ArticlePDF Available

The Effects of Feedback During Exploratory Mathematics Problem Solving: Prior Knowledge Matters

Authors:
Emily R. Fyfe at Indiana University Bloomington
Emily R. Fyfe
Bethany Rittle-Johnson at Vanderbilt University
Bethany Rittle-Johnson
Marci S. DeCaro at University of Louisville
Marci S. DeCaro
Download full-text PDF
Read full-text
Download citation

Abstract and Figures

Providing exploratory activities prior to explicit instruction can facilitate learning. However, the level of guidance provided during the exploration has largely gone unstudied. In this study, we examined the effects of 1 form of guidance, feedback, during exploratory mathematics problem solving for children with varying levels of prior domain knowledge. In 2 experiments, 2nd- and 3rd-grade children solved 12 novel mathematical equivalence problems and then received brief conceptual instruction. After solving each problem, they received (a) no feedback, (b) outcome feedback, or (c) strategy feedback. In both experiments, prior knowledge moderated the impact of feedback on children's learning. Children with little prior knowledge of correct solution strategies benefited from feedback during exploration, but children with some prior knowledge of a correct solution strategy benefited more from exploring without feedback. These results suggest that theories of learning need to incorporate the role of prior knowledge and that providing feedback may not always be optimal. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Figures - uploaded by Marci S. DeCaro
Author content
All figure content in this area was uploaded by Marci S. DeCaro
Content may be subject to copyright.
Content uploaded by Marci S. DeCaro
Author content
All content in this area was uploaded by Marci S. DeCaro on Nov 03, 2018
Content may be subject to copyright.
A preview of the PDF is not available
A preview of this full-text is provided by American Psychological Association.
Learn more
Content available from Journal of Educational Psychology
This content is subject to copyright. Terms and conditions apply.
... However, it is relevant to consider that males had higher pre-test scores than females and that post-test scores were similar across genders. Hence, we can think that females outperforming learning gains were at least partially supported by their lower prior knowledge level, as diverse literature states the idea that lower levels of prior knowledge provide more space for learning improvements [31,40,44,77]. Now, from the perspective of the instructional feedback conditions provided in the present experiment, we have that MTF and STF game versions provided similar results in terms of learning gains for each gender. ...
... Such results do not follow the general idea proposed by SDT-CET theory regarding that competence and autonomy are strong predictors of motivation and learning [65][66][67][68]. These contradicting results may be attributed to the Dunning-Kruger effect [77], where students tend to significantly overestimate their performance, fostering a belief in their adequate knowledge of a given topic. Now, from the perspective of females, despite having higher learning gains, they perceived themselves as less competent compared to males. ...
A Math Digital Game and Multiple-Try Use in Primary Students: A Gender Analysis on Motivation and Performance
Preprint
Full-text available
  • Apr 2024
Gender has been a rarely addressed aspect in digital game-based learning (DGBL). Likewise, mixed results have been presented regarding the effects according to gender and the conditions that generate these effects. The present work studies the effects of a drill-and-practice mathe-matical game on primary students. The study focused on an analysis by gender, measuring learning performance, and motivation in the practice activity. Also, two instructional mechanics were considered regarding the question answering, a multiple-try (MTF) and a single-try (STF) condition, to search for possible differences. A total of 81 students from 4 courses and 2 schools participated in the experiment. The study's main findings were that: (a) the girls outperformed boys in terms of students' learning gains, (b) girls presented lower levels of competence and autonomy than boys, (c) in the MTF, girls presented lower levels of autonomy but no differences in competence contrasted to boys, (d) in the STF, girls presented lower levels of competence but no differences in autonomy against boys, and (e) no differences existed in interest, effort and value among gender overall o per instructional condition. This study enhances the knowledge of gender differences under diverse instructional settings, in particular providing insights into possible differences by gender when varying the number of attempts provided to students.
View
... Bestehende Wissensstrukturen müssen aktiviert werden und neues Wissen muss integriert werden Woolfolk, 2014 Für chemienahe Kontexte und die Mathematik konnten auch bereits Indizien für einen solchen Zusammenhang gefunden werden (Albacete & VanLehn, 2000;Moreno, 2004;Narciss & Huth, 2004). Andere Studien liefern hingegen keine gesicherten Erkenntnisse hinsichtlich des Vorwissenseinflusses auf die Wirksamkeit von Feedback unterschiedlichen Umfangs (Fyfe et al., 2012;Narciss, 2006;Smits et al., 2008). Die Einzelstudien zeigen im Vergleich jedoch ähnliche Auffälligkeiten wie in den bereits zitierten Metastudien (Bangert-Drowns et al., 1991;Hattie & Timperley, 2007;Kluger Bedingungen nicht möglich, da eine direkte Betrachtung der Kognitionen und Berücksichtigung aller Faktoren des Individuums nicht möglich ist. ...
View
... They were able to draw accurate conclusions after considering and evaluating various methods and being able to explain their reasons. It is supported by Fyfe et al. (2012), Pambudi (2022), and Rittle-Johnson et al. (2009), who state that students with high prior knowledge can draw accurate conclusions after considering various methods and can explain their reasons. Medium prior knowledge subjects showed a good understanding of the elimination and substitution methods, used trial and error, and could draw conclusions; however, they needed to be sure about the answer. ...
Prospective mathematic teachers’ reflective thinking in solving numeracy problems at the critical reflection stage
Article
Full-text available
  • Sep 2024
The low numeracy skills in Indonesia are one factor affecting the quality of mathematics education, so reflective thinking is needed to improve this ability. This study aims to describe prospective mathematics teachers' reflective thinking process in solving numeracy problems at the critical reflection stage based on prior knowledge. This study used a qualitative, descriptive research methodology. The research participants were 34 prospective mathematics teachers at the State University of Malang, East Java. The instruments used are numeracy tests and interview guidelines. Data analysis includes data reduction, presentation, and conclusion drawing. The findings revealed notable differences in reflective thinking based on prior knowledge levels at the critical reflection stage. Subjects with high prior knowledge tried various solutions, were confident in their answers, and accurately drew conclusions and explained their reasons. Subjects with medium prior knowledge tried different methods but needed more confidence in their results. They could conclude but struggled to explain their reasons. Subjects with low prior knowledge used the same method, needed more confidence, and needed help explaining their reasons despite concluding. These findings imply creating a better training program for prospective mathematics teachers, emphasizing numeracy and reflective thinking growth.
View
... Learners may possess different types or levels of prior knowledge about related topics, which influence their acquisition of new knowledge and final outcomes (Dinsmore et al., 2014). Learners' prior knowledge moderated the effect of the instructional support (Fyfe et al., 2012). With sufficient background knowledge, learners can use it as a starting point to solve complex problems or make connections to other information (Land & Zembal-Saul, 2003). ...
How Does Students’ Prior Knowledge Affect Learning Behavioral Patterns in CPS-Based STEM Lessons?
Article
Full-text available
  • Sep 2024
In this study, a collaborative problem solving-based STEM course was implemented in a seventh-grade class. This study aimed to examine the effects of students’ prior knowledge on their CPS-based STEM learning processes by using a mixed-methods approach. First, a lag sequential analysis was used to investigate individual cognitive and metacognitive behaviors of students with different prior knowledge levels, while a dialogue analysis was used to explore their social behaviors during discussion. The results indicated that students with sufficient prior knowledge conducted cognitive and metacognitive strategies more effectively during individual thinking. On the contrary, students who lack prior knowledge focused more on social strategy and engaged in cognitive strategies through group contributions. The dialogue analysis revealed different social interaction patterns that were affected by using CPS skills, cognitive tools, and the group dynamics. Second, interviews were conducted and analyzed to provide rational explanations for students’ learning behaviors and further investigate the effects of their prior knowledge. Finally, specific instructional designs are provided to bridge the gap between high and low prior knowledge students.
View
... Prior knowledge is considered a relevant factor that influences how learners process feedback (e.g., Fyfe et al., 2012;Mory, 2004;Narciss & Huth, 2004), which, in turn, can impact subsequent performance (Sitzman et al., 2014(Sitzman et al., , 2015. Learners with high prior knowledge can draw on an existing semantic network, which helps them to integrate new information from feedback more effectively (Clariana & Koul, 2005;Sitzman et al., 2015). ...
How am I going? Behavioral engagement mediates the effect of individual feedback on writing performance
Article
Full-text available
  • Oct 2024
  • LEARN INSTR
Background: Successful feedback should provide learning goals, evaluate current performance and indicate improvement strategies. Furthermore, feedback can only positively affect student performance if students actively engage with it. Thus, it is necessary to consider the feedback reception process in addition to the feedback information itself. Aims: This study compares the effects of different types of feedback information on the writing performance of lower secondary students of English as a foreign language (EFL) in a digital learning environment. Behavioral engagement was considered as a mediator of the feedback effect. Sample: Participants were N = 338 eighth-and ninth-grade EFL students (54.7% female) enrolled in lower-secondary education within the Swiss school system. Methods: We conducted a web-based randomized-controlled experiment, in which students were randomly assigned to four conditions receiving varying amounts of rubric-based feedback information. We used log data (time on feedback page) as a proxy for their behavioral engagement with the feedback. Results: Even though writing performance improved substantially across conditions, there were no differential effects of the type of feedback information on performance. However, EFL learners who received individual performance information spent more time with the feedback, especially those with low prior achievement. Mediation analysis showed that the effectiveness of the feedback was mediated by the time spent on the feedback as an indicator of students' behavioral engagement. Conclusions: Advantages for individual performance feedback over more general information were observed as a function of time spent with the feedback. This finding implies that engagement should be considered in feedback research.
View
... Educational activities had to be carefully chosen to ensure external factors meshed with internal factors such as children's interest and developmental readiness. Consistent with this "principle of interaction," fostering meaningful learning entails identifying what children already know and do not know and building on the former to learn (moderately) new knowledge (Clarke et al., 2014;Fyfe et al., 2012;Ginsburg, 1977;Piaget, 1964;Vygotsky, 1978). ...
View
... The combination of concrete and abstract representations enabled by in-class activities and the "tracker" role, align with several areas of psychological research on learning. There is ample evidence indicating that including both concrete and abstract representations leads to larger learning gains in mathematics compared to interacting with only abstract or only concrete representations (Fyfe et al., 2012;Goldstone & Son, 2005;Kokkonen & Schalk, 2021). However, making connections between two or more representations is challenging. ...
View
... However, research has also shown that some feedback is not always preferred to no feedback. For example, Fyfe et al. (2012) found that learners with little prior knowledge of the correct solution strategy benefitted from some feedback, whereas learners with some prior knowledge of the correct solution strategy benefitted from a learning situation without feedback. Yet, viewing feedback effects in a black-and-white fashion (e.g. ...
A meta-analysis of the effects of context, content, and task factors of digitally delivered instructional feedback on learning performance
Article
Full-text available
  • Jun 2024
  • Learn Environ Res
Even though context, content, and task factors are considered essential parts of digitally delivered instructional feedback, their effects on learning performance are most often studied separately. A meta-analysis was carried out to address the effects of context, content, and task factors of digitally delivered instructional feedback on learning performance. A summary effect of .41 (SE = .05) was found for 116 interventions. Significant influencers on learning performance in the sample were feedback focus, discipline, assessment type, and learner control (amongst others), showing the potential to explain the heterogeneity in effects. Also, any simple feedback (e.g. verification or knowledge of result) is more effective than no feedback. A meta-regression with all significant influencers and feedback focused on the process explained the heterogeneity in learning performance.
View
... However, it is relevant to consider that the males had higher pre-test scores than the females, and that the post-test scores were similar between the sexes. Hence, we can consider that the females' outperforming learning gains were at least partially supported by their lower prior knowledge level, as diverse studies state the idea that lower levels of prior knowledge provide more space for learning improvements [22,34,38,74]. Now, from the perspective of the instructional feedback conditions provided in the present experiment, the multiple-try and single-try game versions provided similar results in terms of the learning gains for each sex. ...
A Digital Math Game and Multiple-Try Use with Primary Students: A Sex Analysis on Motivation and Learning
Article
Full-text available
  • Jun 2024
Sex differences have been a rarely addressed aspect in digital game-based learning (DGBL). Likewise, mixed results have been presented regarding the effects according to sex and the conditions that generate these effects. The present work studied the effects of a drill-and-practice mathematical game on primary students. The study focused on an analysis by sex, measuring motivation and learning in the practice activity. Also, two instructional mechanics were considered regarding the question answering to search for possible differences: a multiple-try feedback (MTF) condition and a single-try feedback (STF) condition. A total of 81 students from four courses and two schools participated in the intervention. The study’s main findings were as follows: (a) the girls outperformed the boys in terms of the students’ learning gains; (b) the girls presented lower levels of competence and autonomy than the boys; (c) under MTF, the girls presented lower levels of autonomy but no differences in competence contrasted with the boys; (d) under STF, the girls presented lower levels of competence but no differences in autonomy contrasted with the boys; (e) no sex differences existed in interest, effort, and value, in general, as per the instructional condition. This study enhances the knowledge of sex differences under diverse instructional settings, in particular providing insights into the possible differences by sex when varying the number of attempts provided to students.
View
Multi-modal quantitative assessment mechanism and intervention of learners’ cognitive engagement in blended classroom
Article
Full-text available
  • Aug 2024
Cognitive engagement refers to the degree of learners’ mental efforts and the application of cognitive strategies during learning, which is the crucial factor affecting learning performance in blended teaching. However, researchers have previously encountered challenges in accurately assessing learners’ cognitive engagement because of problems with the evaluation method, such as subjective and single-mode approaches. Thus, improvement in the learning effect in blended classrooms is restricted. The study aims to combine mathematical modeling, laboratory experiments, and quasi-experiments in teaching to explore the quantification and intervention of cognitive engagement in blended teaching. We will endeavor to establish a multimodal quantitative assessment model to represent learners’ cognitive engagement in blended classrooms and identify strategies for improvement. We will also create teaching schemes for blended teaching in higher education and develop an integrated digital tool for cognitive engagement identification and intervention. We anticipate that the study findings will provide theoretical and practical support for improving the quality and efficiency of blended teaching.
View
Conceptual and Procedural Knowledge of Mathematics: Does One Lead to the Other?
Article
Full-text available
  • Mar 1999
This study examined relations between children's conceptual understanding of mathematical equivalence and their procedures for solving equivalence problems (e.g., 3 + 4 + 5 = 3 + 9). Students in 4th and 5th grades completed assessments of their conceptual and procedural knowledge of equivalence, both before and after a brief lesson. The instruction focused either on the concept of equivalence or on a correct procedure for solving equivalence problems. Conceptual instruction led to increased conceptual understanding and to generation and transfer of a correct procedure. Procedural instruction led to increased conceptual understanding and to adoption, but only limited transfer, of the instructed procedure. These findings highlight the causal relations between conceptual and procedural knowledge and suggest that conceptual knowledge may have a greater influence on procedural knowledge than the reverse. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
View
Emerging Minds: The Process of Change in Children's ThinkingThe Process of Change in Children's Thinking
Book
  • Sep 1996
How do children acquire the vast array of concepts, strategies, and skills that distinguish the thinking of infants and toddlers from that of preschoolers, older children, and adolescents? In this new book, Robert Siegler addresses these and other fundamental questions about children's thinking. Previous theories have tended to depict cognitive development much like a staircase. At an early age, children think in one way; as they get older, they step up to increasingly higher ways of thinking. Siegler proposes that viewing the development within an evolutionary framework is more useful than a staircase model. The evolution of species depends on mechanisms for generating variability, for choosing adaptively among the variants, and for preserving the lessons of past experience so that successful variants become increasingly prevalent. The development of children's thinking appears to depend on mechanisms to fulfill these same functions. Siegler's theory is consistent with a great deal of evidence. It unifies phenomena from such areas as problem solving, reasoning, and memory, and reveals commonalities in the thinking of people of all ages. Most important, it leads to valuable insights regarding a basic question about children's thinking asked by cognitive, developmental, and educational psychologists: How does change occur?
View
View
View
View
View
View
View
View
How children change their minds: Strategy change can be gradual or abrupt
Conference Paper
  • Jan 1999
This study investigated patterns of change in children's strategies for solving mathematical equivalence problems. The strategies children expressed in speech and in gesture were assessed both before and after an instructional intervention. In the intervention, children received either no input, accuracy feedback, or feedback plus instruction about a principle, an analogy, or a procedure. From pretest to posttest, many children changed both the variability of their strategy use and the content of their strategy repertoires. Patterns of change depended on type of instruction and on children's initial level of variability. Children who received instruction were especially likely to generate new strategies, and children with high variability were especially likely to abandon prior strategies. Gradual change was most common; however, many children modified their repertoires abruptly. Abrupt strategy change was especially prevalent among children who received procedure-based instruction and among children with low initial variability.
View