One pedagogical technique that promotes conceptual understanding in mathematics learners is self-explanation integrated with worked examples (e.g., Rittle-Johnson et al., 2017). In this work, we implemented self-explanations with worked examples (correct and erroneous) in a software-based Intelligent Tutoring System (ITS) for learning algebra. We…

Worked examples are effective learning tools for algebraic equation solving. However, they are typically presented in a static concise format, which only displays the major derivation steps in one static image. The current work explores how worked examples that vary in their extensiveness (i.e., detail) and degree of dynamic presentation (i.e.,…

Many teachers labor to distinguish between productive and unproductive struggle; they believe that struggle is productive when it engages students in thinking and communicating metacognitively, which is when students think and communicate about their problem-solving processes, strategies, challenges, and successes. One method that helps ensure…

A lack of college readiness can affect student success in the classroom and impact retention rates. It has been recommended that all students be placed in courses with college-level content but that added support be provided for students identified as underprepared. This study examines the impact of added instructional time and support embedded…

Students with learning disabilities are most typically characterized as struggling readers (i.e., 80-90% of students are identified on the basis of reading failure; LD OnLine, 2008 Lerner, 1989; Lyon, Fletcher, Shaywitz, Torgesen, Wood, et al., 2001); however, as many as 50% of students with learning disabilities have IEP goals in the area of…

As current mathematics standards, such as the Common Core, are being implemented throughout the United States, it has become evident that teachers need support to enact the tenets of those standards. To help in this endeavor, this article was published as a guideline to emphasize to mathematics education stakeholders that "effective teaching…

Intelligent tutoring systems (ITS) support students in learning a complex problem-solving skill. One feature that makes an ITS architecturally complex, and hard to build, is support for strategy freedom, that is, the ability to let students pursue multiple solution strategies within a given problem. But does greater freedom mean that students…

The authors completed a narrative review of studies of mathematics interventions from 1996 to 2010 for helping elementary school students with difficulties in mathematics solve word problems. Key instructional components supported by research are teaching cognitive and metacognitive skills; schema-based instruction focusing on semantic analysis,…

Over the past 2 years, almost 45% of the students attending a local suburban high school failed Algebra 2. The purpose of this study was to compare the impact of a cooperative instructional technique (student teams-achievement divisions [STAD]) to traditional instructional methods on performance in high school algebra. Motivational and cognitive…

The purpose of this paper is to discuss the effectiveness of incorporating study strategies in a developmental mathematics/college algebra program. Both quantitative and qualitative data were collected through a quasiexperimental methodology. Results show that students reported increases on the Learning and Study Strategies Inventory (LASSI)…

Understanding of ratio and proportion is critical to the development of higher level mathematical skills. Following Carpenter, Gomez, et al.'s (1999) proposal of a four-level trajectory in the development of proportional reasoning, a 12-week investigation was undertaken of the developmental trajectory of proportional reasoning of girls in two…

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…

Twelve adolescents with learning disabilities were trained to use a cognitive strategy in algebra problem solving. The two-phase strategy (problem representation and problem solution) was effective in improving algebra performance on algebra word problems, and maintenance and transfer of the strategy were evident. (JDD)

Three studies involving 44 learning-disabled junior high students assessed the impact of strategy instruction in individual, small group, and whole class instruction in one knowledge domain: algebra. The three studies are contrasted, outcome data are compared, and the issue of generality-specificity in strategy instruction is examined. (JDD)