Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.

Algebra is the gateway to college and careers, yet it functions as the eye of the needle because of low pass rates for the middle school/high school course and students’ struggles to understand. We have forty years of research that discusses the ways students think and their cognitive challenges as they engage with algebra. This book is a response to the National Council of Teachers of Mathematics’ (NCTM) call to better link research and practice by capturing what we have learned about students’ algebraic thinking in a way that is usable by teachers as they prepare lessons or reflect on their experiences in the classroom. Through a Fund for the Improvement of Post-Secondary Education (FIPSE) grant, 17 teachers and mathematics educators read through the past 40 years of research on students’ algebraic thinking to capture what might be useful information for teachers to know—over 1000 articles altogether. The resulting five domains addressed in the book (Variables & Expressions, Algebraic Relations, Analysis of Change, Patterns & Functions, and Modeling & Word Problems) are closely tied to CCSS topics. Over time, veteran math teachers develop extensive knowledge of how students engage with algebraic concepts—their misconceptions, ways of thinking, and when and how they are challenged to understand—and use that knowledge to anticipate students’ struggles with particular lessons and plan accordingly. Veteran teachers learn to evaluate whether an incorrect response is a simple error or the symptom of a faulty or naïve understanding of a concept. Novice teachers, on the other hand, lack the experience to anticipate important moments in the learning of their students. They often struggle to make sense of what students say in the classroom and determine whether the response is useful or can further discussion (Leatham, Stockero, Peterson, & Van Zoest 2011; Peterson & Leatham, 2009). The purpose of this book is to accelerate early career teachers’ “experience” with how students think when doing algebra in middle or high school as well as to supplement veteran teachers’ knowledge of content and students. The research that this book is based upon can provide teachers with insight into the nature of a student’s struggles with particular algebraic ideas—to help teachers identify patterns that imply underlying thinking. Our book, How Students Think When Doing Algebra, is not intended to be a “how to” book for teachers. Instead, it is intended to orient new teachers to the ways students think and be a book that teachers at all points in their career continually pull of the shelf when they wonder, “how might my students struggle with this algebraic concept I am about to teach?” The primary audience for this book is early career mathematics teachers who don’t have extensive experience working with students engaged in mathematics. However, the book can also be useful to veteran teachers to supplement their knowledge and is an ideal resource for mathematics educators who are preparing preservice teachers.

The Routledge International Handbook of Innovation Education is the international reference work on innovation education and potentially opens an entirely new direction in education. The overall goal of the handbook is to address the question of how to develop innovators in general and how to develop the innovative potential of today‘s young people

How can you broaden student thinking and help them develop their independence and confidence as problem solvers? Real-life problems are a remarkable tool to stretch student thinking and help them develop a deeper understanding of mathematics and its role in everyday life. Rather than using textbook exercises, the book argues that solving real-world problems promotes flexibility and encourages students to adjust and grow their thinking. It inspires them to consider alternatives and apply math in authentic contexts. You will find practical ways to engage students in critical thinking, develop their independence, and make connections with the world.

Mathematical writing is essential for students’ math learning, but it’s often underutilized due to unclear guidelines. Mathematical writing is a mode of communication that provides teachers access to their students’ thinking and, importantly, offers students an opportunity to deepen their mathematical understanding, engage in mathematical reasoning, and learn a fundamental way to communicate mathematically. Notably, one needs to be able to judiciously combine mathematical symbols, representations, and text. However, more research is needed to exemplify the qualities of mathematical writing, develop implementation methods, and support teachers. Illuminating and Advancing the Path for Mathematical Writing Research, is a necessary comprehensive resource designed to enhance mathematical writing and promote equitable learning. This research book provides a comprehensive understanding of the current state of mathematical writing and illuminates various perspectives on moving the teaching and learning of k-12 mathematical writing forward. Mathematical writing is an important yet underutilized component of mathematical discourse, and this book offers further insight into understanding what it means to write mathematically for mathematics educators and researchers. It informs with research-based implementation strategies and creates purposeful professional learning opportunities. Ultimately, k-12 students will benefit from a more informed field because they will have access to a vital mode of mathematical reasoning and communication.

Hark, Hark! Hear the Story of a Science Educator highlights some compelling ideas on science teaching and learning through the author’s journey and includes evolution and revolution in the growth of scientific knowledge. The book discusses views of McComas et al. and Lederman et al. on the nature of science, as well as the learning theories of Piaget (1926), Vygotsky (1978), and Marton (1981). The three theories of learning frame methods in teaching science. The author is well known in the science education research community for her groundbreaking work in student conceptions and conceptual change, particularly as related to phenomenography. Key Features: Helps science educators explore new avenues related to various innovative curricula, teaching, and learning Presents abstract learning theories, such as social constructivism in personal stories and experiences Bridges the divide between the science education community and the general public on significant ideas of science teaching and learning Uncovers relational conceptual change inquiry learning Discusses current socioscientific community-based issues—other-centeredness—through scientific investigation and engineering design challenges

Publisher’s note: In this 2nd edition: The following article has been added: Jiao H, He Q and Veldkamp BP (2021) Editorial: Process Data in Educational and Psychological Measurement. Front. Psychol. 12:793399. doi: 10.3389/fpsyg.2021.793399 The following article has been added: Reis Costa D, Bolsinova M, Tijmstra J and Andersson B (2021) Improving the Precision of Ability Estimates Using Time-On-Task Variables: Insights From the PISA 2012 Computer-Based Assessment of Mathematics. Front. Psychol. 12:579128. doi: 10.3389/fpsyg.2021.579128 The following article has been removed: Minghui L, Lei H, Xiaomeng C and Potměšilc M (2018) Teacher Efficacy, Work Engagement, and Social Support Among Chinese Special Education School Teachers. Front. Psychol. 9:648. doi: 10.3389/fpsyg.2018.00648