The goal of this project is to identify Algebraic Knowledge for Teaching (AKT) that is useful to develop students’ algebraic thinking. Through an exploration of U.S. and Chinese elementary expert teachers’ video-taped lessons in K-4, this project has discerned a type of AKT named Teaching through Example-based Problem Solving (TEPS).
Algebra readiness is recognized as an important gatekeeper to future success in mathematics. However, many U.S. students are ill-prepared for the study of algebra, indicating a great challenge facing elementary teachers in preparing students for their entry into algebra.
This project aims to help address this issue by identifying necessary AKT that will support teachers to better teach early algebraic concepts, especially those fundamental mathematical ideas. Fundamental ideas such as inverse relations and basic properties are systematically emphasized by the Common Core; however, there is a lack of sufficient guidance on how these fundamentals can be effectively taught to students. Our project contributes to narrowing this gap by identifying an evidence-based approach that can be used to develop students’ algebraic thinking and beyond.
In addition, our project takes the middle ground of two long-debated research assertions: teaching through worked examples and teaching through problem-solving. As indicated by our project lessons, especially those from China, the above two debated assertions can be seamlessly integrated into a lesson to support student learning. By actively engaging students in working out an example task that is situated in a word problem context, students can construct a mental schema to solve subsequent problems.
Main findings of this project are the identified AKT named, Teaching through Example-based Problem Solving (TEPS). This approach emphasizes engaging students in the process of working out an example task through pertinent representation uses and deep questioning. With regard to representation uses, a teacher may situate a worked example in a real-world context (e.g., word problem), which can be modeled through “concreteness fading.” For deep questioning, a teacher may ask concept-specific and comparison questions to promote connection making. The components of TEPS and illustrative lesson episodes are documented in a book and piloted with project teachers who retaught the lessons.