Taking away and determining the difference—a longitudinal perspective on two models of subtraction and the inverse relation to addition

Subtraction can be understood by two basic models—taking away (ta) and determining the difference (dd)—and by its inverse relation to addition. Epistemological analyses and empirical examples show that the two models are not relevant only in single-digit arithmetic. As curricula should be developed in a longitudinal perspective on mathematics learning processes, the article highlights some exemplary steps in which the inverse relation is discussed in light of the two models, namely mental subtraction, the standard algorithms for subtraction, negative numbers and manipulations for solving algebraic equations. For each step, the article presents educational considerations for fostering a flexible use of the two models as well as of the inverse relation between subtraction and addition. In each section, a mathe-didactical analysis is conducted, empirical results from literature as well as from our own case studies are presented and consequences for teaching are sketched.     

GENDER COMPARISONS OF BABY BOOMERS AND FINANCIAL PREPARATION FOR RETIREMENT

This study compared men and women, focusing on three middle‐year age groups incorporating the baby boomers, in relation to the level of savings for retirement and the number of savings vehicles utilized. The research tapped into a study conducted by the National Center for Women and Retirement Research. Usable responses were received from 1,287 persons, 872 females and 415 males. Multiple linear regression identified certain personal characteristics, economic factors, psy‐chosocial factors, attitudes, and investing methods that appeared to be related to the level of savings for retirement. Certain personal characteristics, economics, and psychosocial factors were identified for the investments used. The identified factors were true for both genders, thus a profile of the person most likely to have a higher level of savings for retirement and likely to own investments emerged. The males best fit the savings and investing profiles. Neither gender was saving adequately for retirement or taking full advantage of portfolio diversification, with women the lowest. Recommendations are made, based on the findings, for educators, financial institutions and advisors, employers, and policy makers.     

The sensitivity of native Japanese speakers to On and Kun kanji readings

Japanese kanji reading can be divided into two types: On-readings, derived from the original Chinese pronunciation and Kun-readings, originating from the Japanese pronunciation. Kanji that are normally given an On-reading around 50% of the time were presented in a context of other kanji that had either a highly dominant On-reading or a highly dominant Kun-reading. The reading that was given in this experiment was very much biased toward the type of phonological environment in which it was embedded. So native Japanese speakers easily shifted between On and Kun readings, depending on phonological context, suggesting that separate On and Kun sub-lexica exist within the phonological lexicon.     

Adjustment to College as Measured by the Student Adaptation to College Questionnaire: A Quantitative Review of its Structure and Relationships with Correlates and Consequences

This paper presents a meta-analytic review (k = 237, N = 44,668) of the adjustment to college literature. The review, based on studies using the Student Adaptation to College Questionnaire, is organized around three primary themes: (1) the structure of students’ adjustment to college, (2) the relationship of adjustment to college constructs with possible antecedents and correlates, and (3) the relationship of adjustment to college constructs with college grades and college retention. Meta-analytic results indicate that adjustment to college is multidimensional, predictive of college grades, and an unusually good predictor of college retention. Adjustment to college is also shown to be moderately related to individual traits, social support, and students’ relationships with their parents. Weaker relationships are evident with demographic variables, prior achievement, coping approaches, and variables that reflect students’ psychological independence from their parents. Theoretical and practical implications for the study of students’ adjustment to college, academic performance, and retention are discussed.     

The effects of exemptions to Florida's test-based promotion policy: Who is retained?: Who benefits academically?

We evaluate the impact of Florida's test-based promotion policy on the probability that low-performing students are retained using data on the universe of third-grade students in the state of Florida from 2001 to 2004. We also examine the effect of formal exemptions to the policy on student proficiency in reading two years later. In an evaluation of retention for third-grade students over time with a logit model we find that Florida's policy has increased the probability that minority students are retained to a greater extent than white students. Contrary to previous research, this differential retention occurs after controlling for student academic proficiency. However, in an evaluation of the academic performance of students who were in the first class subject to the retention policy, we find that retained students outperform students who received an exemption from the policy in reading two years after baseline, indicating that on average exemptions have not been granted to those individuals who would benefit from promotion.