数学问题解决教学的基本策略

解决问题是数学教育的重要主题,注重开放性、强调应用味及重视解题策略是问题解决教学改革的趋势。数学问题解决是数学学习要达到的主要目标之一,它对于发展学生的数学思维能力、培养创新精神具有极其重要的意义。     

论中学数学开放题的编制方法、教学策略与模式

当前，数学开放题已经成为初中数学教学改革的一个热点。数学思维活动的开放性，数学思考过程的多样性，决定了数学教学需要适应这种“开放性”和“多样性”。这是一个值得认真思考的问题。开放题是相对于明确条件和结论的封闭型习题而言的，是指能引起学生发散性思维的一种数学习题，它具有“开放性”和“多样性”的特点，在数学教学中应用数学开放题往往会起到很好的教学效果。数学开放题教学是最富有教育价值的，所以在数学教学中要重视开放题的编制、教学模式和策略探究。     

利用开放性问题促进数学教学的实践——以“菱形”的教学为例

创新教育的实施必须抓住课堂教学主渠道。在数学课堂教学中培养学生的创新精神和实践能力是当前教学研究的一个重要课题。数学开放性问题因为其条件、结论或解决策略的不确定性,可以给学生的数学思维提供一个开放的空间,     

开放性问题教学与创新能力的培养

一、开放性问题的教育价值 　　数学开放性问题,大约有以下几类:结论开放型,即指没有惟一确定答案的问题;条件开放型,即指条件不确定的问题;策略开放题,即指由条件推出结论途径不惟一的问题;综合开放题,即指兼有条件开放、结论开放、策略开放的问题. 　　……     

高中数学化归转化解题策略例谈

数学应用题涉及人口、资源、土地、环境等多方面社会生活问题,它将高中数学理论知识与学生阅读理解能力结合在一起,对学生的数学应用水平进行全方面考查与提升,体现了数学教育的功能与价值,且与国际数学教育发展相一致.化归转化策略是一种古老的数学应用策略,然而对其与数学应用题的联系探讨却从未止步,其原因在于它对数学应用题解决策略的辅助作用大有深挖之处.     

开放性问题教学与创新能力的培养

一、开放性问题的教育价值数学开放性问题,大约有以下几类:结论开放型,即指没有惟一确定答案的问题;条件开放型,即指条件不确定的问题;策略开放题,即指由条件推出结论途径不惟一的问题;综合开放题,即指兼有条件开放、结论开放、策略开放的问题。开放性问题具有以下特点:不确定性、探究性、发散性与发展性,其教育价值主要有以下几方面。1.开放性问题的教学符合学生学习知识的生理和心理特点,中学生精力旺盛,好奇心强,有闯劲,好表现自己,他们有探究和创造的潜能。2.开放性问题的教学为培养学生的创新意识提供了可能,开放性问题的挖掘设计,既展…     

小议数学教学过程中开放题的设计

数学课程标准早已明确提出:"我们的数学过程应给学生提供探索与交流的空间.教材可以设置具有挑战性的问题情境,激发学生进行思考;提出具有一定跨度的问题串引导学生进行自主探索;提供一些开放性(在问题的条件,结论,解题策略或应用等方面具有一定的开放程度)的问题,使学生在探索的过程中进一步理解所学的知识".而近年来中考数学试题方向也强调了注重开放性与探究性试题的设置,以便考察学生的思维广阔性和灵活性,综合性.开放式、探索题进     

如何理解数学中的"问题解决"

数学问题一般指对人类具有智力挑战特征的、没有现成方法、程序或算法可以直接套用的那类问题。问题情境状态下，要对学生本人构成问题，必须满足：第一，具有非常规性。第二，具有开放性。第三，具有探索性。第四，具有趣味性。第五，具有适度性。问题解决是数学教育的一个目的，学习数学的主要目的在于问题解决。实施问题解决的教学过程，一般包括以下几个阶段：意识到问题的存在；袁征问题；确定解决问题的策略并尝试某种问题解决的方法：评价与反思。     

浅谈数学开放题的教学

数学开放题是最富有教育价值的一种数学问题类型,设计数学开放题须遵循思维性、开放性、灵活性……等原则,教学时,应讲究策略,做到"六个要".     

浅谈数学开放题的教学

数学开放题是最富有教育价值的一种数学问题类型,设计数学开放题须遵循思维性、开放性、灵活性……等原则,教学时,应讲究策略,做到“六个要”。     

Primary school text comprehension predicts mathematical word problem-solving skills in secondary school

This longitudinal study aimed to investigate the extent to which primary school text comprehension predicts mathematical word problem-solving skills in secondary school among Finnish students. The participants were 224 fourth graders (9–10 years old at the baseline). The children’s text-reading fluency, text comprehension and basic calculation ability were tested in grade four. In grade seven and nine, their skills in solving mathematical word problems were assessed. Overall, the results showed that text comprehension in grade four of primary school predicts math word problem-solving skills in secondary school, after controlling for text-reading fluency and basic calculation ability. Among boys, good text comprehension skills in grade four predicted good math word problem-solving skills in grade seven. Among girls, good text comprehension skills in grade four predicted their subsequent mathematical word problem performance in grade nine. The practical implications of the results are discussed as well.     

An exploratory study contrasting high- and low-achieving students' percent word problem solving

This study evaluated whether schema-based instruction (SBI), a promising method for teaching students to represent and solve mathematical word problems, impacted the learning of percent word problems. Of particular interest was the extent that SBI improved high- and low-achieving students' learning and to a lesser degree on the indirect effect of SBI on transfer to novel problems, as compared to a business as usual control condition. Seventy 7th grade students in four classrooms (one high- and one low-achieving class in both the SBI and control conditions) participated in the study. Results indicate a significant treatment by achievement level interaction, such that SBI had a greater impact on high-achieving students' problem solving scores. However, findings did not support transfer effects of SBI for high-achieving students. Implications for improving the problem-solving performance of low achievers are discussed.     

Impacts of learning inventive problem-solving principles: students’ transition from systematic searching to heuristic problem solving

This paper presents the outcomes of teaching an inventive problem-solving course in junior high schools in an attempt to deal with the current relative neglect of fostering students’ creativity and problem-solving capabilities in traditional schooling. The method involves carrying out systematic manipulation with attributes, functions and relationships between existing components and variables in a system. The 2-year research study comprised 112 students in the experimental group and 100 students in the control group. The findings indicated that in the post-course exam, the participants suggested a significantly greater number of original and useful solutions to problems presented to them compared to the pre-course exam and to the control group. The course also increased students’ self-beliefs about creativity. Although at the beginning of the course, the students adhered to ‘systematic searching’ using the inventive problem-solving principles they had learned, later on they moved to ‘semi-structured’ and heuristic problem solving, which deals with using strategies, techniques, rules-of-thumb or educated guessing in the problem-solving process. It is important to note, however, that teaching the proposed method in school should take place in the context of engaging students in challenging tasks and open-ended projects that encourage students to develop their ideas. There is only little benefit in merely teaching students inventive problem-solving principles and letting them solve discrete pre-designed exercises.     

例谈探究式解题课教学

阐述了解题课的基本功能,指出了目前中学数学教育中解题课存在的问题。通过对一道平面几何题的分析,讨论了解题课环节如何创设一系列探究式问题,引导学生从问题的条件出发通过特例、试错等方法猜测一般规律并找到解决问题的方法,反思是如何想到这样的方法的?进一步对解题方法的优劣进行评判。通过方法的探究过程培养学生的元认知以及提升学生对数学方法的价值与审美判断能力。     

Secondary School Students’ Construction and Use of Mathematical Models in Solving Word Problems

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15–16 years old). Four levels of the development of constructing and using mathematical models were identified using a constant-comparative methodology to analyse the student’s problem-solving processes. Identifying the general in the particular and using the particular to endow the general with meaning were the key elements employed by students in the processes of construction and use of models in the different situations. In addition, attention was paid to the difficulties that students had in using their mathematical knowledge to solve these situations. Finally, implications are provided for drawing upon student’s use of mathematical models as conceptual tools to support the development of mathematical competence from socio-cultural perspectives of learning.     

Unraveling the culture of the mathematics classroom: A video-based study in sixth grade

Changing perspectives on mathematics teaching and learning resulted in a new generation of mathematics textbooks, stressing among others the importance of mathematical reasoning and problem-solving skills and their application to real-life situations. The article reports a study that investigates to what extent the reform-based ideas underlying these mathematical textbooks impact the current teaching of mathematics. Two problem-solving lessons were videotaped in 10 sixth-grade classrooms and a coding scheme was developed to analyze these lessons with regard to three aspects of the classroom culture that are assumed to enhance students’ mathematical beliefs and problem-solving competencies: (1) the classroom norms that are established, (2) the instructional techniques and classroom organization forms, and (3) the set of tasks students are confronted with. Two instruments were administered to measure students’ beliefs about learning mathematical word problem solving, and to assess their problem-solving processes and skills. The results indicate that some reform-based aspects seemed to be easier to implement (e.g., a strong focus on heuristic skills, embedding tasks in a realistic context) than others (e.g., the use of group work, an explicit negotiation of appropriate social norms).     

Case analysis of children's reasoning in problem-solving process

Recognising critical reasoning and problem-solving as one of the key skills for twenty-first century citizenship, various types of problem contexts have been practiced in science classrooms to enhance students’ understandings and use of evidence-based thinking and justification. Good problems need to allow students to adapt and evaluate the effectiveness of their knowledge, reasoning and problem-solving strategies. When students are engaged in complex and open-ended problem tasks, it is assumed their reasoning and problem-solving paths become complex with creativity and evidence in order to justify their conclusion and solutions. This study investigated the levels of reasoning evident in student discourse when engaging in different types of problem-solving tasks and the role of teacher interactions on students’ reasoning. Fifteen students and a classroom teacher in a Grade 5–6 classroom participated in this study. Through case analyses, the study findings suggest that (a) there was no clear co-relation between certain structures of problem tasks and the level of reasoning in students’ problem-solving discourse, (b) students exhibited more data-based reasoning than evidence-based and rule-based justification in experiment-based problem-solving tasks, and (c) teacher intervention supported higher levels of student reasoning. Pedagogical reflections on the difficulties of constructing effective problem-solving tasks and the need for developing teacher scaffolding strategies are discussed.     

Mathematics word problem solving for deaf students: a survey of practices in grades 6-12

One hundred and thirty-three mathematics teachers of deaf students from grades 6-12 responded to a survey on mathematics word problem-solving practices. Half the respondents were teachers from center schools and the other half from mainstream programs. The latter group represented both integrated and self-contained classes. The findings clearly show that regardless of instructional setting, deaf students are not being sufficiently engaged in cognitively challenging word problem situations. Overall, teachers were found to focus more on practice exercises than on true problem-solving situations. They also emphasize problem features, possibly related to concerns about language and reading skills of their students, rather than analytical and thinking strategies. Consistent with these emphases, teachers gave more instructional attention to concrete visualizing strategies than to analytical strategies. Based on the results of this study, it appears that in two of the three types of educational settings, the majority of instructors teaching mathematics and word problem solving to deaf students lack adequate preparation and certification in mathematics to teach these skills. The responses of the certified mathematics teachers support the notion that preparation and certification in mathematics makes a difference in the kinds of word problem-solving challenges provided to deaf students.