Chapter 1: Introduction to Building Thinking Classrooms in Mathematics
Building Thinking Classrooms in Mathematics (BTCM) provides a working model for K-12 math teachers to use to foster critical thinking in their students. The goal of this book is to equip teachers with the tools and frameworks to help their students learn the importance of problem-solving, collaboration, and exploration in mathematics. The book is structured around five key elements of effective teaching practices: evidence-based instruction, cognitive demand, academic discourse, effective questioning, and meaningful assessment. Each chapter begins with a discussion of a key concept of teaching and learning in mathematics, followed by lessons and activities that provide the foundation of a thinking classroom.
For example, Chapter 1 introduces evidence-based instruction, which requires teachers to incorporate research-based instructional strategies to effectively teach mathematics. Specific evidence-based instruction could include classroom discussion of math concepts, inquiry-based learning, and problem-based learning. This chapter also provides an overview of the educational standards related to mathematics instruction and will provide a framework for understanding how to develop an effective math curriculum.
Chapter 2: Aligning Mathematical Content and Instruction
Aligning mathematical content and instruction refers to the process of integrating mathematics instruction into the classroom curriculum. In Chapter 2, this is done by outlining the common core learning standards for mathematics, providing classroom examples that demonstrate how to meet said standards, and emphasizing real-world mathematics applications. As an example, the chapter outlines the standards for applying fractions to real-world problems, which can be accomplished by engaging students with engaging activities and tasks. Through the use of a worksheet, for instance, the teacher could have students select two fractional parts from a menu to split a dish evenly, arriving at the correct answer and thus connecting fractions to a real-world application.
Chapter 3: Cognitive Demand in Mathematics
Cognitive demand in math is a measure of the complexity of a math problem, concept, or activity, with higher cognitive demand meaning it requires more rigorous thinking and problem-solving. In Chapter 3, the book outlines how teachers can increase the cognitive demand of a math lesson by providing options for how students solve a problem, allowing mistakes, and allowing students to work in groups or individually. As an example, the chapter provides an activity involving a Venn diagram representing a mathematical situation. For the activity, students are asked to come up with an equation to solve the problem, creating an opportunity for the teacher to promote the need for analytical thinking and creativity.
Chapter 4: Academic Discourse in Mathematics
The purpose of academic discourse in mathematics is to create an environment in which students can discuss and challenge each other’s ideas and opinions. In Chapter 4, the authors discuss the different types of discourse such as whole group conversations, small group discussions, and one-on-one conversations, as well as the importance of instructional scaffolding. An example of instructional scaffolding provided in the chapter is provided by a teacher introducing a whole-group discussion about a specific math problem. During this conversation, the teacher can model the process for students by asking probing questions and guiding the conversation to ensure students understand the concepts being discussed.
Chapter 5: Effective Questioning in Mathematics
The purpose of effective questioning in mathematics is to encourage students to engage in critical thinking and problem-solving. Chapter 5 explains different strategies on how to do so, such as cueing questions, divergent thinking questions, and patience questions. As a real-world example, the chapter provides an example of a teacher introducing a problem to her students. The teacher cues the questions by starting with the prompt of “How could we calculate the cooking time for a particular recipe?” This allows students to develop the cognitive skills necessary to solve the problem and provides the teacher the opportunity to assess the students’ level of understanding.
Chapter 6: Meaningful Assessment in Mathematics
Meaningful assessment is the process of collecting evidence of student learning in order to ensure they are mastering the material. Chapter 6 explains the basics of how to develop effective assessments, provides strategies for the types of tasks to incorporate in assessments, and outlines the different ways to engage students in the assessment process. As an example, the chapter suggests using performance tasks, which require students to complete a project or task that applies their knowledge of a mathematics concept. Through an activity such as this, the teacher can ensure the students are able to apply their understanding of the material and determine whether or not they mastered it.
