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The article focuses on the conceptual approach to the practice of algebraic procedures which integrates procedures and learning process. It mentions that the nine processes of the cognitive dimension include direct application of procedures, reverse thinking, and global comprehension. Moreover, the approach attempts to maintain an appropriate balance between the skills needed by students to learn and the type of cognitive demands for them.

The article provides information on different factors that affect the strategies used by students when doing algebraic tasks. It notes the three techniques commonly used by students in solving numeric tasks and the factors influencing them such as structure of the mathematical task and students' mathematical knowledge. Moreover, it discusses the elements involved in the goals of classroom instruction that include exploring various strategies to solve problems.

The article presents two methods for teaching middle school students algebraic reasoning: one focuses on the use of number patterns, another on the measurement of real-world qualities. Specific topics discussed include the importance of quantitative reasoning, the creation of an educational unit on linear quantities and suggestions for using number patterns in the classroom. Multiple sample classroom exercises are presented.

The article provides information on the role of computer algebra systems (CAS) in developing new ideas in mathematics. It states that CAS, a multirepresentational tool with symbolic, graphical and numeric capabilities, are becoming essential tools for teaching and learning high school mathematics. In connection, the article illustrates several useful features of CAS, especially when it is incorporated as part of a classroom tool set. The author also notes that a CAS-inclusive environment is conducive to expand the idea of function beyond learner's usual experiences.

The article reports on the teaching of algebra through the use of courses focusing on functions. It argues that algebra should be viewed as a means to providing solutions to actual problems rather than a skill to be memorized. It stresses the importance of educating students on mathematical modeling and its interdisciplinary uses. The article mentions the publication "A Collective Vision: Voice of Partner Disciplines" from the Mathematical Association of America which provides guidelines on teaching courses on the application of algebra. The article also provides examples of courses in algebra including those offered in the Institute for Mathematics Learning in West Virginia University.

The article investigates mathematics tasks that required students to make connections to the Pythagorean theorem, congruence and combinations by stretching a rubber band to form an oblique segment between any two pegs of a geoboard. It also demonstrates how the activity can be extended into algebra by having students find a generalization on how many oblique segments of different lengths can be made on the geoboard.

The article presents an abbreviated version of the methodologies and musings experienced by mathematics educators through a genuine problem-solving investigation. It investigates dimensions of an algebraic concept known to many high school students. It also shows how these dimensions lead to an intuitive understanding of the limit in calculus. It is stated that the readers of the article will experience and come to a deeper understanding of the Process Standards and experience the necessity of using multiple representations to make and solve mathematical conjectures. The article also describes a chronological development of mathematical ideas.

The article presents a Tangent Line problem which is designed to give students an opportunity to think more deeply about the meaning of the concept of velocity. It reports that students tends to overgeneralize the rule d=rt, which is applicable to problems relating to motion at constant velocity. It suggests that the Tangent Line problem presented in the article is designed to allow students to explore accelerated motion and instantaneous velocity by using only familiar tools of algebra. It notes that the purpose of the problem is to engage students in thinking about the concepts of velocity and tangency and how they are represented and computed in a mathematical description. It concludes with some pedagogical comments on the problem and its uses in the classroom.

Research investigating algebra students' abilities to generalize and justify suggests that they experience difficulty in creating and using appropriate generalizations and proofs. Although the field has documented students' errors, less is known about what students do understand to be general and convincing. This study examines the ways in which seven middle school students generalized and justified while exploring linear functions. Students' generalizations and proof schemes were identified and categorized in order to establish connections between types of generalizations and types of justifications. These connections led to the identification of four mechanisms for change that supported students' engagement in increasingly sophisticated forms of algebraic reasoning: (a) iterative action/reflection cycles, (b) mathematical focus, (c) generalizations that promote deductive reasoning, and (d) influence of deductive reasoning on generalizing. [ABSTRACT FROM AUTHOR]

The article presents the argument about what and how algebra and geometry are taught. The author emphasizes that algebra and the geometry are not necessarily the algebra and geometry of importance and most useful to students. An essay is presented which suggested the deletion of the traditional word problems, trinomial factoring, and complicated fractional expressions from the algebra curriculum. It is also recommended to cut the length of time in teaching geometry and that theorems which are not that important be deleted.

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of Mathematics [NCTM] Algebra Working Group, 1998). This study explored a nonrepresentational account of symbolic algebra skills as feature correlation within the visual field. We present evidence that algebra students respond spontaneously to the visual patterns of the notational display apart from engagement with the declarative content of the rules. Thus, persistent algebra errors may reflect disengagement from declarative content rather than an inability to deal with it. We sketch a Lexical Support System designed to sustain students' engagement with the declarative content of algebraic rules and processes, thus complementing the exciting curricular possibilities being developed for referentially rich algebra. [ABSTRACT FROM AUTHOR]

The article discusses the association between algebra and geometry among middle school students in the U.S. It notes that geometric representations help students visualize algebraic expressions. It presents a step-by-step connection of binomials as well as of arithmetic. Formulas in solving the problems and finding their connections are also presented.

The author focuses on computer algebra systems (CAS). The AP Calculus Listserv posted a discussion regarding the use of computer algebra systems (CAS). The author mentions that "pro-CAS" teachers are criticized for making their students complete factoring problems without spending class time on ideas. He also mentions that "anti-CAS" teachers are criticized for making their students use their calculators but would be unable to determine its value. He also discusses the concerns related to CAS such as reduction of skills, and others.

The author reflects on the important role of mathematics teachers in bridging the gap in algebra and calculus learning. She cites her experience in helping students develop an intuitive understanding in the subjects by framing questions within a real-world context. It also suggests the advantage of the process since it develops understanding through real-world scenario and bolster the student's confidence as they work with a concept essential to calculus.

The article discusses the advantage of teaching algebra in the eighth grade. It cites that for students to be competitive, they need for years to study mathematics including calculus that is why students need to start learning algebra in the eighth grade. It also offers ways on how to provide support and how to encourage independence to students in learning algebra.