Framing the Analysis of Written M easurement Curricula Michigan State University

1. Locate Measurement Content Design Basic Framework Generate Knowledge Elements Code Measurement Content Compile Results Framing the Analysis of Written Measurement CurriculaMichigan State University Project Background What is Measurement? Research Questions Types of Measurement Rationale • Why focus on spatial measurement? • Poor national performance (NAEP) • U.S. 8th graders lag further behind other developed countries in this content area (TIMSS; National Center of Education Statistics, 1997) • Largest gap between white students and black and Hispanic students is greatest in this content area (Lubienski, 2003) • Important for both college-bound and work- bound students • Research has documented errors and misconceptions in measurement, but has not given any explanation of the difficulty and the problem cannot be addressed without an explanation • What is the capacity of U.S. K – 8 written and enacted curricula to support students’ robust learning of measurement? Pre-measurement -- Comparative, non-metric measurement, such as determining which of two objects is longer Measurement Proper – The iteration of a spatial unit (and possibly subunit) to quantify the spatial attribute of an object or figure Reasoning with or about measurement -- Reasoning with or about spatial quantities, such as determining the time it takes to travel a certain distance at a given constantrate or using the Pythagorean Theorem to find the length of the side of a triangle Research Team Principal Investigator: Dr. Jack Smith, MSU Project Team: Gulcin Tan Sisman (METU), Kuo-Liang Chang, Leslie Dietiker, Hanna Figueras, Pat Greeley, KoSze Lee, Lorraine Males, Aaron Mosier, Matt Pahl Contexts We have limited our focus to Spatial Measurement of length, area, and volume. Beyond traditional measurement content, several other content strands involve spatial measurement: • Looking at this bar graph, what food is most popular for lunch? • Given part of a figure and the line of symmetry draw the other part • Given a square draw lines that divide the square into fourths. Development Process J E A Types of Knowledge K G C • Conceptual knowledge concerns the basic principles that underlie and justify measurement procedures, systems, notations, and tools. • Procedural knowledge concerns the processes of measuring and estimating the three spatial quantities. • Conventional knowledge concerns the systems, notations, and tools that human have invented to carry out measurement in standardized ways. D F I B H L Everyday Mathematics, 2007, Wright Group/McGraw Hill, Grade 1, p. 287 Saxon Math, 2007,Saxon Publishers, Course 2 (MS), p. 108 Michigan Mathematics, Scott Foresman Addison Wesley, Grade 1, p. 341