Boost young children's problem-solving skills and set them up for long-term success with the second edition of this practical guidebook! Enhanced with new lessons and timely topics--including equity and the use of makerspaces--this book will help you get all children ready for kindergarten by teaching them basic practices of engineering design and…

This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals…

Tangible programming tools (TPTs) are promising teaching aids in programming courses due to their interactivity and ability to enhance early childhood students' computational thinking, spatial reasoning, and executive function skills. However, it remains unclear whether TPTs support these skills simultaneously. This study examines the impact of…

Design thinking--a human-centered approach to problem solving--is a process by which K-12 teachers engage students in solving relevant issues that occur in their schools. In this article, the authors describe a project in which fourth-graders used design thinking to solve an unexpected issue related to a much-anticipated class project. The project…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. "Figuring Out Fluency in Mathematics Teaching and Learning" offers educators the inspiration to develop a deeper understanding of procedural fluency, along with…

Visual literacy is essential for engineers. Technological professions have important visual characterization, both in the transmission of information and problem-solving. This means that future engineers must be proficient at communicating, thinking, and learning visually. However, engineering curricula takes partially the need to have visually…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…

Offering secondary math educators an innovative holistic and process-orientated approach for implementing nonroutine problems into their curriculum, this book defines and establishes practical strategies to develop students' problem-solving skills. The text focuses on the process skills necessary to solve nonroutine problems in mathematics and…

Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…

While reading, writing, and arithmetic remain important, they are no longer enough. For learners to thrive, they must move beyond traditional literacies to modern fluencies--the unconscious mental processes that are learned, adapted, and applied in the context of real-world problems and challenges. In this book, the authors unpack the fluencies…

The mathematical modeling process is also a powerful way to teach students the meaning of data. In mathematical modeling, students are collecting data to answer a question. Data collection is the means to an end and not the end in itself. The author was looking for an engaging way to introduce his third-grade mathematics class to the skill of…

Successful math word-problem solving is difficult for some students. Getting the right answer involves students engaging correctly in an amalgamation of actions. Schema instruction is an instructional approach aimed at supporting students in identifying the underlying math problem structure to yield an appropriate solution plan. The focus of this…

In this article, the authors share the potential for two types of atypical arrays (composite and partially hidden) to stimulate initial multiplicative ideas and strategies from students in a second-grade classroom. Composite arrays are defined here as nonarrays that are composed of multiple smaller complete arrays. The atypical arrays were…