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February 6, 2024**Introduction**

Effective schooling identifies monitoring students' learning as essential to providing high-quality education. The following report highlights significant educational assessment systems used to monitor students' learning while an extensive narrative is also added to clarify the concepts. Careful monitoring is a major component of student progress as it determines the difference between effective and ineffective schools. Further, these analyses offer different instructional practices to identify student progress as it is one of the efficient predictors of student achievement in any institutional practice (Mor, Ferguson, and Wasson, 2015). Furthermore, according to Ysseldyke and Tardrew (2007), implementing an instructional management system and progress monitoring in the mathematics classroom measures students' performance.

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Considering this aspect, the results of this study stated that if these two practices are implemented with integrity or high fidelity, the performance in mathematics for all the students is significantly enhanced. Moreover, assessment is not usually occurring at the end of the course, but it is an integral part of constant classroom practice. It focuses on students' mathematical thinking and attention while taking a mathematical class. Research by Suurtamm (2017) suggested that all assessment methods are the aspects of teaching and learning by making effective instructional decisions.

**Monitoring and Assessment in Mathematics Classroom**

**Diagnostic Assessment**

According to Csapó and Molnár (2019), diagnostic assessment is essential in three domains: education, science, and mathematics. This is a 3D approach that distinguishes between the application, psychological and disciplinary dimensions. Moreover, another research evaluated that if a diagnostic assessment is implemented efficiently, learning mathematics and teaching can be explicitly enhanced in General Education and Training (Sekao, 2011).

Quenette (2014) states that teachers conduct multiple educational assessments to determine students' knowledge, including diagnostic tests.

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The research examined six teachers' diagnostic assessment systems in Year 9 mathematics. The diagnostic assessment system was (Specific Reveals Thinking) SMART system based on two topics: linear graphs and linear equations. This assessment provides teachers with a diagnostic analysis using online diagnostic test teaching advice to meet student's individual learning needs by reducing mathematical ability learning gaps in students.

Furthermore, diagnostic assessment evaluates the existing knowledge of students relevant to the subject, and that's why it is given at the beginning and at the end to identify the improved learning among students. In addition, diagnostic questions help teachers collect data on students' progress related to their class (Csapó and Molnár, 2019). According to Anselmo and Eaton (2017), this practice is an 'evidence-informed' approach in that it impacts decisions about students' pace in understanding insights of the topic.

**Formative Assessment**

Zhou (2017), in his study, said that early education requires a quality monitoring system, and mathematics is the critical content for the early educational assessment and development evaluation of children. Further, he mentioned that formative assessment and evaluation of its results reflect children's problem-solving ability and promote diversity in children's learning methods. According to Wanner (2018), the central aspects of student-centred assessment in higher education are self and peer assessment. He further mentioned that both assessment types are essential in developing key capabilities among students, such as better understanding and more responsibility towards the subject.

Both assessment forms develop critical reflection skills among students by evaluating learning skills. Further, he argued that developing this effective tool requires careful design development through feedback on the capabilities. However, another research by Thomas, Martin, and Pleasants (2011) mentioned that peer assessment is a deeper reflection of an individual's learning, also called independent assessment. It is related partially to self-assessment and partially to other's performances, such as classmates, when students reflect on themselves. On the other hand, Pachler et al. (2010) stated that the core factor in formative assessment is learners' self-regulation, which is directly linked with emotional and motivational factors that affect learners' engagement in learning.

Furthermore, a study has evaluated that formative assessment effectively assesses students' mathematics learning abilities. This study reviewed that in algebra interventions, instructional effectiveness is critical, and the best measure of instructional effectiveness is provided by a formative assessment promoting professional development (Accardo and Kuder, 2017; Hošpesová, 2018). In addition, Lambert, Algozzine, and McGee (2014) stated that in formative assessment, progress monitoring assesses students' performance individually in mathematics with the technology named accelerated math (AM) from grades 1-12 (Suurtamm et al., 2016).

**Summative Assessment**

An educational assessment in which the evaluator identifies what has been learned by an individual or group of students is a summative assessment (Hošpesová, 2018). However, Ofsted put a critical emphasis on 'teaching to the test and stated that "it prepares students to gain qualifications but not in equipping them well enough mathematically for their future". The author argued that achieving good grades does not necessarily involve teaching to the test. Teachers should adopt interesting and engaging approaches to teaching mathematics so that students feel confident applying their knowledge to practical situations (Marley, 2008). Summative classroom assessment is often performed for formative purposes as summative results are used to understand students' misconceptions for large-scale instructional purposes (Suurtamm et al., 2016).

Furthermore, as stated in the study of Schoenfeld (2015), summative assessments in mathematics are performance opportunities or examinations where the primary purpose is to assess the knowledge gained at the end of the course, such as SATs, stakes assessments, etc. However, another research by Marinho, Leite, and Fernandes (2017) on mathematics summative assessment practices presented that summative assessment emphasized competition and beliefs. This could be problematic as it only tells about what a student can and cannot do, nothing about where they should improve themselves.

**The Narrative**

Assessment is considered a critical piece of a learning process, which is essential for both the students and teachers in such a way that teachers can evaluate their teaching process and its effectiveness. In contrast, students learn their course in a much more effective way. Assessments affect multiple facets of education, including placement, student grades, curriculum, instructional needs, etc. (Moore Jr, Green, and Gallis, 2009). The foremost essential component is formulating and communicating goals.

When teachers share clear goals with students, a picture of achievement comes to mind about assessment to measure the achievement of these goals. Furthermore, selecting the correct evaluation at the right time during the course is also very important because the students can be assessed in different ways, such as proficiency, knowledge mastery, skill demonstration, and product creation. In addition, it has been viewed that using educational assessment for feedback is fruitful in improving learning.

**Purpose of narrative**

The primary purpose of this assignment is to assess how I select a range of different AFL strategies and use them effectively to inform my teaching and adapt lessons based on them.

**Assessment for Learning (AFL)**

According to Renkl (2013), educational assessment for learning is the process of interpreting and seeking evidence for teachers and learners to identify where the students stand in their knowledge and how far they need to go for a better understanding of the course. Similarly, as stated by Moore Jr, Green, and Gallis (2009), assessment for learning is beneficial in exploring the clarification of the course to the students because it gives teachers insights into the learning of their pupils and their practice of teaching. Furthermore, AFL also plays an essential role in assessing the learning capabilities of the struggling pupil in the classroom.

Learners can better gain knowledge by improving the learning criteria in the classroom (Renkl, 2013). AFL strategies evaluate whether the learner is on the runway, on target, and flying at cruising altitude; it means the learner has the prerequisite but cannot do the task. A learner can complete the task with some help and efficiently complete the task on his own. Moreover, Moore Jr, Green, and Gallis (2009) presented three key elements of AFL: assessed, diagnosed and remediated. In Assess, EPR (Every Pupil Response) techniques are used to identify misconceptions, see if a pupil needs help, and decide on re-teaching if necessary.

- To diagnose if the incorrect answer by a pupil was a result of a problem in the delivery of the course or if it’s the carelessness of the pupil by his habits or class behaviour.

- To Remediate, carry out some form of task analysis by dividing the task into sub-tasks and then exploring the relevant skills for each subtask, then ask learners to write a reflective journal to know if the pupil requires no more remediation on the specific topic.

**Justification for Choosing Assessment for Learning (AFL) Strategies**

**Baseline Test**

A baseline test is an initial test that teachers use to assess the pre-requisite or the student's existing knowledge. I use the baseline test as a diagnostic test to evaluate the pupils' knowledge of using key terms in mathematics and general calculation knowledge (Dixson and Worrell, 2016). In EAL (English as an Additional Language), students from most of my classes were around 80%. Therefore, it is necessary to check their Knowledge. That’s why I begin with a baseline test to diagnose students learning in every class about the previous class to assess their understanding, and then I switch to the next topic. In my chosen study unit, students learn about the pre-requisite skills needed for the number of branches of mathematics, statistics, and probability to make pupils efficient in catering probability on a number line. This may include Key terminology for probability, Sample space, Venn Diagrams & probability, experimental and theoretical probability, relative frequency, and real-life problem-solving.

It takes a long time for an EAL learner to frequently learn English for Academic Purposes and perform tasks of academic education in English. For this reason, EAL teachers need to track learners' progress at the start, middle, and end of each class and course (Renkle, 2013). When I make baseline assessments, I keep in mind that I need to evaluate the key skill areas of the learners and their knowledge of Mathematics by analyzing their speaking, reading, listening, and writing abilities. For example, I take tests such as written comprehension, oral dictation, and vocabulary after an individual class to identify Literacy, Communication, and Language understanding of EAL maths.

According to Moore Jr, Green, and Gallis (2009), the instrument baseline tests are used by teachers to determine a pupil's natural ability, learning needs, and potential. These tests measure the learners' cognitive abilities, which are essential in generating an expected level of achievement. I have the same perspective for the baseline tests. I take tests to measure students' abilities in Mathematics and fulfil their purpose of taking an EAL course, for example, the students learning it for the General Certificate of Secondary Education (GSCE) level. Moreover, for the test from the diagnostic assessment system designed for learning mathematics and its language, I give students task sheets for numbers, addition, and subtraction, evaluate their understanding of fractions and LCM and identify their knowledge of geometry by giving them word problems to enhance their problem-solving skills.

**Targeted Questioning**

According to Bellman, Byrne, and Sege (2013), one of the integral parts of classroom learning is questioning, and essential for any teacher are questions. One of the effective methods for formative assessment is target questioning, which serves many purposes and enhances student engagement in the learning process. Furthermore, target questioning provides opportunities for the students to ask any query by evaluating their understanding of the topic (Dixson and Worrell, 2016; Hargreaves, Gipps, and Pickering, 2014). I effectively apply this learning strategy assessment in my class as it challenges their levels of thinking and informs whether the knowledge provided in a lecture is clear to most students. Then, I progress further learning in my classroom. Questioning is a straightforward educational assessment technique. However, this differs in EAL as it requires proficient teacher knowledge and is a crucial pedagogical skill. Students, while learning, may think that the teacher has the dominance to talk in the classroom, so an AFL strategy of target questioning gives them a chance to the students to speak up in the class and explore themselves (Dixson and Worrell, 2016).

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I managed to ask such questions from the students related to the management of the classroom, information-recall, and higher-order questions, for example, how could you define probability, and what can you tell about intersection and union? I randomly ask individual pupils a problem-solving question related to the topic taught in class to analyze their familiarity with the topic. Moreover, for active participation in the classroom, I ask questions for the students, and whoever answers first gets bonus marks. Sometimes, during the lecture on Mathematics for EAL students, I ask students to give real-life examples related to the topic that reflect their more profound understanding of the connections of statistics with real-world problems and the use of probability in common games, etc. For example, the likelihood or unlikelihood of rain at times of the year, how financial institutions use it to determine the risk, etc.

**Exit Ticket Question**

As Simpson (2012) stated, exit ticket cards or questions are an easy and quick way to assess students' knowledge and measure their progress during that class. Exit ticket cards are short prompts the teacher uses for quick diagnostic assessments of students. When the students are about to leave the classroom, they are asked to fill out the exit ticket card, designed to collect lesson feedback and check whether they understand a specific topic (Spendlove, 2009). I practice this strategy in my classroom with EAL students daily practice. For example, sometimes, I ask the students to write the key points learned in that particular class in a summarised format. Then, I studied them to evaluate the students' problems or the topic area most students needed help understanding.

According to Creghan and Creghan (2013), exit ticket questions have multiple advantages, such as requiring less preparation time. If the topic is continued till the next class, it is best to attain feedback and improve the need for more understanding of that topic in the next lesson. Moreover, students feel fun with this AFL strategy. At the same time, teachers can be creative with this strategy by designing it like a boarding pass such that students can leave the classroom by showing the boarding pass, or it can be made like train tickets or look like smartphone applications such as a Facebook review post or a Twitter post, etc. I take exit card feedback from students as they leave the classroom, which is extremely useful.

Moreover, I also identify the criteria of how a lesson should go in my class for better information delivery and use it as a benchmark to measure students' learning. After introducing the exit ticket question in my classroom, I consider it a potent tool for me in setting clear objectives for the learners and getting feedback provided at least 80% of success in my students’ performance. For example, I give them exit questions in my M&A class in year 10, as shown below. See Section 1( Venn-Diagrams Lesson plan 2020-03-11). Students in the class performed well in it, and that’s why I was able to teach Venn diagrams and probability combined in my next lesson. I knew I would need more time on this topic if I found any concerns or misconceptions.

**Educational Assessment Strategies**

**Mini Plenaries**

Mini plenaries are the shift from group to class and back to a group in discussion during a small group collaborative activity in the classroom (Creghans and Creghan, 2013). Mini plenaries are the only way to understand the student's needs in the middle of the lesson and to assess if the learners need more input about specific key terminology of mathematics or its operations. The group discussion as mini plenaries allows students to discuss their ideas with their mates and learn something from them that they could not understand during the lecture (Hargreaves, Gipps, and Pickering, 2014). I use mini plenaries once during my lesson to ensure I am going right with my lesson and that students are with me. Moreover, providing the next topic or the next step in the classroom for the pupils would be effective.

Mini plenaries help me get feedback from students. According to Bartlett (2015), mini-plenaries give students the ability and opportunity to reflect on how and what they have learned for the teacher's next steps. I use this technique by using the ‘Give me Five’ quick activity in the middle of the classroom, where the pupil draws a hand. Each finger has a different question regarding the lecture, such as a thumbs up, meaning what you understood up till now in this lecture, or a ring finger for the operation of mathematics taught in class, which is difficult to understand by students. I also used a quick activity of ‘Keyword Bingo’ by randomly questioning pupils about the keywords of the whole topic and how much they remembered from the lecture.

**Self and Peer Assessment**

One of AFL's proven and effective techniques is self-assessment and peer assessment. This technique is about improvement and revision, as students can assess their knowledge and progress rather than relying on the teacher’s judgment (Nicol, 2010). This educational assessment is carried out in my placement school as a compulsory activity because individual self-assessment pupils get actively involved in the learning process. This is one of the major reasons for skill development among students and helps them improve their required areas (Brown, 2015). Therefore, I train my students for self-assessment, make them understand the actual purpose of learning, and grasp the knowledge they want to gain for future achievement in GSCE exams.

Also, some common misconceptions due to peer marking are discussed among pupils, which creates a better understating of the course. I use the self-assessment results to inform teaching as a compulsory AFL strategy in my school. Moreover, students learn through self-assessment and view their mistakes and level of learning in the classroom, making them understand whether they are getting the course material. Teachers also get help from self and peer assessment because frequent assessment allows teachers to evaluate if the learning has been effective by ensuring the information gained by students and where they could improve their understanding of the course (Wong et al., 2015).

**Feedback through Marking**

This AFL strategy in mathematics is purposeful and precise. Learners get to identify the misconceptions, which helps them improve and learn from their mistakes through feedback by marking (Chetwynd and Dobbyn, 2011). On the contrary, according to Hendry, Bromberger, and Armstrong (2011), marking students’ performance has no positive effects on learning and may lower students' self-esteem. My purpose in educating Mathematics to EAL students (The majority of the class is on EAL) is to make pupils understand the concepts of Maths and make them able to solve the problems related to it, for example, using probability in real life to determine the risk.

Therefore, by using feedback through marking, I monitor and assess the individual’s performance and also learn how I should excel in teaching from the most common mistakes of a student. I believe marking learners should also be written feedback, which is more effective and constructive than marking. As Wong et al. (2015) stated, marks may lower confidence and negatively impact students. Still, motivating feedback may help them take the feedback through marking positive and improve in future tests.

**Summative Assessment**

According to Taras (2009), the goal of a teacher is to successfully engage with the learners and make them understand complex problems. Moreover, Dixson and Worrell (2016) stated that summative assessments are essential in analyzing the course curricula and goals by evaluating learners' understanding and skills, measuring their competencies, and assessing their problems. Cilliers et al. (2012) highlighted that summative assessments indicate standards aimed at monitoring students’ performance and raising the current standards of the school. Further, the author also mentioned that these tests motivate students and make them put effort into reducing the gap between their learning skills.

Although summative assessments raise the morale of the high-achieving students, other learners can also be encouraged by their performance and make them better in the remaining learning process of the course. Moreover, according to Taras (2009), to analyze the mastery of the subject area, teachers consider a few components depending upon their course, which carry out a summative assessment to achieve positive influences on students through learning outcomes.

**Conclusion and Evaluation**

M &A assignment for five lessons with this class allowed me to learn and practically implement a broad range of educational assessment strategies such as printed starters, mini plenaries, mini-whiteboards, targeted questions, self-assessment, peer marking, and exit tickets. The assessment and feedback strategies that I mainly used followed school policies. These techniques helped me to develop tailored resources and enhance my capacity to provide effective feedback. These measures enabled me to identify better misconceptions and class ability, which improved my teaching practice throughout the topic. Reflection allowed me to select effective AFL techniques relevant to my class, making a lesson more exciting and challenging. Also, I formulated interesting question AFL questions.

Results from the exit ticket and mini plenaries assessment between the lectures show that understudies made significant progress and their attitude towards learning mathematics improved significantly. Pupils have attained vital knowledge of this topic and have started taking the initiative in their learning. Understudies learned that making mistakes and learning from them is an aspect of progression, which is extremely useful in increasing understanding. Learning through mistakes helps to reduce the risk of them occurring in the real examination. The main lesson learned from this study unit is that the most essential function of the assessment is to move pupils forward in their learning.

**Review the following:**

**References**

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Hošpesová, A., 2018. Formative assessment in inquiry-based elementary mathematics. *Gabriele Kaiser· Helen Forgasz Mellony Graven· Alain Kuzniak*, p.249.

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