Problem-based learning (PBL) fosters both content knowledge and content understanding, improves critical and process thinking skills, and promotes peer-to-peer learning, leadership, and teamwork (Hmelo-Silver 2004). Instructors support the PBL process by guiding students through activities that challenge their current knowledge and understanding…

This chapter focuses on the interaction of two first graders as they attempt to make sense of a particular instructional context for learning negative numbers. The context is one where they move an elevator to a building's floors above and below ground in order to model integer addition and subtraction problems. In particular, the focus of the…

With the goal of improving student success, the chancellor of the California State University (CSU) system issued an executive order that required all CSU campuses to eliminate remedial math courses as of Fall 2018 and place all first-year students into appropriate General Education (GE) mathematics/quantitative reasoning courses. The Mathematics…

In early care and education, a multitiered system of support (MTSS) framework is a way to provide high-quality teaching and responsive caregiving through the delivery of differentiated support for all young children. In an early childhood MTSS framework, the needs of every child, regardless of ability, eligibility status, cultural and linguistic…

In this opinion paper we introduce a school-wide concept at doctoral level aimed at professional practitioners, who wish to stay in their respective areas of work. The rationale behind this school-wide concept is that in Hungary, where its implementation is currently in progress, gaining a PhD automatically means becoming an academic. However,…

There has been increased attention paid to science, technology, engineering, and mathematics also known as STEM. The focus on STEM has been both educational and occupational. Unfortunately, students with disabilities perform below their peers without disabilities in math and science. The authors discuss issues related to STEM and students with…

"Ensuring Mathematical Success for All" (NCTM 2010) outlines eight teaching practices for effective teaching and learning of mathematics. One of the teaching practices, building procedural fluency from conceptual understanding, states the following: Effective teaching of mathematics builds fluency with procedures on a foundation of…

Using Cuisenaire Rods, metric measurement, and mapping, students worked collaboratively to calculate, keep records, build, and problem solve with use of decimal fractions as a key element.

The problem of determining the angle ? at which a point mass launched from ground level with a given speed v[subscript 0] will reach a maximum distance is a standard exercise in mechanics. There are many possible ways of solving this problem, leading to the well-known answer of ? = p/4, producing a maximum range of D[subscript max] = v[superscript…

The theoretical and methodological model of Mathematical Working Space (MWS) is introduced in this paper. For over 10 years, the model has been the object of collaborative research among various researchers, generally coming from French and Spanish speaking countries. Articulating epistemological and cognitive aspects, the MWS model is aimed at…

Every day, 27,000 trees are used to make bathroom tissue. Americans use an average of 23.6 rolls per person per year, and more than 7 billion rolls of toilet paper are sold yearly in the United States alone. Perhaps the amount of bathroom tissue used can be reduced by changing the dimensions of the paper or the core. This brief article presents…

This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…

Intelligence is not fixed. While many of us may not be innately talented in all areas of learning, all of us are capable of learning anything. It is important that teachers help communicate this concept to students and help students to develop this growth mindset. This article first compares growth and fixed mindsets, discussing some of the…

The primary purpose of this paper is to introduce essential elements of cognitive information processing (CIP) theory, research, and practice as they existed at the time of this writing. The introduction that follows describes the nature of career choices and career interventions, and the integration of theory, research, and practice. After the…