The interactions between the variables of instructors, students, curriculum, local context, and other aspects in teaching have an impact on what will occur in courses (Stigler and Hilbert, 1998). Rubenstein (2004) endorsed the idea that teaching is a difficult task. The foundational knowledge for teaching mathematics comprises an understanding of mathematics, the relationships between mathematical concepts, student learning, and school culture. Creating a learning community, pushing students to make sense of mathematical concepts, and fostering students’ growing knowledge are all part of the teaching process. Teachers are one of the most significant variables influencing students’ success and the teaching process, according to Rubenstein (2004).
Math instruction that is effective involves instructors and students interacting in ways that provide pupils the best chance to learn as much as possible. There are many different ways that pupils and instructors communicate in a classroom. Some encounters lead to classroom discussions, teacher- and student-initiated inquiries, and student learning. Cooperative group work, peer tutoring, and a variety of other feedback mechanisms, including assignments, tests, and electronic response mechanisms like the personal responses system (PRS) and the personal data assistant (PDA), are examples of instructional strategies that offer some degree of two-way communication in which knowledge about what is taught and what is learned is exchanged between two people. On the other hand, some teaching systems have students just sitting still in classrooms with one-way communication between the instructor and the pupils. on the campuses of several universities and institutions. As an example, the professor serves as the legendary “Sage on the stage,” and the didactic lecture serves as the ideal method of instruction. Although giving a lecture to a large group of students is an effective way for a teacher to convey information, simply giving information to someone does not guarantee that they will learn it. In order to know whether learning is occurring, in addition to the instructional interactions, there must be teacher-student assessment interactions.
When instructors collect data on students’ learning and use it to assist students better comprehend ideas and principles and apply knowledge, rather than merely learning factor, that is when assessment interactions between students and teachers take place. Formative assessment is characterized as the following sort of assessment interaction: In order to increase students’ accomplishment of the planned instructional goals, instructors and students employ a method called formative assessment, which gives feedback during teaching (council of chief school states officers, 2008). It is evident from this definition that formative assessment is a process that may involve tests or various other types of assessments, but it may also involve interactive instructional strategies like classroom discussion, assignments, homework, quizzes, projects, investigations, electronic response systems, or oral questions in order to direct and enhance students’ learning (Angelo and Cross 1993, Fennell, 2006) It might be difficult to create a math classroom with an engaging learning atmosphere where kids are actively studying arithmetic.
Students may feel self-conscious about their understanding of arithmetic concepts and may be reluctant to speak out during class discussions or in response to instructors’ spoken questions. Also, staying focused while navigating the complicated interactions between instructors’ speak, students’ discussion, and the classroom dynamic requires a specific set of abilities. These classroom dynamics are seen as a social endeavor in certain models of “best practices” in mathematics teaching and learning (Cobb and Bauersfield, 1995), where the classroom functions as a learning community where thinking, criticising, arguing, and agreeing are encouraged. When this dynamic is successful, it may lead to the development of a learning environment where students’ learning flourishes and they assume an increasing amount of responsibility for their own learning.
A effective learning environment, according to Motani and Garg (2002), is one in which instructors and students may engage freely, constantly, and without any restraint. In this kind of learning environment, instructors monitor their pupils’ learning to ensure that they are understanding the concepts being taught. The adoption of an immediate feedback system and its execution are crucial to this achievement. When students misinterpret a concept or principle that is crucial to achieving the learning goals, instructors may step in right away thanks to quick feedback. A teacher may need to change their approach to teaching, provide various examples, or often offer alternate explanations. Teachers demonstrate their understanding and appreciation of the fact that earlier attempts to teach the topic or principle were unsuccessful by making these improvements.
According to Guskey (2003), all students learn better when educational changes are made right away with the goal of reaching all students, including less successful ones. Teachers of mathematics have a variety of tools at their disposal to assess how effectively their pupils are absorbing the subject they are being taught.
There are both non-electronic and electronic mechanisms for receiving feedback, according to Motanic and Garg (2002). Class discussions, collaborative group projects, board assignments, seat assignments, and responding to queries that are put forward verbally are examples of non-electronic mechanisms. Although while these interactive tactics are successful, a significant drawback is that at any one moment, only a portion of the class is actively sharing information with the instructors about what they are learning and getting feedback from the teachers. to encourage more students to participate in the interactive activities. It is important to take precautions to ensure that interactive assessment methods used by teachers—such as assignments and exams—are successful in assessing what and how much pupils have learned.
The fact that pupils are not given feedback during education is one reason why caution must be used. Students may have advanced to “learning” new material when they reply to questions on assignments or exams. The cumulative impact of knowledge coupled with no corresponding feedback might put pupils at risk of subpar performance or even failure. If there were misunderstandings of the previous subject that were not quickly corrected when it was delivered. The fact that students often concentrate on doing whatever is required to receive the best score on assessment methodologies employed by students in this curriculum may also be a contributing factor in how little learning occurs.
Also, the authors agree with Tyler’s (2000) observation that math learning should occur via the students’ engaged behavior and the teacher’s compelling instruction.
Lastly, Tyler (2000) said that learning occurs not as a result of what the instructor does but rather as a result of what the students do.