Early Algebra and the Common Core: What Do Teachers Need to Know?
Susan Jo Russell, TERC and Deborah Schifter, EDC
Abstract: The phrase “properties of the operations” recurs throughout the elementary grades in the Common Core State Standards. How might elementary teachers introduce these properties to their students in ways that support students’ work in computation and provide a link between arithmetic and algebra? What do teachers need to know in order to enact the standards in these ways? In this talk, we will consider a constellation of Common Core content and practice standards that relate to early algebra, offer classroom examples that illustrate how elementary students can engage with these standards, and engage with participants to consider what teachers need to know to enact such lessons.
Comments: Lot’s of interesting video clips on teachers teaching elementary schools, but the focus was on how students learn properties of mathematics as opposed what teachers know about mathematical content and pedagogy. The one insight was that the teachers had been in a program that encouraged them to teach properties to children using different models. The teachers reported a change in attitude and that properties were as important as procedures and computational knowledge.
Achievement in Mathematics Classes for Future Elementary Teachers: What Matters?
Raven McCrory, Michigan State University
Abstract: In this talk, I will address two aspects of undergraduate mathematics courses for future elementary teachers.
- What do these courses look like? That is, who teaches them, what is the content, how are courses organized, how do they differ across institutions, etc.
- What systematic factors explain differences in learning across these courses, with different instructors and at different institutions?
Data come from a study of over 2000 undergraduate students at certifying institutions in four states, and include pre- and post-tests of students taking a mathematics course required for elementary certification; surveys of instructors of these courses; and interviews with mathematics department chairs.
Results suggest that, controlling for students’ prior knowledge, two factors that matter are use of a textbook specifically written for a mathematics course for teachers; and teaching in a way that engages students with doing mathematics. These two factors have differential impact on students depending on students’ prior knowledge. Models will be explained and implications of results for the design and implementation of mathematics classes for teachers will be discussed.
Comment: Great comprehensive study. Students learn better from a textbook and from a student-focused classroom.
Mathematics Teacher Preparation: An International Perspective
Sharon Senk and Maria Teresa Tatto, Michigan State University
Abstract: The Teacher Education and Development Study in Mathematics collected data from approximately 24,000 future primary and secondary mathematics teachers in 17 countries. We will present findings and discuss implications for mathematics teacher preparation in the U.S.
Comments: This is a huge, well-funded study covering policies, learning opportunities for teachers, and the mathematical knowledge of teachers. Invited countries included Singapore, the U.S., Germany, Russia, Chinese Taipai, and Botswana. Japan and Korea were not included. Countries were invited (not selected) to participate. The final report is in the hands of IEA but not yet available to the rest of us.
Chinese Taipai, the Russian Federation, Switzerland, Norway, and Singapore were the highest scoring countries. The U.S. was very low.
National Science Foundation, Common Core Implementation and the Mathematical Education of Teachers: Policy Perspectives and Support
Joan Ferrini-Mundy, NSF
Abstract: The policy formulations that resulted in the establishment of the Common Core State Standards (CCSS) initiative by the National Governors Association and the Council of Chief State School Officers were rooted in the need to provide clear and consistent frameworks to prepare our children for college studies and, ultimately, successful working lives in science, technology, engineering, and mathematics (STEM) careers. Forty-one States, the District of Columbia and the U.S. Virgin Islands have formally adopted the common core standards in mathematics.
We are poised at the doorstep to implementation activities, state-by-state, as well as important policy research to brace the efforts. The new standards in mathematics elicit a well-known problem: If we expect children to demonstrate deeper mathematical understanding and be able to articulate their own reasoning, then we must strengthen programs for the education of both existing and future teachers of mathematics and align that preparation with what is expected by the common core in mathematics.
Scholarly organizations across the country are already at work (the Conference Board of the Mathematical Sciences has issued recommendations on January 1, 2011) and this workshop is part of that national effort. In this talk, I will offer a NSF perspective about the challenges and opportunities in reaching tens of thousands of current mathematics teachers (as well as the undergraduate and graduate students in mathematics education programs that will soon join the workforce). What is NSF planning in terms of support for building the knowledge base to fortify these efforts? What are other federal and non-federal funders planning in terms of providing the resources for both professional development and teacher preparation?
Comments: This was a great overview of what support the federal government (especially NSF) for improvement. Here are the NSF Programs, FY12 requests.
- Increasing numbers: Robert Noyce Teacher Scholarship Program ($45M)
- Using Partnerships: Math and Science Partnership ($48M)
- Research and Development: Discovery Research K-12 (~$35 toward TE)
- Widening Implementation and Demonstration of Evidence-Based Reform ($20M)
- Teacher Learning for the Future ($20M)
- Plus parts of STEP, HBCU-UP, TCUP, LSAMP, TUES, REESE, RET/ENG
Panel on curricula and teacher learning
Navigating Standards: Teacher and Student Learning through Different Instructional Paths
Aki Murata, Stanford University
Abstract: Standards and curricula present varied images of mathematics instruction that may at times seem conflicting and confusing to teachers. By contrasting how mathematics content is treated across grade levels in standards (e.g., Common Core Standards, California Content Standards) and curricula (e.g., Everyday Mathematics, Japanese mathematics textbooks), we will discuss how they can frame students’ learning and experiences in different ways, and how these paths may also guide teachers’ understanding of student learning of mathematics.
Comments: Here are the number of standards for 4th grade mathematics.
- Calfornia Content Standards 54 - Emphasize fluency and computation facts
- CCSSM 28 - Strategies and understanding in addition to computation
- Japan 31- Emphasize understanding. Note: Japanese students may get their computational fluency elsewhere (at home, cram schools, etc.)
Textbooks: math as arbitrary rules
W. Stephen Wilson, Johns Hopkins University
Abstract: Some logic gaps in the development of mathematics in standard texts will be discussed. Examples will be given.