The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it is a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use…

The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…

The purpose of this study was to examine the effects of a schema-based instructional strategy that emphasizes prealgebraic conceptualization of multiplicative relations on solving arithmetic word problems with elementary students with learning disabilities or problems (LP). Introducing symbolic representation and algebraic thinking in earlier…

This article describes several distinct approaches taken by preservice elementary teachers to solving a classic rate problem. Their approaches incorporate a variety of mathematical concepts, ranging from proportions to infinite series, and illustrate the power of all five NCTM Process Standards. (Contains 8 figures.)

The study presented in this paper seeks to investigate the impact of authenticity on the students' disposition to make necessary real world considerations in their word problem solving. The aim is also to gather information about the extent to which different reasons for the students' behaviors are responsible for not providing solutions that are…

Substantial evidence indicates that teacher-delivered schema-based instruction (SBI) facilitates significant increases in mathematics word problem solving (WPS) skills for diverse students; however research is unclear whether technology affordances facilitate superior gains in computer-mediated (CM) instruction in mathematics WPS when compared to…

In this study, children were encouraged to abstract mathematical principles by making connections between procedures. Children from 2 sixth-grade classes (N = 58) were asked to solve and explain subtraction examples in 3 different number domains (whole numbers, fractions, and decimals), solve subtraction word problems, compare the procedures, and…

This study examined the effectiveness of instruction focused on teaching students with learning disabilities (LD) to solve 1- and 2-step word problems of varying types. Three students with LD in Grade 8 participated in the study. During the treatment, students received instruction in diagram generation and a strategy that incorporates diagrams as…

This article describes a task that engages students in the process of creating word problems. Difficulties in having students write problems are described, along with strategies for overcoming these difficulties. Student work and teacher reactions are included.

This study examines 8th grade students' coordination of quantitative units arising from word problems that can be solved via a set of equations that are reducible to a single equation with a single unknown. Along with Unit-Coordination, Quantitative Unit Conservation also emerges as a necessary construct in dealing with such problems. We base our…

We describe how 1 Algebra I teacher and her 8th-grade students used meta-representational knowledge when generating and evaluating equations to solve word problems. Analyzing data from a sequence of 4 lessons, we found that the teacher and her students used criteria for evaluating equations, in addition to other types of knowledge (e.g., different…

The authors explored the effects of teaching conceptual model-based problem-solving instruction on students' ability to solve problems in various situations. Participants were 3 4th-and 5th-grade students with or at risk for mathematics disabilities. The authors used an adapted multiple-probe across-participants design to assess the functional…

Every assessment is a literacy test. It matters not whether the content is science, social studies, or mathematics; if students are not able to make sense of the words, their ability to decipher the meaning of the assessment questions is suspect. Comprehending the language of a task becomes even more important as educators strive to move the…

Mathematics is considered the universal language, but students who speak languages other than English have difficulty doing mathematics in English. For instance, because of a lack of familiarity with the problem's context, many have trouble understanding exactly what operations to perform. In the United States, approximately one in seven students…

We report a case study that explored how three college students mentally represented the knowledge they held of inferential statistics, how this knowledge was connected, and how it was applied in two problem solving situations. A concept map task and two problem categorization tasks were used along with interviews to gather the data. We found that…