1. Mathematics Curricula & Students’ Opportunity to Learn Measurement
Leslie Dietiker
Presenting for
The STEM Project
Michigan State University

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. Feedback No web-site yet Now, in person Later, by e-mail
Jack
Leslie
9/16/2018
STEM, 2007 Pre-Session