Interleaved practice in multi-dimensional learning tasks: Which dimension should we interleave?

Research shows that multiple representations can enhance student learning. Many curricula use multiple representations across multiple task types. The temporal sequence of representations and task types is likely to impact student learning. Research on contextual interference shows that interleaving learning tasks leads to better learning results than blocked practice, but this research has not investigated whether it matters on which dimension we interleave learning tasks. Many educational materials include multiple task types and multiple representations. Should we interleave representations or task types? We conducted a classroom experiment to investigate the effects of interleaving task types (while blocking representations) and interleaving representations (while blocking task types). The participants (158 5th- and 6th-graders) worked with a corresponding version of an intelligent tutoring system for fractions. Our results show an advantage for interleaving task types over interleaving representations. These results extend prior work on contextual interference by showing that this effect is sensitive to the dimension being interleaved. We also extend the literature on learning with multiple representations by investigating the effect of interleaved practice with different representations. The results provide guidance to designers of complex curricula.     

Survey of classroom use of representations: development,field test and multilevel analysis

Because of the multimodal nature of learning, doing and reporting science, it is important that students learn how to interpret, construct, relate and translate scientific representations or, in other words, to develop representational competence. Explicit instruction about multimodal representations is needed to foster students’ representational competence in the classroom. However, only a handful studies have surveyed how representations are actually used in science classes. This might be because of the fact that economical instruments for assessing the use of representations in classrooms are not available. To bridge that gap, an instrument was developed, field-tested in biology classes with 175 and 931 students, respectively, and analysed using exploratory and (multilevel) confirmatory factor analyses. Results supported an instrument with six scales and 21 items at the individual and classroom levels covering the following dimensions: (1) interpretation of visual representations, (2) construction of visual representations, (3) use of scientific texts (verbal representations), (4) use of symbolic representations, (5) number of terms used in class, and (6) the extent to which active social construction of knowledge is possible in the class. The scales showed satisfactory discriminant validity and reliability at each level. Further applications of this instrument for researchers and teachers are discussed.     

DeFT: A conceptual framework for considering learning with multiple representations

Multiple (external) representations can provide unique benefits when people are learning complex new ideas. Unfortunately, many studies have shown this promise is not always achieved. The DeFT (Design, Functions, Tasks) framework for learning with multiple representations integrates research on learning, the cognitive science of representation and constructivist theories of education. It proposes that the effectiveness of multiple representations can best be understood by considering three fundamental aspects of learning: the design parameters that are unique to learning with multiple representations; the functions that multiple representations serve in supporting learning and the cognitive tasks that must be undertaken by a learner interacting with multiple representations. The utility of this framework is proposed to be in identifying a broad range of factors that influence learning, reconciling inconsistent experimental findings, revealing under-explored areas of multi-representational research and pointing forward to potential design heuristics for learning with multiple representations.     

适宜与非适宜表征对应用题解决的影响

为考察小学生的表征类型对应用题解决的影响,作者以四类算术应用题为实验材料,在自由选择和迫选两种条件下对150名四年级小学生进行实验研究。结果表明:在自由选择条件下,四年级小学生倾向采用适宜表征解决不同类型的应用题,且适宜表征的解题正确率较高;在迫选条件下,适宜表征组被试的解题正确率高于自由选择条件下被试的解题正确率,也显著高于非适宜表征组被试的解题正确率,而非适宜表征组被试的解题正确率显著低于自由选择条件下被试的解题正确率。     

Visual‐Spatial Representation,Mathematical Problem Solving,and Students of Varying Abilities

The purpose of this study was to investigate students' use of visual imagery while solving mathematical problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N= 66) participated in this study. Students were assessed on measures of mathematical problem solving and visual‐spatial representation. Visual‐spatial representations were coded as either primarily schematic representations that encode the spatial relations described in the problem or primarily pictorial representations that encode persons, places, or things described in the problem. Results indicated that gifted students used significantly more visual‐spatial representations than the other two groups. Students with LD used significantly more pictorial representations than their peers. Successful mathematical problem solving was positively correlated with use of schematic representations; conversely, it was negatively correlated with use of pictorial representations.     

Understanding teacher knowledge from a Cultural Psychology approach

In this paper we propose a Cultural Psychology approach to teacher knowledge which assumes that: 1) mental representations are directly observable, and 2) the relationship between different kinds of representations is co-mediational. The paper sets out such an approach, providing arguments to support these two alternative premises; outlining a methodology, based on social linguistics, for the direct observation of representations; and articulating the relationship between three types of representations: situational representations, specific propositional representations, and general propositional representations. We discuss the implications of this approach for research and practice in teacher education.     

Early linguistic abilities and reading development: A review and a hypothesis

This article is concerned with aspects of phonological processing and linguistic awareness that may set the stage for initial reading development. The aims are first to provide a current review of phonological processes (both underlying and metaphonological) that have been found to be associated with initial reading achievement, secondly to present a new hypothesis relating differences in the nature of phonological representations in the lexicon to the development of phonological awareness and other phonological processes. The hypothesis is concerned withdistinctness of phonological representations, i.e. the separateness of phonological representations. Phonological representations of high distinctness are distinguished from other representations by many features. The distinctness hypothesis is compared to the lexical restructuring hypothesis which suggests that lexical representations gradually become increasingly segmental between one and eight years of age. Implications of each hypothesis (emphasizing the distinctness hypothesis) for the development of language abilities and reading are presented, along with suggestions regarding future research directions.     

The Past Is Present: Representations of Parents,Friends, and Romantic Partners Predict Subsequent Romantic Representations

This study examined how representations of parent–child relationships, friendships, and past romantic relationships are related to subsequent romantic representations. Two‐hundred 10th graders (100 female; M_age = 15.87 years) from diverse neighborhoods in a Western U.S. city were administered questionnaires and were interviewed to assess avoidant and anxious representations of their relationships with parents, friends, and romantic partners. Participants then completed similar questionnaires and interviews about their romantic representations six more times over the next 7.5 years. Growth curve analyses revealed that representations of relationships with parents, friends, and romantic partners each uniquely predicted subsequent romantic representations across development. Consistent with attachment and behavioral systems theory, representations of romantic relationships are revised by representations and experiences in other relationships.     

Maternal Depression, Children's Attachment Security, and Representational Development: An Organizational Perspective

Relations among maternal depression, child attachment, and children's representations of parents and self were examined. Participants included toddlers and their mothers with a history of major depressive disorder ( n = 63) or no history of mental disorder ( n = 68). Attachment was assessed at 20 and 36 months and representations of parents and self were assessed at 36 and 48 months. Depressive symptoms were assessed at all 3 time points. While early-occurring maternal depression had a negative impact on children's negative and positive representations of parents, attachment security mediated the relation between depressive symptoms and negative representations. Attachment security served as an intervening variable between maternal depression and changes in children's negative representations of self. Implications for prevention are highlighted.     

Conditions for the Effectiveness of Multiple Visual Representations in Enhancing STEM Learning

Visual representations play a critical role in enhancing science, technology, engineering, and mathematics (STEM) learning. Educational psychology research shows that adding visual representations to text can enhance students’ learning of content knowledge, compared to text-only. But should students learn with a single type of visual representation or with multiple different types of visual representations? This article addresses this question from the perspective of the representation dilemma, namely that students often learn content they do not yet understand from representations they do not yet understand. To benefit from visual representations, students therefore need representational competencies, that is, knowledge about how visual representations depict information about the content. This article reviews literature on representational competencies involved in students’ learning of content knowledge. Building on this review, this article analyzes how the number of visual representations affects the role these representational competencies play during students’ learning of content knowledge. To this end, the article compares two common scenarios: text plus a single type of visual representations (T+SV) and text plus multiple types of visual representations (T+MV). The comparison yields seven hypotheses that describe under which conditions T+MV scenarios are more effective than T+SV scenarios. Finally, the article reviews empirical evidence for each hypothesis and discusses open questions about the representation dilemma.     

Students' mental load,stress, and performance when working with symbolic or symbolic–textual molecular representations

In science education, representations are necessary inter alia for the understanding of relationships between structures and systems. However, several studies have identified difficulties of students when working with representations. In the present study, we investigated students' responses (regarding their preference, test performance, mental load (ML), and stress) toward two kinds of representations: symbolic representations, which only use abstract symbols, versus combined symbolic–textual representations, which additionally comprise textual elements. Therefore, students were randomly assigned to one of two treatment groups: one group worked on test tasks accompanied by symbolic representations, and the others worked on the same tasks, but with symbolic–textual representations. Thereafter, the students' test performance and ML were assessed. The level of perceived stress and the salivary cortisol concentration were measured before and after the test and again a few minutes later. Additionally, heart rate variability parameters were assessed continuously. We found a strong preference of the test version with symbolic representations. Additionally, the students showed better test performance and lower ML when they worked with symbolic representations. However, the level of perceived stress was comparable between both groups and there was no strong physiological stress response: The cortisol concentration decreased in both groups and the heart rate was relatively similar. However, during the second half of the test, we observed a significantly higher ratio between low and high heartbeat frequencies in the group with symbolic–textual representations and we found an indirect influence of the kind of representation on test performance through its effect on ML. The poorer test performance and higher ML in connection with symbolic–textual representations confirm previous studies, which found that symbolic–textual representations pose major problems for students. Thus, teachers should enable students to understand symbolic–textual representations and consider carefully whether they can use symbolic representations instead, especially when they teach complex content.     

What are association formation models?

In his presentation of the propositional account of associative learning, De Houwer (2009) argues that association formation models (AFMs) assume excitatory link representations and automatic learning processes. However, the application of AFMs to human causal and contingency learning has assumed propositional forms of representation, although excitatory link representations are also required to explain certain nonrational consequences of associative learning. Moreover, at least two of the AFMs that have been applied to human associative learning invoke processing with nonautomatic characteristics. In conclusion, the distinction between the propositional account and AFMs of associative learning lies not in the form of representations but in the specific details of the learning processes generating the associative representations.     

Representational Tools in Computer-Supported Collaborative Argumentation-Based Learning: How Dyads Work With Constructed and Inspected Argumentative Diagrams

This article investigates the conditions under which diagrammatic representations support collaborative argumentation-based learning in a computer environment. Thirty dyads of 15- to 18-year-old students participated in a writing task consisting of 3 phases. Students prepared by constructing a representation (text or diagram) individually. Then they discussed the topic and wrote a text in dyads. They consolidated their knowledge by revising their individual representation. There were 3 conditions: Students could use either (a) the individual texts they wrote, (b) the individual diagrams they constructed, or (c) a diagram that was constructed for them based on the text they wrote. Results showed that students who constructed a diagram themselves explored the topic more than students in the other conditions. We also found differences in the way collaborating dyads used their representations. Dyads who engaged in deep discussion used their representations as a basis for knowledge construction. In contrast, dyads who engaged in only shallow discussion used their representations solely to copy information to their collaborative text. We conclude that diagrammatic representations can improve collaborative learning, but only when they are used in a co-constructive way.     

感觉经验缺失对视力、听力障碍学生概念表征的影响

通过概念特征自由联想实验,比较了视力、听力障碍学生和普通学生的具体事物概念表征的差异。结果表明:(1)与普通学生相比,视力、听力障碍学生联想的特征数量少,分布分散。(2)视力、听力障碍学生的概念表征受感知觉经验缺失的影响,概念表征具有明显的通道差异。聋生的听觉通道的概念特征显著少于普通学生,盲生的触觉通道的概念特征显著多于普通学生和聋生。(3)在感觉代偿和语言学习的帮助下,视力、听力障碍学生能够形成对缺失感觉通道信息的概念的表征。     

Comparing US and Japanese Elementary School Teachers' Facility for Linking Rational Number Representations

Using cognitive ethnography as a guiding framework, we investigated US and Japanese fourth-grade teachers' domain knowledge of key fraction representations in individual interviews. The framework focused on revealing cultural trends in participants' organization of knowledge and their interpretations of that organization. Our analyses of the interviews, which included a representation sorting task, indicated three major differences that defined US and Japanese teachers' approaches to rational number representation: (1) Japanese teachers interpreted all rational number representations as conveying primarily mathematical information, whereas US teachers interpreted only some representations as conveying primarily mathematical information; (2) the US teachers focused more intently on part-whole relations than Japanese in their interpretations; and (3) Japanese teachers more easily linked rational number representations to more advanced upcoming content in the curriculum. A review of US textbooks used by the teachers reflected their consistency with US teachers' interpretations of the representations. These findings imply that strong cultural differences underlay the approaches that teachers in both nations take to rational number representation and that these differences may help explain established cross-national differences in student reasoning.     

A Comparison of Young Children's Understanding of Contradictory Representations in Pretense, Memory, and Belief

The present study examined the nature of young children's understanding of various mental representations. 3- and 4-year-olds were presented with story protagonists who held mental representations (beliefs, pretenses, and memories) that contradicted reality. Subjects chose 1 of 2 alternate " thought pictures " (depicting either the mental representation or reality) that reflected the mental state. While 4-year-olds performed relatively well on all scenario types, 3-year-olds chose the correct thought picture significantly more often for pretense and memory scenarios than for false belief scenarios. These results suggest that young children conceptualize pretense as involving mental representations, and that they have more difficulty understanding contradictory mental representations that purport to correspond to reality.