Teaching Mathematics Conceptually

Beth L. MacDonald is an associate professor in Early Childhood Mathematics Education in the School of Teaching and Learning at Illinois State University. After completing a Bachelor of Arts degree in Studio Art and Elementary Education (PreK-6) at SUNY Potsdam, Beth taught elementary school for 15 years and served as a K-5 Instructional Specialist for two years in southwest Virginia. In this time, Beth taught in fully inclusive elementary classrooms within Title 1 schools and within all K-5 grade levels. While teaching, Beth completed her Master of Arts in Education degree, with a focus on K-8 Mathematics Education and her Doctor of Philosophy degree, with a Curriculum and Instruction concentration and focus on Mathematics Education, both from Virginia Tech. Her research broadly focuses on PreK-5 students’ development of number, particularly with subitizing activity at the center of this development. Moreover, Beth collaborates often with colleagues who examine teachers’ specialized content knowledge development in mathematics/STEM and collaborates with colleagues who examine marginalized students’ number understanding development. Beth also served as a lead guest editor for Special Issue for the Education Sciences Journal, focusing on STEM in Early Childhood Education.  Jonathan N. Thomas is an associate professor of mathematics education and the chairperson of the department of STEM education at the University of Kentucky. After completing a Bachelor of Arts degree in Elementary Education at the University of Kentucky, Jonathan was a mathematics intervention specialist in public, private, and charter schools in the Cincinnati metropolitan area. While teaching, Jonathan completed a Masters of Arts in Education degree with a focus on education leadership and his Doctor of Education degree in mathematics education, both from the University of Cincinnati. Jonathan’s research focused on responsive and equitable teaching practices in the elementary classroom as well as children’s construction of mental imagery and use of gesture in foundational mathematical experiences. Jonathan has been the principal investigator on several projects, funded by the National Science Foundation, focused on these areas. Jonathan is also an associate editor of the School Science and Mathematics journal and Kentucky Center for Mathematics faculty associate.

Chapter 1: Introduction
Chapter 2: Inquiry-Based Instruction
Chapter 3: Mathematics Learning Progressions And Multiple Student-Created Strategies
Chapter 4: Relationships Between Mathematics Teaching And Learning
Chapter 5: Planning Effective Mathematics Teaching
Chapter 6: Formative Assessments
Chapter 7: Monitoring Mathematics Learning
Chapter 8: Feedback And Discourse In Mathematics Instruction
Chapter 9: Grouping Students To Promote A Productive Struggle In Mathematics Instruction
Chapter 10: The Role Of Children’s Reflection In Mathematics Learning
Chapter 11: Equitable Mathematics Practices
Chapter 12: Connecting Back To NCTM Mathematics Teaching Practices And Common Core State Standards Of Mathematics Practices