The Effects of Verbal Mediation Training on the Problem‐Solving Skills of Children with Partial Sight and Children without Visual Impairments

Thirty children with partial sight and 30 children with unimpaired sight aged between 8 and 12 years were randomly assigned to either verbal mediation or visual mediation training regimes. Participants were asked to complete four variations of the Tower of Hanoi puzzle and success on the task was judged on the basis of the number of moves and time taken to complete the puzzles. Children with visual impairments had some difficulty in adjusting to the requirements of the problem‐solving tasks. However, on the final and most difficult of the tasks (a four‐disc problem), the children with impaired sight performed very much like participants without visual impairments. The effect of verbal mediation training was superior to that of visual mediation training in the final trials of the four‐disc problem‐solving period for both children with partial sight and children without visual impairments.     

The effects of verbal scaffolding instruction on young children's private speech and problem-solving capabilities

This investigation examined the efficacy of a verbal scaffolding instructional program designed to teach young children how to use private speech while working on school tasks and problems. Two different contexts for solving problems were used; common school tasks and analogical reasoning problems. Thirty-four 5-year olds who attended public school kindergartens were assigned to either the comparison group or the treatment group. Comparison group subjects were presented with a series of 8 lessons which focused on a cognitive strategy to be used in the solutions of geometric analogy problems. Treatment group subjects were presented with a series of 8 lessons which employed cognitive self-instruction in a verbal scaffolding format. After initial instruction using self-verbalizations, treatment group subjects were shown how to apply the cognitive self-instruction to routine school tasks and geometric analogy problems. The data analysis revealed that there was an effect on the treatment group's use of 3 of the 4 levels of private speech. When the two groups were compared, the treatment group used significantly less task irrelevant private speech and significantly more task relevant private speech. There were no significant differences between the two groups on the post-assessment of geometric analogy reasoning. Additionally, when the two groups were compared there were positive effects of the instructional program on the treatment group's classroom behavior (near transfer) and locus of control scores (far transfer). The results of this study provide support for the use of cognitive self-instruction to improve young children's problem-solving private speech in the context of a public school classroom.Portions of this paper were presented at the 2nd Annual European Congress of Psychology, Budapest Hungary, July 1991 by the first author.This paper was presented at the 1993 annual meeting of the American Educational Research Association, Atlanta, GA.     

Conceptual Gain and Successful Problem-solving in Primary School Mathematics

This study investigated the effects of children solving addition and subtraction problems collaboratively in comparison with solving problems in the traditional manner of the classroom. Seventy-seven children were divided into experimental and control groups, the experimental children being assigned to groups of four with note taken of the ability and gender mix. Following a pre-test-intervention-post-test design, the experimental children worked together in their groups using problem-solving guidelines to solve a number of problems, thereafter 'teaching' their problem to a fellow pupil. Each child worked on six problems over a 3-week period, three of the problems in their groups subsequently teaching them to another, the other three problems being taught to them by another child. Over the same time period, the control group solved the same problems working individually at their desks. The pre- and post-tests were analysed for number of problems correct or 'score', problemsolving strategy and execution of procedures, with pre-test scores being subtracted from post-test scores to give measures of change. The results indicated a main effect of ability on strategy change and a two-way interaction between gender and condition. They also indicated a main effect of condition for execution of procedures. Dialogue analyses indicated that more below average children improved their strategy understanding by listening to peers. The results themselves revealed variations in the way that children of different ability levels and gender can benefit from collaborative group work and thus have some interesting implications for the organisation of collaborative groups in the classroom.     

Computer-aided self-instruction training with hearing-impaired impulsive students

This study explored the utility of computer-aided, self-instruction training for enhancing reflective problem-solving among impulsive hearing-impaired adolescent students. Sixteen moderate to severely hearing-impaired students were randomly assigned to either a treatment or control condition. The self-instruction treatment condition consisted of training to solve visual problems using a modified version of the LOGO computer language (REFLECT) and videotape feedback. The control condition consisted of LOGO problem-solving without self-instruction. Instruction took place over 12 weeks. On two dependent measures of impulsive problem-solving behaviors, students in the treatment condition demonstrated significantly improved problem-solving ability.     

Effectiveness of the MASTER program for teaching special children multiplication and division

In this study, the utility of a MAthematics Strategy Training for Educational Remediation (MASTER) program, (Van Luit, Kaskens, & Van der Krol, 1993) was examined. The effectiveness of the program, designed to encourage strategy utilization with multiplication and division problems, was investigated for 84 students with poor mathematics skills, some of whom had learning disabilities (n = 42) and others with mild levels of mental retardation (n = 42). The results showed that the use of the self-instruction program resulted in significant improvement over the general instruction program. Furthermore, far transfer was found for the children with learning disabilities in the experimental group when they used effective problem-solving strategies on nontrained tasks. The results are consistent with previous findings suggesting the importance of self-instruction in mathematics training programs.     

大班幼儿加减运算能力的发展特点——以武汉市8所幼儿园为例

选取武汉市8所幼儿园112名大班幼儿作为被试,对幼儿加减运算能力进行测试。结果发现:(1)幼儿笔算、口算、解答应用题和自编应用题四种能力之间均显著相关,解答应用题和自编应用题的能力低于笔算和口算能力。(2)幼儿解答应用题能力的发展有显著的性别差异,男孩的能力优于女孩。(3)省示范园和市示范园幼儿的加减运算能力发展优于私立园幼儿。     

Special education students’ use of indirect addition in solving subtraction problems up to 100—A proof of the didactical potential of an ignored procedure

In this study, we examined special education students’ use of indirect addition (subtraction by adding on) for solving two-digit subtraction problems. Fifty-six students (8- to 12-year-olds), with a mathematical level of end grade 2, participated in the study. They were given a computer-based test on subtraction with different types of problems. Although most students had not been taught indirect addition for solving subtraction problems, they frequently applied this procedure spontaneously. The item characteristics were the main prompt for using indirect addition. Context problems that reflect an adding-on situation and problems that have a small difference between the minuend and subtrahend most strongly elicited the use of the indirect addition procedure. Moreover, indirect addition was identified as a highly successful procedure for special education students, and the best predictor of a correct answer was found in combination with a stringing strategy.     

Teaching Kindergarten Children to Solve Word Problems

A kindergarten teacher's practice was investigated in order to understand her knowledge of her children's mathematical thinking, the ways in which she acquired that knowledge, and the uses she made of that knowledge in making instructional decisions. The focus of the investigation was the teacher's knowledge of her children's thinking about numbers, including counting and addition, subtraction, multiplication, and division. The teacher had attended Cognitively Guided Instruction workshops at which she had the opportunity to learn about research on children's mathematical thinking. She gathered information on her own children's thinking by posing word problems, listening to children as the described their strategies for solving the problems, and talking to other adults about her children. She used that information to select problems to pose in subsequent lessons.     

The effect of instruction on children's solutions of addition and subtraction word problems

This study investigated the effect of initial instruction on the processes children use to solve addition and subtraction word problems. Prior to instruction and following a two-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different addition and subtraction situations. Prior to instruction, the children's solution processes directly modeled the action or relationships described in the problem. Following instruction, they generally used a separating strategy for all subtraction problems. Although they could solve the problems, few children could coordinate their solutions with the arithmetic sentence they wrote to represent the problem.     

Teaching and development: Solving “missing addend” problems using subtraction

The study presented here will examine the connection between teaching and development, focusing in particular on how children solve “missing addend” story problems. Vygotsky’s theory of development will serve as the framework. Ordinarily, when second graders are forced to solve a problem of this type by choosing an arithmetic operation (+ or ?), half of them fail. The most frequent error is choosing addition. The subjects in the experiment presented here were second graders who had always been given the opportunity to use objects or drawings to “act out” (model) the actions expressed in the problem statament. They had never been in the above “forced-choice” situation. Moreover, they had been taught to use a “forward strategy” to solve subtraction problems like 42–36 (to get from 36 to 40, it takes 4; and then to get to 42, it takes 2 more) and a “backward strategy” for subtraction problems like 42–6. When given the following missing-addend problem: “Pierre has 63 pieces of candy and paul has 4. Paul wants to have the same number of pieces as Pierre. How many pieces of candy must Paul buy?” none of these children performed an addition, approximately half did a subtraction, and the others succeeded by using a breakdown strategy or a drawing. The overall success rate was 92%. The results obtained suggest a way of operationalizing the notion of “zone of proximal development” for problem solving of this type.     

Manipulatives and number sentences in computer aided arithmetic word problem solving

In this study we investigated the relative contribution of two main components often used in the instruction of arithmetic word problem solving to first-grade children and children with learning problems, external representation with manipulatives and formal mathematical representation with number sentences. Four computer aided treatments were developed along these dimensions. Furthermore, an assessment control group was formed.It was shown that performance improved significantly after treatment in comparison to the performance of the assessment control group. Comparison of the different training conditions showed that a number sentence treatment was the most effective training component. However, this effect was only present with the relatively high competent children and not with the relatively low performing children.     

Une introduction non classique aux algorithmes d'addition et de soustraction

The aim of our study was to analyze a didactical sequence for the teaching of addition and subtraction procedures and algorithms. In the conception of that sequence, we have taken into account diagnostic and repair models for procedural bugs in addition and subtraction algorithms, as well as learning and teaching methods for multi digit additions and subtractions. The didactical sequence included situations involving many of the characteristics associated with procedural bugs; however, when the children encountered those situations they had many conceptual tools to detect their mistakes and correct them, giving that way a meaning to the actions made in addition and subtraction procedures and algorithms. Our teaching activities were submitted to second grade school children (7–8 years old). The didactical interactions and the procedures used by children in problem solving activities were analyzed in order to get a better understanding of the interaction between numbers, numeration and operations knowledge which are involved in the construction of addition and subtraction procedures and algorithms and to relate children's knowledge acquisition to the didactical situations. This revised version was published online in July 2006 with corrections to the Cover Date.     

数学建模对学生综合素质的影响分析

本文从建模及竞赛分析数学建模在学生素质培养中所起的作用,对学生解决实际问题的能力的影响,阐述了数学建模训练是人们解决实际问题必要的训练和准备的观点,说明数学建模对学生的影响是质变的过程,参加过建模训练的学生必定是“终生难忘,终生受益”。     

Fourth graders’ adaptive strategy use in solving multidigit subtraction problems

Using the choice/no-choice methodology we investigated Dutch fourth graders’ (N = 124) adaptive use of the indirect addition strategy to solve subtraction problems. Children solved multidigit subtraction problems in one choice condition, in which they were free to choose between direct subtraction and indirect addition, and in two no-choice conditions, in which they had to use either direct subtraction or indirect addition. Furthermore, children were randomly assigned to mental computation, written computation, or free choice between mental and written computation. One third of the children adaptively switched their strategy according to the number characteristics of the problems, whereas the remaining children consistently used the same strategy. The likelihood to adaptively switch strategies decreased when written computation was allowed or required, compared to mandatory mental computation. On average, children were adaptive to their own speed differences but not to the accuracy differences between the strategies.     

The role of the working memory and language skills in the prediction of word problem solving in 4- to 7-year-old children

The aim of this study was to analyse the role of verbal and visuo-spatial working memory (WM) and language skills (vocabulary, listening comprehension) in predicting preschool and kindergarten-aged children’s ability to solve mathematical word problems presented orally. The participants were 116 Finnish-speaking children aged 4–7?years. The results showed that verbal WM (VWM) did not have a direct effect on word problems in young children but was indirectly related to word problems through vocabulary and listening comprehension. These results suggest that in young children, VWM resources support language skills which, furthermore, contribute to variation in solving orally presented word problems. The results also showed that visuo-spatial WM had a direct effect on performance in word problems, suggesting that it plays an important role in word problem solving among this age group.     

Self-instruction training: A potential tool for school psychologists

Self-instruction training is a cognitive-behavioral approach to self-control in which children are taught to use covert speech to modify their own behavior. The potential effectiveness of self-instruction training as an intervention technique for school psychologists to enhance student academic and/or social behavior in the classroom is the focus of this review. Research results addressing the practical issues of how, when, and with whom to use this strategy, its generalizability, and its long-term and comparative effectiveness are presented. Implications for further research in the schools are discussed.     

Teaching children how to include the inversion principle in their reasoning about quantitative relations

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research on improving children’s understanding and use of the principle of inversion through interventions has only been applied to the solving of a + b − b = ? sums. The main aim of the intervention described in this article was to study the effects of teaching children about the explicit use of inversion as part of the relational calculus needed to solve inverse addition and subtraction problems using a calculator. The study showed that children taught about relational calculus differed significantly from those who were taught numerical procedures, and also that effects of the intervention were stronger when children were taught about relational calculus with mixtures of indirect and direct word problems than when these two types of problem were given to them in separate blocks.     

A subtraction experiment with six and seven year old children

This paper gives an account of an experiment involving 176 children of 6 and 7 years and their difficulties with subtraction problems. By using two screening questions, four levels of attainment were established and two teaching programmes were then devised to help the children forward to their next level. The results show that it is possible to assess a level of understanding in subtraction quickly and accurately and that, through the teaching programmes, pre-requisite skills needed to establish a sound foundation for subtraction can be taught. The experiment indicates, however, that an attempt to symbolise too soon is a danger to be avoided.     

Examining the Effects of Problem‐solving Training on the Acquisition of Interpersonal Problem‐solving Skills by 5‐Year‐old Children in Turkey

This study was designed and carried out to examine the effect of problem‐solving training on the acquisition of interpersonal problem‐solving skills by 5 year‐old children. The subjects consisted of 74 5 year‐olds (34 girls and 40 boys) attending a kindergarten in Ankara, Turkey. Of these children 38 were assigned to the experimental group and 36 to the control group. The procedure consisted of pre‐testing, training and post‐testing activities. The training phase involved a programme of activities that required working with children for a certain period of time every day for 14 weeks. In the statistical analysis of the data collected ‘Chi‐Square (x²) test for significance’ was used for the evaluation of the differences between the experimental and control groups. The results were also evaluated on the basis of ‘the significance test for the difference between two means’. This was used to study the relationship between variables. The results showed that problem‐solving training was effective in helping 5 year‐old kindergarten children acquire interpersonal problem‐solving skills.     

Children’s solving of ‘Tower of Hanoi’ tasks: dynamic testing with the help of a robot

Abstract

The present study investigated the usefulness of a pre-programmed, teleoperated, socially assistive peer robot in dynamic testing of complex problem solving utilising the Tower of Hanoi. The robot, in a ‘Wizard of Oz’ setting, provided instructions and prompts during dynamic testing to children when they had to solve 3?D Tower of Hanoi puzzles. Participants were 37?second grade 8-year-old children, of whom half received graduated prompts training between pre-test and post-test, delivered by the robot, and half did not. It was found that children’s progression in task accuracy varied considerably, depending on whether or not children were trained in solving Tower puzzles. Trained children showed greater progression in the number of Tower problems that they could solve accurately, made considerably fewer steps, although the Tower puzzles increased quickly in difficulty level. The mean completion time of trained children decreased at a slower rate than that of the untrained children, but both groups of children took considerably more time to think and plan ahead before they started the solving process. Only moderate relations with planning behaviour were found. In general, the study revealed that computerised dynamic testing with a robot as assistant has much potential in unveiling children’s potential for learning and their ways of tackling complex problems. The advantages and challenges of using a robot in educational assessment were discussed.