Introduction to special issue on contributions of mathematical psychology to clinical science and assessment

Evolution of clinical mathematical psychology, exemplifying integrative, translational psychological science, is considered in light of target, idealized scientific systems. It is observed that mutual benefits to psychological clinical science, and quantitative theory, potentiated through their interlacing as exemplified in this special issue, stand to parallel the historical symbiosis between older disciplines and mathematics. Enumerated are the range of psychological processes and clinical groups addressed, forms of modeling implemented, and clinical issues engaged, the latter ranging from intervention, to elucidation of deviant basic processes. A denouement comprising cogent quotations from historical figures in science concludes this Introduction.     

Working memory resources in young children with mathematical difficulties

Kyttälä, M., Aunio, P. & Hautamäki, J. (2010). Working memory resources in young children with mathematical difficulties. Scandinavian Journal of Psychology, 51 , 1–15.
Working memory (WM) ( Baddeley, 1986, 1997 ) is argued to be one of the most important cognitive resources underlying mathematical competence ( Geary, 2004 ). Research has established close links between WM deficits and mathematical difficulties. This study investigated the possible deficits in WM, language and fluid intelligence that seem to characterize 4- to 6-year-old children with poor early mathematical skills before formal mathematics education. Children with early mathematical difficulties showed poor performance in both verbal and visuospatial WM tasks as well as on language tests and a fluid intelligence test indicating a thoroughly lower cognitive base. Poor WM performance was not moderated by fluid intelligence, but the extent of WM deficits was related to language skills. The educational implications are discussed.     

THE DYNAMICS OF THE LAW OF EFFECT: A COMPARISON OF MODELS

Dynamical models based on three steady‐state equations for the law of effect were constructed under the assumption that behavior changes in proportion to the difference between current behavior and the equilibrium implied by current reinforcer rates. A comparison of dynamical models showed that a model based on Navakatikyan's (2007) two‐component functions law‐of‐effect equations performed better than models based on Herrnstein's (1970) and Davison and Hunter's (1976) equations. Navakatikyan's model successfully described the behavioral dynamics in schedules with negative‐slope feedback functions, concurrent variable‐ratio schedules, Vaughan's (1981) melioration experiment, and experiments that arranged equal, and constant‐ratio unequal, local reinforcer rates.     

Multidimensional adaptive testing

Maximum likelihood and Bayesian procedures for item selection and scoring of multidimensional adaptive tests are presented. A demonstration using simulated response data illustrates that multidimensional adaptive testing (MAT) can provide equal or higher reliabilities with about one-third fewer items than are required by one-dimensional adaptive testing (OAT). Furthermore, holding test-length constant across the MAT and OAT approaches, substantial improvements in reliability can be obtained from multidimensional assessment. A number of issues relating to the operational use of multidimensional adaptive testing are discussed.     

The spatial mapping of concepts in English and Mandarin

ABSTRACT

English speakers have been shown to map abstract concepts in space, which occurs on both the vertical and horizontal dimensions. For example, words such as God are associated with up and right spatial locations, and words such as Satan with down and left. If the tendency to map concepts in space is a universal property of human cognition, then it is likely that such mappings may be at least partly culturally-specific, since many concepts are themselves language-specific and therefore cultural conventions. Here we investigated whether Mandarin speakers report spatial mapping of concepts, and how these mappings compare with English speakers (i.e. are words with the same meaning associated with the same spatial locations). Across two studies, results showed that both native English and Mandarin speakers reported spatial mapping of concepts, and that the distribution of mappings was highly similar for the two groups. Theoretical implications are discussed.     

小学生数学问题解决中视觉空间表征的研究

本研究区分了两类数学应用题:非视觉化题目与视觉化题目,采用数学测验与个别访谈相结合的方法,考察了54名小学四、五、六年级不同学业水平学生的视觉空间表征。结果表明:图式表征在非视觉化题目与视觉化题目上都极大地促进了问题解决,图像表征妨碍非视觉化题目的解决但与视觉化题目的解决无关,并提出图式表征和图像表征在两类题目上有不同的含义。六年级学生的解题成绩及图式表征有显著的提高,但图像表征与年级因素无关。差生的图式表征能力很差,而在视觉化题目上使用图像表征显著地多于优生及中等生。在非视觉化题目的非视觉空间表征与图式表征之间的转换灵活性上,优生表现了明显的优势。     

初中生的数学估计能力及其与元认知监控的关系

抽取济南市四所中学初一至初三年级547名学生为被试,采用自行设计的数学估计任务和元认知状态问卷(SMI),考察了初中生数学估计能力的现状及其与元认知监控的关系。结果表明:初中生的估计能力总体较差,未显示出稳定的性别差异。元认知监控的四个维度与数学估计表现均存在显著的正相关。从元认知监控对估计成绩的回归分析来看,自我意识可以显著正向预测估计整体表现。其中,计划可以正向预测估数和估算成绩,自我意识可以正向预测估测和估算成绩。文章特别讨论了数学估计与元认知加工之间的具体联系。     

问题表征、工作记忆对小学生数学问题解决的影响

以104名小学六年级学生为被试, 采用4个相对独立的研究探讨了工作记忆广度、问题表征方式与小学生数学应用题解决的关系。结果表明：(1)言语工作记忆广度只影响高难度应用题的解决, 在低难度、中等难度的应用题解决上, 高、低言语工作记忆广度者不存在显著差异; (2)视觉-空间工作记忆广度对低难度、中等难度、高难度应用题的解决都存在影响; (3)问题表征方式影响数学应用题的解决, 应用题的解题成绩与问题表征方式的使用有关; (4)言语工作记忆广度对应用题的表征方式没有影响, 高、低言语工作记忆广度者在三种难度水平应用题的表征方式上不存在显著差异; (5)视觉-空间工作记忆广度对应用题的表征方式存在影响, 高、低视觉-空间工作记忆广度者在三种难度水平应用题的表征方式上均存在组间差异。     

Mapping an HIV/STD prevention curriculum for Zambian in-school settings

HIV/AIDS poses grave risk to human development in sub-Saharan Africa. Evidence-based interventions that are rooted in local culture could help efforts to prevent threats to human development from HIV/AIDS. We used concept mapping (Concept System, 2006 ) to construct the components and content of a locally developed HIV/AIDS curriculum for use by secondary schools in Lusaka, Zambia. Participants were school counsellors (n = 14), youth health program officers (n = 7), and regular education teachers (n = 3) from the education, health, and youth development agencies in Lusaka, Zambia (males = 11; females = 13; mean age 38; SD = 15 years). Concept mapping yielded six statement clusters defining preliminary components of a locally grounded in-school HIV/AIDS prevention curriculum and the content items that define these components: (1) life skills education (18 items), (2) sexuality and reproductive health (10 items), (3) treatment, care and support (13 items), (4) counselling (12 items), (5) basic facts about HIV/AIDS (11 items), and (6) dissemination of information about HIV/AIDS (11 items). Zambian locally constructed constructs for an HIV/STD prevention curriculum overlap those promoted by public health programs in the country and internationally.