Expectancy-Value Models of Attitude: Measurement and Combination of Evaluations and Beliefs1

Two studies investigated methodological issues arising from the use of the Fishbein-Ajzen expectancy-value model of attitudes. Different expectancy-value models— based on manipulations of scoring procedure (bi-polar vs. uni-polar scoring of beliefs) and combinatorial rule (multiplication vs. addition of value and expectancy components) -were explicitly compared. Although they used different attitudinal items and samples, both studies obtained significantly lower correlations with overall attitude by using the multiplicative/bi-polar belief model than by using multiplicative/uni-polar belief and additive models. Linear transformations of the belief component had a dramatic effect on the multiplicative model, but had no impact on the additive model. The findings are discussed in terms of their practical and theoretical importance.     

Reducing cognitive biases in probabilistic reasoning by the use of logarithm formats

Research on probability judgment has traditionally emphasized that people are susceptible to biases because they rely on “variable substitution”: the assessment of normative variables is replaced by assessment of heuristic, subjective variables. A recent proposal is that many of these biases may rather derive from constraints on cognitive integration, where the capacity-limited and sequential nature of controlled judgment promotes linear additive integration, in contrast to many integration rules of probability theory (Juslin, Nilsson, & Winman, 2009). A key implication by this theory is that it should be possible to improve peoples’ probabilistic reasoning by changing probability problems into logarithm formats that require additive rather than multiplicative integration. Three experiments demonstrate that recasting tasks in a way that allows people to arrive at the answers by additive integration decreases cognitive biases, and while people can rapidly learn to produce the correct answers in an additive formats, they have great difficulty doing so with a multiplicative format.     

Teaching Children to Confront Peers’ Sexist Remarks: Implications for Theories of Gender Development and Educational Practice

Elementary-school children (81 boys, 72 girls, aged 5–10 years) in the Southwest United States were taught to challenge peers’ sexist remarks to (a) improve school climate for gender nontraditional children, (b) decrease children’s gender-typed attitudes, and (c) test hypotheses linking gender identity and peer-directed gender role behaviors. Children either practiced using retorts to peers’ sexist remarks (practice condition) or heard stories about others’ retorts (narrative condition). At pretest, children rarely challenged peers’ sexist remarks. At posttest, children’s challenges were significantly more common in the practice than narrative condition. At the 6-month posttest, data showed intervention effects had become more widespread. Behavioral changes led to decreases in gender-typing of others among girls but not boys.     

Story Remembering Among Children

Abstract

The hypothesis that belief in the paranormal is related to reasoning errors was tested. College students were administered the Belief in the Paranormal Scale (Jones, Russell, &; Nickel, 1977) and a syllogistic reasoning test. A slight but statistically significant correlation was observed between BPS scores and the number of errors made on the reasoning test. This relationship was larger but not significantly so for reasoning items with paranormal content than for symbolic content. An a priori comparison indicated that the relationship between BPS scores and reasoning errors was significantly greater for problems that required subjects to determine the validity of hypotheses given statements of evidence than for problems that required subjects to determine the validity of deduced empirical predictions given hypotheses. Thus, belief in the paranormal among college students was very moderately correlated with reasoning ability and was observed most clearly when the reasoning problems contained paranormal content and when they required subjects to determine the validity of hypotheses given evidential statements.     

Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions

Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college‐educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse primes for the equation that immediately followed it (e.g., 4 × 3/4 = 3 followed by 3 × 8/6 = 4). Students with relatively high math ability showed relational priming (speeded solution times to the second of two successive relationally related fraction equations) both with and without high perceptual similarity (Experiment 2). Students with relatively low math ability also showed priming, but only when the structurally inverse equation pairs were supported by high perceptual similarity between numbers (e.g., 4 × 3/4 = 3 followed by 3 × 4/3 = 4). Several additional experiments established boundary conditions on relational priming with fractions. These findings are interpreted in terms of componential processing of fractions in a relational multiplication context that takes advantage of their inherent connections to a multiplicative schema for whole numbers.     

Consistency measures for pairwise comparison matrices

We propose new measures of consistency of additive and multiplicative pairwise comparison matrices. These measures, the relative consistency and relative error, are easy to compute and have clear and simple algebraic and geometric meaning, interpretation and properties. The correspondence between these measures in the additive and multiplicative cases reflects the same correspondence which underpins the algebraic structure of the problem and relates naturally to the corresponding optimization models and axiom systems. The relative consistency and relative error are related to one another by the theorem of Pythagoras through the decomposition of comparison matrices into their consistent and error components. One of the conclusions of our analysis is that inconsistency is not a sufficient reason for revision of judgements. © 1998 John Wiley & Sons, Ltd.     

Mental representations of arithmetic facts: evidence from eye movement recordings supports the preferred operand-order-specific representation hypothesis

There are three main hypotheses about mental representations of arithmetic facts: the independent representation hypothesis, the operand-order-free single-representation hypothesis, and the operand-order-specific single-representation hypothesis. The current study used electrical recordings of eye movements to examine the organization of arithmetic facts in long-term memory. Subjects were presented single-digit addition and multiplication problems and were asked to report the solutions. Analyses of the horizontal electrooculograph (HEOG) showed an operand order effect for multiplication in the time windows 150-300?ms (larger negative potentials for smaller operand first problems than for larger operand first ones). The operand order effect was reversed in the time windows from 400 to 1,000?ms (i.e., larger operand first problems had larger negative potentials than smaller operand first problems). For addition, larger operand first problems had larger negative potentials than smaller operand first in the series of time windows from 300 to 1,000?ms, but the effect was smaller than that for multiplication. These results confirmed the dissociated representation of addition and multiplication facts and were consistent with the prediction of the preferred operand-order-specific representation hypothesis.     

Mental representations of arithmetic facts: Evidence from eye movement recordings supports the preferred operand-order-specific representation hypothesis

There are three main hypotheses about mental representations of arithmetic facts: the independent representation hypothesis, the operand-order-free single-representation hypothesis, and the operand-order-specific single-representation hypothesis. The current study used electrical recordings of eye movements to examine the organization of arithmetic facts in long-term memory. Subjects were presented single-digit addition and multiplication problems and were asked to report the solutions. Analyses of the horizontal electrooculograph (HEOG) showed an operand order effect for multiplication in the time windows 150–300 ms (larger negative potentials for smaller operand first problems than for larger operand first ones). The operand order effect was reversed in the time windows from 400 to 1,000 ms (i.e., larger operand first problems had larger negative potentials than smaller operand first problems). For addition, larger operand first problems had larger negative potentials than smaller operand first in the series of time windows from 300 to 1,000 ms, but the effect was smaller than that for multiplication. These results confirmed the dissociated representation of addition and multiplication facts and were consistent with the prediction of the preferred operand-order-specific representation hypothesis.     

Pragmatic reasoning schemas

We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wason's selection paradigm for subjects who have had no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals (must, can) totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain.     

知识图式对贝叶斯推理的影响

选取具有概率知识的大学生(专家)和没有概率知识的大学生(新手)为被试,进行贝叶斯推理中的概率估计,探讨知识图式对贝叶斯推理的影响。结果表明,具有概率知识背景的大学生比没有概率知识背景的大学生概率估计的准确性更高,反应时更长,说明知识图式影响概率信息的搜索和判断。     

Does the cue help? Children's understanding of multiplicative concepts in different problem contexts

Background: Understanding arithmetical principles is a key part of a conceptual understanding of mathematics. However, very little attention has been paid to children's understanding of multiplicative, as compared to additive, principles. Aims: This study investigated(a) children's ability to use commutative and distributive cues to solve multiplication problems, (b) whether their ability to use these cues depends on the problem context, and(c) whether separate mechanisms might underlie children's understanding of commutativity and distributivity. Sample: Twenty‐seven 9‐year‐olds (Year 5) and thirty‐two 10‐year‐olds (Year 6). Methods: Forty‐eight multiplication problems (with a multiple‐choice response format) were presented to children. There were four types of problem: Commutative, Distributive, Combined commutative‐distributive(all preceded by a cue) and No cue problems. Each type of problem was presented in three different contexts: Isomorphism of measures, Area, and Cartesian product. Results: Children demonstrated a good understanding of commutativity but a very poor understanding of distributivity. A common mistake in the distributive problems was to select the number that was one more, or one less, than the answer in the cue. Children's understanding of distributivity (butnot commutativity) seemed to depend on the problem context. Factor analysis suggested that separate factors underlie the ability to solve commutative and distributive problems. Conclusions: Nine‐ and 10‐year‐olds understand commutativity, but are unable to use the distributive principle in multiplication. Their errors suggest that they may confuse some of the principles of multiplication with those of addition. When children do begin to understand the principle of distributivity, they most easily apply it in the context of Isomorphism of measures multiplication problems. The implications for mathematical education are discussed.     

Evaluating parent-implemented behavioral skills training for teaching firearm safety skills

Research shows that behavioral skills training (BST) and in situ training (IST) are effective interventions for teaching safety skills to children. In addition, the efficiency of these interventions can be increased when parents, teachers, or peers are taught to implement them. The purpose of this study was to replicate Novotny et al. (2020) and evaluate a web-based program for teaching parents to conduct BST to teach safety skills to prevent gunplay. We randomly assigned 18 children to the parent-conducted BST group or a control group and evaluated the intervention in a posttest only control group design. Children in the control group or treatment group who did not score a three in the in situ assessment (do not touch, get away, and tell an adult) received IST from their parents and were assessed again. Results showed that safety skill scores were statistically significantly higher in the treatment group than in the control group. Furthermore, there was a statistically significant increase in safety skills scores following IST for children who received it.     

小学一年级数感不良儿童的筛查与动态干预

首先编制测查小学一年级儿童数感发展水平的测验, 以筛查出数感发展不良儿童并进行数量转换和数量估计的动态干预。将数感不良儿童分为干预组(29人)和控制组(27人), 并以数感正常儿童作为对照组(40人), 以比较干预训练对儿童数感水平和与之密切相关的计算流畅性的促进作用。同时进一步考查数感和计算流畅性的作用方向。结果发现：(1)所编制的儿童数感发展测验信效度良好, 能有效评估一年级儿童的数感水平; (2)数感不良儿童经干预后, 其数感水平较控制组有了明显改善, 计算流畅性水平也显著提高, 甚至达到正常组儿童的水平; (3)数感对计算流畅性有明显的预测作用, 是计算流畅性的基础。     

The logic of social exchange: has natural selection shaped how humans reason? Studies with the Wason selection task

In order to successfully engage in social exchange--cooperation between two or more individuals for mutual benefit--humans must be able to solve a number of complex computational problems, and do so with special efficiency. Following Marr (1982), Cosmides (1985) and Cosmides and Tooby (1989) used evolutionary principles to develop a computational theory of these adaptive problems. Specific hypotheses concerning the structure of the algorithms that govern how humans reason about social exchange were derived from this computational theory. This article presents a series of experiments designed to test these hypotheses, using the Wason selection task, a test of logical reasoning. Part I reports experiments testing social exchange theory against the availability theories of reasoning; Part II reports experiments testing it against Cheng and Holyoak's (1985) permission schema theory. The experimental design included eight critical tests designed to choose between social exchange theory and these other two families of theories; the results of all eight tests support social exchange theory. The hypothesis that the human mind includes cognitive processes specialized for reasoning about social exchange predicts the content effects found in these experiments, and parsimoniously explains those that have already been reported in the literature. The implications of this line of research for a modular view of human reasoning are discussed, as well as the utility of evolutionary biology in the development of computational theories.     

Interactive effects of numerical surface form and operand parity in cognitive arithmetic

In Experiment 1, adults (n = 48) performed simple addition, multiplication, and parity (i.e., odd-even) comparisons on pairs of Arabic digits or English number words. For addition and comparison, but not multiplication, response time increased with the number of odd operands. For addition, but not comparison, this parity effect was greater for words than for digits. In Experiment 2, adults (n = 50) solved simple addition problems in digit and word format and reported their strategies (i.e., retrieval or procedures). Procedural strategies were used more for odd than even addends and much more for word than digit problems. The results indicate that problem encoding and answer retrieval processes for cognitive arithmetic are interactive rather than strictly additive stages.     

To What Extent Do Pragmatic Reasoning Schemas Affect Performance on Wason's Selection Task?

Cheng and Holyoak's (1985) most persuasive evidence for pragmatic reasoning schema theory has been the finding that an abstract permission version of Wason's selection task yields higher rates of solution than a nonpragmatic control. Experiment 1 presented two problem sets, one modelled after Cheng and Holyoak's abstract permission problem, which is relativley rich in extraneous features, and one after Wason's, relatively impoverished, standard problem. Each problem set varied type of rule (permission, obligation, or nonpragmatic) and task type (to reason from or about a rule). Results revealed that enriched problems were solved more often than impoverished ones, that reasoning-from problems were solved more often than reasoning-about problems, and that there was a beneficial interaction between enriching features and the permission rule. Experiment 2 demonstrated that although explicit negatives were crucial for solution of reasoning-from permission problems, they played no role in solution of enriched nonpragmatic-rule problems. Experiment 3 provided a replication of the enriched reasoning-from permission problem, again revealed no beneficial effect for obligation-rule problems, and further revealed no influence of instructions to provide brief written justifications. We argue that the results show that the scope of pragmatic reasoning schema theory needs to be narrowed, that although a permission rule does have an effect, an obligation rule does not, and that some beneficial task features are independent of anything explained by pragmatic reasoning schema theory.     

Strategy Use in Reasoning Training With Older Adults

The relationship between strategy use and cognitive training gains on reasoning ability is examined in a sample of 393 older participants in the Seattle Longitudinal Training Study. Pre- and posttest gains on the use of strategies specific to reasoning ability were compared for the elderly trained on reasoning versus spatial orientation ability. The present study involves an objective behavioral method of measuring strategy use on tests of inductive reasoning. Results showed that participants trained on reasoning significantly increased strategy use from pre- to posttest on two reasoning outcome measures compared to participants trained on spatial orientation. Higher strategy use by inductive reasoning trainees was also associated with greater training gain on reasoning outcome measures, suggesting strategy use as a possible mechanism of training gain. In addition, young–old participants and those with higher education, irrespective of training condition, exhibited greater pre- to posttest gain in strategy use.     

DEGREE OF CONSTRUCTED-RESPONSE INTERACTION IN COMPUTER-BASED PROGRAMMED INSTRUCTION

This investigation evaluated the importance of frequent responding in computer-based programmed instruction. Instructional computer programs that taught the use of an authoring language were administered to 155 undergraduate college students. One group experienced frequent (dense) situations requiring them to supply key components of the subject taught. A second group experienced half as many response requirements, and a third “passive” group simply tapped any key to progress. To control for time in contact with presentations, individuals in a fourth group were yoked to the members of the high-density requirement group. Statistically significant differences on both posttest and application performances indicated that students who experienced the high density of overt response contingencies scored the best and the passive group score the worst. The yoked control revealed that time on task alone could not account for the superior performance of students in the high-density group. Results suggest that inclusion of a high rate of constructed-response contingencies within instructional computer programs increases performance.     

Learning multiplication facts: a study of children taught by discovery methods in England

The development of multiplication skills was examined in a group of children ages 8 to 12 years who were taught by discovery methods. Strategies used by the children included direct retrieval, retrieval + calculation, and counting-in-series. Repeated addition was not observed. Retrieval was the fastest and least error-prone strategy; counting-in-series was the slowest and most error prone. Children ages 8 and 9 years used mainly mixed strategies. Children ages 10 to 12 years used mainly retrieval or retrieval and calculation for low operands, but reverted to back-up strategies for high operands based on the strategies available for low operands. There was a general shift away from less effective strategies across ages 8 to 12 years but, by the end of the primary school (age 11 years), relatively few children used the most effective strategy of retrieval for all operands. The development of effective strategies was related to nonverbal reasoning ability and to working memory capacity. The results are considered with reference to experiential and pedagogical models of multiplication.     

New aspects of the probabilistic evaluation of hypotheses and experience

The probabilistic corroboration of two or more hypotheses or series of observations may be performed additively or multiplicatively . For additive corroboration (e.g. by Laplace's rule of succession), stochastic independence is needed. Inferences, based on overwhelming numbers of observations without unexplained counterinstances permit hyperinduction , whereby extremely high probabilities, bordering on certainty for all practical purposes may be achieved. For multiplicative corroboration, the error probabilities (1 - Pr) of two (or more) hypotheses are multiplied. The probabilities, obtained by reconverting the product, are valid for both of the hypotheses and indicate the gain by corroboration.. This method is mathematically correct, no probabilities > 1 can result (as in some conventional methods) and high probabilities with fewer observations may be obtained, however, semantical independence is a prerequisite. The combined method consists of (1) the additive computation of the error probabilities (1 - Pr) of two or more single hypotheses, whereby arbitrariness is avoided or at least reduced and (2) the multiplicative procedure . The high reliability of Empirical Counterfactual Statements is explained by the possibility of multiplicative corroboration of “all-no” statements due to their strict semantical independence.