Comparison of Linear Functions in Middle Grades Textbooks from Singapore and the United States

Many U.S. students do not perform well on mathematics assessments with respect to algebra topics such as linear functions, a building-block for other functions. Poor achievement of U.S. middle school students in this topic is a problem. U.S. eighth graders have had average mathematics scores on international comparison tests such as Third International Mathematics Science Study, later known as Trends in Mathematics and Science Study, (TIMSS)-1995, -99, -03, while Singapore students have had highest average scores. U.S. eighth grade average mathematics scores improved on TIMMS-2007 and held steady onTIMMS-2011. Results from national assessments, PISA 2009 and 2012 and National Assessment of Educational Progress of 2007, 2009, and 2013, showed a lack of proficiency in algebra. Results of curriculum studies involving nations in TIMSS suggest that elementary textbooks in high-scoring countries were different than elementary textbooks and middle grades texts were different with respect to general features in the U.S. The purpose of this study was to compare treatments of linear functions in Singapore and U.S. middle grades mathematics textbooks. Results revealed features currently in textbooks. Findings should be valuable to constituencies who wish to improve U.S. mathematics achievement. Portions of eight Singapore and nine U.S. middle school student texts pertaining to linear functions were compared with respect to 22 features in three categories: (a) background features, (b) general features of problems, and (c) specific characterizations of problem practices, problem-solving competency types, and transfer of representation. Features were coded using a codebook developed by the researcher. Tallies and percentages were reported. Welch's t-tests and chi-square tests were used, respectively, to determine whether texts differed significantly for the features and if codes were independent of country. U.S. and Singapore textbooks differed in page appearance and number of pages, problems, and images. Texts were similar in problem appearance. Differences in problems related to assessment of conceptual learning. U.S. texts contained more problems requiring (a) use of definitions, (b) single computation, (c) interpreting, and (d) multiple responses. These differences may stem from cultural differences seen in attitudes toward education. Future studies should focus on density of page, spiral approach, and multiple response problems.

Analysis of Land Use Change as a Method of Predicting Water Demands in an Urbanizing Environment: Redland, Miami-Dade County, Florida

The fluctuation in water demand in the Redland community of Miami-Dade County was examined using land use data from 2001 and 2011 and water estimation techniques provided by local and state agencies. The data was converted to 30 m mosaicked raster grids that indicated land use change, and associated water demand measured in gallons per day per acre. The results indicate that, first, despite an increase in population, water demand decreased overall in Redland from 2001 to 2011. Second, conversion of agricultural lands to residential lands actually caused a decrease in water demand in most cases while acquisition of farmland by public agencies also caused a sharp decline. Third, conversion of row crops and groves to nurseries was substantial and resulted in a significant increase in water demand in all such areas converted. Finally, estimating water demand based on land use, rather than population, is a more accurate approach.