## Introduction

Social class backgrounds has a significant impact on the level of education attained by certain individuals. It is widely believed that individuals from higher socio-economic backgrounds tend to outperform those that are not from such privileged backgrounds. This will be investigated in further detail through analysing various sources

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## Problem Solving as a Means toward Mathematics for All: An Exploratory Look through a Class Lens

This article by Sarah Lubienski focuses on how differences in the Social Class of students affects their learning of mathematics. Lubienski discusses two aspects, one relates to the openess whereby there is no direct mathematical solution and the other relates to context. The tests that were conducted resulted in the finding that higher SES (Soci-Economic Status) students tended to possess more confidence in solving mathematical problems whereas the lower SES students found more difficulty in finding mathematical solutions to problems. Hence this highlights that the varying approaches may have been brought about by the differences in class cultures. It was discovered that the lower SES students focused on individual problems without thoroughly understanding the mathematical concepts and were therefore unable to apply the mathematical rules. The ranking showed the lower SES students lacked self-esteem and preferred a more directive role from the text and teacher.

## Developing Mathematical Thinking and Self-Regulated Learning: a Teaching Experiment in a Seventh-Grade Mathematics Classroom

The main focus of the article by S.J. Pape is made on the notion, that the maths teachers and educators have made an essential emphasis on the socio-cultural models of tutoring and studying processes in order to be powerful in their capability to explain and support the pursuit of instruction based on recent standards documents. Nevertheless, these models have been seriously criticized for the essential lack of explicitness. Thus, the authors of the article make an emphasis on the matters of detailed and thorough descriptions of the cognitive processes in the co within the self-regulated learning process and ascription concepts of the teaching theory lend support for and provide instances of explicit instruction embedded within socio-cultural models of maths instruction. Moreover, the authors make an emphasis on the matters of equal opportunities in socio-economic classes. Self-regulated learning and the matters of mathematical thinking are originally associated with the matters of background thinking and the logical reasoning of the students, as Socioeconomic classes shape different ways of thinking from those, which math classes offer. On the other hand, the authors offer that the main principle of equal opportunities is the personal approach of the tutor. Thus, the experimental model, described in the paper reveals the concept of socio-cultural modeling in the teaching process.

## “Highly Qualified” to Do What? The Relationship between NCLB Teacher Quality Mandates and the Use of Reform Oriented Instruction In Middle School Mathematics

This article is aimed at reviewing the legislative issues of teaching mathematics, and the authors emphasize the importance of the No Child Left Behind Act of 2001 (NCLB). This act presupposes the necessity of a highly qualified teachers in every classroom. In accordance with the legislation and the stated act, Socio-Economic classes are generally subjected to another mathematics teaching approach than the students of mathematics classes. No Child Left Behind Act presupposes that highly qualified is generally defined as the full certificated. Smith and Desimone claim that states, districts, and schools are spending considerable resources addressing these provisions, nevertheless, the degree of the standard-based reform penetration into the teaching process is unknown. In the context of Socio-Economic class teaching, it should be emphasized that equal learning opportunities should be provided to anyone, nevertheless, the specification of Socio-Economic mathematics studies should be taken into consideration. The analysis of the authors in this aspect suggests that the preparation of the mathematics content-related professional development activities and the teaching process in general. These are claimed to be the matters of reform-oriented teaching, measured here as increased emphasis on conceptual learning goals for students and increased use of reform-oriented teaching strategies.

## Using Transactional Reading Strategies to Support Sense-Making and Discussion in Mathematics Classrooms: An Exploratory Study

The authors here focus on the necessity of thoroughly elaborated mathematics teaching strategies and the instructions for the teachers, for they could implement these strategies. Originally, a special emphasis is made on the matters of equality and equal opportunities for teaching mathematics in classes with different students (of different social, racial and cultural backgrounds), and with the students of different classes (Math and socio-economic specification). The paper illustrates how encouraging mathematics students to talk, write, draw, and enact texts can provide them with concrete ways to construct and negotiate interpretations of what they read. The strategies, which are recommended in the paper presuppose the use of Mathematics and Science Vocabulary Wheels. These are reflective of the issues that students learn and think about in multiple ways. This is especially associated with the specification of how socio-economic classes and maths classes differ as they require various approaches towards teaching maths in general and providing equal opportunities for teaching and learning. The specific strategies include oral, written, visual, auditory, and kinesthetic approaches which are included on the wheels and in the main strategic approach, regarded in the paper. The information, derived from the application of the strategies is used as the methodological basis of the paper and may be regarded as the research innovation approach.

## Secondary School Mathematics Teachers’ Conceptions of Proof

The paper is mainly aimed at discovering the matters of teaching mathematics in secondary schools. The conception of proof, which represents the main idea of the author suggests that teachers recognize the variety of roles that proof plays in mathematics. The matters of proof are generally regarded as the tool for teaching mathematics in schools. The author also relates the teaching process with maths teaching in socio-economic classes. The data for the research was collected from a series of interviews and articles by teachers who wrote their responses for the proof tool. The results of the research suggest that the teachers mainly recognize the differences between teaching math for math classes and classes with the socio-economic backgrounds. Nevertheless, some teachers, who practice this tool for socio-economic classes admit the wrong understanding of the proof tool among students, while teachers themselves often constitute inadequate understanding of the importance and the essence of the proof tool for teaching mathematics. The results of the research also suggest that these teachers mainly regarded the proof tool in a pedagogically restricted manner, thus, the emphasis of the article is also made on the matters of communication in the context of studying and teaching mathematics, applying the proof tool.

## Different Goals, Similar Practices: Making Sense of the Mathematics and Literacy Instruction in a Standards-Based Mathematics Classroom

The paper is mainly aimed at describing the matters of the teaching process in the light of the notion of cooperative inquiry between literacy and maths education. Originally, the approaches of teaching both aspects of basic skills depend on the proficiency of a teacher and presuppose the increased attention towards the matters of the standards-basing in the arrangement of the maths class. Part of the research is dedicated to the concepts of teaching mathematics in socio-economic classes, as the approaches of these teachings differ from the original strategies of teaching maths. In the light of the fact that the original standard-based teaching strategy, practiced in the socio-economic classes and maths classes are shaping the original approach towards understanding the taught material, it should be emphasized that teachers should pay special attention to understanding among students. The fact is that only attention towards understanding jointly with the individual approach and properly observed teaching strategy is able to provide equal opportunities for teaching mathematics.

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The data for the research was collected during the observation of the teaching processes in different classes, and the drawbacks of standard-based technologies and approaches were analyzed along with the positive sides of these approaches.

## “New Math” Implementation: A Look Inside the Classroom

The authors discuss the procedure, findings, and summary of a study conducted through the use of anonymous questionnaires in an attempt to determine what actual classroom practice is in second- and fifth-grade mathematics classes. Originally, the New Math approach, associated with the implementation of new teaching strategies will help to overcome the problem of standardization in teaching approaches. Originally, this innovation would be rather helpful for Socio-Economic Classes, as the specification of their teaching should differ from the teaching approaches of the math classes. Thus, the student of all classes will be able to develop strong math skills and develop a strong, working knowledge of mathematical content. In the light of this fact, it should be emphasized that the main principle of such an approach will be based on various proof, explanation and solution tools, which are relevant for developing the understanding process within students. Nevertheless, this innovation has an essential drawbacks, as teachers will have to change their elaborated methodologies and refuse to form traditional teaching practices.

## Reference

Sarah Theule Lubienski. Problem Solving as a Means toward Mathematics for All: An Exploratory Look through a Class Lens. Journal for Research in Mathematics Education, Vol. 31, No. 4 (2000), pp. 454-482.

Stephen J. Pape. Clare V.Bell. Iffet Elif Yetkin. Developing Mathematical Thinking and Self-Regulated Learning: a TeachingExperiment in a Seventh-Grade Mathematic Classroom. Educational Studies in Mathematics, Vol. 53, No. 3 (2003), pp. 179-202.

Thomas M. Smith, Laura M. Desimone and Koji Ueno. “Highly Qualified” to Do What? The Relationship between NCLB Teacher Quality Mandates and the Use of Reform Oriented Instruction In Middle School Mathematics. Educational Evaluation and Policy Analysis, Vol. 27, No. 1 (2005), pp. 75-109.

Raffaella Borasi, Marjorie Siegel, Judith Fonzi and Constance F. Smith. Using Transactional Reading Strategies to Support Sense-Making and Discussion in Mathematics Classrooms: An Exploratory Study. Journal for Research in Mathematics Education, Vol. 29, No. 3 (1998), pp. 275-305.

Eric J. Knuth. Secondary School Mathematics Teachers’ Conceptions of Proof. Journal for Research in Mathematics Education, Vol. 33, No. 5 (2002), pp. 379-405.

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Roni Jo Draper and Daniel Siebert. Different Goals, Similar Practices: Making Sense of the Mathematics and Literacy Instruction in a Standards-Based Mathematic Classroom. American Educational Research Journal, Vol. 41, No. 4 (2004), pp. 927-962.

Jack Price, John L. Kelley and Jonathan Kelley. “New Math” Implementation: A Look inside the Classroom. Journal for Research in Mathematics Education, Vol. 8, No. 5 (1977), pp. 323-331. Published by: National Council of Teachers of Mathematics.