Departure from normal assumptions: A promise for future psychometrics with substantive mathematical modeling

Normal assumptions have been used in many psychometric methods, to the extent that most researchers do not even question their adequacy. With the rapid advancement of computer technologies in recent years, psychometrics has extended its territory to include intensive cognitive diagnosis, etcetera, and substantive mathematical modeling ha become essential. As a natural consequence, it is time to consider departure from normal assumptions seriously. As examples of models which are not based on normality or its approximation, the logistic positive exponent family of models is discussed. These models include the item task complexity as the third parameter, which determines the single principle of ordering individuals on the ability scale.     

The Nctm Standards and the Philosophy of Mathematics

It is argued that the philosophical and epistemological beliefs about the nature of mathematics have a significant influence on the way mathematics is taught at school. In this paper, the philosophy of mathematics of the NCTM's Standards is investigated by examining is explicit assumptions regarding the teaching and learning of school mathematics. The main conceptual tool used for this purpose is the model of two dichotomous philosophies of mathematics-absolutist versus- fallibilist and their relation to mathematics pedagogy. The main conclusion is that a fallibilist view of mathematics is assumed in the Standards and that most of its pedagogical assumptions and approaches are based on this philosophy.     

The Effects of Response Repetitions on Sight Word Acquisition for Students with Mild Disabilities

Single response learning trials, defined in terms of the three-term contingency model, were compared with repeated response learning trials. The purpose of Study 1 was to assess the effectiveness and efficiency of single and repeated response learning trials on sight word remediation. In Study 1, one single response learning trial having one response opportunity per word was compared to one repeated response learning trial having five response opportunities. In Study 2, three single response trials were compared to three repeated response trials. In both studies, the training conditions were compared using an alternating treatments design. Measuring the cumulative number of sight words mastered showed the training conditions equally effective. However, measuring (a) the mean duration of training sessions, (b) the cumulative frequency of words mastered per session duration, (c) the mean number of training sessions per word required for mastery, and (d) the training time per mastered word showed that the single response condition was more efficient. Discussion focuses on the need to include training data when determining best practices for teaching.     

Conditional discrimination in mentally retarded adults: the development of generalized skills.

The development of generalized conditional discrimination skills was examined in adults with retardation. Two subjects with histories of failure to acquire arbitrary matching under trial-and-error procedures were successful under procedures that trained one or more prerequisite skills. The successive discrimination between the sample stimuli was established by training the subjects to name the stimuli. The simultaneous discrimination between the comparison stimuli was established using either (a) standard simple discrimination training with reversals or (b) a procedure in which each of the two sample-comparison relations in the conditional discrimination was presented in blocks of trials, with the size of the blocks decreasing gradually until sample presentation was randomized. The amount of prerequisite training required varied across subjects and across successive conditional discriminations. After acquiring either two or three conditional discriminations with component training, both subjects learned new conditional discriminations under trial-and-error procedures. In general, each successive conditional discrimination was acquired more rapidly. Tests showed that conditional responding had become a generalized skill. Symmetry was shown for almost all trained relations. Symmetry trial samples were ultimately named the same as the stimuli to which they were related in training.     

Analysis of discriminative control by social behavioral stimuli

Visual discriminative control of the behavior of one rat by the behavior of another was studied in a two-compartment chamber. Each rat's compartment had a food cup and two response keys arranged vertically next to the clear partition that separated the two rats. Illumination of the leader's key lights signaled a “search” period when a response by the leader on the unsignaled and randomly selected correct key for that trial illuminated the follower's keys. Then, a response by the follower on the corresponding key was reinforced, or a response on the incorrect key terminated the trial without reinforcement. Accuracy of following the leader increased to 85% within 15 sessions. Blocking the view of the leader reduced accuracy but not to chance levels. Apparent control by visual behavioral stimuli was also affected by auditory stimuli and a correction procedure. When white noise eliminated auditory cues, social learning was not acquired as fast nor as completely. A reductionistic position holds that behavioral stimuli are the same as nonsocial stimuli; however, that does not mean that they do not require any separate treatment. Behavioral stimuli are usually more variable than nonsocial stimuli, and further study is required to disentangle behavioral and nonsocial contributions to the stimulus control of social interactions.     

Creative reasoning in formal discussion

Systems of formal dialectics articulate methods of conflict resolution. To this end they provide norms to regulate verbal exchanges between the Proponent of a thesis and an Opponent. These regulated exchanges constitute what are known as formal discussions.One may ask what moves, if any, in formal discusions correspond to arguing for or against the thesis. It is claimed that certain moves of the Proponent's are properly designated as arguing for the thesis, and that certain moves of the Opponent purport to criticize the tenability or the relevance of the reasons advanced. Thus the usefulness of formal dialectic systems as models for reasonable argument is vindicated.It is then proposed to make these systems more realistic by incorporating in them a norm of Creative Reasoning that removes the severe restrictions to which the Proponent's arguing was hitherto subject. As a consequence, a certain type of irrelevant reason is no longer automatically excluded. Therefore, it is proposed to extend the Opponent's rights to exert relevance criticism. The new dialectic systems are shown to be strategically equivalent to the original ones. Finally, it is stressed that the Opponent's criticism should not be designated as arguing against the thesis. The Opponent criticizes, but does not argue.     

Stimulus control of the pigeon's ability to peck a moving target.

Two pigeons were trained to peck whichever of eight keys displayed a white field (SD). The other seven keys displayed a white "X" on a black background (S delta). Each peck to SD produced three-second access to grain, a three-second intertrial interval (ITI), and the next trial. Pecks to S delta produced a three-second timeout (TO) and the same trial. During later sessions the key displaying SD changed every t seconds (t = 3, 2, 1, .5, and .25 sec), requiring the birds to track the position of the SD. Pecks on a ninth key increased t. Several sessions employed novel stimuli to ascertain the controlling stimulus dimensions. Both birds made few errors acquiring the original discrimination. During the tracking sessions, both birds made few errors when t = .5 sec. Only one reliably lengthened t. Data from sessions with novel stimuli indicate that color and form were important aspects of SD and S delta respectively; movement contributed to the final performance.     

家长参与在家庭社会经济地位和高中生学习品质之间的中介作用——师生关系的调节作用

为了考察在中国背景下,家长参与在家庭社会经济地位与高中生学习品质之间的中介作用,以及师生关系对上述中介效应的调节。以东部某省13442名高中二年级学生为被试,采用家长的受教育程度、家长的职业以及家庭拥有物三个指标测量家庭社会经济地位。采用家长参与子女学习和家长参与子女日常生活两个指标测试家长参与度。采用学习兴趣、学习自信心、学习策略、自主学习能力、学习习惯五个分指标测量学生的学习品质。采用师生关系量表测量师生关系。结果表明：（1）家庭社会经济地位可以正向显著预测高中生的学习品质;（2）家长参与在家庭社会经济地位与高中生学习品质之间起完全中介作用;（3）家庭社会经济地位经由家长参与影响高中生学习品质的中介作用受到师生关系的调节;（4）因家庭社会经济地位不同造成的学生学习品质的差异,在一定程度上会受到师生关系的弥补作用。