Pizzas or no pizzas: An advantage of word problems in fraction arithmetic?

Fractions are an important but notoriously difficult domain in mathematics education. Situating fraction arithmetic problems in a realistic setting might help students overcome their difficulties by making fraction arithmetic less abstract. The current study therefore investigated to what extent students (106 sixth graders, 187 seventh graders, and 192 eighth graders) perform better on fraction arithmetic problems presented as word problems compared to these problems presented symbolically. Results showed that in multiplication of a fraction with a whole number and in all types of fraction division, word problems were easier than their symbolic counterparts. However, in addition, subtraction, and multiplication of two fractions, symbolic problems were easier. There were no performance differences by students’ grade, but higher conceptual fraction knowledge was associated with higher fraction arithmetic performance. Taken together this study showed that situating fraction arithmetic in a realistic setting may support or hinder performance, dependent on the problem demands.     

Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth graders (12-year-olds) use shortcut strategies in solving multidigit addition, subtraction, multiplication, and division problems, to what extent student factors and task instructions affected this frequency of shortcut strategy use, and to what extent the strategies differed in performance. A sample of 648 sixth graders from 23 Dutch primary schools completed a paper-and-pencil task of 12 multidigit arithmetic problems, designed to elicit specific shortcut strategies such as compensation. Based on the students’ written work, strategies were classified into whether a shortcut strategy was used or not. Results showed that the frequency of shortcut strategies ranged between 6 and 21% across problem types, and that boys and high mathematics achievers were more inclined to use shortcut strategies. An explicit instruction to look for a shortcut strategy increased the frequency of these strategies in the addition and multiplication problems, but not in the subtraction and division problems. Finally, the use of shortcut strategies did not yield higher performance than using standard strategies. All in all, spontaneous as well as stimulated use of shortcut strategies by Dutch sixth graders was not very common.     

Misconceptions about Motion: Development and Training Effects

2 experiments were performed to examine whether children and adults possess a single-object/single-motion intuition. This intuition involves the view that because all parts of a rigid object move together, they all must move at the same speed. We found that third graders, sixth graders, ninth graders, and adults all responded in accord with this intuition. On problems where the intuition led to errors, a large majority of subjects of all ages answered incorrectly. On problems where it led to successful performance, subjects answered more accurately than on problems where the intuition was not applicable. In addition, the specific errors were those that the intuition yielded, and the intuition fit individual patterns of performance. The intuition not only influenced speed judgments but also judgments of distance traveled. Experiment 2 demonstrated that making sixth graders aware of the intuition and providing them kinesthetic experience that contradicted it produced significant improvements in the children's understanding. Implications for how scientific misconceptions in general can be overcome were discussed.     

Learning from analogy-enhanced science text

The present study examined the role that an elaborate analogy can play when middle school students learn a major concept from a science text. The elaborate analogy had both graphic and text components that integrated and mapped key features from an analog (a factory) to the target concept (an animal cell). The target features were the functions of the cell parts. In Experiment 1, eighth graders who studied an analogy-enhanced text had greater immediate and 2-week recall of cell-part functions than students who studied a control text. In Experiment 2, sixth graders who studied an analogy-enhanced text considered the target concept to be more understandable than students who studied a control text. The sixth graders who studied the analogy-enhanced text also had greater immediate and 2-week retention, as measured by both recall and recognition. In both experiments, the analogy was interpreted as acting as a mediator between the students' existing knowledge and the new knowledge in the text. The analogy mapped a familiar, concrete schema onto that of the target concept, making the target concept more understandable and memorable. Implications for the meaningful learning of science text are discussed. © 1998 John Wiley & Sons, Inc. J Res Sci Teach 35: 1129–1149, 1998.     

Early learning and awareness of division: A phenomenographic approach

Interviews with 72 pupils in grade 2–6 were used to investigate awareness of the relation between situation and computation in simple quotitive and partitive division problems as informally and formally experienced. The research approach was phenomenographic. Most second graders counted or made drawings, and related these methods to the situation described in the problems. Several of the older children, on the contrary, experienced a conflict between computation and situation in partitive division. Most second graders, but also some third, fourth and sixth graders, could still not carry out repeated addition, the precursor of multiplication. The data are finally viewed from two theoretical perspectives other than phenomenography. It was concluded that formal division, understood as related to everyday situations, only develops in interplay with informal knowledge.This revised version was published online in September 2005 with corrections to the Cover Date.     

The Relative Merits of Explicit and Implicit Learning of Contrasted Algebra Principles

Knowledge representations that result from practicing problem solving can be expected to differ from knowledge representations that emerge from explicit verbalizing of principles and rules. We examined the degree to which the two types of learning improve problem-solving knowledge and verbal explanation knowledge in classroom instruction. We presented algebraic addition and multiplication problems to 153 sixth graders randomly assigned to two conditions. Students in the explicit learning condition had to verbally compare contrasted algebra problems. Students in the implicit learning condition had to generate and solve new problems. On three follow-up tests over 10 weeks, students in the explicit learning condition exhibited better problem-solving knowledge than students in the implicit learning condition, as well as some advantages in verbal concept knowledge. Implicit learning showed some advantages on not directly taught but incidentally learned aspects. Overall, this outcome favors the explicit learning of concepts. Explicit comparison fostered student performance on non-verbal and verbal measures, indicating that verbalization facilitates effective comparison.     

To Me It’s Like Having a Kid,Kind Of: Analysis of Student Reflections in a Developmental Mentoring Program

This qualitative longitudinal study focuses on analyses of journals written by 31 sixth grade students who participated in the Chapel Buddy program. The Chapel Buddy program is a developmental mentoring program that pairs sixth graders with kindergarten students. Mentors responded to guided writing prompts three times during the course of the year. Prompts were designed to encourage mentors to explore their role as mentors and their understanding of the mentor–mentee relationship. Results indicated that the program presented a rich, experiential learning opportunity for the sixth graders to develop a relationship with a younger child, to reflect on what it means to be in a helping relationship, and to examine their experiences as “big kids.” Sixth graders varied in their ability to successfully engage and manage their kindergarten mentees, which in turn meaningfully affected the mentors’ satisfaction. Strategies to maximize the educational value of developmental mentoring programs with younger mentors are discussed.     

Experimental Effects of Word Generation on Vocabulary,Academic Language,Perspective Taking,and Reading Comprehension in High-Poverty Schools

Abstract

With a sample of 7,752 fourth- to seventh-grade students in 25 schools which were randomized at the school level to condition, this article reports experimental impacts of an enhanced version of Word Generation on student outcomes at the end of Year 1 and of Year 2. Word Generation employs analysis, synthesis, critique, and problem-solving activities to build students’ academic language, perspective taking, and ultimately their reading comprehension. Results indicate that the program improves the proximate outcome of academic vocabulary included in the curriculum after the first and second year of implementation for all students (Y1 effect size (ES)?=?.22, Y2?=?.28 for fourth and fifth graders; Y1 ES?=?.13, Y2?=?.16 for sixth and seventh graders). For those in the fourth and fifth grades, their perspective positioning skills also improved at the end of the first year (ES?=?.14), and their academic language skills (ES?=?.06), perspective articulation and positioning skills (ES?=?.12, .19), and reading comprehension (ES?=?.15) improved at the end of the second year. Among sixth and seventh graders, there were improvements in perspective positioning skills (ES?=?.19) and reading comprehension (ES?=?.10) at the end of Year 2. Effects after both Years 1 and 2 were stronger in high-exposure classrooms.     

Using Self-Generated Drawings to Solve Arithmetic Word Problems

Abstract

In this article, two intervention studies are described that were set up to investigate whether encouraging elementary students to generate drawings of arithmetic word problems facilitates problem-solving performance. The interventions consisted of 60 to 90 min of practice and showed the usefulness of self-generated drawings for solving word problems. The subjects in the first study were first and second graders, and in the second study, fifth graders. The results indicated that the fifth graders improved problem solutions after the intervention, whereas the first and second graders did not. Unlike the first and second graders, the fifth graders generated lots of drawings of word problems. The findings suggest that the nature of the difficulties children experience when solving arithmetic word problems influences their decision to generate drawings.     

Developing and evaluating a strategy for learning from animations

Based on current theories of multimedia learning, we propose a strategy for learning from animations. Two different experimental studies were conducted in order to evaluate the strategy. In the first study, 22 sixth graders learned from an animation without the strategy while 21 students were encouraged to make use of the proposed strategy during learning; use of the strategy was not monitored. The students who were encouraged to take advantage of the strategy learned significantly more than the students who were not asked to do so. In the second study, three groups of sixth graders were investigated. The first group consisted of 49 students who learned from an animation without the strategy. The second group consisted of 52 students who were encouraged to make use of the strategy during learning; but use of the strategy was not monitored. The third group consisted of 53 students who were also encouraged to make use of the strategy during learning and their use of the strategy was monitored. The results of the second study replicated the findings of the first study. Furthermore, learning was most successful when the students' use of the learning strategy was monitored.     

No Difference in the Neural Underpinnings of Number and Letter Copying in Children: Bayesian Analysis of Functional Near‐Infrared Spectroscopy Data

It is under debate whether the neural representation of numbers and letters might rely on distinct neural correlates, or on a mostly shared neural network. In the present study, a total of 47 children in fifth grade (Experiment 1) and sixth grade (Experiment 2) simply copied numbers and letters on a touch screen while brain activation changes were recorded by means of functional near‐infrared spectroscopy (fNIRS). fNIRS data of both experiments and a joint analysis revealed that a shared neural network, particularly in the left hemisphere, was activated in response to both number and letter copying. Interestingly, no difference was observed in brain activation patterns between these two stimuli, as revealed by Bayesian analysis. Our findings indicate that both number and letter copying lead to similar brain activation in children. We further suggest methodological and applied applications of these findings in the frame of educational neuroscience.     

Developing Sixth Graders’ Inquiry Skills to Construct Explanations in Inquiry‐based Learning Environments

The purpose of this study is to investigate how sixth graders develop inquiry skills to construct explanations in an inquiry‐based learning environment. We designed a series of inquiry‐based learning activities and identified four inquiry skills that are relevant to students’ construction of explanation. These skills include skills to identify causal relationships, to describe the reasoning process, to use data as evidence, and to evaluate explanations. Multiple sources of data (e.g., video recordings of learning activities, interviews, students’ artifacts, and pre/post tests) were collected from two science classes with 58 sixth graders. The statistical results show that overall the students’ inquiry skills were significantly improved after they participated in the series of the learning activities. Yet the level of competency in these skills varied. While students made significant progress in identifying causal relationships, describing the reasoning process, and using data as evidence, they showed slight improvement in evaluating explanations. Additionally, the analyses suggest that phases of inquiry provide different kinds of learning opportunities and interact with students’ development of inquiry skills.     

Fostering students’ evaluation behaviour while searching the internet

A program for teaching 9th graders course content (history) and how they should evaluate information found on the WWW was designed and tested. Goal of the program was to teach content, evaluations skills, and to achieve transfer of these skills to a different domain. In the design of the program the principles of two transfer theories were combined using a design-based research approach. Results revealed that the program improved students’ evaluation behaviour. Compared to the students of the control condition, the evaluation skills of students in the experimental condition improved to a higher level, but did not lead to transfer. Students in the experimental classes scored higher on the final content exam than students in the control class.     

Learning to Make Good Decisions: A Self-Regulation Perspective

Two studies were conducted to determine the extent to which feedback could improve the decision-making of adolescents and adults. In Experiment 1, 96 eighth graders and adults engaged in a task that required a choice between easy and hard questions. Two types of feedback (i.e., verbal and outcome) were used to help participants identify the type of question that would be most likely to earn them points. Results showed that (1) neither group benefited from verbal feedback, and (2) adults benefited more from outcome feedback than eighth graders. In Experiment 2, two types of feedback were once again employed in the context of a medical decision-making task. Fifty-five adults and adolescents participated. As was found in Experiment 1, adults seemed to benefit more from feedback than adolescents. In addition, intelligence was unrelated to performance. The results are interpreted within the perspective of a self-regulation model of decision-making.     

The impact of preprimary school on primary school achievement in Bangladesh

Evidence was collected regarding changes over 3 years in the quality of a preprimary program in rural Bangladesh and differences in school achievement of children who did and did not attend. The quality of 30 preprimary schools was evaluated using the ECERS-R (Early Childhood Environment Rating Scale - Revised) and ECERS-E (- Extension). Results indicated that the quality improved overall from 3.50 in 2006 to 5.24 in 2008. Samples of 180 graduates of these schools were annually followed into first and second grades and tested for five competencies: speaking, writing, reading, oral mathematics and written mathematics. Their achievement scores were compared with students in their classrooms and students in neighboring schools who did not have the opportunity to attend preprimary schools. First graders in 2008 performed significantly better than comparisons in all competencies, and better than earlier graduates. Second graders performed significantly better than comparisons on all but Reading. Qualities of the math preprimary program correlated with math achievement in Grade 1 only. Consequently the quality of the preprimary program improved over time along with higher achievement for its graduates. The findings support efforts to expand high-quality programs in developing countries to help children succeed in the early primary grades.     

Acquiring meaning for decimal fraction symbols: A one year follow-up

Fourth graders with differing achievement records participated in a specially designed two week unit on decimal fractions. Students were encouraged to connect meaningful referents with decimal fraction symbols and use these meanings to develop procedures for adding and subtracting decimal numbers. One year later these students and a matched set of fifth graders were interviewed and given paper-and-pencil tests. Three questions were of interest: (1) Do short term changes in the processes students use to solve problems remain stable over time; (2) Do students who have been instructed in conceptually-based processes exhibit a higher level of performance one year later than their conventionally taught peers; and (3) What is the relationship between entry achievement level and the year-long effects of conceptually-based instruction? The results suggest that: (1) If students used the meanings of written symbols as a basis for solving problems immediately after instruction, they used these processes to solve problems one year later, regardless of entering achievement; (2) Compared to their conventionally taught peers, students in the lower achievement group benefitted relatively more from the conceptually-based instruction than students in the higher achievement group; (3) However, higher achieving students were more likely to exhibit use of conceptually-oriented processes one year later than the lower achieving students.     

Student-Created Digital Media and Engagement in Middle School History

In this study, student engagement during classroom activities was investigated where sixth graders created digital media projects using historical images. The study employed a qualitative design involving observations, student artifacts, and interviews while students were creating digital storyboards using a Web-based application developed for this research. Several patterns of student engagement were identified, such as time on task, level of detail, and extra effort, which subsequently led to the development of four distinct profiles among the students. Applications of these findings and directions for future studies are discussed.     

Monitoring learning-disabled students in mainstream science classes

While science classes are believed to be interactive learning environments, offering varied ways for students to learn, some experts believe that learning disabled (LD) students should be monitored closely in such settings because of difficulties adjusting to the social, behavioral, and academic demands. The purpose of this paper is to determine whether LD fourth and sixth graders show difficulties adjusting to the demands of their mainstream science classes and to investigate two means of assessing LD students’ functioning in these classes: paired questionnaires for teachers and students and a science curriculum-based assessment (CBA). Subjects include 31 fourth graders (9 LD) and 38 sixth graders (13 LD). Results show that the LD students had significant weaknesses on some subtests of the science CBA relative to their peers; additionally, they rated themselves and were rated by their teachers significantly more negatively than their Non-LD peers. These results suggest the potential value of monitoring LD students in mainstream science classes. Case studies of LD students reveal mismatches in the perception of the student and teacher regarding the student’s adjustment and classroom habits. Examination of these case studies is used to suggest ways in which the collaboration of student and teacher as well as regular and special education teachers might aid the student.     

The Efficacy of Using Diagrams When Solving Probability Word Problems in College

Previous experiments have shown a deleterious effect of visual representations on college students’ ability to solve total- and joint-probability word problems. The present experiments used conditional-probability problems, known to be more difficult than total- and joint-probability problems. The diagram group was instructed in how to use tree diagrams to solve conditional probability problems; the equation-only group was instructed only in the formulation of equations. Results indicated that the diagram group outperformed the equation-only group on a posttest of 10 near- and far-transfer problems given immediately and as long as 1 week later (Experiment 2). In addition, when rating their experience with the training phase the equation-only group reported significantly higher levels of frustration and lower levels of perceived success than the diagram group.