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Mathematics Curricula & Students’ Opportunity to Learn Measurement
Leslie Dietiker Presenting for The STEM Project Michigan State University
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Personnel & Support (in addition to NSF)
Project Staff PI: Jack Smith Graduate Students: Gulcin Tan (Turkey), Kosze Lee (Singapore), Hanna Figueras (Finland/US), Leslie Dietiker (US) Financial & Intellectual support from the Center for the Study of Mathematics Curriculum (NSF, CLT) Note our international character! 9/16/2018 STEM, 2007 Pre-Session
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What is STEM? “Strengthening Tomorrow’s Education in Measurement” (funding from NSF/REESE) Project Goal: Assess the capacity of U.S. written and enacted curricula to support students’ robust learning of measurement Elementary & Middle school years Focus on Spatial quantities: Length, Area, & Volume 9/16/2018 STEM, 2007 Pre-Session
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Why Measurement? (of length, area, & volume)
Important mathematics for both college-bound & work-bound students Our poorest national performance (NAEP, TIMSS) Largest gap between white and minority students Research documents errors & misconceptions, but has given no explanation of difficulty Can’t address the problem without an explanation Last item: We don’t know where to focus (teacher preparation, curriculum, professional development) or what to focus on 9/16/2018 STEM, 2007 Pre-Session
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The Big Picture (Contributing Factors)
Research evidence suggests that many factors contribute: Limitations in written curricula Chosen content & allotted instructional time Problems in teacher-led classroom discourse Miscommunication about quantities Shift from spatial to numerical focus Static representations (area, volume) Limitations in elementary teachers’ knowledge Chosen content & allotted time are both driven by state standards’ guidelines; basic reality: more GLEs to cover than available time Static representations do not easily support students’ development of dynamic imagery of continuously changing quantities 9/16/2018 STEM, 2007 Pre-Session
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Why Examine Written Curricula?
Textbooks are foundational For students’ learning For teachers’ teaching & learning If textbook content is OK, move on to other factors If content is problematic, addressing the limits could have a wide ripple Textbook content may not engage what we know about learning measurement 9/16/2018 STEM, 2007 Pre-Session
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Which Curricula? Can’t analyze every series; Must pick
Goal: approximate national “report card” Elementary Curricula (K–6) Everyday Mathematics (#1) Scott Foresman/Addison Wesley Mathematics (#2) Saxon Mathematics Middle School Curricula (6–8) Glencoe’s Mathematics, Concepts & Applications (#1) Connected Mathematics Project (#2) 9/16/2018 STEM, 2007 Pre-Session
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Phase I: Overview (written curriculum analysis)
Analyze all target measurement content in 6 written curricula Step 1: Identify the content Pages in the texts Lessons & Individual problems Step 2: Analyze the capacity of content to support learning Step 3: Compile results and communicate with authors Core of the work: Conceptual Framework 9/16/2018 STEM, 2007 Pre-Session
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Phase II: Overview (enacted curriculum analysis)
Analyze classroom teaching of target topics from chosen curricula 5 topics: intro to length, complex lengths, intro to area, area & perimeter, intro to volume, volume & surface area Step 1: Locate local classrooms using curricula & target lesson sequences Step 2: Document sequences (3–5 days) Step 3: Analyze enacted content using the framework (from Phase I) “Locate” means (1) find the school and gain access, (2) work with teachers to locate lesson sequences (grade and time during the year) Some topics may be taught at the same grade level 9/16/2018 STEM, 2007 Pre-Session
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The Cornerstone: Our Conceptual Framework
Currently under development 5 components General curricular approach Measurement core: concepts, properties, & relationships (General & Specific to L, A, V) Relationships between quantities (Area & Perimeter, Surface Area & Volume) Descriptive vocabulary Attention to student difficulties Motivation for measurement?? Development has focused thus far on Dimensions 1–3 General curricular approach: not measurement directly, need to understand approach (list some elements) and demonstrate it to authors Measurement core: Generally applies to all 3 quantities (L, A, V), but typically is not stated to the student in general terms Relationships between these pairs of quantities have been clear weak spots in students’ learning; worthy of special attention Descriptive vocabulary is an assessment of the language permitted and supported for talking about L, A, V, especially in early years Attention to student difficulties (e.g, “misconceptions”) is more likely in Teacher Editions (and materials for teachers) For Motivation: the specific question is how to curricula introduce and motivate measurement, that is, the need to measure; We don’t expect that there will be a great deal of content devoted to this issue 9/16/2018 STEM, 2007 Pre-Session
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Key Stances in Framework
Curricula should build on what we know about learning (e.g., student difficulties) Quantities are fundamental (debt to Pat Thompson, Rich Lehrer, others) L, A, V are quantities prior to measurement Can think about & talk about them without units, iteration, and enumeration Building/choosing units is key step Understanding is a key instructional goal “Understanding” supports novel problem solving, application to measurement of new quantities, higher-level mathematics and science 9/16/2018 STEM, 2007 Pre-Session
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Closing: Our hopes We will find gaps and limitations, but….
How substantial? Variation across curricula? “National report card” will be compelling assessment Authors & publishers will be open to feedback Results will help orient future steps, in research and development 9/16/2018 STEM, 2007 Pre-Session
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Feedback No web-site yet Now, in person Later, by e-mail
Jack Leslie 9/16/2018 STEM, 2007 Pre-Session
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