数形结合的思想方法在数学解题教学中的应用

数形结合作为重要的数学思想方法,在数学解题中起着举足轻重的作用.本文介绍了数形结合的思想方法在函数、几何、方程与不等式、数列、集合等方面的应用,为进一步提高学生的解题能力抛砖引玉.     

浅议高中数学解题后的思考

现在高中生普遍反映有这样的问题:1.好多题目老师不仅是讲了,而且是讲了好多遍,可是学生的解题能力不见得进步!也常听见学生这样说:老师一讲就会.学生一做就错.解题能力却得不到提高!2.不少同学题目会做但考试时得不到分,这些问题确实应该引起我们的反思.要想真正提高学生的解题能力,例题教学的解后反思应该成为例题教学的一个重点内容.我想主要从以下几个方面谈些看法.     

数学教学反思略谈

反思是一线老师常规教学工作的重要环节,它是提升教师素质的重要手段,也是学生学习的重要方法,对学生稳固原有知识,提升理解深度有着重量作用.教学老师要不断从自身观念、教学对象、教学方式上进行反思,以提升教学水平,提高自身素质.要引导学生学会反思,反思学习方式和对知识的掌握,可以帮助学生提高学习效率.     

小学数学的解题方法探讨

《数学课程标准》指出：“培养学生的探索意识，使学生初步学会运用所学的数学知识和方法解决一些简单的实际问题。”把“解决问题”的教学过程当作数学教学的一种基本形式，即在解决问题的过程中学数学，以解决问题的形式学数学，从而培养学生运用数学知识解决实际问题的能力。     

浅谈英语课堂教学反思的意义及其途径

教师专业化是时代与社会发展的内在要求,而教学反思则是教师专业化发展的重要途径.教学反思不仅能使学生受益,还可调动教师的综合思维,不断激发教师的积极性和创造性,进而提升自身素质和教学专业化水平.     

浅谈初中数学教学中的教学反思

教学反思作为一种意识时刻指导我们的教学实践,我们的教学水平和专业技能只有在不断的反思中才得到提高.新课改要求教师,不断钻研、探索、反思自己的教学实践,发现得失,总结经验.只有善于探索反思的教师才能成为有利于任新课改的优秀教师.本文结合教学实践就初中数学教学中的教学反思进行探讨,以教师的日常教学为切入点,分析了教学反思的基本理论和在实践中的体现.     

倡导教学反思提提高教学效果

教学反思是教师有益的思维活动和再学习活动.一个优秀教师的成长离不开教学反思.在新课程理念的指导下,倡导教学反思,提高教师的教学水平和科研水平,不仅促进学生发展,而且促进教师发展.本文围绕教学反思的内涵、必要性、内容、及策略方面来阐述.     

教育随笔——构建语文教师反思的平台

教育随笔具有简便性、易操作性和有效性等特点,是语文教师以叙事、讲故事的方式表达对教育理解的有效手段,它从实践层面启迪语文教师重新认识并反思自己的教育教学实践活动,对促使语文教师快速成长为反思型教师具有重要意义.本文旨在探讨如何撰写教育随笔,包括其涉及的内容及遵守的原则,期望教育随笔能够成为促进语文教师的专业反思的平台.     

五年制高职数学教学的反思及探索

五年高等职业教育是高等教育的特殊类型,相比五年制高职院校尤其要注重教学质量的提高.在课程实施中,为了提高教学效率,教师必须改变以前的单一教学模式,在研究教法与学生的同时,尝试运用如下几种方式创新教学方法:在专业情境中理解概念、进行教学模式创新的实践与探索等.     

Schema Induction in Problem Solving: A Multidimensional Analysis.

The present research examined the processes of schema formation in problem solving. In 4 experiments, participants experienced a series of tasks analogous to A. S. Luchins' (1942) water jar problems before attempting to solve isomorphic target problems. Juxtaposing illustrative source instances varying in procedural features along multiple dimensions promoted the construction of a general schema that facilitated solving an isomorphic problem requiring a novel procedure. Exposure to less variant problems led to faster initial learning, but narrower and fixed schemas (mental set), whereas exposure to variant procedures led to slower initial learning, but broader and more flexible schemas. The findings support the dimensional specificity hypothesis: Generalization along 1 dimension facilitates transfer to a target problem differing from the source problems in that dimension. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

More on the Fragility of Performance: Choking Under Pressure in Mathematical Problem Solving.

In 3 experiments, the authors examined mathematical problem solving performance under pressure. In Experiment 1, pressure harmed performance on only unpracticed problems with heavy working memory demands. In Experiment 2, such high-demand problems were practiced until their answers were directly retrieved from memory. This eliminated choking under pressure. Experiment 3 dissociated practice on particular problems from practice on the solution algorithm by imposing a high-pressure test on problems practiced 1, 2, or 50 times each. Infrequently practiced high-demand problems were still performed poorly under pressure, whereas problems practiced 50 times each were not. These findings support distraction theories of choking in math, which contrasts with considerable evidence for explicit monitoring theories of choking in sensorimotor skills. This contrast suggests a skill taxonomy based on real-time control structures. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Enhancing Mathematical Problem Solving Among Third-Grade Students With Schema-Based Instruction.

The purposes of this study were to assess the effects of schema-based instruction (SBI) in promoting mathematical problem solving and to investigate schema induction as a mechanism in the development of mathematical problem solving. Twenty-four 3rd-grade teachers, with 366 students, were assigned randomly to conditions that provided instruction on 4 types of word problems. The 3 16-week conditions were contrast, SBI, and SBI with practice in sorting word problems into schemas. Students were pre- and posttested on mathematical problem-solving tests and were posttested on schema development. Students receiving SBI, with and without sorting practice, improved more than the contrast group on problem-solving measures. Concurrently, the SBI groups' schema development exceeded that of the contrast group, and schema development explained a substantial portion of unique variance in students' posttreatment problem-solving performance. Results also suggested the need for additional research testing the contribution of practice in sorting word problems. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effectiveness of Collaborative Problem Solving in Affectively Dysregulated Children With Oppositional-Defiant Disorder: Initial Findings.

Oppositional-defiant disorder (ODD) refers to a recurrent pattern of negativistic, defiant, disobedient, and hostile behavior toward authority figures. Research has shown that children with ODD and comorbid mood disorders may be at particular risk for long-term adverse outcomes, including conduct disorder. In this study, the authors examined the effectiveness of a cognitive-behavioral model of intervention--called collaborative problem solving (CPS)--in comparison with parent training (PT) in 47 affectively dysregulated children with ODD. Results indicate that CPS produced significant improvements across multiple domains of functioning at posttreatment and at 4-month follow-up. These improvements were in all instances equivalent, and in many instances superior, to the improvements produced by PT. Implications of these findings for further research on and treatment selection in children with ODD are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Problem Solving Deteriorates Following Mood Challenge in Formerly Depressed Patients With a History of Suicidal Ideation.

The authors divided 34 participants who had a history of depression into 2 groups, those having previous suicidal ideation or behavior (n = 19) and those having no such symptoms (n = 15), then compared the 2 groups with a group of participants who had no history of depression (n = 22). Assessment of interpersonal problem-solving performance using the Means-Ends Problem-Solving (MEPS) task before and after a mood-induction procedure showed that only those formerly depressed people with a history of suicidal ideation shifted in MEPS performance, producing significantly less effective problem solutions following mood challenge, consistent with a differential activation account of vulnerability for recurrence of suicidal ideation and behavior. The deterioration in effectiveness following mood challenge was moderated by lack of specificity in autobiographical memory. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Preventing adolescent depression: An evaluation of the Problem Solving For Life program.

This study evaluated the effectiveness of the Problem Solving For Life program as a universal approach to the prevention of adolescent depression. Short-term results indicated that participants with initially elevated depressions scores (high risk) who received the intervention showed a significantly greater decrease in depressive symptoms and increase in life problem-solving scores from pre- to postintervention compared with a high-risk control group. Low-risk participants who received the intervention reported a small but significant decrease in depression scores over the intervention period, whereas the low-risk controls reported an increase in depression scores. The low-risk group reported a significantly greater increase in problem-solving scores over the intervention period compared with low-risk controls. These results were not maintained, however, at 12-month follow-up. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Evaluating the Readiness of Pre-Referral Intervention Teams for Use in a Problem Solving Model.

Scholars have suggested that school psychologists should implement a problem solving approach to practice (Reschly & Ysseldyke, 2002). Pre-referral intervention teams (PITs) are a frequently used model in education and are a preferred service option among school psychologists. Thus, the PIT model could be expanded to more effectively function within a problem solving approach, but research is needed to examine the use of PITs in this format. Ellis (2001) suggested that educational innovations require research that demonstrates sound theoretical basis, proven effectiveness, and consistent widespread implementation. The current article reviewed research and concluded that the PIT model was developed from a solid theoretic base and data exist to support its effectiveness. However, consistent implementation has not been achieved and remains a significant barrier to moving toward a problem solving approach. Research is needed regarding team format, assignment of staff, training, and treatment fidelity to better assure consistency through recommendations for practice. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Relationships Among Health Factors and Everyday Problem Solving in African Americans.

This study examined whether measures of health status enhance the prediction of performance on everyday problem solving in adult African Americans. The sample consisted of 209 community-dwelling African American adults with a mean age of 66.82 years (SD=7.95). The following variables were included in the analysis: Everyday Problems Test (EPT), summary index of chronic illnesses (cardiovascular disease, hypertension, arthritis, stroke, and diabetes), self-rated health (current health, health in the past month, health compared with others, health compared with 5 years ago), and demographic information. Using hierarchical regression and follow-up communality analysis, the authors found that the number of chronic illnesses and self-rated health as compared with 5 years prior were significant and unique predictors of performance on the EPT but did not account for all of the demographic-related variance. The results indicate that health indices contribute to the variability in everyday cognition in this understudied population. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of Motivational Cues on Perceptual Asymmetry: Implications for Creativity and Analytical Problem Solving.

In 4 experiments, participants were led to focus on either the prospect of positive outcomes (approach anticipation) or the prospect of negative outcomes (avoidance anticipation) and were subsequently administered behavioral measures of relative hemispheric activation. It was found that approach, relative to avoidance-related anticipatory states, produced greater relative right (diminished relative left) hemispheric activation. Experiment 3 additionally demonstrated that this pattern of activation was reversed when approach and avoidance states were not merely anticipatory but were also emotionally arousing. Finally, Experiment 4 replicated earlier findings demonstrating an influence of approach and avoidance anticipatory states on creativity and analytical problem solving (R. S. Friedman & J. F?rster, 2001, 2003) and provided evidence that such effects are mediated by differences in relative hemispheric activation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Having the Memory of an Elephant: Long-Term Retrieval and the Use of Analogues in Problem Solving.

The authors report 4 experiments exploring long-term analogical transfer from problem solutions in folk tales participants heard during childhood, many years before encountering the target problems. Substantial culture-specific analogical transfer was found when American and Chinese participants' performance was compared on isomorphs of problems solved in European versus Chinese folk tales. There was evidence of transfer even among participants who did not report being reminded of the source tale while solving the target problem. Comparisons of different versions of a target problem indicated that similarity of solution tool affected accessing, mapping, and executing components of problem solving, whereas similarity of goal object had only a moderate effect on accessing. High school students also evidenced greater transfer than did middle school students. (PsycINFO Database Record (c) 2010 APA, all rights reserved)