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Teachers’ knowledge of student mathematical thinking in written instructional products

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Douglas L. Corey at Brigham Young University
Douglas L. Corey
Steven R. Williams at Brigham Young University
Steven R. Williams
Eula Monroe at Brigham Young University
Eula Monroe
Michelle Wagner
Michelle Wagner
Michelle Wagner
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Abstract and Figures

The successful use of lesson plans as the primary vehicle for storing and sharing teachers’ instructional knowledge in Japan has given impetus to calls by US researchers for the development of a system for sharing teachers’ knowledge through instructional products to improve teachers’ capacity to implement high-quality instruction and to build a knowledge base for instruction. These products would be created by, and for, teachers to use in guiding instruction, thus building and sharing teachers’ instructional knowledge. In this study, we try to characterize one aspect of teacher knowledge that is central in building a knowledge base for instruction, knowledge of student mathematical thinking. We analyze ten written instructional products from the USA and Japan to better understand what knowledge of student mathematical thinking can be shared in such products. We also look at how knowledge of student mathematical thinking is used to guide and justify instructional decisions. One key finding is that the knowledge of student mathematical thinking shared in the top written instructional products is specific to a task or mathematical topic, varied with descriptions of multiple solutions or ways of reasoning, and sufficiently detailed to make the knowledge usable for teachers.
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Vol.:(0123456789)
Journal of Mathematics Teacher Education (2021) 24:613–639
https://doi.org/10.1007/s10857-020-09476-y
1 3
Teachers’ knowledge ofstudent mathematical thinking
inwritten instructional products
DouglasLymanCorey1 · StevenWilliams1· EulaEwingMonroe2,3·
MichelleWagner1
Published online: 3 August 2020
© Springer Nature B.V. 2020
Abstract
The successful use of lesson plans as the primary vehicle for storing and sharing teach-
ers’ instructional knowledge in Japan has given impetus to calls by US researchers for the
development of a system for sharing teachers’ knowledge through instructional products to
improve teachers’ capacity to implement high-quality instruction and to build a knowledge
base for instruction. These products would be created by, and for, teachers to use in guiding
instruction, thus building and sharing teachers’ instructional knowledge. In this study, we
try to characterize one aspect of teacher knowledge that is central in building a knowledge
base for instruction, knowledge of student mathematical thinking. We analyze ten writ-
ten instructional products from the USA and Japan to better understand what knowledge
of student mathematical thinking can be shared in such products. We also look at how
knowledge of student mathematical thinking is used to guide and justify instructional deci-
sions. One key finding is that the knowledge of student mathematical thinking shared in the
top written instructional products is specific to a task or mathematical topic, varied with
descriptions of multiple solutions or ways of reasoning, and sufficiently detailed to make
the knowledge usable for teachers.
Keywords Student mathematical thinking· Lesson plans· Knowledge base for teaching·
Japanese lesson study
Electronic supplementary material The online version of this article (https ://doi.org/10.1007/s1085
7-020-09476 -y) contains supplementary material, which is available to authorized users.
* Douglas Lyman Corey
corey@mathed.byu.edu
1 Department ofMathematics Education, Brigham Young University, Provo, UT84602, USA
2 Department ofTeacher Education, Brigham Young University (Emerita), Provo, USA
3 Todd County School District, Elkton, KY, USA
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... LS was most often conducted within a single school (Takahashi & McDougal, 2016), although it could also occur at district, regional, and national levels (Groves et al., 2016). It was frequently conducted by in-service (81.4%) elementary and middle school teachers (Corey et al., 2021), although a growing body of research has explored the implementation of LS in secondary classrooms (e.g., Huang, Barlow, et al., 2017) and with preservice teachers (e.g., Guner & Akyuz, 2020;Hernández-Rodríguez et al., 2021). LS cycles were often led by expert teachers (Seino & Foster, 2021) or supported by "knowledgeable others" who provided feedback during the process (Hernández-Rodríguez et al., 2021;Lewis & Perry, 2017). ...
... Second, those LS studies that reported positive changes primarily emphasized the effects of LS on teachers' changes in the personal/collective domain such as increased professional knowledge and more positive teaching attitudes and beliefs (e.g., Akiba et al., 2019;Corey et al., 2021;Leavy & Hourigan, 2016;Nguyen & Tran, 2022;Vermunt et al., 2019 (2019) reported that no changes took place in teachers' initial and final lesson plans (practice domain) after one cycle of LS. ...
... This may explain why LS is one of the most effective PD approaches (Gersten et al., 2014;Lewis & Perry, 2017) and has drawn global attention. Our review also shows that adapted LS in other countries could improve teachers' knowledge (e.g., Corey et al., 2021;Lewis & Perry, 2017) and improve school environments in some places with needed supports from the district (e.g., Aas, 2021;Groves et al., 2016). Despite the reported successes of teacher learning through LS, our findings echoed prior reviews (Cheung & Wong, 2014;Willems & Van den Bossche, 2019), indicating various research gaps and implementation challenges in the lens of IMPG. ...
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... In the other eleven papers, although theoretical frameworks were mentioned in the literature review, these were not used to substantiate the study. For example, Corey et al.'s (2020) approach to teachers' instructional knowledge of lesson planning is similar (but not identical) to the approach used in our study. Although their analyses was based on rich empirical data about lesson plans and contains a particular model they used to analyse their data, their study pays scant attention to developing theoretical approaches within well-established frameworks beyond the literature review. ...
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