Abstract
Learning is fundamentally about growth and change. Longitudinal studies of mathematics learning must therefore conceptualize, measure, analyze, and interpret changes in students’ mathematical thinking. This chapter provides a perspective on how researchers can deal with issues entailed in researching such change over time, drawing on the authors’ experiences with two longitudinal projects in the USA and China. Both the LieCal (Longitudinal Investigation of the Effect of Curriculum on Algebra Learning) project and the China project studied the effects of curriculum on student learning. Based on these projects, several challenges are discussed, including the complexity of conceptualizing and measuring change in mathematical thinking, the importance of appropriate analytic techniques, the need to consider long-term change, and critical concerns when interpreting the correlates or causes of observed change.
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Acknowledgments 
Preparation of this article was supported by grants from the National Science Foundation (ESI-0454739 and DRL-1008536) and Research Grant Council of HKSAR, China (CERG-462405; CERG-449807) and the National Center for School Curriculum and Textbook Development, Ministry of Education of People’s Republic of China. Any opinions expressed herein are those of the authors and do not necessarily represent the views of the funding agencies.
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Cai, J., Ni, Y., Hwang, S. (2015). Measuring Change in Mathematics Learning with Longitudinal Studies: Conceptualization and Methodological Issues. In: Middleton, J., Cai, J., Hwang, S. (eds) Large-Scale Studies in Mathematics Education. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-07716-1_13
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