When learning a new math concept, should learners be first taught the concept and its associated procedures and then solve problems, or solve problems first even if it leads to failure and then be taught the concept and the procedures? Two randomized-controlled studies found that both methods lead to high levels of procedural knowledge. However,…

It is understandable that misuse of the terms "specially designed instruction" (SDI), "high-leverage practices" (HLPs), "explicit instruction" (EI), and "intensive instruction"(II) has bred confusion among professionals, and this confusion may lead to miscommunication and misunderstandings in the field.…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the writing of the guidance report "Improving Mathematics in the Early Years and Key Stage One" (ED612298). The review aimed to synthesise the best available international evidence regarding teaching and learning of mathematics for…

This article investigates the effects of fraction word problem-solving instruction involving explicit teaching of the concrete-representational-abstract sequence with culturally relevant teaching examples for 3 low-performing Asian immigrant English learners who spoke a language other than English at home. We used a multiple probe design across…

The purpose of this investigation was to identify strategies used by effective instructors of developmental mathematics, and to discover the perceptions developmental mathematics students have about these strategies. While there are research projects focusing solely on developmental mathematics achievement, this study fills a need by incorporating…

Students with mathematics difficulties and learning disabilities (LD) typically struggle with solving word problems. These students often lack knowledge about efficient, cognitive strategies to utilize when solving word problems. Cognitive strategy instruction has been shown to be effective in teaching struggling students how to solve word…

This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…

The production of an effective mathematics curriculum begins with a scientific development, evaluation, and revision framework. The purpose of this study was to conduct an initial investigation of a recently developed Tier 2 mathematics curriculum designed to improve the outcomes of first grade students at risk for mathematics difficulties (MD).…

The production of an effective mathematics curriculum begins with a scientific development, evaluation, and revision framework. The purpose of this study was to conduct an initial investigation of a recently developed Tier 2 mathematics curriculum designed to improve the outcomes of 1st grade students at-risk for mathematics difficulties. The…

This paper examines how particular teaching and learning strategies are related to student performance on specific PISA test questions, particularly mathematics questions. The report compares teacher-directed instruction and memorisation learning strategies, at the traditional ends of the teaching and learning spectrums, and student-oriented…

This qualitative single exploratory case study explored instructional practices of third, fourth, and fifth grade teachers to explore how Florida students with learning disabilities at the elementary school level perform on statewide mathematics assessments of learning following both cognitive and metacognitive skills development. Theoretical…

We examined the effectiveness of (a) a working memory (WM) training program and (b) a combination program involving both WM training and direct instruction for students with geometry difficulties (GD). Four students with GD participated. A multiple-baseline design across participants was employed. During the Phase 1, students received six sessions…

This study investigated the effect of different methods of guidance with anchored instruction on students' mathematical problem-solving performance. The purpose of this research was to iteratively design a learning environment to find the optimal level of guidance. Two iterations of the software were compared. The first iteration used explicit…

How best to promote fluency with basic sums and differences is still not entirely clear. Some advocate a direct approach--using drill to foster memorization of basic facts by rote. Others recommend an indirect approach that first involves learning reasoning strategies. The purpose of the present study was to evaluate the efficacy of 2…

I advance a theoretically and empirically-grounded case for designing for and learning from failure, and instantiate it in a learning design called Productive Failure (PF). I describe the key mechanisms and the design principles of PF. The PF learning design comprises a generation and exploration phase followed by a consolidation and knowledge…