压轴题解答:行进在求“简”的道路上

在中考试卷中,压轴题是“拦路虎”,影响着学生答卷的心情和答卷的速度.此类考题一般涉及的考点较多,具有较强的综合性,是中考中区分度最大的试题,是学生的应试难点.在试题类型上,填空题、选择题和解答题均有压轴问题.解答题的压轴题,一般为全卷最后一题,由一个题干和多个问题组成,问题之间难度不断增加.中考时,解答这道压轴题一般在规定时段的最后阶段,解答的时间并不充裕.所以,很多学生没能给出解题     

从分析高考试卷中存在的问题所想起的

从1981年高考数学试卷相当数量的一些答卷中,暴露出学生在学习数学上的弱点,以及在当前中学数学教学中值得研究的一些倾向性的问题。     

浅谈求解高考客观题的策略

学生解答客观题特别是填空题,失分较多,这是近年来高考数学答卷中较为突出的问题,因此探索解答客观题的策略,以促进高三复习,提高学生解题正确率,是极为迫切与必要的,本文旨在用变格策略探索高考客观题的解题途径,以期帮助学生提高解题的     

悬链线模型在系泊系统设计中的应用--2016年全国大学生数学建模竞赛A题解答评述

通过力和力矩的平衡、悬链线方程等给出2016年全国大学生数学建模竞赛A题的一种解答,并对学生答卷的不同方法和结果进行简单的点评。     

从一道题的解答看新课程平面几何的教学

一、问题与背景:2007年3月11日我参加了2007年全国初中数学竞赛(浙江赛区)初赛试题绍兴市的阅卷工作,我负责批阅了第17题,从学生的答卷的     

一道中考数学题的正误解析及启示

笔者长期从事高中数学教学工作,多次参加高考阅卷工作,经常发现学生存在令人遗憾的错误．今年一次偶然的机会参加了泰州市中考阅卷工作,发现初中生的答卷中有许多让人眼睛一亮的解法,同时也看到大量的不可思议的错误．因而要解决学生高考中产生的问题,除了注意心理调节等因素外,还要从源头上,即初中数学教学中找原因、想办法．以第26题为例．     

由一道题的典型错解引发的教学思考

文章通过对2022年西藏自治区初中学业水平考试中一道统计与概率题的答卷分析，整理学生用列表法或树状图求概率时出现的典型错解，深入剖析典型错解背后的原因，结合发展学生数学核心素养对教学提出四点思考和建议.     

柴油机供喷油过程的压力变化与控制

针对2019年全国大学生数学建模竞赛A题高压油管的压力控制问题,在一些简化的假设下给出了描述柴油机高压共轨管内燃油进入和喷出过程压力变化的数学模型,得到了几种情况下维持压力稳定的策略,并对学生竞赛答卷中的一些情况进行了评述.     

2012年CUMCM A 题解答评析

根据评卷过程中收集到的信息对2012年全国大学生数学建模竞赛的“葡萄酒的评价”问题进行分析,展示了一些较好的模型和结果,并针对答卷中反映的问题提出一些建议。     

高中学生解数学应用题的困难症结分析

近年来 ,数学应用题正越来越引起广大师生的关注和重视 ,其原因是 :( 1)科学技术突飞猛进 ,促使我们对数学应用重要性有了更深刻的认识 .应用数学知识解决实际问题的能力是新世纪青年重要的科学素质 .( 2 )高考数学应用题得分率一直偏低 ;应用数学竞赛每年都要举行一次 .笔者在课堂教学中比较重视对学生数学应用能力的培养 ,特别是通过课堂教学实践、测试答卷形式、与学生交流等途径 ,探究学生解应用题困难症结所在 ,分析原因 .为广大同行提供第一手资料 ,共同剖析症结 ,寻求对策 ,增强学生实际应用能力 .一、学生对应用题的认识存在较大偏…     

Use of Inappropriate and Inaccurate Conceptual Knowledge to Solve an Osmosis Problem

Two outstanding high school science students each generated a correct answer to an osmosis problem. The solution processes are noteworthy because the problem solvers did not blindly use algorithms. They relied, instead, on conceptual knowledge which was inaccurate and inappropriate to the problem. They thought the osmosis problem was about air pressure, and some of their knowledge about air pressure was inaccurate. Thus, even when students rely on conceptual knowledge to solve a problem, correct answers need not indicate adequate understanding. Characteristics of the problem solvers, salient properties of the problem that could contribute to the problem misrepresentation, and spurious correct answers are identified. Finally, some instructional recommendations and research questions are presented.     

High School Biology Students' Knowledge and Certainty about Diffusion and Osmosis Concepts

The purpose of this study was to investigate students' understanding about scientifically acceptable content knowledge by exploring the relationship between knowledge of diffusion and osmosis and the student's certainty in their content knowledge. Data was collected from a high school biology class with the Diffusion and Osmosis Diagnostic Test (DODT) and Certainty of Response (CRI) scale. All data was collected after completion of a unit of study on diffusion and osmosis. The results of the DODT were dichotomized into correct and incorrect answers, and CRI values were dichotomized into certain and uncertain. Values were used to construct a series of 2 × 2 contingency tables for each item on the DODT and corresponding CRI. High certainty in incorrect answers on the DODT indicated tenacious misconceptions about diffusion and osmosis concepts. Low certainty in incorrect or correct answers on the DODT indicated possible guessing; and, therefore no understanding, or confusion about their understanding. Chi‐square analyses revealed that significantly more students had misconceptions than desired knowledge on content covering the Influence of Life Forces on Diffusion and Osmosis, Membranes, the Particulate and Random Nature of Matter, and the Processes of Diffusion and Osmosis. Most students were either guessing or had misconceptions about every item related to the concepts osmosis and tonicity. Osmosis and diffusion are important to understanding fundamental biology concepts, but the concept of tonicity not be introduced to high school biology students until effective instructional approaches can be identified by researchers.     

煤矸石堆积模型

本文就煤矿堆积煤矸石费用问题建立数学模型 ,就不同的征地方式 (建矿初期一次性征完 2 0年所需用地和分批征地方式 )和煤矸石堆数进行了分析讨论 ,得出结论 :在建矿初期一次性征完所需用地 ,且所有煤矸石全堆成一堆的方案是最优的 ,并就不同的出矸率计算出该最优方案的总费用 ,最后给出对不同的出矸率处理矸石的最低年度平均费用公式     

煤矸石堆积问题的电费计算

本文设计了一种矸石堆的成堆方法 :在堆积若干年之后 ,后移一定距离重新堆积并将之前的矸石堆覆盖 ,这一方法在文 [1 ]的基础上使电费的值继续减少 ,并计算了两次成堆情况下不同出矸率对应的电费值 .     

Promoting productive mathematical classroom discourse with diverse students

Productive mathematical classroom discourse allows students to concentrate on sense making and reasoning; it allows teachers to reflect on students’ understanding and to stimulate mathematical thinking. The focus of the paper is to describe, through classroom vignettes of two teachers, the importance of including all students in classroom discourse and its influence on students’ mathematical thinking. Each classroom vignette illustrates one of four themes that emerged from the classroom discourse: (a) valuing students’ ideas, (b) exploring students’ answers, (c) incorporating students’ background knowledge, and (d) encouraging student-to-student communication. Recommendations for further research on classroom discourse in diverse settings are offered.     

Understanding and representing the arithmetic averaging algorithm: an analysis and comparison of US and Chinese students' responses

Analysing the responses of 311 sixth-grade Chinese students and 232 sixth-grade US students to two problems involving arithmetic average, this study explored students' understanding and representation of the averaging algorithm from a cross-national perspective. Results of the study show that Chinese students were more successful than US students in obtaining correct numerical answers to each of the problems, but US and Chinese students had similar cognitive difficulties in solving the second task. The difficulties were not due to their lack of procedural knowledge of the averaging algorithm, rather due to their lack of conceptual understanding of the algorithm. There were significant differences between the US and Chinese students in their solution representations of the two average problems. Chinese students were more likely to use algebraic representations than US students; while US students were more likely to use pictorial or verbal representations. US and Chinese students' use of representations are related to their mathematical problem-solving performance. Students who used more advanced representations were better problem solvers. The findings of the study suggest that Chinese students' superior performance on the averaging problems is partly due to their use of advanced representations (e.g. algebraic).     

Inequalities,assessment and computer algebra

The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students’ own answers to such problems are correct. We review how inequalities arise in contemporary curricula. We consider the formal mathematical processes by which such inequalities are solved, and we consider the notation and syntax through which solutions are expressed. We review the extent to which current CAS can accurately solve these inequalities, and the form given to the solutions by the designers of this software. Finally, we discuss the functionality needed to deal with students’ answers, i.e. to establish equivalence (or otherwise) of expressions representing unions of intervals. We find that while contemporary CAS accurately solve inequalities there is a wide variety of notation used.     

How students use the ‘see similar example’ feature in online mathematics homework

Homework is one of students’ opportunities to learn mathematics, but we know little about what students learn from homework. This study employs the instructional triangle and didactic contract to explore how students used the ‘see similar example’ feature in an online homework platform and how that use reflected their learning goals. Findings indicate students used similar examples to troubleshoot, to check if they were on the right track, and to see the form of the answer. Students also sought to unpack the reasoning in solution steps, used solutions as templates for solving their own problems, and sometimes copied answers. One student did a ‘see similar example’ problem for more practice. Students’ goals included completing the homework, maximizing their score, and understanding the content. This research lays groundwork for future work characterizing what students learn from homework and how features that provide students with similar examples help or hinder their learning.     

On the continuity of functions

In this paper, results of a questionnaire about continuity of functions are analysed. The tested students attend Novi Sad grammar school. The aim of this test was to check the student's theoretical and visual knowledge of continuous functions at the end of their high school education. The questions were given with and without the graphs of functions. The main conclusion is that the graph of a function has a significant influence on the students opinion about continuity. Looking at the graphs of functions mostly led to correct answers, but sometimes it causes problems, if it has a break. The idea came from a 1981 paper by Tall and Vinner, where the “concept image” of a continuous functions was examined.