Permutations and combinations are generally taught by requiring students to memorize formulas and solve problems using the appropriate formula. Students who learn these topics may succeed in gaining high scores on end-of-chapter exams in textbooks, while lacking the conceptual understanding required to deal with problems in the real world.…

This chapter discusses three main topics: (1) volunteer as a form of civic engagement, (2) Science, Technology, Engineering and Mathematics (STEM), and (3) basic skills including literacy, numeracy and digital problem-solving skills. Volunteering, STEM background, and basic skills are important social and economic indicators of societies. Yet,…

This randomized controlled study investigated the efficacy of a Tier 1 intervention, schema-based instruction (SBI), designed to help students with and without mathematics difficulties (MD) develop proportional reasoning. Twenty seventh-grade teachers/classrooms were randomly assigned to a treatment (SBI) or control (business-as-usual) condition.…

Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…

Since the National Council of Teachers of Mathematics ([NCTM], 2000) and the National Research Council ([NRC], 2005) revealed that problem posing needed to be incorporated into mathematics classrooms, the importance of teachers' roles in problem posing has been emphasized in K-12 mathematics curriculum because of instructors' impact on students'…

Giftedness in numeracy skills in young children is a phenomenon that is not always visible and easily identifiable. However, these numeracy skills should be recognised in the early years of pre-school education for adequate enrichment on curriculum and pedagogy in teaching young children. Numeracy skills in young children at pre-schools involves…

Historically there has always been a lively research discussion on whether the development of number concept should be considered as innate, or whether the catalyst for the development of the number concept -- and for counting -- is hearing number words combined with seeing concrete examples. One can recognize these theories as the nativist view…

Proportional relationships and geometric similarity are two of the critical topics in school mathematics. Students and even teachers often struggle with recognizing the proportional relationships in geometric similarity problems. The purpose of this study was to investigate preservice middle-grades mathematics teachers' (PSTs) strategies when…

There is a substantial body of knowledge on the importance of language for learning in general, and for learning mathematics in particular. Hence, language skills and collaborative learning are emphasised in the Norwegian curriculum. Even so, we have few studies on what supports and what impedes mathematical progress in authentic learning…

"Deepening Students' Mathematical Understanding with Children's Literature" is an important addition NCTM's books that focus on high quality children's books to create engaging and meaningful tasks that deepen mathematics learning for pre-K and elementary students. Classroom teachers in early childhood and elementary grades will find the…

We introduce a class of second-order ordinary differential equations (ODEs) with variable coefficients whose closed-form solutions can be obtained by the same method used to solve ODEs with constant coefficients. General solutions for the homogeneous case are discussed.

This study explored what kind of mathematics is needed in cabinetmakers' everyday work and how problem solving is intertwined in it. The informants of the study were four Finnish cabinetmakers and the data consisted of workshop observations, interviews, photos, pictures and sketches made by the participants during the interviews. The data was…

This "Math Snacks" intervention measured 741 fifth grade students' gains in conceptual understanding of core math concepts after game-based learning activities. Teachers integrated four "Math Snacks" games and related activities into instruction on ratios, coordinate plane, number systems, fractions and decimals. Using a…