Recent reform movements have emphasized students making meaning of algebraic relationships; however, research on student thinking and learning often remains disconnected from the design of widely used curricular materials. Although a previous examination of algebra textbooks (Nathan, Long, & Alibali, 2002) demonstrated a preference for a…

Three studies explore arithmetic tasks that support both substitutive and basic relational meanings for the equals sign. The duality of meanings enabled children to engage meaningfully and purposefully with the structural properties of arithmetic statements in novel ways. Some, but not all, children were successful at the adapted task and were…

This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written…

Knowledge of the equal sign as an indicator of mathematical equality is foundational to children's mathematical development and serves as a key link between arithmetic and algebra. The current findings reaffirmed a past finding that diverse items can be integrated onto a single scale, revealed the wide variability in children's knowledge of the…

Responses to rate-of-change problems were collected during and after 24 hours of conceptual calculus instruction given to first-year university students. Analysis revealed three categories of error in which variables were treated as symbols to be manipulated rather than quantities to be related. Contains test questions. (Author/MKR)

Investigates whether three cognitive components of language proficiency--metalinguistic awareness of symbol, syntax, and ambiguity--are associated with students' success in learning algebraic notation. Reports that very few students with low metalinguistic awareness scores achieved high algebra scores in a total sample of more than 1500 students.…

An exploratory investigation of various incorrect solution procedures used by students attempting to solve a variety of forms of open sentences is reported. The study identifies specific incorrect strategies, indicates their relative frequency of occurrence, and attempts to offer some explanation for certain of the incorrect procedures used. (MK)

The relationship between first grade students' understanding of written mathematical symbolization and readiness to learn was investigated. Results suggest students' readiness influences meaningful learning of the written symbolization of addition and subtraction. (MP)

The major conclusion of this study is that students understand mathematics better when concepts are written with more common grammatical structures and without symbols. (MP)

Four third-grade and three fourth-grade students received individualized instruction on addition and subtraction of fractions for three weeks. Students overgeneralized the meanings of symbolic representations for whole numbers to fractions and vice versa. (MKR)

In this article, I argue for a renewed focus in mathematics education research on procedural knowledge. I make three main points: (1) The development of students' procedural knowledge has not received a great deal of attention in recent research; (2) one possible explanation for this deficiency is that current characterizations of conceptual and…

Teaching in a manner consistent with reform recommendations is a challenging and often overwhelming task. Part of this challenge involves using students' thinking and understanding as a basis for the development of mathematical ideas (cf. NCTM, 2000). The purpose of this article is to address this challenge by developing the notion of "pedagogical…

Given its important role in mathematics as well as its role as a gatekeeper to future educational and employment opportunities, algebra has become a focal point of both reform and research efforts in mathematics education. Understanding and using algebra is dependent on understanding a number of fundamental concepts, one of which is the concept of…

This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. The instruction primarily concerned representing fractions and ordering fractions on number lines. (Author/PK)

College students were asked to write equations using one of two sets of notational systems. Results indicate that the use of more explicit notation did not help problem-solving performance. (Author/PK)