1. Why Study Written Mathematics Curricula (when you care About Learning)?
Jack Smith & Raven McCrory
Michigan State University
NCTM Research Pre-Session Presentation
April 20, 2010; 3 – 3:40pm
Support from the National Science Foundation gratefully acknowledged
(REESE & CAREER Programs)

2. Overview
Our Session Goal: support discussion about research on mathematics curriculum (written, enacted, & otherwise)
Structure of the talk (≤ 20 minutes of presentation)
List of reasons with brief rationale
Dialogue thereafter
Discussion of reasons
Discussion of issues related to research on mathematics curriculum more generally (e.g., relations between written & enacted)
Do personal background orally: Focus on learning; long path to curricula
Use the inside and outside the talk language

3. Framing for “Curriculum”
Influence from and homage to Stein, Remillard, & Smith for How Curriculum Influences Student Learning (2007)
Written curriculum
Intended curriculum
Enacted curriculum
Student learning
Temporal order with transformations at each step
“Written curriculum” is broader than term than “textbook”
Mary Kay Stein, Janine Remillard, Peg Smith, chapter 8, Handbook of Teaching and learning Mathematics, 2nd edition—great review chapter
They acknowledge that they use the term almost interchangably.

4. Source: Two Projects
STEM Project: Detailed analysis of the spatial measurement content in three elementary (K–5) mathematics curricula (length, area, & volume)
Do current curriculum materials in the U.S. adequately support students’ learning of spatial measurement?
What measurement knowledge is presented & how is it expressed?
MEET Project: Detailed analysis of textbook content in pre- service elementary teachers mathematics content courses
Treatment of problematic concepts (fractions & rational numbers)
How much does this content shape classroom instruction?

5. Reason #1: Effect on Student Learning
Written curricula (textbook content) directly influence what mathematics students learn (via opportunity to learn)
Presence (or absence) of core content matters
Direct effects & mediated effects (via teachers’ enactments)
STEM: Unit Iteration in measurement
MEET: Varying definitions of fractions

6. Reason #2: Effect on Teacher Learning
What is true for students is doubly true for teachers
Round #1: Written curricula as representations of knowledge (in their student years)
Round #2: Written curricula as representations of knowledge (in their teaching years)
Common focus, emphasis, approach can have strong delimiting effects
Caveat: Teachers also experience variability in curricula; but how many and how much?

7. Reason #3: Help to Understand Difficulty
Mathematical activities in school are one source of students’ (and teachers) mathematical experience & learning
Careful examinations of written curricula can contribute to our understanding of where and why students struggle
Core issues: Conceptual clarity and completeness
STEM:
The failure to problematize units
The failure to unpack multiplication (L x W = # of squares)
MEET: Variability in fraction definitions matter

8. Learning to Variability
The first three reasons have all concerned the fundamental issue of how curricula shape students’ and teachers’ mathematical experience & learning
The second three reasons all concern issues of variability, at present and across time
Curricular variability can provide insights into choices; make them more visible
Heuristic: Make the familiar a bit more strange
Shift in the argument

9. Reason #4: Variability exists In U.S. Curricula
Despite the dampening effects of state standards (since NCLB), U.S. curricula are not identical in content, emphasis, and approach
NCTM Standards (1989) led to considerable variability and much of that diversity remains
Examine variability at the level of particular topics
STEM: EM’s investment in rectangular arrays => options for unpacking multiplication of lengths
Quote Stein, Smith, & Remillard on item 2

10. Reason #5: Historical Changes Provide insight
Both continuity and change over time in the content and approach of U.S. mathematics curricula
New math’s emphasis on mathematical structure
Geometry via transformations
Standards-based enrichment of middle school content
But we should not forget or ignore the past (beyond a single lifetime)
Past choices can locate, highlight, and even question current choices
[Example?]

11. Reason #6: Variability Exists Across nations
Cross-national curricular comparisons has recently focused on linking curricular content & performance
That’s unfortunate; simplifies a very complex system
Curricular choices of different nations can highlight our own choices and widen our sense of possibility
Choices should carry supportive arguments; not just the “wisdom of history”
STEM Example: Russian approach to elementary mathematics via measurement

12. Conclusion
We are not arguing for a single-minded focus on written curricula, present and/or past
Written curricula are but one factor influencing students’ and teachers’ mathematical experience
Other important factors
Content expectations & assessments
Issues of enactment (especially classroom discourse)
Teacher knowledge
Our message: Let’s be aware of what we can learn

13. Questions
Does enactment move us closer to students’ learning (at least most of the time)?
Does enactment move us closer to teachers’ learning?
Does research on written curricula carry a risk of supporting a view that content is more important than interaction, activity, and sense-making (enactment)?
Other reasons for studying written curricula?
Return to the initial issue (the title)