Heather C. Hill

Reconstructing Research in Teacher Education to Provide Usable Knowledge and Support Teacher Education Improvement (2019-2022)
National Science Foundation

Overview. Over the past decade, scholars have developed promising new practices for STEM teacher education. These new practices, however, have not been accompanied by advances toward more rigorous evaluative research, leaving practitioners and policymakers with little evidence to assess the promise of these new approaches. We trace this problem to three underlying factors. The first relates to teacher education’s most prevalent research designs, which generally do not feature comparisons that enable the identification of causal impacts. Second, very few studies assess teaching outcomes that result from the piloted approach or program, perhaps because very few standardized measures of K-12 STEM teacher skills exist. Finally, there is little social and informational infrastructure, so to speak, from which teacher educators can draw to improve their research practice. These three issues – current research norms, a lack of standardized measures of skills and practice, and poor infrastructure for improvement – prevent the field from identifying, improving, and scaling innovative approaches effectively.

Learning Practice: A Seminar on Magdalene LampertÂ’s Scholarship on and for Teaching (2017-2018)
Spencer Foundation

Dr. Magdalane Lampert has devoted her career to working on two tightly linked problems: How does one conceptualize the complexities of teaching, in economical, theoretically sound, and pragmatically useful ways? And how then does one use that conceptualization to drive the design of the materials, pedagogies, and practices needed to support candidates in learning to teach? The Spencer Foundation is subsidizing a working seminar designed to bring together scholars and teachers who have contributed to Dr. Lampert’s work over time. Our goal is to collectively bear down on central questions concerning this practice-based approach to analyzing teaching and preparing teachers. Dr. Lampert’s career has stretched across multiple contexts: Harvard University, Michigan State University, the University of Michigan, the Boston Public Schools, and the New Visions for Public Schools Network in New York City. Across those venues, she has collaborated with researchers, teachers, and graduate students in exploring teaching and teacher education. We are together colleagues from across those parts of her career and designing a set of tasks that would engage them in several core questions, including: •How does one conceptualize and parse teaching in ways that capture its complexity and highlight its technical core, while avoiding mechanization and anti-intellectualism? •What have we learned about the central instructional activities that best prepare new teachers for their learning and teaching over time? •How do we take those activities and test their robustness and relevance across grade levels, subject matters, developmental differences, linguistic and cultural differences, and the like?

The Mathematical Knowledge for Teaching Measures: Refreshing the Item Pool (2016-2019)
National Science Foundation

This study describes an assessment strand late-stage design project that focuses on improving existing measures of teachersÂ’ mathematical knowledge for teaching. Original measure development, which occurred at the University of Michigan during the period 2002-2010, had several goals: to identify the knowledge useful to teachersÂ’ work with students and to explore the possibility that this knowledge is unique to teaching; to provide a set of measurement instruments that could be used in research on teachersÂ’ knowledge; and to provide evaluators with an easy-to-use online administration and scoring system. These efforts resulted in widely disseminated instruments, numerous academic papers, and theoretical progress regarding the mathematical knowledge teachers use in their work. We now seek to update these measures. One reason is their wide use: anecdotal evidence suggests that up to 25% of our target teacher population may have taken a version of these instruments in pre-service training or in-service professional development. To respond to this issue, we will create over 300 items and 10 new sets of parallel forms in the most frequently tested grades and topics. Another reason to update the measures relates to new mathematics content and practice standards; a review of existing forms suggests we could better align our item pools to this key instructional guidance. We also seek to respond to a variety of user requests, and to also make our online delivery system, the Teacher Knowledge Assessment System (TKAS), more flexible in both the item formats it can accommodate and in responding to additional form updates.

Survey of U.S. Middle School Mathematics Teachers and Teaching (2014-2018)
National Science Foundation

For the last 25 years, three major goals have animated the U.S. mathematics education community: more knowledgeable teachers, more challenging curricula for students, and more ambitious instruction in classrooms. Yet despite volumes of policy guidance, on-the-ground effort and research over the past decades, few comprehensive and representative portraits of teacher and teaching quality in U.S. mathematics classrooms exist. Instead, most research into these topics has been conducted with small samples, non-representative samples (e.g., Kane & Staiger, 2012) or by research projects that use diverse instruments, meaning that it is difficult to ascertain what, if any, progress has been made toward the three goals. To provide information on such progress, we will collect data on teacher content knowledge, curriculum use, and instruction from a nationally representative sample of U.S. middle school mathematics teachers. A written survey component of this study will build on a similar study conducted in 2005 – 06 (Hill, 2007), allowing for the comparison of teachers’ curriculum use and content knowledge – and more specifically, their mathematical knowledge for teaching (MKT) –across time periods. An observational component will record and score videotapes of instruction, allowing for a description of current instruction as well as a comparison of current instruction with that observed during the TIMSS video study (Heibert et al., 2005). The new video dataset will also serve as a baseline for future studies of instruction, for instance ones comparing current instruction to that in 2025, to assess whether Common Core State Standards have been met. This study is largely descriptive, as are many other studies of its kind (Hiebert et al., 2005). However, as in our past research (Hill, 2007; Hill et al., 2008), we can inquire into relationships between key variables (e.g., curriculum use, MKT, and instructional quality). Such inquiry can form the basis for future research. We can also describe instruction as it exists across a wide variety of U.S. classrooms, for example, asking whether – as is often assumed – instruction in urban districts is inferior to those in other areas and whether differences in instructional or teacher quality by academic track (honors, general, or remedial) exist. Finally, we believe that describing the mean and range of U.S. instruction can have a profound effect on the field, much as the TIMSS video studies (Stigler & Hiebert, 1999; Hiebert et al., 2005) did over a decade ago. We argue that timely information on these topics would be useful for three reasons. First, mathematics educators have both researched and attempted to improve teacher knowledge, curriculum, and instruction for over two decades; examining current levels of each would provide evidence about the extent to which these goals have been met. Second, the Common Core has set new goals for teachers and teaching; it is important to establish a baseline for future research by describing the status quo as new curriculum materials and assessments reach classrooms. Finally, we believe that the work described in this proposal will demonstrate that teacher and teaching quality in the U.S. can be effectively tracked, similar to other national indicators such as NAEP.

Exploring Methods for Improving Teachers' Mathematical Quality of Instruction (2012-2015)
National Science Center

In this exploratory study, we will develop and test professional development aligned with the Mathematical Quality of Instruction observational instrument. In the program, teachers will learn to score videotapes of instruction using the MQI framework first by completing online training and then through participating in a series of groups meetings with others at their school. These meetings will combine aspects of video clubs (Borko, Jacobs, Eiteljorg & Pittman, 2008; van Es and Sherin, 2006) and lesson analysis (Santagata & Angelici,2010), using the MQI framework to view and score portions of lessons. A comparison group will enable us to understand the effects of the MQI on several measures, including teachersÂ’ talk,their analysis of videotapes, and reflections on their own lessons. Owing to cost constraints, we will leave the collection of data on instructional or student outcomes to a future study. However, we believe that the outcomes of interest noted above will provide adequate proxies to practice, in that they have been linked to practice or are precursors to the improvement of practice. In addition, we will systematically vary the conditions under which the MQI-based professional development is delivered in order to gain knowledge about the best design for a scaled-up implementation. To do so, we will expose fifteen groups of fourth and fifth grade teachers to MQI-based lesson analysis. These fifteen groups will be randomly assigned into five conditions (three groups per condition), with each group engaging in weekly or bi-weekly lesson analysis using the MQI. However, the amount of facilitator intervention (less vs. more), the origin of the videotape (teachersÂ’ own video vs. video from a library), and the delivery method (face-to-face vs. internet) will vary by condition.

Hill, H.C. & Grossman, P. (2013). Learning from Teacher Evaluations: Challenges & Opportunities. Harvard Education Review 83, 371-384.,(2013)

Hill, H. C., Beisiegel, M., & Jacob, R. (2013). Professional Development Research Consensus, Crossroads, and Challenges. Educational Researcher, 42(9), 476-487.,(2013)

Hill, H.C. & Grossman, P. (2013). Learning from Teacher Evaluations: Challenges & Opportunities. Harvard Education Review 83, 371-384.,(2013)

Hill, H.C. (in press). The nature and effects of middle school mathematics teacher learning experiences. Teachers’ College Record.,(2012)

Hill, H.C., Umland, K. L. & Kapitula, L.R. (2011). A validity argument approach to evaluating value-added scores. American Educational Research Journal.,(2011)

Hill. H.C. (2010). The nature and predictors of elementary teachers’ Mathematical Knowledge for Teaching. Journal for Research in Mathematics Education, 41 (5), 513-545.,(2010)

Hill, H.C. & Shih, J. (2009) Research commentary: Examining the quality of statistical mathematics education research. Journal for Research in Mathematics Education.,(2009)

Hill, H.C. & Ball, D.L. (2009) The curious — and crucial — case of Mathematical Knowledge for Teaching. Phi Delta Kappan ,  91, 68-71.,(2009)

Hill, H.C. (2009). Evaluating value-added models: A measurement perspective. Journal of Policy and Management, 28, 702-209.,(2009)

Delaney. S. F., Ball, D. L., Hill, H. C., Schilling, S.G., & Zopf, D. A. (2008). Adapting U.S. measures of “Mathematical Knowledge for Teaching” for use in Ireland. Under review at Journal of Mathematics Teacher Education,11, 171-197..,(2008)

Hill, H.C., Blunk, M. Charalambous, C., Lewis, J., Phelps, G. C. Sleep, L. & Ball, D.L. (2008). Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study. Cognition and Instruction, 26, 430-511.,(2008)

Hill, H.C., Ball, D.L. & Schilling, S.G. (2008) Unpacking “Pedagogical Content Knowledge”: Journal for Research in Mathematics Education,39, 372-400.,(2008)

Schilling, S.G. & Hill, H.C. (2007). Assessing Measures of Mathematical Knowledge for Teaching: A Validity Argument Approach. Measurement: Interdisciplinary Research and Perspectives (5), 2-3, 70-80.,(2007)

Hill, H.C., Ball, D.L., Blunk, M. Goffney, I.M. & Rowan, B. (2007). Validating the ecological assumption: The relationship of measure scores to classroom teaching and student learning. Measurement: Interdisciplinary Research and Perspectives (5), 2-3, 107-117.,(2007)

Hill, H.C., Dean, C. & Goffney, I.M. (2007). Assessing Elemental and Structural Validity: Data from Teachers, Non-teachers, and Mathematicians. Measurement: Interdisciplinary Research and Perspectives (5), 2-3, 81-92.,(2007)

Schilling, S.G., Blunk, M. & Hill, H.C. (2007). Test Validation and the MKT Measures: Generalizations and Conclusions. Measurement: Interdisciplinary Research and Perspectives (5), 2-3, 118-127.,(2007)

Hill, H.C., Ball, D.L., Sleep, L. & Lewis, J.M. (2007) Assessing Teachers’ Mathematical Knowledge: What Knowledge Matters and What Evidence Counts? In F. Lester (Ed.), Handbook for Research on Mathematics Education (2nd ed), p. 111-155. Charlotte, NC: Information Age Publishing.,(2007)

Hill, H.C. (2007). Mathematical knowledge of middle school teachers: Implications for the No Child Left Behind Policy initiative. Educational Evaluation and Policy Analysis (29), 95-114.,(2007)

Hill, H.C. (2007). Teachers’ Ongoing Learning: Evidence from Research and Practice. The Future of Children, 17, 111-128.,(2007)

Hill, H.C. & Lubienski, S.T. (2007) Teachers’ mathematics knowledge for teaching and school context: A study of California teachers. Educational Policy 21(5), 747-768.,(2007)

Learning Mathematics for Teaching. (2006). A Coding rubric for measuring the Quality of Mathematics in Instruction. Ann Arbor, MI: Authors.,(2006)

Hill, H.C. (2006) Language matters: How characteristics of languagecomplicate policy implementation. In M.I. Honig (Ed.), New directions in education policy implementation: Confronting complexity. Albany, NY: SUNY Press.,(2006)

Hill, H.C. (2005). Content across communities: Validating measures of elementary mathematics instruction. Educational Policy 19, 447-475.,(2005)

Hill, H.C., Rowan, B., & Ball, D.L. (2005) Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal 42, 371-406.,(2005)

Ball, D.L., Hill, H.C. & Bass, H. (2005) Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, Fall 2005, 14-22.,(2005)

Hill, H.C., Schilling, S.G., & Ball, D.L. (2004) Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal 105, 11-30.,(2004)

Hill, H. C. (2004) Professional development standards and practices in elementary school mathematics. Elementary School Journal 104, 215-31.,(2004)

Hill, H. C. & Ball, D. L. (2004) Learning mathematics for teaching: Results from California’s Mathematics Professional Development Institutes. Journal of Research in Mathematics Education 35, 330-351.,(2004)

Hill, H.C. (2003) Understanding implementation: Street-level bureaucrats’ resources for reform. Journal of Public Administration Research and Theory 13, 265-282.,(2003)

Hill, H .C. (2001) Policy is not enough: Language and the interpretation of state standards. American Educational Research Journal 38, 289-320.,(2001)

Cohen, D.K. & Hill, H.C. (2001) Learning policy: When state education reform works. New Haven, CT: Yale University Press.,(2001)

Cohen D. K. & Hill, H.C. (2000) Instructional policy and classroom performance: The mathematics reform in California. Teachers College Record 102, 296-345.,(2000)