This research paper aims to characterize Mathematical Reasoning (MR) in teaching and learning of mathematics in high-school education. To achieve this goal and reveal the status of Mathematical Reasoning as a concept, we analyze the content of curricula and official textbooks of the initial and second year of high school in Morocco. Our analytical…

Building upon the work of Zieffler, Garfield, DelMas and Reading (2008) and others, we developed a framework for assessing informal inferential tasks in middle school mathematics textbooks. The framework both embodies the key recommendations for developing informal inferential reasoning and captures common trimming attributes, which lower the…

The transfer of learning has been the subject of much scientific inquiry in the social sciences. However, mathematics education research has given little attention to a subclass called backward transfer, which is when learning about new concepts influences learners' ways of reasoning about previously encountered concepts. This study examined when…

The aim of this study is to determine the distribution of the questions in an 8th grade mathematics textbook in terms of the categories (mathematical content, mathematical literacy contexts, mathematical processes, PISA mathematics proficiency scale levels, and item types) within the PISA mathematics literacy framework. Investigation of the…

The purpose of this research was to show open-ended questions about surface area and beam volume which valid and practice, have potential effect. This research is research development which consists of two main phases: preliminary phase (preparation phase and problem design) and formative evaluation phase (evaluation and revision phases). The…

This study investigated proportional reasoning and the related concepts of decimal, percent, and ratio. In particular, the research focused on analyzing the gaps and understandings that grades 6, 7, and 8 students have and advanced factors for such gaps and understandings. The study employed a mixed method approach in which quantitative data was…

This article examines research to explore whether the use of manipulatives is an effective tool in teaching mathematics concepts and reasoning to middle-grades students.

Ratio, rate, and proportion are central ideas in the Common Core State Standards (CCSS) for middle-grades mathematics (CCSSI 2010). These ideas closely connect to themes in earlier grades (pattern building, multiplicative reasoning, rational number concepts) and are the foundation for understanding linear functions as well as many high school…

The mathematical reasoning ability is one of the essential hard skills of a student, especially in solving everyday problems. In supporting the achievement of this mathematical reasoning ability, meaningful teaching materials are an essential part of keeping exciting and not dull a learning process. This study aimed to design and develop an…

Research has shown that prediction has the potential to promote the teaching and learning of mathematics because it can be used to enhance students' thinking and reasoning at all grade levels in various topics. This article addresses the effectiveness of using prediction on students' understanding and reasoning of mathematical concepts in a middle…

The present study explored 285 11th-grade students' preconceptions, misconceptions, and errors in solving mathematics tasks by graphical method. A descriptive-explorative study design was adopted. Cluster sampling was used to select students from sampled secondary schools in eastern and central Uganda. Students' paper and pen solution sketches…

The purpose of this study is to examine secondary school students' mathematical reasoning about the area of the circle. Mathematical tasks designed using GeoGebra were performed within the context of the 5E-based flipped classroom approach. The participants of the study are 13 secondary school students. The tasks, video and audio recordings…

Teachers are continually in search of tasks that balance the dual priorities of rigorous thinking and fluency development. These often-competing priorities are emphasized by national-level organizations as well as by state-level standards and assessments. The National Council of Teachers of Mathematics (NCTM) calls for school mathematics…

This work presents the result of the application of a didactic sequence designed to understand the concept of the Cavalieri's Principle, supported by the GeoGebra application in its version for mobile phones -- 3D Calculator. For this study, the Theory of Categories of Intuitive Reasoning, by Efraim Fischbein, was used as a conceptual basis. The…

A common goal for mathematics teachers at any grade level is for "all" students--not just future mathematics teachers--to develop deep understanding of the mathematics they are learning and using. To that end, this lesson can be used in an upper-level high school mathematics course to introduce the concept of a radian in a way that…