Group activities as formative assessment in mathematics classrooms

¶ … 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 enhancing mathematics learning in every grade level. School administrators usually refer to formative mathematics assessment as assessment for learning, which is a cyclic teaching process where teachers constantly collect information regarding students' knowledge and plan. Information about students' knowledge and plan in mathematics is in turn used to develop and execute instructional activities in a suitable manner. Formative assessment in mathematics also entails the use of various activities to enhance students' learning and experiences. These activities may be channeled towards individual students, various student groups or the entire class depending on various factors in the teaching process.

In the past few years, several studies have been conducted regarding assessment in mathematics, especially formative assessment with regards to its implementation and effectiveness. Formative assessment in mathematics goes beyond numbers, shapes, and symbols to incorporate what students know and think about the instructional process (Benjamin, 2013, p.78). This assessment helps in understanding students' knowledge and thoughts in mathematics since it provide opportunities for verbal and written feedback in mathematics. The need for students' feedback is important in mathematics since class discussion is not adequate to provide the various dynamics related to a student's learning, comprehension, and understanding. Actually, formative assessment in mathematics helps in generating three types of feedback through which learning is effected. These types of feedback include student to teacher, teacher to student, and student to student feedback.

The provision of feedback is one of the most important elements of formative assessment in mathematics because it promotes communicative interactions within the classroom environment. Through communicative interaction, students are able to grasp the lessons clearly and understand what is expected of them, students receive feedback about their performance and how to improve, and students obtain guidance on making necessary improvements. The other important dimensions of communicative interaction brought by formative assessment include full incorporation of students in the decision making process and awareness of available help (Clark, 2008, p.6). Therefore, formative mathematics assessment provides a new way for implementing the concept of student centered learning. Formative mathematics assessment essentially positions students at the core of learning and assessment interactions given that they are most significant and vulnerable stakeholders in the learning process.

Group Activities in Formative Assessments in Mathematics Classroom

Given the significance of formative assessments in enhancing students' learning and knowledge in mathematics, there are various strategies and activities that can be implemented to perform the evaluation in mathematics classroom. Some of the most commonly used strategies for formative mathematics assessments in the classroom environment include presenting open questions and tasks to students, conducting students' observations, listening to students, and evaluating student work. Group activities can be used as formative assessments in mathematics classroom because they incorporate various resources that are designed to develop mathematical comprehension and activity.

Formative assessment classroom techniques such as group activities in mathematics classroom are valuable because these techniques promote the development of communicative interaction in the class. As previously mentioned, communicative interaction between the various stakeholders in the learning process is vital towards understanding learning needs and shaping instructional techniques for enhanced learning. The complexity of mathematics lessons contribute to the need for ensuring communicative interaction takes place within the classroom. As a result of communicative interactions, teachers effectively determine the students' learning needs and strengths and weaknesses in mathematics as well as identify the learning gaps in instructional practices. Similar to other subjects, the collected information in mathematics classroom is in turn used to develop effective learning strategies and practices.

The daily work of mathematics teachers entails asking questions, listening to students carefully, observing students during group work, evaluating the writing and representations by students, and initiating classroom discourse to promote sharing of ideas between students (Keeley & Tobey, 2011, p.3). The interactions between students and teachers, teachers and students, and students incorporate the use of various assessment methods. The use of these techniques such as group activities in formative assessment in mathematics classroom is geared towards various learning objectives. One of these objectives is to enable students to think deeply regarding their ideas and concepts in mathematics. Secondly, the techniques help in understanding the contribution of students' thoughts to the learning process, which can utilized as the beginning point for developing instruction. Third, the techniques help instructions to identify the progress of individual students and class towards developing mathematical understanding and comprehension.

There are various group activities that can be used as formative assessment in mathematics classroom. The various group activities are developed and implemented based on various learning outcomes towards enhancing mathematical comprehension and understanding. Teachers or instructors should develop the group activities based on the specific learning outcomes they seek to achieve as well as in consideration of the various characteristics related to the classroom environment. Some of the most common examples of group activities that can be used as formative assessment in mathematics classroom include

Classifying Mathematical Objects

This type of group activity can be utilized as formative assessment in mathematics classroom since this subject is characterized by conceptual objects like shapes, numbers, and functions. When using classification of mathematical objects as group activity in formative mathematical assessment, students should develop their own categories for these objects and utilize the classifications developed by other students and/or teachers. In this kind of group activity, the students examine mathematical objects carefully before categorizing them depending on their varying characteristics. During this process teachers gain understanding of students' comprehension of the meaning of several mathematical symbols and terms as well as the procedure through which these symbols and terms are created (Swan, 2005). The most common examples of group activities in formative mathematics assessment include odd one out and categorizing using two-way tables.

Interpreting Multiple Representations

The second type of group activity in formative assessment in mathematics classroom is the interpretation of several representations. This activity entails matching cards with varying representations of relatively similar mathematical concepts and ideas. The assessment is geared towards enabling students to identify the relations between the various representations and creation of new mental images for mathematical concepts and ideas. The need to develop such links emerges from the fact that mathematical concepts have various representations like graphs, words, tables, diagrams, and algebraic symbols. The group activity helps in enabling the representations to be interpreted, compared, shared, and classified in ways through which meaning is understood.

Mathematics teaching and learning largely entails providing instruction regarding essential technical skills for developing and manipulating representations. However, this process requires balancing the technical skills with activities that provide a platform of reflection on the meaning of the mathematical representations. Group activity in formative assessment in mathematics classroom help provide the balance in learning technical skills and deriving meaning of mathematical representations. The activities help students to not only interpret these representations but also help in constructing meanings of the representations. The activities vary from simple ones such as domino-like activities to complex ones that incorporate aligning at least three representations of a similar object.

Evaluating Mathematical Statements

Group activities on formative mathematical assessments enable students to gain an understanding of several mathematical generalizations or statements. Once students are presented with these generalizations or statements, they are required to determine whether they are true or not and provide reasons for their arguments. This group activity is very crucial towards enhancing students' learning and knowledge with regards to mathematical generalizations and statements. The explanations that students need to provide always entail creating examples and counter-examples to support their arguments (Swan, 2005).

The significance of this activity is attributed to the fact that it enables students to develop their ability to explain, persuade, and prove. These mathematical statements can be created in a manner that enables students to deal with common mathematical misconceptions and difficulties. The statements and generalizations can be developed at any difficulty level or grade to help ensure students' progress towards the achievement of a learning objective. Some of the various difficulty levels with which group activities for formative assessment in mathematics classroom can be developed include the size of numbers, number operations, algebraic generalizations, calculus, area and perimeter, and sequences.

Creating Problems

In this kind of group activity in formative mathematic assessment, students are given the chance to generate their own mathematical problems. During this process, students attempt to develop problems that are difficult or challenging and those that they can solve precisely. The students first solve their own mathematical problems before the engage others in solving them. This implies that students provide support and act as instructors when the student solving the problem experiences some difficulties. Some of the problems that can be created include variants of current problems and exploring several mathematical procedures.

Analyzing Reasoning and Solutions

The analysis of reasoning and solutions is also an important way of assessing students' knowledge and learning in mathematics by providing a different approach towards understanding mathematics. Unlike the other activities, these kinds of group activities are developed to provide a different focus from obtaining an answer to a situation where students develop capability to assess and compare varying forms of reasoning. Some examples of activities include comparing various solution strategies, correcting mistakes in reasoning and prioritizing reasoning. When analyzing reasoning and solutions, students have the opportunity to experiment and make mistakes without harsh consequences (Seaton, 2013, p.965).

Integrating Group Activities in Formative Mathematical Assessments

Based on the above analysis, the integration of group activities in formative mathematical assessments is crucial towards enhancing the effectiveness and overall result of these kinds of assessments. It is crucial to incorporate group activities in formative mathematical assessments because of their role in promoting learning. Generally, in mathematics, students are constantly tested and ranked though these measures do little to enhance learning. This implies that effective assessment initiatives should be developed to enable teachers develop students' previous knowledge and align their teaching practices to the students' learning needs. Through integrating group activities into formative mathematical assessments, learning is improved through providing students with opportunity to experiment with different strategies. According to Hudesman et. al. (2013), the assessments help students to start understanding that learning is directly linked to experimenting with various strategies (p.3). As previously mentioned, formative assessments are effective assessment strategies in mathematics that generate huge gains. These assessments have proven effective in generating huge achievement gains across a spectrum of content domains as compared to other academic interventions that have been used to enhance learning (Hudesman et. al., 2013, p.2).

While the integration of group activities in the classroom environment is important towards enhancing the effectiveness of formative assessments, the process requires adherence to certain principles and processes. In mathematics, teachers need to ensure adherence to these principles because they do not plan in a vacuum and need to consider the students' previous achievement and potential. The integration process also involves developing lesson plans that become the basis of implementing the series of proposed group activities for formative assessment in mathematics classroom. Moreover, the consideration of these principles and processes helps in ensuring that the activities are developed and implemented based on the individual student's learning needs. However, the process also helps in ensuring that the lessons plans have adequate built-in flexibility for students to respond to various emerging issues in order to widen their mathematical comprehension and understanding. Some of the necessary principles and processes to undertake as part of integrating group activities in formative assessment in mathematics classroom include