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.

Evaluating heavy episodic drinking effects on educational attainment

Adolescence and emerging adulthood are transition points that offer both opportunities and constraints on individual development. The purpose of this study is threefold: First, to examine two models (i.e., young adolescents in grades 7 and 8 and older adolescents in grade 12) of heavy episodic drinking and examine how heavy episodic drinking affects subsequent educational attainment. By utilizing two different developmental transitions, i.e., middle school to high school and high school to college, it may be possible to better understand the temporal effects of alcohol use and subsequent educational attainment. The second purpose of this study is to examine how alcohol use at Time 1 may lead to the problems in the adolescent's immediate context due to alcohol (i.e., problems with parents, peers, romantic relationships, problems at school) and to examine if these problems affect educational attainment over and above alcohol use alone. The third purpose of this study is to examine the potential gender differences in these models. The study uses data from the National Longitudinal Study of Adolescent Health, which is a large scale, nationally representative school based sample of 20,745 adolescents who were interviewed in grades 7 to 12. Two longitudinal mediational models were evaluated utilizing structural equation modeling. Binge drinking and number of days drunk were used as indicators for a latent variable of heavy episodic drinking (i.e., LHED). In the 7th and 8th grade model, direct effects of LHED were found to predict educational attainment at grade 12. Additionally, in the 7th and 8th grade sample, a mediated relationship was found whereby educational attainment was predicted by problems with parents. Problems with parents were predicted by number of days drunk in the past year. In the 12th grade sample, there were no direct effects or indirect effects of alcohol on educational attainment. This study highlights the need for using a longitudinal framework when examining heavy episodic drinking's effects on educational attainment. ^