Student,teacher, and instructional characteristics related to students' gains in flexibility

Flexibility in problem solving has been widely recognized as an important skill for students' mastery of mathematics. Here we utilize the Opportunity-Propensity framework to investigate student characteristics, teacher characteristics, and teacher instructional practices that may be associated with students' gains in flexibility in algebra. Teacher and student data were collected from 8th and 9th grade Algebra I teachers in Massachusetts as part of a larger study on the impact of a researcher-developed year-long supplementary curriculum that focused on improving students' flexibility. We explore student demographics, teacher background characteristics and teacher instructional practices as predictors of student gains in flexibility. We further investigate instructional practices associated with flexibility gains through an analysis of teacher questioning in the classroom for teachers whose students achieved the greatest gains in flexibility and those whose students achieved the least gains. Our results indicate that prior knowledge is a reliable predictor of flexibility gains and that gender is an important student background characteristic associated with the development of flexibility. In addition, although high and low gain teachers did not differ in their implementation fidelity, high flexibility gain teachers asked more open-ended questions that prompted students to verbalize the main ideas of the lesson.     

The Possibilities of Historical Research

ABSTRACT

The authors outline results of 3 studies conducted to examine the structure of disciplinary knowledge from reading measured through proximity data. In Study 1, 168 third-grade students were asked to read a science text and rate the relationships of keywords from the passage. From these ratings, comprehension scores were calculated that related well to a free-recall measure of science reading comprehension and differentiated poor and proficient readers. In Study 2, 176 third-grade students were given the proximity data measure on science text along with measures of prior knowledge, questioning, and text searching. In Study 3, 160 ninth-grade students were given the proximity data measure after reading a social studies text that varied on the presence of text signals and familiarity. The findings of this study extend the literature on the cognitive processing that contributes to higher order comprehension of information text among elementary and secondary students.     

Investigating the mechanisms of learning from a constrained preparation for future learning activity

Many studies have shown benefits associated with engaging students in problem-solving activities prior to administering lessons. These problem-solving activities are assumed to activate relevant knowledge and allow students to develop some initial knowledge structures, which support understanding of the lesson. In this paper we report the results of two studies in which we investigated the underlying benefits of engaging in a preparatory activity—setting up experiments without running them or receiving feedback—prior to an interactive computerized lesson on experimental design compared to only engaging in the interactive lesson. We predicted that the seventh-grade participants who demonstrated some initial knowledge of the topic—experimental design—would benefit more from spending the whole time engaged in instructional activities. However, we expected students who did not demonstrate initial knowledge would benefit more from engaging in the preparatory activity, which would allow them to activate or develop initial knowledge that would aid their understanding of the subsequent instruction. The predicted condition by initial knowledge interaction was found in both studies. In Study 1, the benefit of only engaging in the instruction was found only for the lowest-knowledge of students who demonstrated initial knowledge. For students who did not demonstrate some initial knowledge, the benefit of completing the preparatory activity appeared to be due to the development of an understanding of the general goal of the activity rather than of specific knowledge of experimental design. Based on this finding, in Study 2, we investigated an initial goal by condition interaction. In fact, students who did not express an understanding of the task goal on the pretest benefited from engaging in the preparatory activity and students who did benefited more from the instruction. Again, this benefit appeared to be due to students’ development of an appropriate understanding of the task goal during the preparatory activity.     

Keep DRAGging ON: Is solving more problems in DragonBox 12+ associated with higher mathematical performance during the COVID-19 pandemic?

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12–13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between students' progress within DragonBox and their algebraic knowledge and general mathematics achievement, (b) the moderating effects of students' prior performance on these relations and (c) the potential factors associated with students' in-game progress. Among students with higher prior algebraic knowledge, higher in-game progress was related to higher algebraic knowledge after the intervention. Higher in-game progress was also associated with higher end-of-year mathematics achievement, and this association was stronger among students with lower prior mathematics achievement. Students' demographic characteristics, prior knowledge and prior achievement did not significantly predict in-game progress beyond the number of intervention sessions students completed. These findings advance research on how, for whom and in what contexts game-based interventions, such as DragonBox, support mathematical learning and have implications for practice using game-based technologies to supplement instruction.

Practitioner notes

What is already known about this topic

• DragonBox 12+ may support students' understanding of algebra but the findings are mixed.
• Students who solve more problems within math games tend to show higher performance after gameplay.
• Students' engagement with mathematics is often related to their prior math performance.

What this paper adds

• For students with higher prior algebraic knowledge, solving more problems in DragonBox 12+ is related to higher algebraic performance after gameplay.
• Students who make more in-game progress also have higher mathematics achievement, especially for students with lower prior achievement.
• Students who spend more time playing DragonBox 12+ make more in-game progress; their demographic, prior knowledge and prior achievement are not related to in-game progress.

Implications for practice and/or policy

• DragonBox 12+ can be beneficial as a supplement to algebra instruction for students with some understanding of algebra.
• DragonBox 12+ can engage students with mathematics across achievement levels.
• Dedicating time and encouraging students to play DragonBox 12+ may help them make more in-game progress, and in turn, support math learning.

     

Learning a mathematical concept from comparing examples: the importance of variation and prior knowledge

In experiment 1, novice fourth-grade students (N????2) who compared multiple examples that separately varied each critical aspect and then simultaneously varied all critical aspects developed better conceptual knowledge about the altitude of a triangle than students who compared multiple examples that did not separately vary each critical aspect but simultaneously varied all critical aspects. In experiment 2, this pattern was the same for fourth-grade students (N????0) but not for sixth-grade students (N????4) who had greater prior knowledge about the concept. Aspects that are critical for learning should be varied first separately and then simultaneously, and students with different levels of prior knowledge may perceive different aspects as critical for their learning and thus benefit differently from the identical instruction.     

The conceptions of learning science by laboratory among university science-major students: qualitative and quantitative analyses

Background: The sophistication of students’ conceptions of science learning has been found to be positively related to their approaches to and outcomes for science learning. Little research has been conducted to particularly investigate students’ conceptions of science learning by laboratory.

Purpose: The purpose of this research, consisting of two studies, was to explore Taiwanese university science-major students’ conceptions of learning science by laboratory (CLSL).

Sample: In Study I, interview data were gathered from 47 university science-major students. In Study II, 287 university science-major students’ responses to a CLSL survey were collected.

Design and methods: In Study I, the interview data were analyzed using the phenomenographic method. Based on the findings derived from Study I, Study II developed an instrument for assessing students’ CLSL by exploratory factor analysis.

Results: Study I revealed six categories of CLSL, including memorizing, verifying, acquiring manipulative skills, obtaining authentic experience, reviewing prior learning profiles, and achieving in-depth understanding. The factor analysis in Study II revealed that the ‘verifying’ category was eliminated, but found another new category of ‘examining prior knowledge.’

Conclusions: This study finally proposes a framework to describe the variations of CLSL, consisting of three features: cognitive orientation, metacognitive orientation, and epistemic orientation. Possible factors influencing students’ CLSL are also discussed.     

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.     

Situational interest and learning: Thirst for knowledge

The objective of the three studies presented here was to investigate how situational interest is related to knowledge acquisition. Situational interest is construed as a motivational response to a perceived knowledge deficit. It is triggered in situations where this knowledge deficit becomes manifest, such as in the confrontation with a problem. In Study 1 we manipulated prior knowledge of 32 secondary-school students about a particular problem (i.e., reasons for the conquest of Singapore by the Japanese during the Second World War). Only students who lacked the appropriate knowledge showed an increase in situational interest after the problem was presented. In Study 2 (N = 60), students who showed awareness that they lacked knowledge to understand a problem (i.e., causes of erosion of an island) showed increased situational interest in that problem. In Study 3 (N = 86), situational interest and knowledge acquisition were monitored over the course of a 3-h lesson in a natural classroom. We were able to demonstrate that situational interest decreased with increasing knowledge of the problem-at-hand. We argue that the findings support a knowledge-deprivation account of situational interest. Our findings are at variance with the broadly held conviction that situational interest and knowledge necessarily influence each other positively.     

Unrealistic responses to realistic problems with missing information: what are important barriers?

Abstract

It is a well-documented finding that students tend to neglect their real-world knowledge when solving word problems, even when realistic assumptions are needed. Although studies have successfully shown the extent to which students tend to provide unrealistic responses, the question of where this tendency comes from has yet to be answered. We focused on two major steps needed to solve realistic word problems: noticing missing information and making realistic assumptions. We conducted two studies with fifth graders (Study 1, N?=?108; Study 2, N?=?60) in which we compared students’ (un-)realistic responses to problems that differed in how obvious the missing information was. Study 1 fostered only students’ ability to make assumptions. Study 2 fostered this ability plus the ability to notice missing information. The results indicate that, if the missing information is not obvious, students’ failure to notice it seems to be what prevents them from arriving at a realistic solution.     

‘Is it like one of those infectious kind of things?’ The importance of educating young people about HPV and HPV vaccination at school

Abstract

The National Human Papillomavirus (HPV) Vaccination Program in Australia commenced in 2007 for girls and in 2013 for boys, using the quadrivalent HPV [4vHPV] vaccine. In Australia, students are primarily vaccinated en masse, on school grounds, after parental/guardian consent is obtained. Students most often receive little, or no, education at school about HPV or HPV vaccination prior to immunisation. There is also some uncertainty about where young people can and should obtain reliable information about the vaccine, outside of school. We conducted a cluster randomised controlled trial of a complex intervention in schools. This study aimed to improve: (1) student knowledge about HPV vaccination; (2) psycho-social outcomes and (3) vaccination uptake. In this paper, we briefly outline our educational intervention and discuss its implementation by educators including facilitators and barriers. We also discuss the study findings pertaining to student knowledge about HPV and HPV vaccination and their attitudes to vaccination across control and intervention schools. Study results showed students in intervention schools demonstrate greater knowledge and understanding of HPV and HPV vaccination. Greater knowledge and understanding of HPV and HPV vaccination appeared to promote positive attitudes towards vaccination and supported confidence with vaccination.     

Moving Beyond Solving for “x”: Teaching Abstract Algebra in a Liberal Arts Mathematics Course

Abstract

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context, identifying patterns, and venturing conjectures. A sequence of open-ended instructional tasks that aim to capitalize on students’ prior experiences with equation solving is provided along with notes and sample student responses for prospective instructors.     

Toward Stewardship of Democratic Ideals: Using students' perspectives to improve school‐university collaboration and model democratic practice

A healthy democracy values and depends on diverse perspectives to maintain flexibility and to make ongoing improvements that better serve its various groups. Our analysis of qualitative data from interviews conducted with students in two professional development school settings (school-university partnerships) showed that students were not regularly asked to provide their views of schooling or of school renewal efforts. The analysis further showed that students in this study, both young children and maturing adolescents alike, held personal knowledge that could contribute to adults' understandings of their work. The article is organized into five sections. First, we describe the innovation that provided the impetus for the study. Second, we describe the study's design. The third and fourth parts—students' perspectives on their schools and on the changes they were experiencing—represent the heart of the article. We conclude by placing the students' perspectives in the larger context of schooling for democracy—the theoretical framework for the study.     

From childhood nature experiences to adult pro-environmental behaviors: An explanatory model of sustainable food consumption

Abstract

In two studies, the role of nature experiences and social norms during childhood is explored next to adulthood biospheric values, connectedness to nature, environmental identity, and objective knowledge in relation to pro-environmental behaviors. Study 1 (N?=?185) tested the hypothesized model in the realm of general pro-environmental behaviors and sustainable fruit consumption on a sample of students. Study 2 (N?=?155) tested the model in the realm of sustainable seafood consumer choice on a general population sample. Path analyses show consistent results across samples. Results show that childhood nature experiences and exposure to pro-environmental social norms during childhood are related to adulthood development of connectedness with nature and biospheric values; these, in turn, help in shaping adulthood environmental self-identity ultimately influencing the enactment of sustainable food choices during adulthood. These findings point toward the relevance of childhood experiences for pro-environmental behaviors as compared to the provision of information. The role of objective knowledge across samples is inconsistent, thus requiring future investigations.     

The Effect of Knowledge and Strategy Training on Monitoring Accuracy

Abstract

The effect of prior knowledge and strategy training on monitoring accuracy among college students was investigated. The authors compared the debilitative, no-impact, and facultative hypotheses. The authors predicted that prior knowledge and strategy training would facilitate monitoring accuracy because both variables help students assess their performance. Experiment 1 revealed that mathematics knowledge was related positively to performance and monitoring accuracy. In Experiment 2, the trainable and no-trainable hypotheses were tested; the authors found that strategy training increased performance and monitoring accuracy immediately, but not after a 1-week delay. Measures of general ability and mathematics self-efficacy were not related to monitoring accuracy in either experiment.     

The role of orthographic flexibility in Chinese word reading among kindergarten children

Abstract

The present study aimed to examine the potential importance of orthographic flexibility for Chinese reading acquisition. Orthographic flexibility is a novel concept that represents the ability to manage and switch attention among multiple aspects of orthographic information. A total of 92 Chinese kindergarten children at age 6 were assessed on measures of orthographic flexibility, orthographic knowledge, executive functions (EF) skills (i.e. cognitive flexibility and working memory) and Chinese word reading. Results of hierarchical regressions showed that orthographic flexibility uniquely and significantly contributed to word reading beyond the effects of established predictors, namely orthographic knowledge and EF skills. Path analysis further indicated that orthographic flexibility significantly mediated the contribution of EF skills to word reading. These findings provided theoretical insights into the linkage between domain-general EF skills and domain-specific reading ability. The present study also provided practical implication that training on orthographic flexibility in addition to orthographic knowledge could be beneficial to early acquisition of Chinese word reading.     

A Systematic Approach in Student Reading

Abstract

The Faculty Writing Fellows Seminar was designed to develop university instructors’ skill in writing instruction: The 2015–16 professional development project offered faculty at Southern Oregon University a chance to read writing-pedagogy research, collaboratively develop their teaching practices, and—most importantly—put themselves in the shoes of student writers. The seminar had a positive impact on instructors’ teaching and students’ writing. Instructors showed growth in confidence, empathy, knowledge, and instruction. Their students’ essays outscored essays by students in nonparticipating instructors’ classes. The study argues for professional development that simultaneously builds pedagogical knowledge and skills and incorporates emotional and psychosocial aspects of teaching and learning.     

KNOWLEDGE USE IN THE CONSTRUCTION OF GEOMETRY PROOF BY SRI LANKAN STUDENTS

Within the domain of geometry, proof and proof development continues to be a problematic area for students. Battista (2007) suggested that the investigation of knowledge components that students bring to understanding and constructing geometry proofs could provide important insights into the above issue. This issue also features prominently in the deliberations of the 2009 International Commission on Mathematics Instruction Study on the learning and teaching of proofs in mathematics, in general, and geometry, in particular. In the study reported here, we consider knowledge use by a cohort of 166 Sri Lankan students during the construction of geometry proofs. Three knowledge components were hypothesised to influence the students’ attempts at proof development: geometry content knowledge, general problem-solving skills and geometry reasoning skills. Regression analyses supported our conjecture that all 3 knowledge components played important functions in developing proofs. We suggest that whilst students have to acquire a robust body of geometric content knowledge, the activation and the utilisation of this knowledge during the construction of proof need to be guided by general problem-solving and reasoning skills.     

Developing knowledge intensive ideas in engineering education: the application of camp methodology

Background: Globalization, technological advancement, environmental problems, etc. challenge organizations not just to consider cost-effectiveness, but also to develop new ideas in order to build competitive advantages. Hence, methods to deliberately enhance creativity and facilitate its processes of development must also play a central role in engineering education. However, so far the engineering education literature provides little attention to the important discussion of how to develop knowledge intensive ideas based on creativity methods and concepts.

Purpose: The purpose of this article is to investigate how to design creative camps from which knowledge intensive ideas can unfold.

Design/method/sample: A framework on integration of creativity and knowledge intensity is first developed, and then tested through the planning, execution and evaluation of a specialized creativity camp with focus on supply chain management. Detailed documentation of the learning processes of the participating 49 engineering and business students is developed through repeated interviews during the process as well as a survey.

Results: The research illustrates the process of development of ideas, and how the participants through interdisciplinary collaboration, cognitive flexibility and joint ownership develop highly innovative and knowledge-intensive ideas, with direct relevance for the four companies whose problems they address.

Conclusions: The article demonstrates how the creativity camp methodology holds the potential of combining advanced academic knowledge and creativity, to produce knowledge intensive ideas, when the design is based on ideas of experiential learning as well as creativity principles. This makes the method a highly relevant learning approach for engineering students in the search for skills to both develop and implement innovative ideas.     

Self-regulated learning processes vary as a function of epistemic beliefs and contexts: Mixed method evidence from eye tracking and concurrent and retrospective reports

The objective of the current studies was to investigate how epistemic cognition related to specific phases and components of self-regulated learning and its adaptation to learning conditions of varying quality. In a multi-study, mixed method design, we presented university students with science content that relayed conceptual discrepancies and collected quantitative and qualitative data to study how students responded to discrepancies. In Study 1 (n = 42), we collected eye tracking patterns, study times, and metacognitive ratings and found that participants adapted their behavioral processing as a function of their epistemic cognition and discrepancy type. In Study 2 (n = 20), we collected concurrent think-aloud protocols and retrospective interviews to further explore why discrepancies were noticed (or not) and how they were resolved. Results revealed that prior knowledge and epistemic self-efficacy in oneself as an evaluator of knowledge emerged as important themes to detecting and efficiently resolving discrepancies. We conclude with a discussion of theoretical and methodological implications.     

The Post-Modern Student

Abstract

The differences between present-day post-modern students and educators from older generations require changes in educational approach, but also challenge post-modern trends. Students' postmodern experiences may lead them to seek individuality among diverse sources of identity, seeing knowledge as a throwaway consumption good, and education promotes flexibility and “edutainment.” However, professional education trains people for structured managerialist organisations and the accumulation of shared professional knowledge. Social work education needs to be reframed as a process of emergence in which educators and students work jointly to create knowledge and identity in their professional area. To operate in an increasingly complex and changing society, students need to create a strong professional identity and learn how to transfer knowledge and values from one situation to another. In this way, social work education connects with the Danish managerial concept of “chaos pilots” in which students are prepared to deal with cultural and social change.