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This study investigated the methods that pre-service teachers employed while finding volume using integration and the reasons why they utilized these methods (problems); the accuracy of their solutions was also analyzed in this study. Case study design, a qualitative research method, was used for this study. 45 sophomore pre-service teachers studying for the Middle School Mathematics Education degree programme at an Education Faculty in Anatolia. It is used to mean 45-second class preservice teachers studying for the Middle School Mathematics Education degree programme at an Education Faculty in Anatolia. It is used to mean 45-second class preservice teachers studying for the Middle School Mathematics Education degree programme at an Education Faculty in Anatolia. Pre-service teachers were provided with a training programme that made use of GeoGebra software for four weeks as part of their mathematical analysis course. Pre-service teachers were provided with a written form containing five open-ended questions and given time to answer them. Data from the study was analyzed using the content analysis method. Results from these analyses showed that half of the pre-service teachers chose problems that requires the shell method to calculate volume and that the main determining factor was the ease of mathematical calculation provided by the shell method. Also, it was found out that the mistakes made by pre-service teachers originated from issues such as the inability to fully comprehend the subject at hand, errors in formulization and/or graphing, and problems taking the integral. [ABSTRACT FROM AUTHOR]

Modern mathematics education used a different approach when dealing with word problems in algebra because of how people perceive mathematics. The teacher can aid students in honing their problem-solving abilities to assist them build mathematical concepts that can be applied in real-world situations. This research is a case study involving junior high school (JHS) pupils in Ghana's Tema Metropolis. For the study, data collection and analysis used a qualitative methodology. Using a purposive sample technique, data from 12 participants-six JHS mathematics teachers and six students-were gathered. Data were gathered through observation, interviews, and document analysis. The primary finding is that JHS pupils at Tema Education Metropolis are unable to present their own issues as proof of conceptual knowledge of algebra word problems. [ABSTRACT FROM AUTHOR]

This study aims to investigate the non-algebraic solution strategies that prospective mathematics teachers use to solve word problems and their thought process while they were solving the problems. A total of 76 prospective mathematics teachers were asked to solve two word problems without using algebraic solutions and, then, clinical interviews were conducted with a sub-sample of 20 participants. The solutions used by the participants were analysed according to the type and frequency of the strategy. The results show that prospective mathematics teachers did not use various non-algebraic solutions for word problems and that they used the guess and check strategy most often. According to the findings obtained from the interviews, it was found that the participants tended to rely on solutions that used algebraic equations related to the problem while producing solution strategies. Furthermore, the participants were found to have a limited understanding of how to interpret the algebraic equations within their context, the difference between algebraic and non-algebraic solutions, and problem-solving strategies, which prevented the participants from producing alternative solution strategies. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present a characterization of algebraic competence articulated in levels and development indicators. This characterization was used to analize the mathematical practice of inservice teachers of mathematics. Through a qualitative and exploratory research design, the algebraic competence in the teachers on high school (with students between 16 and 19 years old) is investigated and described. The results suggest that teachers present inconsistencies when solving tasks that demand a level three of algebraic competence, so the articulation of training programs based on this proposal will contribute to the development of algebraic competences in teachers of mathematics. [ABSTRACT FROM AUTHOR]

There is a compelling need to develop an algebra teacher self‐efficacy instrument (ATSEI) as algebra continues to be considered a gatekeeper course for postsecondary educational and career opportunities, which is seen as a crucial piece in closing the achievement gap. This paper reports on the development and validation of the ATSEI, an instrument that measures two domains, Efficacy To Do School Algebra (Knowledge Efficacy, KE‐A) and Efficacy to Teach Algebra (Personal Teaching Efficacy, PTE‐A) along six categories. Four of the categories represented content standards (variables, functions, patterns, and modeling) and two of the categories represented process standards (technology and concrete models, and multiple representations). Through conducting an exploratory factor analysis across two phases, the instrument was reduced and refined from an initial 118 items developed from a curriculum analysis to 36 items that reflected two significant categories, Functions and Technology. The ATSEI measure is validated for in‐service mathematics teachers and thus provides an instrument to examine need and impact in professional development venues. The specificity of the ATSEI allows those working with teachers to be better able to support them in the field and in return positively influence the learning outcomes of the students they teach. [ABSTRACT FROM AUTHOR]

The article examines the methods that use the associative rule for mathematics students to use a range of efficient mental and written strategies for mathematical problems. It seeks to make the transition to using the associative rule in algebra in the future. The associative rule is one way to restructure a numerical sentence, commonly used in the early years.

We investigated prospects for reported sustainable adoption and sharing of an educational innovation through survey research including online questionnaires and telephone interviews. This investigation is part of the Scaling-Up SimCalc experimental program, which combines dynamic representational algebra software (SimCalc MathWorlds) with integrated curriculum and small professional development workshops focused on how to use the software and how to integrate this intervention into the larger year-long curriculum. Teachers who (1) perceived the usefulness of the SimCalc professional development as being consistent with personal aims and (2) perceived specific affordances of the software/curriculum to be valuable were more likely to report continued use of the innovation after the research had ended and that they had shared it with colleagues over time. [ABSTRACT FROM PUBLISHER]

The object of this study fits into the relationships of the concept of number and translates into the question: What differentiates the teaching that adopt the proposal of Davydov from that who following other references? The data has been collected in interviews with teachers and billboards indicators of the teaching the concept of number . The analysis turns to the possibilities for the development of two ways of thought: 1) theoretical, peculiarity of the education system by Davydov interrelate the meanings of geometry, algebra and arithmetic; 2) empirical, proper from other references to the focus on everyday notions expressed in the meaning of count. [ABSTRACT FROM AUTHOR]

This study examined the effect of computer-assisted instruction, used as a supplement to traditional classroom instruction, on students' understanding of selected algebra topics, their attitude towards mathematics, and computer-assisted instruction at a laboratory high school. Four classes received supplementary instruction on factoring, radicals and simple quadratics expressions delivered via a computer-assisted instruction. A mixed method approach was employed where both qualitative and quantitative data collection techniques were used. The data were analyzed using both quantitative and qualitative methods. The study found that students' scored significantly higher in posttests than pre- tests both in terms of content and attitudes towards mathematics and use of computer-assisted instruction. [ABSTRACT FROM AUTHOR]

We describe how 1 Algebra I teacher and her 8th-grade students used meta-representational knowledge when generating and evaluating equations to solve word problems. Analyzing data from a sequence of 4 lessons, we found that the teacher and her students used criteria for evaluating equations, in addition to other types of knowledge (e.g., different interpretations of the equal sign) previously reported in the literature. Moreover, the teacher and her students had trouble understanding one another's proposed algebraic models of problem situations due to differences in the criteria that each applied, and this impeded learning. These findings (a) extend an accumulating body of evidence for the role meta-representation plays in mathematics and science learning and (b) add a new dimension to researchers' growing understanding of what teachers must know in order to teach algebra and other complex mathematics and science topics effectively. [ABSTRACT FROM AUTHOR]

The article focuses on the importance of storytelling in teaching algebra 1 and helping students integrate their mathematical experience with their understanding of the human condition. Mathematics teachers can start their lessons by citing the cave paintings early hunter-gatherers as an early example of myth making and scientific reasoning and how they use their powers of observation to build a general model of animal behavior. Teachers can evaluate the effectiveness of enrichment topics and the extent to which students have mastered critical thinking by letting students write essays describing how humans make sense of the world. Students gain confidence and the flow of ideas moves easily into solving equations that have a single unknown by having a sense of numeracy.

The article presents a reprint of the article "Algebra in the Elementary Schools," by James H. Shipley, which originally appeared in the June 1912 issue of "Mathematics Teacher." The article expresses the author's dissatisfaction with students' knowledge of fractions. He provides his suggestions on what should be included in elementary school curriculum, including mechanical drawing and algebra. He believes that introducing algebra in elementary school will make the subject more easy to understand.

The article offers reflections on the teaching of algebra in elementary schools in reference to the article "Algebra in the Elementary Schools," by James H. Shipley in 1912. Shipley proposed an algebraic approach to teaching arithmetic. The author of this article addresses issues related to mathematics curriculum, mathematics testing, misconceptions of students' capabilities, and the purpose of mathematics study. The author remarks that the goal of teachers today is to educate everyone and believes that the education system of the United States is resistant to change.

This article arises from a study whose overall purpose was to investigate the relationship between Colombian mathematics teachers' conceptions of beginning algebra and their conceptions of their own teaching practices. The teachers' understandings of their teaching practices were explored with a view to unraveling their conceptions of change in their teaching. Focusing on the perspectives of teachers afforded opportunities that exposed the powerful role that the teachers' conceptions of social/institutional factors of teaching played in their conceptions of their practices. The degree to which they attributed these (external) factors as crucial reasons for what they do in their teaching was the basis of a categorisation of their conceptions of the crucial determinants of their teaching practices into three types. The findings are particularly relevant to our understanding of the stability of mathematics teaching approaches in the Colombian context but have likely implications for a range of international education contexts. Specific implications for the development of the research into teachers' conceptions of mathematics and its teaching, and for teacher education programmes are presented. [ABSTRACT FROM AUTHOR]

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.