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The article focuses on the significance of proof in learning and teaching mathematics. It notes that the understanding of students in proving can be supported by learning how to build arguments. It points out that learning how to mathematically argue can be attained through organized classroom discourse. It adds that organizing transactive classroom discussions can be a powerful tool to make proof vital in mathematics instruction and learning.

This article explores how teachers can use literature to integrate algebraic thinking and illustrates how these tasks, connected to literature, can be integrated across the curriculum. Today teachers find it difficult to teach all the subjects to the students in span of time given to them. With testing and accountability on everyone's mind, teachers are looking for creative ways to teach all subjects. Literacy is on the top of the list for testing, so it seems to get top priority. But the main focus is on how the crucial area such as algebraic thinking can be integrated into the literature. Integrating subject matter is one answer, and children's literature seems to be a great place to start. Good, rich children's books enhance reading and communication as well as demonstrate how mathematics is relevant in real life situations. Algebraic thinking can be supported through the use of "algebrafied" tasks that help children look for general relationships. Although other ways exist for students to think algebraically, the type of algebrafying approach described in the article offers a simple way for teachers to algebrafy their existing arithmetic curriculum.

This research focuses on the retention of students' algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3-5. The results show that, as was the case at the end of Grades 3,4, and 5, treatment students significantly outperformed control students at the end of Grade 6 on a written assessment of algebraic understanding. However, treatment students experienced a significant decline and control students a significant increase in performance relative to their respective performance at the end of Grade 5. An item-by-item analysis performed within condition revealed the areas in which students in the two groups experienced a change in performance. [ABSTRACT FROM AUTHOR]

The article describes an activity program which aims to help elementary school students understand the concept of functions.

The haloacetic acids (HAAs) are a family of xenobiotics found in tap water as a result of drinking water disinfection. Administration of HAAs to rats produces a variety of adverse effects, including developmental toxicity. The dysmorphogenic potencies of all nine bromo/chloro-acetic acids have been determined in rodent whole embryo culture using standard 26-h exposure. Since the half-lives of the HAAs in vivo are typically <8 h, the developmental effects of short-term exposures to dihaloacetates were evaluated. Gestation day 8 (3-6 somite pairs) CD-1 mouse conceptuses were exposed to 11,000 microM dichloroacetic acid (DCA), 300 microM dibromoacetic acid (DBA) or 300 microM bromochloroacetic acid (BCA) for culture periods of 1, 3, 6 or 26 h. Following 1, 3 or 6 h of exposure to HAAs, conceptuses were transferred to control medium to complete a 26-h culture period. The amounts of HAAs present in embryos after 1, 3 and 6h of exposure were determined. Increased incidences of dysmorphic embryos were produced by 6 or 26-h exposures to DCA; a 26-h exposure to DBA; or 3, 6 or 26-h exposures to BCA. The dysmorphology produced was dependent upon the length of exposure and chemical. The embryonic concentration of each HAA (104.5, 2.5 and 2.6 pmol/microg protein for DCA, DBA and BCA, respectively) was reached by 1h of exposure and did not change at the subsequent time points examined. The current studies demonstrate that BCA is more potent than DBA or DCA at disrupting embryogenesis since shorter exposures alter morphogenesis. Since the embryonic HAA concentrations were the same at the three time points measured, the time-dependence in dysmorphogenesis does not appear to be a simple function of increasing embryonic concentration of these chemicals. These studies demonstrate that for these dihaloacetic acids relatively high concentrations and long exposures are needed to alter rodent development in vitro.