## Introduction

Gifted education has significantly improved learning not only in highly able students, but also in regular students. In the last few years, several modern teaching methods have been developed and used in classrooms. Teaching methods such as project work, providing meaningful choices for students, self-directed learning, literature-based reading, and problem-based curriculum were developed to cater for gifted education.

Empirical studies show that gifted children work well within a well-prepared learning environment. Thus, Montessori education is based on the concept of learning in a well-prepared environment.

In this context, the learning environment should enable students to learn by exploring and engaging in different learning experiences. This research attempts to analyze the extent to which an authentic Montessori environment is compatible with the learning needs of gifted students in mathematics.

In action research, data should be collected through triangulation. Teachers should maintain the highest quality standards in their research work due to the following reasons. First, teachers have an obligation to their students. This reason is based on the premise that children’s education is a sacred trust placed upon the educator.

Hence, teachers should not expose children to the risk of poor performance by making decisions that are based on sloppy research. Second, teachers need to contribute to the body of knowledge. In this regard, teachers should produce quality research findings, which can be accepted by other educators.

Third, high standards facilitates personal and collective efficacy. Concisely, personal and collective perceptions of efficacy can improve if the teacher understands his or her influence on educational outcomes.

Teacher-made evaluations for regular and Montessori math curriculum can be summative or formative. Formative evaluations are essentially assessments, reviews, and observations that are administered continuously in a classroom. Formative evaluations help teachers to improve their instructional methods, as well as, students’ feedback during the learning process.

Summative evaluations, on the other hand, are conducted at the end of the learning period in order to assess the effectiveness of instructional programs. Summative assessments help teachers to evaluate the competency of their students at the end of an instructional phase.

Scoring rubrics are methods of illustrating evaluation criteria in the context of the expected students’ performance. They are external standards that facilitate objective assessment of students’ performance. Rubrics are commonly used to grade oral and written assignments. Table 1 summarizes the use of scoring rubrics.

*Table 1*

Teaching journals help teachers to generate new ideas, to find solutions to pedagogical problems and to reflect on their classroom experiences. Furthermore, they enable teachers to incorporate their past insights in future course plans.

Teaching journals are important tools for recording the marginalia that are often omitted in formal teaching documents. Teachers usually record observations in the journals immediately after completing each teaching session in order to avoid omitting anything. These observations enable the teachers to reflect on their experiences and to evaluate each lesson.

Learning outcomes can be measured using student behavioral scales that are based on organization, as well as, presentation of hands-on math materials. Measuring learning outcomes (SLO) involves verifying the occurrence of the desired learning.

In order to measure learning outcomes, teachers or educators must state the objectives of the measurements. Moreover, the objectives must be stated in measurable terms. Learning encompasses the process of acquiring skills, mastering concepts, and development of life perspectives.

Montessori education uses an elementary curriculum that motivates young students to develop interest in learning. In this regard, the curriculum promotes physical and social development of the students. It also enhances the spiritual and cognitive development of the young learners. In academics, the curriculum enables students to cover a series of Montessori learning materials in a sequential manner.

The students begin at a concrete level by improving their understanding of previous learning experiences and knowledge. This prepares them for the introduction of more abstract concepts. The lessons are provided at individual level and in groups of different sizes. One of the strengths of the Montessori teaching methodology is that it facilitates flexibility.

Continuous work sessions can be scheduled for morning hours, whereas lessons and group activities can be performed in the afternoons.

This leads to the development of independent students who are interested in learning and are able to manage their timely well. In this regard, the students complete assignments in notebooks, which must be evaluated on a daily basis. Furthermore, third year students have to take supplementary tests so that they can be prepared to join fourth grade.