The effectiveness of using incorrect examples to support learning about decimal magnitude

Comparing common mathematical errors to correct examples may facilitate learning, even for students with limited prior domain knowledge. We examined whether studying incorrect and correct examples was more effective than studying two correct examples across prior knowledge levels. Fourth- and fifth-grade students (N = 74) learned about decimal magnitude in a brief tutoring session. Students were randomly assigned to two conditions: 1) comparing correct and incorrect examples (incorrect condition) or 2) comparing correct examples only (correct condition). The incorrect condition helped students learn correct procedures and key concepts more than the correct condition, including reducing misconceptions. Students’ prior knowledge of decimals did not interact with condition. Students’ explanations during the intervention revealed that those in the incorrect condition more frequently discussed correct concepts (e.g., the magnitude of a decimal and identifying misconceptions). Overall, contrasting incorrect examples with correct examples can help students learn correct concepts and procedures.     

PRE-SERVICE PHYSICS TEACHERS’ UNDERSTANDING OF THE RELATIONAL STRUCTURE OF PHYSICS CONCEPTS: ORGANISING SUBJECT CONTENTS FOR PURPOSES OF TEACHING

Good conceptual understanding of physics is based on understanding what the key concepts are and how they are related. This kind of understanding is especially important for physics teachers in planning how and in what order to introduce concepts in teaching; connections which tie concepts to each other give direction of progress—there is “flux of information” so that what was learned before provides the basis for learning new ideas. In this study, we discuss how such ordering of concepts can be made visible by using concept maps and how they can be used in analysing the students’ views and ideas about the inherent logic of the teaching plans. The approach discussed here is informed by the recent cognitively oriented ideas of knowledge organisation concentrating on simple knowledge organisation patterns and how they form the basis of more complex concept networks. The analysis of such concept networks is then very naturally based on the use of network theory on analysing the concept maps. The results show that even in well-connected maps, there can be abrupt changes in the information flux in the way knowledge is passed from the initial levels to the final levels. This suggests that handling the information content is very demanding and perhaps a very difficult skill for a pre-service teacher to master.     

From Words to Concepts: Focusing on Word Knowledge When Teaching for Conceptual Understanding Within an Inquiry-Based Science Setting

This qualitative video study explores how two elementary school teachers taught for conceptual understanding throughout different phases of science inquiry. The teachers implemented teaching materials with a focus on learning science key concepts through the development of word knowledge. A framework for word knowledge was applied to examine the students’ level of word knowledge manifested in their talk. In this framework, highly developed knowledge of a word is conceptual knowledge. This includes understanding how the word is situated within a network of other words and ideas. The results suggest that students’ level of word knowledge develops toward conceptual knowledge when the students are required to apply the key concepts in their talk throughout all phases of inquiry. When the students become familiar with the key concepts through the initial inquiry activities, the students use the concepts as tools for furthering their conceptual understanding when they discuss their ideas and findings. However, conceptual understanding is not promoted when teachers do the talking for the students, rephrasing their responses into the correct answer or neglecting to address the students’ everyday perceptions of scientific phenomena.     

Elementary teachers’ use of content knowledge to evaluate students’ thinking in the life sciences

Science learning environments should provide opportunities for students to make sense of and enhance their understanding of disciplinary concepts. Teachers can support students’ sense-making by engaging and responding to their ideas through high-leverage instructional practices such as formative assessment (FA). However, past research has shown that teachers may not understand FA, how to implement it, or have sufficient content knowledge to use it effectively. Few studies have investigated how teachers gather information to evaluate students’ ideas or how content knowledge factors into those decisions, particularly within the life science discipline. We designed a study embedded in a multi-year professional development program that supported elementary teachers’ development of disciplinary knowledge and FA practices within science instruction. Study findings illustrate how elementary teachers’ life science content knowledge influences their evaluation of students’ ideas. Teachers with higher levels of life science content knowledge more effectively evaluated students’ ideas than teachers with lower levels of content knowledge. Teachers with higher content exam scores discussed both content and student understanding to a greater extent, and their analyses of students’ ideas were more scientifically accurate compared to teachers with lower scores. These findings contribute to theory and practice around science teacher education, professional development, and curriculum development.     

The impact of incorrect examples on learning fractions: A field experiment with 6th grade students

Educational research indicates that error reflection, especially reflection on incorrect examples, has a positive effect on knowledge acquisition. The benefit of error reflections might be explained by the extended knowledge of incorrect strategies and concepts (negative knowledge) which fosters the learning of new content. In a field experiment with a pre-post-design we taught fractions to N = 195 6th grade students and compared two conditions that encouraged reflection on either incorrect or correct examples. We found that incorrect examples supported students’ negative knowledge more than correct examples. However, regarding the knowledge of fractions, only advanced students could benefit from incorrect examples; students with low prior knowledge learned more from correct examples. Even though negative knowledge showed a partial mediation effect for knowledge acquisition, it did not mediate the effect of error reflections on the acquisition of knowledge of fractions. The implications for school instruction are discussed.     

Students’ Perceptions of Dynamics Concept Pairs and Correlation with Their Problem-Solving Performance

A concept pair is a pair of concepts that are fundamentally different but closely related. To develop a solid conceptual understanding in dynamics (a foundational engineering science course) and physics, students must understand the fundamental difference and relationship between two concepts that are included in each concept pair. However, all existing research in dynamics and physics education has been focused on the identification and repair of students?? misunderstanding of individual concepts, but not concept pairs. The present research fills the gap of existing research by studying students?? perceptions of dynamics concept pairs and correlation with their problem-solving performance in both particle and rigid-body dynamics. A total of 88 engineering undergraduate students participated in the present study. Students?? perceptions were assessed using a 40-item instrument that included 20 dynamics concept pairs at fundamental Level One and higher-order Level Two. Students?? problem-solving performance was assessed using four exams that included 66 dynamics problems. The coefficients of reliability (Cronbach??s ??) of assessment instruments vary between 0.69 and 0.93. The research findings from the present study show that students were not confident in their understanding of Level-Two concept pairs, especially the relationship between the Principle of Linear Impulse and Momentum and the Principle of Angular Impulse and Momentum, and the relationship between the Principle of Angular Impulse and Momentum and the Conservation of Angular Momentum. A statistically significant correlation exists between students?? perceptions of Level-Two concept pairs and their problem-solving performance on both particle dynamics (r?=?0.355, p?<?0.01) and rigid-body dynamics (r?=?0.351, p?<?0.01). The research findings made from the present study imply that educational efforts should be focused on improving students?? understanding of Level-Two dynamics concept pairs.     

Secondary Students’ Stable and Unstable Optics Conceptions Using Contextualized Questions

This study focuses on elucidating and explaining reasons for the stability of and interrelationships between students’ conceptions about Light Propagation and Visibility of Objects using contextualized questions across 3 years of secondary schooling from Years 7 to 9. In a large-scale quantitative study involving 1,233 Korean students and 1,149 Singaporean students, data were analyzed from responses to the Light Propagation Diagnostic Instrument consisting of four pairs of items, each of which evaluated the same concept in two different problem situations. Findings show that only about 10–45 % of students could apply their conceptions of basic optics in contextualized problem situations giving rise to both stable and unstable alternative conceptions. Students’ understanding of Light Propagation concepts compared with Visibility of Objects concepts was more stable in different problem situations. The concepts of Light Propagation and Visibility of Objects were only moderately correlated. School grade was not a strong predictive variable, but students’ school achievement correlated strongly with their conceptual understanding in optics. The teaching and learning approach and education systems in the two countries may have had some influence on students’ conceptual understanding.     

Empirical validation of a modern genetics progression web for college biology students

ABSTRACT

Research in learning progressions (LPs) has been essential towards building understanding of how students’ ideas change over time. There has been little work, however, into how ideas between separate but related constructs within a multi-faceted LP relate. The purpose of this paper is to elaborate on the idea of progression webs to model connections within and between related constructs simultaneously, and to explain and demonstrate the efficacy of path analysis towards validating a hypothesised progression web for understanding of modern genetics. Specifically, we evaluate strength of evidence for a progression web based upon multiple related constructs within a multi-faceted LP describing undergraduate biology students’ understanding of genetics. We then utilise the progression web to generalise theory around how undergraduate students understand relationships between related genetics concepts, and how they use simpler concepts to scaffold those which are more complex.     

Tools for Reflection: Video-Based Reflection Within a Preservice Community of Practice

Current reform in science education calls for teachers to understand student thinking within a lesson to effectively address students’ needs (NRC in A framework for K-12 science education: practices, crosscutting concepts, and core ideas. National Academy Press, Washington, DC, 2012; NRC in Guide to implementing the Next Generation Science Standards. The National Academies Press, Washington, DC, 2015). This study investigates how to scaffold preservice teachers with learning to attend to students’ thinking for the purpose of guiding curricular decisions. The study focuses on one team teaching a science unit during their early field experience. We sought to understand how participants’ thoughts and abilities changed through participation in a moderated community of practice using video of their own teaching as a reflective tool. We examined how these changes affected both their classroom practice and their decision-making for future lessons. Evidence shows growth in participants’ ability to identify opportunities to elicit, assess, and use students’ thinking to guide instructional decisions. Implications for use of the approach used in this study to begin developing novice teachers’ pedagogical content knowledge for teaching science are discussed.     

Making the invisible visible: enhancing students’ conceptual understanding by introducing representations of abstract objects in a simulation

This study aimed to identify if complementing representations of concrete objects with representations of abstract objects improves students’ conceptual understanding as they use a simulation to experiment in the domain of Light and Color. Moreover, we investigated whether students’ prior knowledge is a factor that must be considered in deciding when to use representations of abstract objects. A pre-post comparison study design was used, involving 69 participants assigned to two conditions. The first condition consisted of 36 students who had access to a simulation with representations of concrete objects, whereas the second condition consisted of 33 students who had access to a simulation with representations of both concrete and abstract objects. Both conditions used the same inquiry-oriented curriculum materials, consisting of three sections that included physical phenomena with increasingly complex underlying mechanisms, so that the third section’s mechanisms were more complex in nature than those in the first two sections. Tests were administered to assess students’ conceptual understanding before and after the presentation of the curricular material as a whole, as well as before and after each of its three sections. Results revealed that the presence of representations of abstract objects was helpful for the first two sections, but only for students with low prior knowledge. On the third, most complex section, also the students with higher prior knowledge profited from the presence of abstract objects. From these findings, we conjecture that for physical phenomena with a lower level of complexity, students with high prior knowledge are able to mentally construct the necessary abstract concepts on their own, whereas for higher levels of complexity they need an explicit representation of the abstract objects in the learning environment.     

A Technology‐Enhanced Unit of Modeling Static Electricity: Integrating scientific explanations and everyday observations

What trajectories do students follow as they connect their observations of electrostatic phenomena to atomic‐level visualizations? We designed an electrostatics unit, using the knowledge integration framework to help students link observations and scientific ideas. We analyze how learners integrate ideas about charges, charged particles, energy, and observable events. We compare learning enactments in a typical school and a magnet school in the USA. We use pre‐tests, post‐tests, embedded notes, and delayed post‐tests to capture the trajectories of students’ knowledge integration. We analyze how visualizations help students grapple with abstract electrostatics concepts such as induction. We find that overall students gain more sophisticated ideas. They can interpret dynamic, interactive visualizations, and connect charge‐ and particle‐based explanations to interpret observable events. Students continue to have difficulty in applying the energy‐based explanation.     

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.     

Planning Instruction to Meet the Intent of the Next Generation Science Standards

The National Research Council’s Framework for K-12 Science Education and the Next Generation Science Standards (NGSS Lead States in Next Generation Science Standards: For states, by states. The National Academies Press, Washington, 2013) move teaching away from covering many isolated facts to a focus on a smaller number of disciplinary core ideas (DCIs) and crosscutting concepts that can be used to explain phenomena and solve problems by engaging in science and engineering practices. The NGSS present standards as knowledge-in-use by expressing them as performance expectations (PEs) that integrate all three dimensions from the Framework for K-12 Science Education. This integration of core ideas, practices, and crosscutting concepts is referred to as three-dimensional learning (NRC in Division of Behavioral and Social Sciences and Education. The National Academies Press, Washington, 2014). PEs state what students can be assessed on at the end of grade level for K-5 and at the end of grade band for 6–8 and 9–12. PEs do not specify how instruction should be developed nor do they serve as objectives for individual lessons. To support students in developing proficiency in the PEs, the elements of the DCIs will need to be blended with various practices and crosscutting concepts. In this paper, we examine how to design instruction to support students in meeting a cluster or “bundle” of PEs and how to blend the three dimensions to develop lesson level PEs that can be used for guiding instruction. We provide a ten-step process and an example of that process that teachers and curriculum designers can use to design lessons that meet the intent of the Next Generation of Science Standards.     

Activity Structures and the Unfolding of Problem-Solving Actions in High-School Chemistry Classrooms

In this paper, we argue for a more systematic approach for studying the relationship between classroom practices and scientific practices—an approach that will likely better support the systemic reforms being promoted in the Next Generation Science Standards in the USA and similar efforts in other countries. One component of that approach is looking at how the nature of the activity structure may influence the relative alignment between classroom and scientific practices. To that end, we build on previously published research related to the practices utilized by five high-school chemistry teachers as they enacted problem-solving activities in which students were likely to generate proposals that were not aligned with normative scientific understandings. In that prior work, our analysis had emphasized micro-level features of the talk interactions and how they related to the way students’ ideas were explored; in the current paper, the analysis zooms out to consider the macro-level nature of the enactments associated with the activity structure of each lesson examined. Our data show that there were two general patterns to the activity structure across the 14 lessons scrutinized, and that each pattern had associated with it a constellation of features that impinged on the way the problem space was navigated. A key finding is that both activity structures (the expansive and the open) had features that aligned with scientific practices espoused in the Next Generation Science Standards—and both had features that were not aligned with those practices. We discuss the nature of these two structures, evidence of the relationship of each structure to key features of how the lessons unfolded, and the implications of these findings for both future research and the training of teachers.     

Increasing Student Accounting Self‐Efficacy,Interest, and Knowledge Using the DuPont Model

This research describes a DuPont Model activity used in an introduction to business course. An in‐class activity stimulated students’ confidence in their ability to apply the fundamental accounting principles building upon students’ knowledge of a lemonade stand. Accounting is often viewed by students in introductory courses as “a foreign language,” with common reactions by students of fear and anxiety about financial statements and financial ratios (Borja; Brazelton; Deer, Gohn, and Kanaya; Eber and Parker; and Goh and Scerri). The DuPont Model was developed to visually connect an income statement and the balance sheet to five common financial ratios. Using a preactivity and a postactivity questionnaire and 76 matched pairs of student responses, changes or differences in two student self‐efficacy measures were found. Over one‐half of these student pairs showed increases or improvements in these two self‐efficacy measures from preactivity to postactivity, implying that the DuPont Model positively influenced these self‐efficacy measures. Correlation analysis also showed meaningful, positive correlations among students’ self‐efficacy differences and their attitudes toward accounting. Furthermore, students’ perceived characteristics of the DuPont activity are significantly and positively correlated with students’ attitudes toward accounting. Finally, the results of the study are encouraging to the authors to continue using the DuPont Model activity.     

Promoting Shifts in Preservice Science Teachers’ Thinking through Teaching and Action Research in Informal Science Settings

The purpose of this study was to investigate the influence of an integrated experiential learning and action research project on preservice science teachers’ developing ideas about science teaching, learning, and action research itself. The qualitative, interpretive study examined the action research of 10 master’s degree students who were involved in service learning with children in informal education settings. Results indicated that all of the participants enhanced their knowledge of children as diverse learners and the importance of prior knowledge in science learning. In-depth case studies for three of the participants indicated that two developed deeper understandings of science learners and learning. However, one participant was resistant to learning and gained more limited understandings.     

Conceptual continuity and the science of baseball: using informal science literacy to promote students’ science learning

This project explores conceptual continuity as a framework for understanding students’ native ways of understanding and describing. Conceptual continuity suggests that the relationship between the use of words in one genre and the scientific genre can exist at varying levels of association. This perspective can reveal the varied relationships between ideas explained in everyday or vernacular genres and their association to scientific explanations. We conducted a 2-year study involving 15 high school baseball players’ understanding of the physics involved in baseball. First, we conducted a quantitative assessment of their science understanding by administering a test prior to season one (2006) and season two (2007). Second, we examined the types of linguistic resources students used to explain their understanding. Third, we revisited our data by using conceptual continuity to identify similarities between students’ conceptual understanding in the informal contexts and their similarities to canonical scientific ideas. The results indicated students’ performance on the multiple-choice questions suggested no significant improvement. The qualitative analyses revealed that students were able to accurately explain different components of the idea by using a diversity of scientific and non-scientific genres. These results call attention to the need to reconstruct our vision of science learning to include a more language sensitive approach to teaching and learning.     

Consistency of Students’ Ideas across Evaporation, Condensation, and Boiling

Existing research on students’ conceptions contain competing philosophical positions concerning the nature of students’ ideas—whether those ideas are coherent, systematic and theory-like, or fragmented and incoherent. Existing research has also focused primarily on studies of individual conceptions rather than investigating multiple, related conceptions. Nevertheless, there is wide agreement among researchers and teachers alike that the ideas students bring to a learning situation are fertile ground for investigation, and that students’ ideas should be taken into consideration when planning science instruction. The purpose of this study was to examine the representational, conceptual framework, and contextual consistency aspects of two students’ ideas across concepts of evaporation, condensation, and boiling. Knowing the consistency students express for each specific concept, and how well they integrate these related concepts, would offer insights that could potentially impact student learning. We present two case studies here that highlight the degree of consistency expressed by two students across different representations for each target concept and in instances where these conceptions are related to one another. Findings from this study highlight the need for attention to the consistency of students’ ideas across multiple, related concepts. Implications from this study support our recommendation for metaconceptual teaching strategies that would help students examine different representations for the same concept and also to examine the consistency of their ideas across multiple conceptions.