Self-explanation in the domain of statistics: an expertise reversal effect

This study investigated the effects of four instructional methods on cognitive load, propositional knowledge, and conceptual understanding of statistics, for low prior knowledge students and for high prior knowledge students. The instructional methods were (1) a reading-only control condition, (2) answering open-ended questions, (3) answering open-ended questions and formulating arguments, and (4) studying worked-out examples of the type of arguments students in the third group had to formulate themselves. The results indicate that high prior knowledge students develop more propositional knowledge of statistics than low prior knowledge students. With regard to conceptual understanding, the results indicate an expertise reversal effect: low prior knowledge students learn most from studying worked-out examples, whereas high prior knowledge students profit most from formulating arguments. Thus, novice students should be guided into the subject matter by means of worked-out examples. As soon as students have developed more knowledge of the subject matter, they should be provided with learning tasks that stimulate students to solve problems by formulating arguments.     

The expertise reversal effect in prompting focused processing of instructional explanations

Providing prompts to induce focused processing of the central contents of instructional explanations is a promising instructional means to support novice learners in learning from instructional explanations. However, within research on the expertise reversal effect it has been shown that instructional means that are beneficial for novices can be detrimental for learners with more expertise if the instructional means provide guidance that overlaps with the internal guidance provided by the prior knowledge of learners with more expertise. Under such circumstances, prompts to induce focused processing might even be detrimental for learners with expertise whose prior knowledge already provides internal guidance to learn from explanations. On this basis, we aimed at experimentally varying expertise by developing prior knowledge. Specifically, we used a preparation intervention with contrasting cases to enhance learners’ prior knowledge (expertise). Against this background, we tested 71 university students in a 2 × 2 factorial experimental design: (a) Factor of expertise. Working with contrasting cases to develop prior knowledge and expertise to provide internal guidance to learn from instructional explanations (with vs. without), (b) Factor of prompts. Prompts to induce focused processing of the explanations (with vs. without). The results showed that prompts to induce focused processing fostered conceptual knowledge for novice learners whereas prompts hindered the acquisition of conceptual knowledge for learners with expertise that was developed by working with contrasting cases beforehand. Moreover, measures of subjective cognitive load and learning processes suggest that the instructional guidance provided by prompts compensated for the low internal guidance of novice learners and overlapped with the internal guidance of learners with expertise.     

The impact of guidance during problem-solving prior to instruction on students’ inventions and learning outcomes

Multiple studies have shown benefits of problem-solving prior to instruction (cf. Productive Failure, Invention) in comparison to direct instruction. However, students’ solutions prior to instruction are usually erroneous or incomplete. In analogy to guided discovery learning, it might therefore be fruitful to lead students towards the discovery of the canonical solution. In two quasi-experimental studies with 104 students and 175 students, respectively, we compared three conditions: problem-solving prior to instruction, guided problem-solving prior to instruction in which students were led towards the discovery of relevant solution components, and direct instruction. We replicated the beneficial effects of problem-solving prior to instruction in comparison to direct instruction on posttest items testing for conceptual knowledge. Our process analysis further revealed that guidance helped students to invent better solutions. However, the solution quality did not correlate with the posttest results in the guided condition, indicating that leading students towards the solution does not additionally promote learning. This interpretation is supported by the finding that the two conditions with problem-solving prior to instruction did not differ significantly at posttest. The second study replicated these findings with a greater sample size. The results indicate that different mechanisms underlie guided discovery learning and problem-solving prior to instruction: In guided discovery learning, the discovery of an underlying model is inherent to the method. In contrast, the effectiveness of problem-solving prior to instruction does not depend on students’ discovery of the canonical solution, but on the cognitive processes related to problem-solving, which prepare students for a deeper understanding during subsequent instruction.     

The influence of cognitive reasoning level,cognitive restructuring ability,disembedding ability,working memory capacity,and prior knowledge on students' performance on balancing equations by inspection

Eighty-three (83) high school chemistry students were administered tests of cognitive reasoning level, cognitive restructuring ability, disembedding ability, working memory capacity, and prior knowledge before a learning segment on balancing chemical equations by inspection. After a four-day instructional segment utilizing direct teaching methodology, participants were given a posttest on balancing equations. Initial regression analysis indicated that a multicollinearity problem existed. Factor analysis and correlational data indicated that the reasoning, restructuring, and disembedding variables could be collapsed and redefined as a single restructuring variable. A hierarchial regression analysis was then performed, and the following conclusions were derived: (1) when prior knowledge alone is considered, students' understanding of chemical formulas significantly (p < 0.05) influences overall equation balancing performance; (2) when prior knowledge, restructuring, and working memory are considered, only restructuring ability significantly (p < 0.05) influences overall performance; (3) working memory capacity does not significantly (p < 0.05) influence overall performance but does on certain posttest items; (4) prior knowledge and restructuring ability also significantly (p < 0.05) influence performance on certain posttest items. Discussion includes the rationale for identifying the collapsed variable as restructuring and the absence of working memory capacity as a significant influence on overall performance.     

Effects of explicit and implicit prompts on students’ inquiry practices in computer-supported learning environments in high school earth science

The study explored how to best use scaffolds for supporting students’ inquiry practices in computer-supported learning environments. We designed a series of inquiry units assisted with three versions of written inquiry prompts (generic and context-specific); that is, three scaffold-fading conditions: implicit, explicit, and fading. We then examined how the three scaffold-fading conditions influenced students’ conceptual understanding, understanding of scientific inquiry, and inquiry abilities. Three grade-10 classes (N?=?105) participated in this study; they were randomly assigned to and taught in the three conditions. Data-collection procedures included a pretest–posttest approach and in-depth observations of the target students. The findings showed that after these inquiry units, all of the students exhibited significant learning gains in conceptual knowledge and performed better inquiry abilities regardless of which condition was used. The explicit and fading conditions were more effective in enhancing students’ understanding of scientific inquiry. The fading condition tended to better support the students’ development of inquiry abilities and help transfer these abilities to a new setting involving an independent socioscientific task about where to build a dam. The results suggest that fading plays an essential role in enhancing the effectiveness of scaffolds.     

Distinguishing complex ideas about climate change: knowledge integration vs. specific guidance

We compared two forms of automated guidance to support students’ understanding of climate change in an online inquiry science unit. For specific guidance, we directly communicated ideas that were missing or misrepresented in student responses. For knowledge integration guidance, we provided hints or suggestions to motivate learners to analyze features of their response and seek more information. We guided both student-constructed energy flow diagrams and short essays at total of five times across an approximately week-long curriculum unit. Our results indicate that while specific guidance typically produced larger accuracy gains on responses within the curriculum unit, knowledge integration guidance produced stronger outcomes on a novel essay at posttest. Closer analysis revealed an association between the time spent revisiting a visualization and posttest scores on this summary essay, only for those students in the knowledge integration condition. We discuss how these gains in knowledge integration extend laboratory results related to ‘desirable difficulties’ and show how autonomous inquiry can be fostered through automated guidance.     

Completion problems can reduce the illusions of understanding in a computer-based learning environment on genetics

Inaccurate judgments of task difficulty and invested mental effort may negatively affect how accurate students monitor their own performance. When students are not able to accurately monitor their own performance, they cannot control their learning effectively (e.g., allocate adequate mental effort and study time). Although students' judgments of task difficulty and invested mental effort are closely related to their study behaviors, it is still an open question how the accuracy of these judgments can be improved in learning from problem solving. The present study focused on the impact of three types of instructional support on the accuracy of students' judgments of difficulty and invested mental effort in relation to their performance while learning genetics in a computer-based environment. Sixty-seven university students with different prior knowledge received either incomplete worked-out examples, completion problems, or conventional problems. Results indicated that lower prior knowledge students performed better with completion problems, while higher prior knowledge students performed better with conventional problems. Incomplete worked-out examples resulted in an overestimation of performance, that is, an illusion of understanding, whereas completion and conventional problems showed neither over- nor underestimation. The findings suggest that completion problems can be used to avoid students' misjudgments of their competencies.     

Using Evidence‐Based Practices to Build Mathematics Competence Related to Conceptual,Procedural, and Declarative Knowledge

Abstract Mathematics continues to be one of the most difficult components of the school curriculum for students with learning disabilities (LD). The National Council for Teachers of Mathematics, in conjunction with current educational legislation, challenges teachers to maintain high standards for student performance in mathematics. Fortunately, over the past two decades, researchers have identified and validated a number of instructional practices that help students with LD understand and use mathematics in meaningful ways. The purpose of this article is to discuss instructional guidelines and evidence‐based practices for building conceptual, procedural, and declarative knowledge within a comprehensive mathematics curriculum. The importance of balancing these three knowledge areas across mathematics content areas is noted.     

The Function of a Research Bureau in a State Department of Education

ABSTRACT

A hands-on instructional approach with medium-achieving 10th-grade students (N = 294) successfully demonstrated the achievement of a conceptual change. Two teaching variations were applied (I-1, I-2), both dealing with a hands-on gene technology lesson in an out-of-school laboratory. I-2 additionally confronted the participants with alternative conceptions to some of the central issues involved in gene technology following a constructivist teaching model. The authors monitored the percentage of alternative conceptions by pretest, posttest, and delayed posttest. In the long term, I-2 abandoned more of students’ alternative conceptions in favor of the orthodox scientific view. Furthermore, a gender effect appeared: In the short term, more young men within I-2 were forced to shift to more scientific conceptions. Young women filed their alternative conceptions also in the long term, independently of the applied instructional method.     

The effects of hands-on and teacher demonstration laboratory methods on science achievement in relation to reasoning ability and prior knowledge

The present study compared the relative effects of hands-on and teacher demonstration laboratory methods on declarative knowledge (factual and conceptual) and procedural knowledge (problem-solving) achievement. Of particular interest were (a) whether these relationships vary as a function of reasoning ability and (b) whether prior knowledge and reasoning ability predict student achievement. Ninth-grade physical science students were randomly assigned to classes taught by either a hands-on or a teacher demonstration laboratory method. Students' reasoning ability and prior knowledge of science were assessed prior to the instruction. The two instructional methods resulted in equal declarative knowledge achievement. However, students in the hands-on laboratory class performed significantly better on the procedural knowledge test than did students in the teacher demonstration class. These results were unrelated to reasoning ability. Prior knowledge significantly predicted performance on the declarative knowledge test. Both reasoning ability and prior knowledge significantly predicted performance on the procedural knowledge test, with reasoning ability being the stronger predictor.     

Prospective teacher learning: recognizing evidence of conceptual understanding

This study examined prospective teachers’ (PSTs) ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. It also investigates the role PSTs’ content knowledge plays in their ability to recognize children’s mathematical understanding. Results of content knowledge assessments administered at the beginning of the study revealed that content knowledge did seem to support PSTs’ analyses of children’s understanding when the child’s response demonstrated understanding or demonstrated a misconception. Content knowledge did not seem to support PSTs’ analyses of children’s procedural responses, as many PSTs with good content knowledge initially characterized procedural solutions as evidence of conceptual understanding. Similarly, content knowledge did not seem to support PSTs’ analyses of children’s responses with features commonly associated with understanding but not evidence of understanding. After the instructional intervention consisting of three multifaceted lessons in which PSTs examined many examples of student thinking, they showed improved ability to analyze responses with conceptual features and no evidence of conceptual understanding and responses demonstrating procedural knowledge. Results suggest that content knowledge is not sufficient for supporting PSTs’ analysis of children’s thinking, and that building activities such as the intervention into content courses may help develop this ability. Implications for teacher education programs and future research are considered.     

Secondary School Students Learning From Reflections on the Rationale Behind Self-Made Errors: A Field Experiment

Thus far, it is unclear how students can learn most effectively from their own errors. In this study, reflections on the rationale behind self-made errors are assumed to enhance knowledge acquisition. In a field experiment with pre/post/follow-up design, the authors practiced fractions with 174 seventh- and eighth-grade students who were randomly assigned to one of two conditions: The students reflected on either the rationale behind their own errors or on the correct solution corresponding to their own errors. Students in the first condition group demonstrated a greater procedural knowledge at the posttest and at the follow-up test. Furthermore, at the follow-up test, these students demonstrated a higher conceptual knowledge. The implications for theory and school instruction are discussed.     

Inquiring scaffolds in laboratory tasks: an instance of a “worked laboratory guide effect”?

The study explores if established support devices for paper–pencil problem solving, namely worked examples and incremental scaffolds, are applicable to laboratory tasks. N?=?173 grade eight students solved in dyads a physics laboratory task in one of three conditions. In condition A (unguided problem solving), students were asked to determine the mass of an unknown object by applying Hooke’s law. In condition B (laboratory guide), students received a guide which instructed and explained each solution step. In condition C (incremental scaffolds), the solution steps were presented incrementally on learner demand and were preceded by strategic prompts. Dependent variables were learning outcomes (solution, retention, knowledge) and motivational learning experiences (basic needs, situational interest, deeper level processing). The laboratory guide (B) led to better learning outcomes (d?=?0.42) but lower motivation (d?>?0.38) compared to unguided problem solving (A). Incremental scaffolds (C) led to higher motivation (d?>?0.44) but similar learning outcomes compared to a laboratory guide.     

Learning Algebra by Example in Real-World Classrooms

Abstract

Math and science textbook chapters invariably supply students with sets of problems to solve, but this widely used approach is not optimal for learning; instead, more effective learning can be achieved when many problems to solve are replaced with correct and incorrect worked examples for students to study and explain. In the present study, the worked example approach is implemented and rigorously tested in the natural context of a functioning course. In Experiment 1, a randomized controlled study in ethnically diverse Algebra classrooms demonstrates that embedded worked examples can improve student achievement. In Experiment 2, a larger randomized controlled study demonstrated that improvement in posttest scores as a result of the assignments varies based on students’ prior knowledge; students with low prior knowledge tend to improve more than higher knowledge peers.     

Role of environmental interaction in interdisciplinary thinking: from knowledge resources perspectives

This article examined the role of environmental interaction in interdisciplinary thinking and the use of different knowledge resource types. The case study was conducted with two classes (N?=?40) of 8th-grade students, ages 13 to 14. The outdoor trail aimed to help students synthesize history, geography, and science knowledge. Two groups’ discourse from each class was audio-­recorded and transcribed for content analysis. We coded the discourse to examine: (i) the use of different knowledge resource types (i.e., contextual resource, new conceptual resource, prior knowledge resource); (ii) the relationship among these knowledge resource types; and (iii) evidences of interdisciplinary thinking. Findings showed that contextual resources enhanced students’ capacity to develop new conceptual resources and to activate prior knowledge resources. Further, about 80% of students’ discourse demonstrated interdisciplinary connections of two subjects.     

A comparison of students' conceptual understanding of electric circuits in simulation only and simulation‐laboratory contexts

The aim of this experimental study was to compare learning outcomes of students using a simulation alone (simulation environment) with outcomes of those using a simulation in parallel with real circuits (combination environment) in the domain of electricity, and to explore how learning outcomes in these environments are mediated by implicit (only procedural guidance) and explicit (more structure and guidance for the discovery process) instruction. Matched‐quartets were created based on the pre‐test results of 50 elementary school students and divided randomly into a simulation implicit (SI), simulation explicit (SE), combination implicit (CI) and combination explicit (CE) conditions. The results demonstrated that the instructional support had an expected effect on students' understanding of electric circuits when they used the simulation alone; pure procedural guidance (SI) was insufficient to promote conceptual understanding, but when the students were given more guidance for the discovery process (SE) they were able to gain significant amount of subject knowledge. A surprising finding was that when the students used the simulation and the real circuits in parallel, the explicit instruction (CE) did not seem to elicit much additional gain for their understanding of electric circuits compared to the implicit instruction (CI). Instead, the explicit instruction slowed down the inquiry process substantially in the combination environment (CE). Although the explicit instruction was able to improve students' conceptual understanding of electrical circuits considerably in the simulation environment, their understanding did not reach the level of the students in the combination environment. These results suggest that when teaching students about electricity, the students can gain better understanding when they have an opportunity to use the simulation and the real circuits in parallel than if they have only a computer simulation available, even when the use of the simulation is supported with the explicit instruction. © 2010 Wiley Periodicals, Inc. J Res Sci Teach 48: 71–93, 2011     

Enhancing transfer by learning generalized domain knowledge structures

Transferring one’s knowledge in new situations is usually associated with cognitively demanding processes. The paper explores an approach to facilitating transfer of knowledge by explicitly instructing learners in medium-level generalized but yet domain-connected knowledge structures that are applicable to a broader range of tasks in the domain and could be essential in managing the cognitive load associated with transfer. The paper includes a theoretical analysis of the potential role of the generalized domain knowledge in transfer and an experimental study designed to investigate the effectiveness of explicit instruction in a generalized domain knowledge structure (function–process–structure schema) in technical areas. Forty-nine undergraduate university students with low or no prior knowledge in the domain participated in the randomised 2 (schema-based vs. non-schema-based instruction)?×?2 (general-to-specific vs. specific-to-general knowledge sequences) experiment investigating the effects of these two factors on posttest transfer performance and subjective ratings of learning difficulty (interpreted as indicators of cognitive load). The results indicated a significant (p?<?0.05) main effect of schema-based instruction; a possible trend (p?<?0.1) favouring general-to-specific instructional sequence for posttest test performance; and a significant interaction between the two factors for ratings of difficulty. The paper concludes that (a) transfer within a domain could be facilitated by explicitly instructing learners in generalized domain schemas; (b) general-to-specific approach could possibly be used as a preferred instructional sequence for enhancing transfer; and (c) cognitive load perspective could add some valid arguments to explain the role of generalized domain knowledge in transfer.     

You Learn by your Mistakes. Effective Training Strategies Based on the Analysis of Video-Recorded Worked-out Examples

This paper presents an empirical study on procedural learning from errors that was conducted within the field of vocational education. It examines whether, and to what extent, procedural learning can benefit more from the detection and written analysis of errors (experimental condition) than from the correct elements (control group). The study involved 136 commercial employee apprentices who were working on a videorecorded, worked-out example of a professional procedure involving customer counselling. The results showed no differences between the conditions with regards to declarative knowledge acquisition during the procedure. Additionally, the analysis of errors was demonstrated to be more effective than the analysis of correct behaviours in terms of (1) representing a much more detailed and correct procedure and (2) developing anticipatory knowledge about possible errors to be avoided. The results highlighted the value of the inductive instructional strategy (from the analysis of a single worked-out example to the learning of the general procedure) and opened the field up for future applications of a similar instructional approach combining roleplaying and video analysis of errors in vocational education to develop communication skills.     

Instructional strategies and tactics for the design of introductory computer programming courses in high school

This article offers an examination of instructional strategies and tactics for the design of introductory computer programming courses in high school. We distinguish the Expert, Spiral and Reading approach as groups of instructional strategies that mainly differ in their general design plan to control students' processing load. In order, they emphasize topdown program design, incremental learning, and program modification and amplification. In contrast, tactics are specific design plans that prescribe methods to reach desired learning outcomes under given circumstances. Based on ACT^* (Anderson, 1983) and relevant research, we distinguish between declarative and procedural instruction and present six tactics which can be used both to design courses and to evaluate strategies. Three tactics for declarative instruction involve concrete computer models, programming plans and design diagrams; three tactics for procedural instruction involve worked-out examples, practice of basic cognitive skills and task variation. In our evaluation of groups of instructional strategies, the Reading approach has been found to be superior to the Expert and Spiral approaches.The authors wish to express their gratitude to Sanne Dijkstra, Otto Jelsma and Georg Rakers for their helpful comments on a draft of this article. Correspondence concerning this article should be addressed to Jeroen J. G. van Merrienboer.Notes