¶ … Group Activities as Formative Assessment in Mathematics Classroom The modern educational system is characterized by an increase demand for accountability and high-stakes testing. The demand for such accountability and testing is demonstrated in the quest for the use of summative assessments that provide a summary of the learning progress of students. Generally, the push for increased accountability and high-stakes testing has contributed to the use of different kinds of assessments that are administered at the state, district, school, and national levels. The use of these various kinds of assessments is not only geared towards realization of increased accountability but also act as a means for comparing and ranking students and schools. An example of the type of assessments that can be used in this process is formative assessments for various topics such as mathematics. Formative assessments are defined as systematic procedures of collecting evidence regarding students' learning to inform teaching practices and help students progress towards the achievement of a learning goal. There are various kinds of activities used in formative assessments including group activities.

Overview of Formative Assessments

As previously mentioned, formative assessments can be described as systematic processes of collection of evidence regarding students' learning (Nunn, 2011). The information derived from the formative assessments is used to inform teaching practices and act as a guideline for ensuring students' progress towards the achievement of a specific learning objective. Formative assessments are usually very crucial in situations where the student learning is objective of education. This is primarily because the teaching process and these kinds of assessments are inseparable and cannot take place without the other.

Formative assessments are regarded as feasible and effective procedures to enhance learning in every grade level. As a result, this type of assessment has received considerable attention from school administrators and teachers in the past few years. The increased attention on formative assessments is also fueled by the fact that these assessments are criterion or subject referenced and pupil referenced (Hall & Burke, 2004, p.78). This implies that the variables of formative assessments are the effort the pupil puts into the work, context and content of learning, and student's progress over time towards achieving a learning goal. In this case, the conceptual ability of the student and relevant criteria influence judgment regarding the work and response given to the student.

Formative assessments act as important tools in enhancing the learning process and students' performance since they are diagnostic tools for every student and important elements in teaching. Through these assessments, the student identifies small ideas as they are generated in a particular activity whereas teachers identify bigger ideas towards enhancing student's progress and performance in learning. Moreover, formative assessments play a crucial part in the summative process because they are administered by the teacher. Students are usually encouraged to be involved in formative assessments because it helps them recognize their personal strengths and weaknesses in order to make significant and valuable progress. The valuable progress emanates from the fact that formative assessments are developed with regards to where the students are in their learning i.e. The specific skills and content.

The effective implementation of formative assessments necessitates teachers to re-conceptualize their roles as teachers, students' roles, and interactions between teachers and students. There are various strategies used to implement formative assessments effectively including determining, sharing, and understanding learning goals and objectives for success, developing effective classroom discussions and activities, and providing feedback that promotes progress in learning. The other strategies used in this process include enabling students to own the learning process and creating an environment where students act as learning resources for each other. In essence, teachers tend to be more productive in implementing formative assessments through focusing on a single area or topic of change at a given time (McGatha, Bush & Rakes, 2009, p.33).

Assessment of Mathematics

In the United States, the current public education system is largely based on the use of standardized testing as a crucial component for evaluating students' learning and academic progress. Currently, students' learning and knowledge is assessed on an annual basis through the use of open-response or multiple-choice testing methodology, which are also used as the basis for evaluating the efficacy of teachers based on the results of the tests. While teachers in the classroom have the liberty to choose the kinds of assessments to use, mathematics teachers tend to use multiple-choice tests as compared to other forms of assessments. Multiple-choice tests have largely been used as part of standardized testing methods for assessing students' knowledge of mathematics....

However, multiple-choice tests for mathematics have sometimes been used in combination with other tests while they have sometimes been used exclusively.
The exclusive use of standardized assessments in mathematics classroom can generate several problems since multiple-choice assessments do not offer teachers a comprehensive and all round means of the whole level of skill and ability of a student (Walsh, 2013). The conventional means of assessing mathematics have been based on the premise that it is an endeavor that entails the determination of a quick answer through the use of predetermined and internalized methods. These conventional means of assessment of mathematics such as multiple-choice tests do not reflect the actual complexity of the subject. This implies that standardized assessments, especially multiple-choice tests do not meet teachers' needs and contribute to the need for developing and establishing alternative forms of assessment in order to meet teachers' needs and help in providing important information for decision-making.

Generally, teaching mathematics presupposes that students do not reach classrooms or conclusions as blankly. Students need to engage in the topic as actively thinking individuals with a broad range of skills and conceptions ("Formative Assessment," 2012). This implies that assessing mathematics is more effective when it evaluates and utilizes prior learning in order for teaching to be adapted to students' needs. In this case, prior learning can be tapped through the use of activities that provide the students with various opportunities to express their thought processes and understanding. Therefore, the process does not necessarily require more testing but generating a series of explanations for a written question or during classroom discussions.

Formative Assessment in Mathematics

The concept of formative assessment originated from Michael Scriven use of the term to refer to evaluation procedures that play an important role in constant improvement of the curriculum (William, 2014). When introducing this concept, Scriven stated that evaluation of assessment may act as a means of enabling administrators to make decisions on whether the whole curriculum reflected adequately significant progress on the existing alternatives for justifying the adoption of a school system. During this process, he suggested that formative and summative assessment need to be incorporated into these roles.

Since the introduction of this concept, several researchers in the field of education have attempted to define formative assessment. The difference in definitions is fueled by the fact that the term itself is subject to differences in interpretations and usually means that it is carried out exclusively and at a time when teaching is taking place. One of the definitions of formative assessment is that it is a term used to describe constant, interactive evaluation of students' progress and knowledge in order to recognize learning needs and make changes to the teaching or instructional process suitably. Secondly, formative assessment is defined as a technique used by teachers to assess student comprehension of certain topics and skills they taught. In this case, the evaluation tool also helps in detecting certain student misconceptions and errors during the teaching or learning process. Despite the differences in definition, there are various characteristics associated with formative assessment including the fact that it helps teachers to identify gaps in student learning and teaching practice. In addition, this type of assessment helps students to identify their specific strengths and weaknesses in comprehending and understanding the topic or subject being taught.

Formative assessment in mathematics is increasingly considered as an alternative form of assessment of the subject because of the seeming ineffectiveness of the conventional methods of assessments. According to Walsh (2013), formative assessment in mathematics is a means of evaluating students' learning in which students are given instant feedback or response and provided with ideas on how to enhance their performance. Nonetheless, student feedback must be valuable and beneficial in a manner that encourages the student to think and in turn enhance his or her learning experience. This implies that the feedback should be specific, precise, clear, and timely so that students can make necessary corrections and enhance their learning.

The significance of using formative assessments in mathematics is its ability to offer teachers new insights and information about students' problem-solving skills and abilities and help influence teachers' instructional practices towards improved learning. This is mainly because formative mathematics assessments provide students the opportunity to demonstrate their skills and abilities in a better way than the conventional assessment methods. Notably, this kind of assessment can be used in a mathematics classroom to evaluate immediate student grasp and understanding of a whole lesson or part of the lesson.

In mathematics, formative assessment is a practical and effective tool or process for…