement] [Covering and Counting] (b) have many experiences covering quantities with appropriate measurement units and counting those units [Covering and Counting] [Spatial Structuring] (c) structure spatially the object they are to measure [Spatial Structuring] [Unit Measure Compensation] (d) construct the inverse relationship between the size of a unit and the number of units used in the measurement [Unit Measure Compensation] ©STEM @ MSU 2011 – PME Ankara, Turkey

20. Textual Expression of Recommendations 20 ©STEM @ MSU 2011 – PME Ankara, Turkey

21. Summary 21 ©STEM @ MSU 2011 – PME Ankara, Turkey Procedural focus Procedures were often in the form of Queries in which students were expected to engage Concepts were often in the form of Statements in which students were told or merely read the content Significant direct access to procedural elements in student materials but not conceptual elements Students positioned more as “doers” and less as “knowers”

22. Thank you! We want to thank the National Science Foundation for funding this work We want to thank you for coming! For more information :http://www.msu.edu/~stemprojhttp://www.msu.edu/~stemproj Please fill out our contact form on our website If you have any questions please e-mail us at: stemproj@msu.edustemproj@msu.edu 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 22 ©STEM @ MSU 2011 – PME Ankara, Turkey