The purpose of the present study is to examine the effectiveness of the Conceptual Model-based Problem-Solving intervention program (COMPS) along with instructional scaffolds to enhance the performance of English learners (ELs) with learning difficulties in mathematics (LDM) to solve word problems. The participants were three third-grade ELs with…

Purpose: Math word problem solving, a form of reading comprehension, is complicated by mathematical lexical ambiguity (e.g., the word "difference" can mean "dissimilarity" in everyday discourse but "the answer in a subtraction problem" in math). This study examined the role of mathematical lexical ambiguity in math…

Identifying mathematical interventions that practitioners can implement to improve the mathematical problem solving (PS) of students is a need for the field. Literature on the PS performance of students with disabilities has grown; recently, schema instruction (SI) has been suggested as an evidence-based practice. The purpose of this study was to…

How can a cognitively demanding real-world task such as the Seven Billion People problem promote productive struggle "and" help shape students' mathematical dispositions? Driving home from school one evening, Jaclyn Murawska heard a commentator on the radio announce three statements: (1) experts had determined that the world population…

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

English learners (ELs) experience difficulty with mathematical problem solving because word problems require complex processes beyond basic math skills, such as the use of linguistic information, identifying relevant information, and constructing the appropriate problem statement. This study used a combined multiple baseline design and criterion…

There is a call for enabling students to use a range of efficient mental and written strategies when solving addition and subtraction problems. To do so, students should recognise numerical structures and be able to change a problem to an equivalent problem. The purpose of this article is to suggest an activity to facilitate such understanding in…

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 ubiquity of the subject of percentages in our everyday life demands that math teachers and pre-service math teachers demonstrate a profound knowledge and thorough understanding of the concept of percentages. This work, which originated from one specific lesson in an 8th grade math class, studies the conceptual understanding and problem-solving…

This article aims to describe the transition process from procedural understanding to conceptual understanding in solving mathematical problems. Subjects in this study were three students from 20 fifth grade students of SDN 01 Sumberberas Banyuwangi selected based on the results of the students' answers. The transition process from procedural to…

In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his "Key to Arithmetic", a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life…

Researchers have proposed a variety of methods to make a connection between real life and mathematics so that it can be learned in a practical way and enable people to utilise mathematics in their daily lives. Model-eliciting activities (MEAs) were developed to fulfil this need and are very capable of serving this purpose. The reason MEAs are so…

This study aims at determining to what extent visuals contribute to success in non-routine problem solving process and what types of errors are made when solving with visuals. Comparative model was utilized for identifying the effect of visuals on student achievement, and clinical interview technique was used to determine the types of errors. In…

Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…