共查询到20条相似文献，搜索用时 515 毫秒
1.
代数式的内容，在七年级数学课程中是极为重要的部分，同时又是以往使学生感到枯燥乏味的部分。新世纪版实验教材，一反传统上代数式的内容主要以运算为主的设计，突出了代数式的表示功能、突出了代数式与现实问题的联系、突出了学生对代数式意义的理解。对于代数式的运算，一方面降低了运算的难度，一方面突出了代数式运算的意义。 相似文献
2.
田宇 《中学生数理化(高中版)》2009,(3):74-75
有理数的加法是有理数运算的开始,是进一步学习有理数运算的基础,也是今后学习实数运算、代数式的运算、解方程以及函数知识的基础。同时,学好这部分内容,对减少学生之间两极分化、增强学生学习代数的信心具有十分重要的意义。 相似文献
3.
教材分析:《合并同类项》是第三章用字母表示数中的重要内容。该内容结合学生已有的生活经验,在介绍了代数式的定义,代数式的书写规范,列代数式,代数式的分类的基础上,对代数式的运算的探索和研究,是以后学习解方程,解不等式的基础。 相似文献
4.
一、教材分析本章教材分四节:列代数式、代数式的值、整式、整式的加减.两个阅读材料:有趣的“3x 1”问题、用分离系数法进行整式的加减运算.一个课题学习:身份证号码与学籍号.本章教材的教学思路是:从学生对数的认识入手,使学生经历探索规律并用字母表示数量关系的过程和用代数式表示规律的过程;能够用字母表示数,体会字母表示数的意义,形成初步的符号感,并在现实情境中通过进一步理解字母表示数的意义,发展符号感;能够用字母和代数式表示以前学过的运算律,并将运算律运用到整式的运算中,通过探索整式运算法则的过程,使学生理解整式运算的算理,发展学生观察、归纳、类比、概括等能力,发展比较有条理的思考以及语言表达能力.本章知识在整个初中数学学习中的地位很重要:前面是有关有理数的系统的学习,七年级下册一开始就是一元一次方程和二元一次方程组,在义务教育第二学段的第一年就很完整地构建了一个数、式、方程的链接,将课标中初中“数与代数”部分的五大知识块(数、式、方程、不等式、函数)中的三块呈现了出来.所以本章实际上起到了承前启后的作用,是今后进一步研究各种代数式的恒等变形的基础,也是研究函数与方程的重要工具.在整个初一代数知识部分,本章是很关... 相似文献
5.
中学数学的代数部分,初一上学期是入门阶段,而学好《代数式》这一节又是这个阶段的关键。学生在以后学习中的缺陷,很多都和这一节内容掌握得不好有关。那么在《代数式》的教学中要注意些什么呢? 一、要化大气力教好“用字母表示数”对这部分内容,课本上先举了三个例子:长方形的面积表示式、数的运算律和汽车的速度、时间、路程的关系式,然后小结:“用字母表示数,能够把数量或数量关系一般地而又简明地表达出来。”这句话含义很丰富,教师要使学生能够深刻领会,就得在上面三个例子的讲解中精心引导。以数的运算律中的加法交换律 相似文献
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一、教材分析
本章教材分四节：列代数式、代数式的值、整式、整式的加减。两个阅读材料：有趣的“3x＋1”问题、用分离系数法进行整式的加减运算。一个课题学习：身份证号码与学籍号。
本章教材的教学思路是：从学生对数的认识入手，使学生经历探索规律并用字母表示数量关系的过程和用代数式表示规律的过程；能够用字母表示数，体会字母表示数的意义，形成初步的符号感，并在现实情境中通过进一步理解字母表示数的意义，发展符号感；能够用字母和代数式表示以前学过的运算律，并将运算律运用到整式的运算中，通过探索整式运算法则的过程，使学生理解整式运算的算理，发展学生观察、归纳、类比、概括等能力，发展比较有条理的思考以及语言表达能力。 相似文献
8.
数学课堂目标教学步骤初探宿松县柳溪初中王仰曾步从具体数量抽象为更一般意义的代数式，并突出数量之间运算关系，即由数的运算发展到形式运算。对初一学生来说，这是最基本、最简单，也是最重要的抽象。但在人的认识上，由具体数字运算发展到字母的运算，学生初学时也最... 相似文献
9.
祝永良 《成都教育学院学报》2000,14(1):56-56,59
“因式分解”是初中阶段代数式中的一个重要内容，它对代数式的运算以及解方程，函数等知识的掌握起着举足轻重的作用。不少学生因为这部分知识的掌握不牢或不熟练而影响了其它相关知识的学习。究其原因：一方面学生初学；另一方面学生虽然对分解因式的方法都能较好地理解，学习一种方法并应用这种方法容易掌握，但几种方法学习以后，面对因式分解的题目反而不知用哪种方法了。 相似文献
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Several researchers suggest that students' difficulties with the algebraic structure are in part due to their lack of understanding of structural notions in arithmetic. They assume that the algebraic system used by students inherits structural properties associated with the number system with which students are familiar. This study explored this assumption. In an attempt to discover whether wrong interpretations of the algebraic structure found in an algebraic context occur in a purely numerical one, we interviewed 53 sixth-graders individually. The assessment confirms the assumption: students' difficulties with the algebraic structure were found in purely numerical contexts. However, the study also confirms two, seemingly, contradictory observations. On the one hand, the students' interpretations of the structures of the expressions were very consistent; that is, the same tendencies were found in many students' answers. In this sense the students' behaviour was consistent. On the other hand, it was clearly observed that the same student may give an incorrect answer in one context and a correct answer in another. In this sense, it often seemed that the students were inconsistent.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
12.
Luis Radford 《Educational Studies in Mathematics》2000,42(3):237-268
The purpose of this article, which is part of a longitudinal classroom research about students' algebraic symbolizations,
is twofold: (1) to investigate the way students use signs and endow them with meaning in their very first encounter with the
algebraic generalization of patterns and(2) to provide accounts about the students' emergent algebraic thinking. The research
draws from Vygotsky's historical-cultural school of psychology, on the one hand, and from Bakhtin and Voloshinov's theory
of discourse on the other, and is grounded in a semiotic-cultural theoretical framework in which algebraic thinking is considered
as a sign-mediated cognitive praxis. Within this theoretical framework, the students' algebraic activity is investigated in the interaction of the individual's
subjectivity and the social means of semiotic objectification. An ethnographic qualitative methodology, supported by historic,
epistemological research, ensured the design and interpretation of a set of teaching activities. The paper focuses on the
discussion held by a small group of students of which an interpretative, situated discourse analysis is provided. The results
shed some light on the students' production of (oral and written) signs and their meanings as they engage in the construction
of expressions of mathematical generality and on the social nature of their emergent algebraic thinking.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
Michal Ayalon Ruhama Even 《International Journal of Science and Mathematics Education》2016,14(3):575-601
This study examines how students’ opportunities to engage in argumentative activity are shaped by the teacher, the class, and the mathematical topic. It compares the argumentative activity between two classes taught by the same teacher using the same textbook and across two beginning algebra topics—investigating algebraic expressions and equivalence of algebraic expressions. The study comprises two case studies in which each teacher taught two 7th grade classes. Analysis of classroom videotapes revealed that the opportunities to engage in argumentative activity with the topic investigating algebraic expressions were similar in each teacher's two classes. By contrast, substantial differences were found between one teacher's classes with regard to the opportunities to engage in argumentative activity with the topic equivalence of algebraic expressions. The discussion highlights how the interplay between the characteristics of the mathematical topic, the characteristics of the class, and the characteristics of the teacher contributed to the shaping of students’ opportunities to engage in argumentative activity. 相似文献
14.
Ayalon Michal Even Ruhama 《International Journal of Science and Mathematics Education》2014,12(2):285-305
This study compares students’ opportunities to engage in transformational (rule-based) algebraic activity between 2 classes taught by the same teacher and across 2 topics in beginning algebra: forming and investigating algebraic expressions and equivalence of algebraic expressions. It comprises 2 case studies; each involves a teacher teaching in two 7th grade classes. All 4 classes used the same textbook. Analysis of classroom videotapes (15–19 lessons in each class) revealed that the opportunities to engage in transformational algebraic activity related to forming and investigating algebraic expressions were similar in each teacher’s 2 classes. By contrast, substantial differences were found between 1 teacher’s classes with regard to the opportunities to engage in transformational algebraic activity related to equivalence of algebraic expressions. The discussion highlights the contribution of the interplay among the mathematical topic, the teacher, and the class to shaping students’ learning opportunities. Specifically, the mathematical topic appeared to play a prominent role in certain situations, with the topic involving deductive reasoning generating high variation in classes of 1 teacher but not in the other’s.
相似文献15.
Michal Ayalon Ruhama Even 《International Journal of Science and Mathematics Education》2015,13(2):285-307
This study compares students’ opportunities to engage in transformational (rule-based) algebraic activity between 2 classes taught by the same teacher and across 2 topics in beginning algebra: forming and investigating algebraic expressions and equivalence of algebraic expressions. It comprises 2 case studies; each involves a teacher teaching in two 7th grade classes. All 4 classes used the same textbook. Analysis of classroom videotapes (15–19 lessons in each class) revealed that the opportunities to engage in transformational algebraic activity related to forming and investigating algebraic expressions were similar in each teacher’s 2 classes. By contrast, substantial differences were found between 1 teacher’s classes with regard to the opportunities to engage in transformational algebraic activity related to equivalence of algebraic expressions. The discussion highlights the contribution of the interplay among the mathematical topic, the teacher, and the class to shaping students’ learning opportunities. Specifically, the mathematical topic appeared to play a prominent role in certain situations, with the topic involving deductive reasoning generating high variation in classes of 1 teacher but not in the other’s. 相似文献
16.
Thomas W. Jones Barbara A. Price Cindy H. Randall 《Decision Sciences Journal of Innovative Education》2011,9(3):379-394
A study was conducted at a southern university in sophomore level production classes to assess skills such as the order of arithmetic operations, decimal and percent conversion, solving of algebraic expressions, and evaluation of formulas. The study was replicated using business statistics and quantitative analysis classes at a southeastern university. The intent of the study was to determine math deficiencies among college students and to ascertain whether or not these deficiencies impact grades. Data analyses compared students’ test results and grades from the different classes at the two universities and identified surprising patterns across classes, universities, and professors.These results support the need for curriculum modifications to address the identified deficiencies. 相似文献
17.
Wallace Feurzeig 《Instructional Science》1986,14(3-4):229-254
For many students the ideas and methods of algebra appear obscure and mysterious, their sense and purpose unclear, and their applicability to anything genuinely real or interesting very remote. Students often fail to acquire an understanding of the key concepts, despite their inherent simplicity. Even when they gain the notion of variables, expressions and equations, students often lack the strategic knowledge required to motivate and direct the global planning and detailed execution of an attack on a problem. These conceptual and strategic difficulties are compounded by the needs for precise performance of the arithmetic and symbolic operations required in manipulating expressions. Extended operations like subtracting an expression from both sides of an equation or expanding a product of three terms, are very difficult for beginning students. Their buggy performance in carrying out the detailed manipulative work greatly confounds and frustrates their acquisition and assimilation of the most important and central ideas.In an effort to confront these difficulties and show how they can be overcome, we are developing a Logo-based introductory algebra course for sixth graders. Our approach has three major components: work on Logo programming projects in algebraically rich contexts whose content is meaning ful and compelling to students, the use of algebra microworlds with concrete iconic representations of formal objects and operations, and the introduction of the algebra workbench, an expert instructional system to aid students in performing extended algebraic operations.The algebra workbench will employ a set of powerful symbolic manipulation tools for performing the standard manipulations of high school algebra. It will have two main modes of use: demonstration mode, which uses an expert tutor program to solve algebra problems incrementally, explaining its strategy and its step by step operations in straightforward terms along the way; and practice mode, in which the student tries to solve a problem with the assistance of the tutor, which performs the operations requested by the student at each step and which can be called at any point to advise the student of the correctness of a step, to perform or explain any step, to evaluate the student's solution, or to perform a problem that she poses.These powerful aids make it possible to effectively separate out the difficulties in performing the formal and manipulative aspects of algebra work from those encountered in learning the central conceptual and strategic content. Distinctly different kinds of instructional tools and activities-Logo programming, expert tutors, or algebra microworlds-can thus be brought to bear where each is most appropriate and effective. 相似文献
18.
This study examines eighth grade students’ use of a representational metaphor (cups and tiles) for writing and solving equations
in one unknown. Within this study, we focused on the obstacles and difficulties that students experienced when using this
metaphor, with particular emphasis on the operations that can be meaningfully represented through this metaphor. We base our
analysis within a framework of referential relationships of meanings (Kaput 1991; Kaput, Blanton, and Moreno, et al. 2008). Our data consist of videotaped classroom lessons, student interviews, and teacher interviews. Ongoing analyses of these
data were conducted during the teaching sequence. A retrospective analysis, using constant comparison methodology, was then
undertaken in order to generate a thematic analysis. Our results indicate that addition and (implied) multiplication operations
only are the most meaningful with these representational models. Students also very naturally came up with a notation of their
own in making sense of equations involving multiplication and addition. However, only one student was able to construct a
“family of meanings” when negative quantities were involved. We conclude that quantitative unit coordination and conservation
are necessary constructs for overcoming the cognitive dissonance (between the two representations—drawn pictures and the algebraic
equation) experienced by students and teacher. 相似文献
19.
Tammy Eisenmann Ruhama Even 《International Journal of Science and Mathematics Education》2011,9(4):867-891
The aim of this study was to examine how teachers enact the same written algebra curriculum materials in different classes.
The study addresses this issue by comparing the types of algebraic activity (Kieran, 2004) enacted in two 7th grade classes taught by the same teacher, using the same textbook. Data sources include lesson observations
and an interview with the teacher. The findings show that students in the two classes were offered somewhat different algebraic
experiences. At one school, more emphasis was placed on global/meta-level activities (activities that are not exclusive to
algebra and suggest general mathematical processes), whereas at the other school, more emphasis was placed on transformational
activities (“rule-based” algebraic activities). Analysis of the sources of the differences related to the ways in which the
teacher used and enacted the curriculum materials in the two classes revealed that these were linked to the teacher’s attempts
to be attentive to the students in the class and to the nature of the students’ work. 相似文献
20.
Jihyun Lee Diane Pedrotty Bryant Min Wook Ok Mikyung Shin 《Learning disabilities research & practice》2020,35(2):89-99
Improving the algebraic concepts and skills of secondary school students with learning disabilities is critical for their success in college and in the job market. This research reviewed 12 studies to examine interventions for students with learning disabilities in relation to algebraic notions and competencies. The results indicate that in regard to the Common Core State Standards for Mathematics (CCSSM) Content Standards, the majority of the studies address linear equations and expressions, linear inequalities, and quadratic expressions; they show that following interventions, students’ performance improved with respect to algebraic concepts and skills. The Tau-U and Hedges’ g of the intervention effects computed were typically large or very large. The most commonly used instructional components in the interventions were multiple representations, a sequence and/or range of examples, and explicit instruction. Limitations and suggestions for future research are discussed. 相似文献