The proposed program of research focuses on the mathematics prospective elementary teachers have opportunities to learn during their undergraduate education and what they actually learn as a result of their mathematics courses. Although research has identified the problem of teacher knowledge as a significant contributing factor in the generally inadequate quality of K-6 mathematics education, more is known about what teachers do not know than about what they know or have had opportunities to learn. This study will look across institutions and states to examine what prospective teachers are being taught and what they are actually learning.
The project will investigate both opportunities to learn and learning from undergraduate mathematics courses through a set of multi-method, multilevel case studies. The work will include an analysis of textbooks written for undergraduate mathematics courses for prospective elementary teachers; an examination of textbook topical coverage and how that correlates with states' mathematics student learning standards; surveys of mathematics departments and instructors of those courses in selected states; case studies of selected courses at institutions within the states; and pre- and post-assessments of student (preservice teacher) learning in those courses. The focal mathematical domains will be multiplication, fractions, and reasoning and proof.
This research will contribute to understanding whether prospective elementary teachers are exposed to content that they need for successful teaching, and whether they are learning that content. The findings will include whether, and to what extent, instructors are teaching content that contributes to mathematical knowledge for teaching. This is new research in areas about which little is known, with important implications for teacher education.
The proposer's education plan includes teaching undergraduate mathematics courses for elementary teachers at Michigan State University using two approaches currently supported by the Mathematics Department and using that teaching as a site for studying opportunity to learn and teacher knowledge. She will revise a course to introduce PhD students to theoretical and practical issues in assessing teacher knowledge and opportunities to learn.
The Mathematical Education of Elementary Teachers (MEET) project explored what mathematics is taught, and how it is taught, to future elementary teachers in undergraduate mathematics courses required for certification. The MEET project spanned the years 2006 – 2012. We collected data from 57 institutions in 4 states; 75 instructors of mathematics classes for future elementary teachers; and over 2000 students. Pre and post tests from students showed significant learning of relevant mathematics, an average effect size of over 0.7 (very large for educational research). Outcomes were measured using an instrument developed and validated at the University of Michigan. Analysis (manuscript in preparation) showed that using any one of the textbooks written specifically for a mathematics class for future elementary teachers was the strongest correlate of student learning in these classes, stronger than prior knowledge of the student or qualifications of the instructor. Another strong correlate was the teaching method: students did better in classes with less lecturing and more direct engagement with math problems. The project provided solid evidence that mathematics courses can be key leverage points for improving the mathematical knowledge of elementary teachers. Teacher knowledge can be increased through adequate teacher preparation courses. A surprising result was that the teaching method matters: the most successful courses were those in which instructors reported more "student-centered" methods directly engaging students with mathematics rather than having them listen to instructor explanations of mathematics (manuscript in preparation, 2013). The results of this project suggest that certifying institutions could improve outcomes for future elementary teachers by providing mathematics courses specifically designed for that population, using textbooks that include content elementary teachers need, and using instructional methods that do more than reteach the content the same way it was taught to the future teachers when they were children. Within a range of instructors with solid mathematics preparation, who teaches these courses (in terms of rank, type of degree, years of experience, and similar demographic characteristics) is less important than what they teach (content specifically aimed at future elementary teachers) or how they teach it (using methods that engage the future teachers in doing mathematics). Instruments and technical reports are available on the project Web site, http://meet.educ.msu.edu Other findings: 1) 75% of responding institutions required only one mathematics course for elementary certification (McCrory & Cannata, 2010). 2) More courses were required for middle school certification or endorsement, an average of 6.9 courses at institutions that offer such an option (McCrory & Cannata, 2010). 3) Most instructors were full time, almost entirely in mathematics departments (McCrory & Cannata, 2010). 4) Mathematics department chairs in the survey were highly knowledgeable about and involved in the mathematical education of future teachers (McCrory & Cannata, 2010). 5) Textbooks written for these courses follow one of three different patterns: a) comprehensive, encyclopedic coverage of the domain of K-8 mathematics, including arithmetic, geometry, pre-algebra, and data; b) problem based books with fewer explanations and more complex problems for use in class; c) comprehensive but less encyclopedic books that present a coherent perspective on K-8 mathematics (McCrory, 2006). 6) Fractions are represented in a variety of ways across the textbooks, some inconsistent with developing a coherent understanding of fraction as number (McCrory, 2006). 7) Reasoning-and-proving is not adequately presented in most of the textbooks, often relegated to a chapter on logic or problem solving and infrequently referred to in the rest of the book. (McCrory & Stylianides, in review 2013). 8) A study of multiplication of integers in the textbooks yielded a method for textbook analysis using published standards, advanced mathematics texts, and policy documents. This study concluded that many of the textbooks do not include important aspects of integer multiplication and do not make important mathematical connections to other concepts in arithmetic and algebra (Siedel, 2010). 9) Other results cover how textbooks are used in these classes; correlation of textbook with student achievement; control of instructors over textbook selection; and instructors’ familiarity with and use of key policy and standards documents (manuscripts in preparation). 10) Expert teachers use strategies for classroom discourse similar to those that are successful in K-12 classrooms (Young, dissertation in progress, 2013). 11) Teaching reasoning and proving strategies to future teachers requires attention to well-research elements of proof, and also to the unique situations found in K-8 classroom (Lo, et al, 2010). 12) Case studies of two mathematics classes suggest that instructors may miss opportunities to teach fractions as numbers, and to make connections across multiple conceptions of fractions (Park, et al, 2012). 13) Semiotics can be a useful tool for helping future teachers realize and cope with the complexities of fractions. One instructor’s explicit use of semiotics helped draw future teachers’ attention to the importance of the "unit" and the considerable ambiguity that often surrounds words used to talk about fractions (Francis, et al., 2009).
