This study explores how teachers understand and translate curriculum statements into concepts that are better suited to supporting student progress with rich mathematical problem-solving tasks. We report the actions of one experienced teacher of primary mathematics in charting the sequence of concepts and processes relevant to the above issue. We…

This study examines patterns in middle-grade boys' and girls' written problem solving strategies for a mathematical task involving proportional reasoning. The students participating in this study attend a coeducational charter middle school with single-sex classrooms. One hundred nineteen sixth-grade students' responses are analyzed by gender…

In order to achieve their course learning outcomes, public affairs instructors can train students to solve real community problems (SRCP). This approach focuses on the learners themselves and aims to transform the role of college professors from traditional teaching (lecturing) to facilitating and coaching students' learning activities. This study…

Knowledge restructuring refers to changes in the strategy with which people solve a given problem. Two types of knowledge restructuring are supported by existing category learning models. The first is a relearning process, which involves incremental updating of knowledge as learning progresses. The second is a recoordination process, which…

What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…

Teaching how to solve problems--from solving simple equations to solving difficult competition tasks--has been one of the greatest challenges for mathematics education for many years. Trying to find an effective method is an important educational task. Among others, the question arises as to whether a method in which students help each other might…

Research has shown that for acquiring problem-solving skills, instruction consisting of studying worked examples is more effective and efficient for novice learners than instruction consisting of problem-solving. This study investigated whether worked examples would also be a useful instructional format for the acquisition of visual perceptual…

The eight mathematical practices explored in the Common Core Math Standards are the following: (1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (4) Model with mathematics; (5) Use appropriate tools strategically; (6) Attend to…

Background: Context-based learning approaches are used to enhance students' interest in, and knowledge about, science. According to different empirical studies, students' interest is improved by applying these more non-conventional approaches, while effects on learning outcomes are less coherent. Hence, further insights are needed into the…

Bilingual Latino students engage multiple languages, cultures and environments as they pursue educational and professional goals. For this underrepresented group, pursuing a post-secondary degree is a "lucha" (fight) to negotiate the complex interplay of historical, educational, and cultural variables and achieve academic success.…

Using a means-means-ends problem-solving task, this study examined whether 16-month-old walking infants (N = 28) took into account the width of a bridge as a means for crossing a precipice and the location of a handrail as a means for augmenting balance on a narrow bridge. Infants were encouraged to cross from one platform to another over narrow…

This paper presents the results of a study designed to facilitate teacher candidates' shift from students of mathematics to teachers of mathematics. We develop a series of tasks each of which encourages candidates to reconsider rich tasks from increasingly teacher-centric points of view. The results show that using authentic high school student…

This qualitative study considers middle grades mathematics teachers' reasoning about drawn representations of fractions and decimals. We analyzed teachers' strategies based on their response to multiple-choice tasks that required analysis of drawn representations. We found that teachers' flexibility with referent units played a significant role in…

Fluid intelligence (Gf) predicts performance on a wide range of cognitive activities, and children with impaired Gf often experience academic difficulties. Previous attempts to improve Gf have been hampered by poor control conditions and single outcome measures. It is thus still an open question whether Gf can be improved by training. This study…

Many factors influence a student's performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils' real-world knowledge, which support the construction of a…