Remediating Computational Deficits at Third Grade: A Randomized Field Trial

Abstract

The major purposes of this study were to assess the efficacy of tutoring to remediate 3rd-grade computational deficits and to explore whether remediation is differentially efficacious depending on whether students experience mathematics difficulty alone or concomitantly with reading difficulty. At 2 sites, 127 students were stratified on mathematics difficulty status and randomly assigned to 4 conditions: word recognition (control) tutoring or 1 of 3 computation tutoring conditions: fact retrieval, procedural computation and computational estimation, and combined (fact retrieval + procedural computation and computational estimation). Results revealed that fact retrieval tutoring enhanced fact retrieval skill, and procedural computation and computational estimation tutoring (whether in isolation or combined with fact retrieval tutoring) enhanced computational estimation skill. Remediation was not differentially efficacious as a function of students' mathematics difficulty status.     

Factors contributing to success in mathematical estimation in preservice teachers: Types of problems and previous mathematical experience

Variables that may affect success in mathematical estimation in preservice elementary teachers were studied. A multiple regression analysis was performed in order to predict success on a 25 problem estimation test. Subjects' answer to the question, “Are you good at math?” was the best predictor of success on the estimation test. Other important variables were college grade point average, years of study of mathematics, and enjoyment of mathematics. Not only were average mathematics grades not related to estimation score, but they were negatively correlated to estimation score. Half the subjects saw problems in an applied format, and half saw the same problems in a computational format. The number of subjects answering problems correctly in the application format was significantly greater than the number of subjects answering questions correctly in the computational format. This result was contradictory to results usually found for finding exact answers with pencil and paper. A reason for greater success on problems in the application format may be related to the fact that the applied problems involved money, a very relevant type of problem in which to quickly estimate an answer.     

Personalized Verbal Problems: An Application of the Language Experience Approach

Abstract

Overall mathematics achievement is declining nationwide. One of the main weaknesses of students appears to be their solution of word problems. In this study an interest inventory was administered to 99 fourth-grade students. The investigators developed a computer program to utilize the results of the interest inventory to personalize a pool of problems previously selected by a panel of experts. Subjects were administered tests with standard textbook problems and personalized problems. The analysis of the results indicated that personalization improved performance in the selection of the correct process but was of little or no benefit in the computation of correct answers,     

Withholding answers during hands-on scientific investigations? Comparing effects on developing students’ scientific knowledge,reasoning, and application

As more concerns have been raised about withholding answers during science teaching, this article argues for a need to detach ‘withholding answers’ from ‘hands-on’ investigation tasks. The present study examined students’ learning of light-related content through three conditions: ‘hands-on’ + no ‘withholding’ (hands-on only: HO), ‘hands-on’ + ‘withholding’ (hands-on investigation with answers withheld: HOW), and no ‘hands-on’ + no ‘withholding’ (direction instruction: DI). Students were assessed in terms of how well they (1) knew the content taught in class; (2) reasoned with the learned content; and (3) applied the learned content to real-life situations. Nine classes of students at 4th and 5th grades, N?=?136 in total, were randomly assigned to one of the three conditions. ANCOVA results showed that students in the hands-on only condition reasoned significantly better than those in the other two conditions. Students in this condition also seemed to know the content fairly better although the advance was not significant. Students in all three conditions did not show a statistically significant difference in their ability to apply the learned content to real-life situations. The findings from this study provide important contributions regarding issues relating to withholding answers during guided scientific inquiry.     

Chinese number‐naming advantages? Analyses of Chinese pre‐schoolers' computational strategies and errors

Simplicity in number naming in a language (e.g. ‘ten‐two’ in Chinese is simpler than the irregular ‘twelve’ in English) has been used to explain cross‐cultural disparities in children's computational competence. In contrast to previous research focusing only on whether children can provide the correct answers, in this study (N?=?117 and 92) we examined Chinese pre‐schoolers' computational strategies in depth and individually so as to examine their understanding of the base‐10 system and place value. The results showed that despite the fact that many can give the correct answers, there is strong evidence that Chinese pre‐schoolers do not have adequate understanding of the base‐10 number system and place value, suggesting that the advantages of the simpler number‐naming system are limited.     

Using model-based scaffolds to support students solving context-based chemistry problems

ABSTRACT

Context-based learning aims to make learning more meaningful by raising meaningful problems. However, these types of problems often require reflection and thinking processes that are more complex and thus more difficult for students, putting high demands on students’ problem-solving capabilities. In this paper, students’ approaches when solving context-based chemistry problems and effects of systematic scaffolds are analysed based on the Model of Hierarchical Complexity. Most answers were initially assigned to the lowest level of the model; higher levels were reached without scaffolds only by few students and by most students with scaffolds. The results are discussed with regard to practical implications in terms of how teachers could make use of context-based tasks and aligned scaffolds to help students in this activity.     

Exploring doctorate holders’ perceptions of the non-academic labour market and reputational problems they relate to their employment

Doctoral employment outside universities has been increasing, as universities cannot employ all doctorate holders. Nevertheless, it has been argued that the shift from doctoral programs to the non-academic labour market has been limited. In this qualitative study, more than 800 verbal answers given by doctorate holders to a pair of open-ended questions were content-analysed to explore doctorate holders’ perceptions of the non-academic labour market and the reputational problems they relate to their employment. The study identifies four reputational problems which doctorate holders relate to their employment: the oversupply problem, the overeducation problem, the consistency problem and the communication problem. By identifying potential reputational problems on the doctorate holders level, this research contributes novel information in terms of both theory development and practitioner insights.

     

Maternal adverse childhood experiences,attachment style,and mental health: Pathways of transmission to child behavior problems

BackgroundInvestigations have found mothers’ adverse childhood experiences (ACEs) confer an intergenerational risk to their children's outcomes. However, mechanisms underlying this transmission have only been partially explained by maternal mental health. Adult attachment insecurity has been shown to mediate the association of ACEs and mental health outcomes, yet an extension of this research to children's behavioral problems has not been examined.ObjectiveTo examine the cascade from maternal ACEs to risk for child behavioral problems at five years of age, via mothers’ attachment insecurity and mental health.Participants and settingParticipants in the current study were 1994 mother-child dyads from a prospective longitudinal cohort collected from January 2011 to October 2014.MethodsMothers retrospectively reported their ACEs when children were 36 months of age. When children were 60 months of age, mothers completed measures of their attachment style, depression and anxiety symptoms, and their children's behavior problems.ResultsPath analysis demonstrated maternal ACEs were associated with children's internalizing problems indirectly via maternal attachment avoidance, attachment anxiety, and depression symptoms, but not directly (β = .05, 95% CI [−.001, .10]). Maternal ACEs indirectly predicted children's externalizing problems via maternal attachment avoidance, attachment anxiety, and depression. A direct effect was also observed from maternal ACEs to child externalizing problems (β = .06, 95% CI [.01, .11]).ConclusionsMaternal ACEs influenced children's risk for poor behavioral outcomes via direct and indirect intermediary pathways. Addressing maternal insecure attachment style and depression symptoms as intervention targets for mothers with histories of ACEs may help to mitigate the intergenerational transmission of risk.     

Exploring pre-service science teachers’ pedagogical capacity for formative assessment through analyses of student answers

Background: There has been an increasing emphasis on empowering pre-service and in-service science teachers to attend student reasoning and use formative assessments to guide student learning in recent years. Purpose: The purpose of this study was to explore pre-service science teachers’ pedagogical capacity for formative assessment. Sample: This study took place in Turkey. The participants include 53 pre-service science teachers in their final year of schooling. All but two of the participants are female. Design and methods: We used a mixed-methods methodology in pursing this inquiry. Participants analyzed 28 responses to seven two-tiered questions given by four students of different ability levels. We explored their ability to identify the strengths and weaknesses in students’ answers. We paid particular attention to the things that the pre-service science teachers noticed in students’ explanations, the types of inferences they made about students’ conceptual understanding, and the affordances of pedagogical decisions they made. Results: The results show that the majority of participants made an evaluative judgment (i.e. the answer is correct or incorrect) in their analyses of students’ answers. Similarly, the majority of the participants recognized the type of mistake that the students made. However, they failed to successfully elaborate on fallacies, limitations, or strengths in student reasoning. We also asked the participants to make pedagogical decisions related to what needs to be done next in order to help the students to achieve academic objectives. Results show that 8% of the recommended instructional strategies were of no affordance, 64% of low-affordance, and 28% were of high affordance in terms of helping students achieve the academic objectives. Conclusion: If our goal is to improve pre-service science teachers’ noticing skills, and the affordance of feedback that they provide, engaging them in activities that asks them to attend to students’ ideas and reasoning may be useful.     

Open-ended problem solving in school chemistry: A preliminary investigation

This paper uses a new set of 14 open-ended problems, designed for 14-17-year-old pupils studying chemistry, to attempt to gain some initial insights into the ways pupils solve open-ended chemistry problems. The emphasis is on how concepts and linkages between concepts influence success in solving such open-ended problems. Pupils worked in groups of three attempting to solve the problems and were encouraged to talk freely, to make notes of their progress, and to note their agreed answers. Evaluation sheets were also completed individually by the pupils after each problem. By studying the interactions between pupils by means of written materials, observation and audiotapes, it was possible to build up a picture of the way the pupils approached the problems and to explore some of the reasons for difficulties they experienced. In the light of the evidence, it is suggested that creating the links between 'islands' of knowledge is an important skill in solving open-ended problems and that this skill is not easily achieved by pupils at these ages. The notion that problem solving is a generic skill which can be taught is questioned.     

Character Making in the Brick Church Institute

The question Dr. Yoder asks in his title, and then answers in his paper, has been canvassed several times in Religious Education. Other answers than this one have been given, and by persons equally thoughtful and equally sincere. In coming issues of the Journal this year further answers will be given. Editor     

Addressing computational estimation in the Kuwaiti curriculum: teachers’ views

Computational estimation has not yet established a place in the Kuwaiti national curriculum. An attempt was made to include it during the early 1990s, but it was dropped by the Kuwaiti Ministry of Education because of the difficulties teachers had teaching it. In an effort to provide guidance for reintroducing the concept into the curriculum, this study reports on mathematics teachers’ understanding of the meaning of computational estimation and their views about its significance in the elementary and middle school curricula in Kuwait. Data gathered from 59 elementary and middle schools teachers in Kuwait revealed that more than 60% of teachers equate computational estimation with rounding. While two-thirds of the teachers viewed computational estimation to be an important skill for daily life; only one-fifth (20%) saw it as important in mathematics education. More than half of the teachers either disagreed with the idea of teaching computational estimation or only wanted to teach it in limited situations. Most were concerned about the difficulty of learning computational estimation or feared that teaching computational estimation would cause problems with students’ development of standard algorithms for determining an exact answer. These findings reveal the challenge that mathematics educators face in introducing computational estimation into the mathematics curriculum. In order for computational estimation to be taught in elementary and middle school classrooms, teachers need to understand the concept and its value in education. Teacher education needs to focus on helping teachers better understand the concept of computational estimation and appreciate its value for instruction.     

Key issues in educational policy for secondary schools in federated Belgium 1

Belgian educational policy for secondary schools was a national matter until 1989, although the polarized structure had already given rise to some decentralization. When educational policy became the responsibility of the Communities in 1989, it became clear that each Community would deal with their problems differently, even when confronting the same problems. The Communities did not abolish the influence of the polarized structure. Analysis of four key issues of educational policy in relation to secondary schools confirms the typical approach to the problems by each community. They gave different political answers to the problems of the protection of the position of teachers, of the quality of education, and local schools administration. Only the problem of the integration of immigrant children is being tackled similarly.

     

Generating multiple answers for a word problem with insufficient information

In mathematics learning, word problems always include sufficient information; however, in everyday situations, people sometimes encounter problems with insufficient information. Previous studies suggest that people cannot successfully handle word problems with insufficient information because they believe a word problem has only one answer and avoid considering multiple answers. The present study examined whether university students (n?=?98) can develop the skill to generate multiple answers for word problems with insufficient information. A new learning method, reduced insufficiency learning, was designed and tested to examine whether the participants can learn to generate multiple answers for a set of target problems (high level of insufficiency) after exposure to an exercise problem (low insufficiency level). Results of this study suggest that people can develop the skill to handle insufficient problems with higher levels of insufficiency by means of reduced insufficiency learning.     

Interactive Learning Using Expert System Quizzes on the Internet

Abstracts

English: HTML and JavaScript web pages interactively pose questions at random with multiple choice answers. Questions are ranked for difficulty based on prior student tests. During a quiz, the system tracks the percentage of correct answers and adjusts the difficulty of questions appropriately. A compiled BASIC program allows teachers to make specialized web quizzes from text files of questions and answers, without needing to know HTML, JavaScript and BASIC programming languages.     

EXAMINING EIGHTH GRADE KUWAITI STUDENTS’ RECOGNITION AND INTERPRETATION OF REASONABLE ANSWERS

This research documents Kuwaiti eighth grade students’ performance in recognizing reasonable answers and the strategies they used to determine reasonableness. The results from over 200 eighth grade students show they were generally unable to recognize reasonable answers. Students’ performance was consistently low across all three number domains (whole numbers, fractions, and decimals). There was no significant difference in students’ performance on items that focused on the practicality of the answers or on items that focused on the relationships of numbers and the effect of operations, or on both. Interview data revealed that 35% of the students’ strategies were derived from two criteria for judging answers for reasonableness: the relationships of numbers and the effect of operations, and the practicality of the answers. They used strategies such as estimation, numerical benchmarks, real-world benchmarks, and applied their understanding of the meaning of operations. However, over 60% of the students’ strategies were procedurally driven. That is, they relied on algorithmic techniques such as carrying out paper-and-pencil procedures. Additionally, some of the students’ strategies reflected misunderstandings of how and when to apply certain procedures. Given these findings, mathematics education in Kuwait should shift the emphasis from paper-and-pencil procedures and provide systematic attention to the development of number sense and computational estimation so Kuwaiti students will be more adept at recognizing reasonable answers.     

Modeling teachers’ reactions to unexpectedness

BackgroundEven experienced teachers make inconsistent classroom decisions in unexpected situations. From the cognitive load theory perspective, the effective handling of the novel, unexpected events by teachers depends on the cognitive load of the task, the teaching context in which the unexpectedness appears, and the available cognitive capacity.AimsTeachers’ reactions to unexpected mathematical events, in particular the unexpectedness of the arithmetic calculation, was modeled, investigated experimentally, and explained within the theoretical framework of cognitive load theory.Sample64 mathematics teacher trainees took part in the experiment.MethodsIn a dual-task arrangement, participants verified alternative answers to simple mathematical questions while memorizing task-irrelevant information. The answers represented low (schematic good responses), and high (unexpected good responses) processing load conditions, and control condition (incorrect responses). The memory load was low or high representing levels of extraneous load. The participants’ cognitive capacity was estimated by a complex working memory span task.ResultsThe verification of unexpected but correct answers was slow and more error-prone as compared with the processing speed and accuracy of schematic answers, presumably due to elevated processing (intrinsic) load. The increase in memory load resulted in slower and more inaccurate verifications. However, working memory capacity was found to mediate the extraneous load effect.ConclusionsThe results stress the importance of well-organized schemas for effective reactions to unexpected classroom events. Furthermore, it highlights the importance of accurately understanding and being aware of the impact of cognitive load on teachers to improve teaching practice.     

Assessing students’ understanding about levers: better test instruments are not enough

This study was designed to investigate variations in students’ responses to lever problems across multiple assessment contexts and formats. Prior to and at the end of a four‐month science unit on simple machines, grade 6/7 students prepared semantic maps, wrote responses to application questions, discussed their written answers, and modelled solutions to practical problems using physical materials. We present data from pre‐ and post‐instruction interviews to show that students’ responses varied in kind and extent across assessment contexts and formats. Such variations in performance are consistent with situated cognition theories which assert that competence is heterogeneous across situations and is a function of interactions between individuals and the contexts in which they perform. Based on these findings, implications are drawn regarding more productive means of assessing students’ understanding in classrooms.     

Exploring student study behaviours in engineering: how undergraduates prepared textbook problems for online submission

ABSTRACT

While textbooks serve as a primary source of content material and problem-solving practice for undergraduates in engineering, studies that investigate how engineering students prepare assignments based on textbook problems are limited. To examine how engineering students complete textbook-based assignments outside of class, this exploratory qualitative study retrospectively investigated the study behaviours of six undergraduates enrolled in a required, second-year undergraduate engineering course at a mid-size, public university in the western United States. Within the course, students solved textbook problems and electronically submitted problem answers for graded credit. Findings from in-depth, semi-structured interviews showed that students identified and used a variety of non-traditional and unsupported resources in personalised approaches to preparing assignments. Resource choice and use was affected by students’ preferences for timely support, convenience, and social connections. The online submission process seemed to influence students’ adoption of study behaviours and resources considered less effective for deep, conceptual learning.     

Measurement of College Level Reading Competence in A Content Area

Abstract

The effects of overt verbalization anti practice on problem solving ability were examined. The 100 secondary school students who served as Ss were divided into four groups: (1) those who received practice word problems and solved problems while thinking aloud, (2) those who did not practice but solved problems while thinking aloud, (3) those who practiced but did not verbalize, and (4) those who received no practice and did not verbalize. Analysis of variance revealed that neither overt verbalization nor practice significantly influenced problem solving scores. However, Ss who were required to think aloud made significantly more computational errors than those who worked without verbalizing.