**5. What makes a good mathematics classroom assessment?**

A good classroom assessment plan gathers evidence of student learning that informs teachers' instructional decisions. It provides teachers with information about what students know and can do. Students should, at all times, have access to the assessment, so they can use it to inform and guide their learning. However, how can assessment be used to improve mathematics teaching?

Using classroom assessment to improve both teaching and student learning is not a new concept. But assessments designed for evaluating student performance through scrutiny of examination results (test scores) will not help improve instructional practices of teachers that enhance students' learning. Assessment for learning should be treated as an integral part of an instructional process and as an essential element in teachers' effort to help students learn. It is encouraged that before teaching students, teachers should employ baseline assessment to see what students already know. During the learning experience, teachers should employ formative assessment to address the misconceptions that may arise and after the learning experience; summative assessment should be employed for evaluating the effect of the instructional process on student knowledge. There is then a need for balanced packages of assessment tools, with all the elements of fair testing in it. A teacher can use concept maps, concept tests, examinations, oral and poster presentations, peer and self-assessment, portfolios, rubrics or written reports investigations, projects, class activity, and weekly or fortnightly concept tests as forms of assessment instead of using only tests as forms of assessments. However, to use classroom assessment to make improvements, a teacher should employ all forms of assessments, i.e., baseline, formative, diagnostic, and summative assessments. The choice of methods of scoring students in these different forms of assessments is guided by the purpose of assessment. Methods of scoring students should be such that they enable the student to demonstrate what they know rather than what they do not know. A teacher may elect to use a rubric because it enables him/her to score students on all their thinking processes and not only focus on one correct answer [6]. In that way teachers would be able to identify the misconceptions that students have and employ appropriate teaching strategies when addressing the misconceptions. Very often testing is meant to find out what the students do not know. This is a rather negative approach, and it does not give the students a chance to show what they do know [6]. One result may be that the student loses confidence. Assessment should support learning; it should not be a judgment. Therefore the techniques a teacher

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*Formative Assessment in Mathematics Education in the Twenty-First Century*

their instructional approaches (techniques) in three ways:

• *Give students second chances* to demonstrate success.

as opportunities for reconstruction of their knowledge.

and that helped them to broaden and expand their learning.

**5.3 Give students second chances to demonstrate success**

may use in a mathematics classroom to make students understand better help them become more independent and stimulate their critical thinking [8]. Therefore, what stands out to be a good mathematics classroom assessment for teachers is to change

• Use *assessments* to establish and describe the students' misconceptions.

• Turn these misconceptions into teaching and learning opportunities.

**5.1 Use assessments to establish and describe the students' misconceptions**

**5.2 Turn these misconceptions into teaching and learning opportunities**

Assessment must be followed by corrective instruction designed to help students remedy whatever learning errors are identified with the assessment [10]. Using corrective instruction is *not* the same as reteaching, which often consists simply of restating the original explanations louder and more slowly [12]. Instead, the teacher must use strategies that accommodate differences in learning styles and intelligences [13]; for example, to teach circle geometry, I gave the students all the different circle theorems and then showed them several circle questions to identify the theorems within and find missing angles using these theorems. There was no success in this type of instruction as students did not remember the theorems; hence, they could not identify or apply them in questions. I decided to alter instruction by creating different circle handouts where students were directed to draw lines to create the theorems, measure the angles with groups, and infer circle theorems based on what they observed. This new instruction of circle geometry gave far better results as students were remembering most of the theorem since they discovered them on their own. However, students who had few or no learning errors to correct also participated in the enrichment or extension activities

Teachers should strive to help their students become lifelong students and to develop learning-to-learn skills [10]. What better learning-to-learn skill is there than learning from one's mistakes? Mistakes should not mark the end of learning; rather, they can be the beginning. As such, assessments must be part of an ongoing effort to help students learn. If teachers follow assessments with corrective instruction, then students should be provided a second chance to demonstrate their new level of competence and understanding [11]. This second chance determines the effectiveness of the corrective intervention while giving students another opportunity to experience success in learning, thus providing additional motivation [11].

Teachers' knowledge of students' misconceptions should go a long way in equipping them to prepare mathematics activities in their classroom. This will allow them to plan instruction targeting the student misunderstandings. I can conclude that formative assessment, like homework, can be used to locate mistakes and to figure out why they were made and how to provide support to students by way of explanation and tutoring [19]. This approach can help teachers learn some pedagogical lessons from exploring the content of students' procedural knowledge and understanding [9]. That is, when students make mistakes, they must be considered

*DOI: http://dx.doi.org/10.5772/intechopen.88996*

*Theorizing STEM Education in the 21st Century*

reflections, or asking students to summarize lesson taught. The assessment tools they may choose to apply to assess student learning may differ depending on the stage of learning. However, assessment only *of* learning (summative assessment) and not *for* learning (formative assessment) is not enough to promote students' integrated understanding. They may use concept maps (connections between and among mathematical ideas), concept tests, examinations, oral and poster presentations (use different representations of mathematical ideas to support and deepen mathematical understanding), peer and self-assessment (introduce the peer or self-marking of home/ classwork in the classroom, and allow for discussion if there is a disagreement of an answer), portfolios, rubrics, or written reports. All these forms of assessment tools in mathematics allow for ways of assessment that motivate students to learn and thereby avoid damage to student self-esteem [7]. Besides, these different forms of assessment tools give helpful feedback to students in that they are guided on how to avoid making similar mistakes in the main examination. Furthermore, students are guided on how to

improve their performance, and this impacts positively on student learning [7].

A good classroom assessment plan gathers evidence of student learning that informs teachers' instructional decisions. It provides teachers with information about what students know and can do. Students should, at all times, have access to the assessment, so they can use it to inform and guide their learning. However, how

Using classroom assessment to improve both teaching and student learning is not a new concept. But assessments designed for evaluating student performance through scrutiny of examination results (test scores) will not help improve instructional practices of teachers that enhance students' learning. Assessment for learning should be treated as an integral part of an instructional process and as an essential element in teachers' effort to help students learn. It is encouraged that before teaching students, teachers should employ baseline assessment to see what students already know. During the learning experience, teachers should employ formative assessment to address the misconceptions that may arise and after the learning experience; summative assessment should be employed for evaluating the effect of the instructional process on student knowledge. There is then a need for balanced packages of assessment tools, with all the elements of fair testing in it. A teacher can use concept maps, concept tests, examinations, oral and poster presentations, peer and self-assessment, portfolios, rubrics or written reports investigations, projects, class activity, and weekly or fortnightly concept tests as forms of assessment instead of using only tests as forms of assessments. However, to use classroom assessment to make improvements, a teacher should employ all forms of assessments, i.e., baseline, formative, diagnostic, and summative assessments. The choice of methods of scoring students in these different forms of assessments is guided by the purpose of assessment. Methods of scoring students should be such that they enable the student to demonstrate what they know rather than what they do not know. A teacher may elect to use a rubric because it enables him/her to score students on all their thinking processes and not only focus on one correct answer [6]. In that way teachers would be able to identify the misconceptions that students have and employ appropriate teaching strategies when addressing the misconceptions. Very often testing is meant to find out what the students do not know. This is a rather negative approach, and it does not give the students a chance to show what they do know [6]. One result may be that the student loses confidence. Assessment should support learning; it should not be a judgment. Therefore the techniques a teacher

**5. What makes a good mathematics classroom assessment?**

can assessment be used to improve mathematics teaching?

**132**

may use in a mathematics classroom to make students understand better help them become more independent and stimulate their critical thinking [8]. Therefore, what stands out to be a good mathematics classroom assessment for teachers is to change their instructional approaches (techniques) in three ways:

