Diagnostic Assessment Conducted on Student in Mathematics, Number and Place Value Content Strand - Case Study Example

Running head: INTERVENTION REPORT Intervention Report Following Diagnostic Assessment Conducted on Student in Mathematics, Number and Place Value Content Strand Name Course Information Professor Information Date Due Table of Contents Table of Contents ii 1.0 Introduction This paper is an intervention report focused on establishing the grade of a primary school child using diagnostic assessment and laying down a foundation for a lesson plan which will reflect student’s level of learning and Australian Curriculum requirement. Both the parent and the teacher were consulted for consent. For purposes of producing this report, number and place value content strand in Mathematics was selected. The report further sought to shade light on how formative and summative assessment was integrated in the planned lesson. Later, a reflection on assessment cycle will be made which will lay a floor for a follow up lesson. 2.0 Student Profile In diagnostic assessment, student’s prior knowledge and difficulties are deduced with an intention of improving learning experience and achievement level. Failure to conduct diagnostic assessment hampers level of student’s engagement with learning consequently reducing achievement. Australian Curriculum Assessment and Reporting Authority (2013) give an outline of proficiencies required for number and algebra strand for a Year 1 child. These proficiencies are majorly cognitive since they entail use of the mind. Mark Anthony was selected to undergo diagnostic assessment in order to understand his achievement level specifically in number and place value content strand. Aged between five and six years, Mark had already gone through kindergarten and pre-primary stages thus able to recognize number of objects by simply making an observation. This meant that the student was in a position to identify one, two, three objects by making a glance. It is therefore evident that Mark could quantify a collection of objects, a skill that was developed either before schooling or during kindergarten and pre-primary stages. Besides, Mark was secured in his mind that regardless of changing arrangement of objects, their sizes remained intact. This demonstrates that Mark had a strong foundation for operations such as additions and subtractions, which are vital for proficiency in problem solving. The second element characterizing abilities of Mark was the acquired skill of counting, both forward and backwards. This student was not only able to count numbers to at least five, but was also confident in aligning number of objects with number name i.e. two for two objects. Apparently, Mark seemed to count numbers sequentially and any attempt by a teacher to change sequence did not result in confusion. This is a demonstration of fluency in dealing with numbers an element credited to classroom learning activities such as songs and chants. Thirdly, Mark had developed the capacity to sort and classify objects in line with similarity and difference. By putting together different objects with varying shapes, Mark classified the objects into groups of similar shapes. Moreover, Mark related shapes with real life objects i.e. circles for wheels of a bicycle. This was evidenced by the way he responded to questions asked. Mayring and Rhöneck (2003) note that besides the cognitive variables, affective factors also influences learning. In line with affective domain, teacher behavior influences learner behavior and mental development. This implies that a warm and receptive teacher affectively imparts in a learner positive behavior. It therefore explains why a Year 1 teacher is always considerate, understanding, receptive, friendly, and loving. By extension, orderliness in a classroom setting is also explained by teacher behavior which has affective impact on a student. This was elicited during contact with the student. To end a certain learner behavior, it was necessary to send particular behavior that conveyed a message to the student. Affective domain, particularly in Year 1 classroom, works efficiently in classroom management behavioral change. 3.0 Diagnostic Phase The intention of diagnostic assessment is to identify student’s prior knowledge while pointing out misconceptions (Gough, 2002). It further serves the purpose of bringing forward interests and learning styles preferred by a learner. Diagnostic assessment is often conducted before executing classroom instruction thus acts as a guide for planning and differentiating instructions. This assessment can be done by subjecting a student to a short answer or multiple choice questions. In the context of Mark Anthony, an assessment was conducted through questioning tool. The achievement standard for Year 1 student, as provided by Australian Curriculum, requires that at the end of the year, such student ought to be able to give a description of sequence of numbers that result from skipping some digits, say 2s, 5s and 10s. At the end of the year, the student was further expected to be in a position to offer a description of data displayed before him. In relation to place value, Mark should be capable of counting numbers from and to 100 and to further locate the digits on the number line. By using counting techniques, the student was expected to confidently execute additions and subtractions. To add on this, it is envisioned in Australian Curriculum that at the end of the grade Mark should have mastered the skill of place value to partition numbers. To assess Mark on the aforementioned standard provided by Australian Curriculum, a number of tasks covering number and place value content strand were formulated. The approach of using tasks was chosen because children in Year 1 normally have short concentration span thus the need to use brief and practical tasks. The approach also gives immediate feedback on a child’s ability to conduct tasks required for the grade. The first task was for the student to capitalize on various strategies to count and record numbers. Secondly, Mark wrote sequentially two digit numbers on a paper. So as to take care of student’s ability to count, starting point was fixed at 9. Mark was left alone to complete the grid. It was observed that the student counted the numbers loudly as he filled the provided grid paper. This was attached as work sample 1. The other task was for the student to skip counting by a value of 2s starting from 10. To conduct this task, the student was provided with a new piece of paper with a number line drawn. The starting point on the number line was 10 and student was to skip counting by 2s and indicate the result on the number line. Practically, the student was provided with numbered cards and required to place the cards sequentially on a number line at an interval of 2. The student correctly placed the cards in the correct position. Thirdly, the student was subjected into the task of partitioning numbers i.e. 12 in terms of place value of ones and tens. During the entire exercise behaviors elicited by the student was noted. In the first task of counting numbers sequentially from 9, Mark demonstrated the ability to count the numbers correctly from 9 to 100. In the second task, the student managed to execute the task correctly by skipping numbers by 2s and placing the numbers on the number line. The student however misconceived the place value of digits in the number 12 by reading it directly as one and two. This acted as pointer on the where the student required assistance thus the need to create a lesson place for place value. The lesson plan is addressed in subsequent section of this report. It is essential to appreciate that besides assessing the student on whether he was able to execute the task required for his grade, observation was made on activities that the student used. This acted as a guide on improving teaching strategies and activities. 4.0 Lesson Plan The diagnostic assessment conducted showed that the student had not captured the concept of place value in Year 1 thus the necessity to plan a lesson on place value. The overall objective of the lesson was for the student to understand that a two digit number, 12, was comprised of tens and ones. At the end of the lesson, the student was expected to understand that 10 was a collection of ten ones. Secondly the numbers beginning 11 to 19 were made up of ten and 1, 2,3,4,5,6,7,8, and 9 ones. Thirdly, the learner was supposed show that the numbers 10, 20, to 90 implied one, two, to nine tens. It was apparent from diagnostic assessment that the student required skills on partitioning numbers into tens and ones. Guided by Australian Curriculum, the strategy of composing and decomposing numbers into various place values was necessary. The starting point for acquisition of place value skills is the use of tens to compose numbers (Westwood, 2008). In such a case, number of tens and the remaining ones are represented. Through a process of decomposition of a two digit number in terms of tens, a student develops number sense consequently securing knowledge that order of digits is critical. To enhance mental operation and flexibility, numbers are composed and decomposed, which eventually establishes relationship that exists in a two digit number. In the first instance, a student must develop an understanding that placing ten ones results in a single ten. It is at this point that the student was informed of ways of writing down place values such that knowledge acquired in writing down the ten is applied in other numbers such as 15, 18, 21, 89 etc. Several representations were necessary at this learning stage thus deployment of base-ten blocks, collections of tens and ones, and ten frames. In learning place value, aspect of progression was vital i.e. moving from concrete to abstract (Chambers, 2008). The starting point was therefore to instruct the student to place a collection of small cubes on one side and another on the other side. This was followed by counting number of cubes on each side and representing the results numerically. Basically, the student began by drawing objects or representing the objects on a piece of paper then comparing the drawn picture directly with the object. The student proceeded to quantify the drawn pictures using number. The student noticed the need to group counting in a collection of say four, five etc. After a repeated process, the student realized that a group of five objects can be termed as one-five. This was an aspect of unitizing. By extension, the student noticed that he could disintegrate 12 into 10 and 2. Resources to be used in this lesson comprise of the following: A table and enough space Linking cubes Numbered cards Sheet of paper Pencil Base-ten blocks Ten frames 5.0 Assessment To assess progress, a variety of tools including formative, summative, and transformative assessment was deployed. According to Alastair (2007), formative assessment is more concerned with future achievement thus it produces evidence that shows student’s achievements and how instructions can be adopted to satisfy learner needs. Since formative assessment takes place as part daily instructions, some of the strategies employed in the case of Mark include observing the student, presenting him with tasks, and listening to what he was saying. The student was regularly diagnosed and subsequently given feedback which facilitated improved learning. The benefit of formative assessment was that a student was able to learn from mistakes after a session of trial and error. Besides, the learner understood his area of difficulties, highlighted his learning needs, and thought about what he really wanted to learn. Through formative assessment areas of misconception specifically with regard to reading place value from right to left was rectified subsequently improving learning. Secondly, summative assessment was used. In a study by Harlen (2007), summative assessment examines student’s achievement for the entire week or term. Testing and scoring the test according to specified standard criteria was integrated in the design of instruction. The result indicated weakness, which was later assessed formatively. A review of student’s work for the entire season and assigning a grade was conducted. Summative assessment often forms the basis for informing parents and other stakeholders on a child’s progress. As provided by Australian Curriculum, integrated evidence was collected for the entire week and term which facilitated formulation of objective judgment on student progress. Research by Popham (2008) shows that transformative assessment relies on institutional goals and are factored into institutional programs with an intention to change teaching and learning in a systematic manner. Through transformative assessment, the student was able to reflect on learning analyses progress consequently establishing future learning goals. Department of Education and Early Childhood Development (2013) acknowledge that assessment focused on improved learning ought to integrate formative, summative and transformative assessment. This formed part of the reasons for bringing together all the three forms assessment. 6.0 Reflection on Assessment Cycle There was need to appreciate the fact that successful learning depended on a deep understanding of variables surrounding teaching strategies. As an educator it was imperative to continuously reflect on assessment, planning, teaching and revising strategies (Santiago, et al, 2011). Assessment provided feedback on student learning thus informed on the design of a lesson and instruction integrated in class. The assessment cycle further provided an avenue for the teacher to review instruction and progress to disseminate learning from an informed angle. This indicates that the process of assessment, reflection, planning, and teaching is continuous. In a nutshell, assessment stage enables a teacher to comprehend the relationship between instruction and outcomes from learning. 7.0 Follow up Lesson Assessment conducted both during and after instruction informed on the nature of follow up lesson. Additional exercise on place value was necessary. Through assessment, most objectives were met but those that were not met were noted down and requisite content factored into the next lesson. It was incumbent upon the instructor to examine the ability of the learner to complete homework. This provided feedback on sections that a student needed further assistance. These areas of deficiencies will be addressed at the beginning of the next lesson such that while a student progress to other content, the lower level will have been mastered. 8.0 Conclusion This report began with a discussion covering on student profile. For purposes of research, the student was assigned the name Mark Anthony. Various characteristics of the learner were identified. The factors revolved around number and place value content strand in addition to other external variables. At the second stage, diagnostic assessment was carried out to identify student’s prior knowledge while pointing out misconceptions. This diagnosis showed that the point of entry was place value, a section were the student elicited confusion. A lesson plan was then constructed to guide in instruction. Assessment was necessary throughout the session since they provide insights on instructional design. Informed by assessment, a follow up lesson was necessary which facilitated achievement of learning objectives identified at the start of the lesson. 9.0 References  Alastair, I. (2007). Enhancing Learning through Formative Assessment and Feedback. London, UK: Routledge. Australian Curriculum Assessment and Reporting Authority. (2013). Mathematics. Retrieved from http://www.acara.edu.au/curriculum/worksamples/Year1MathematicsPortfolioSati sfactory.pdf.    Chambers, P. (2008). Teaching Mathematics. London: Sage Public. Department of Education and Early Childhood Development. (2013). Assessment Advice. Retrieved from http://www.education.vic.gov.au/school/teachers/support/pages/advice.aspx. Gough, J. (2002). Diagnostic Mathematical Tasks. New South Wales: UNSW Press. Harlen, W. (2007). Assessment of Learning. London: Sage. Mayring, P, & Rhöneck, C.V. (2003). Learning Emotions: The Influence of Affective Factors on Classroom Learning. New York: Peter Lang Publishing. Popham, W. J. (2008). Transformative Assessment. Alexandria, Virginia: ASCD. Santiago, P., Donaldson, G., Herman, J., & Shewbridge, C. (2011). OECD Reviews of Evaluation and Assessment in Education OECD Reviews of Evaluation and Assessment in Education: Australia 2011. Wellington: OECD Publishing. Westwood, P. (2008). What Teachers Need to Know About Numeracy. Camberwel, Vic: Australian Council for Ed Research Ltd. 10.0 Appendices A. Work Sample 1: Counting 9 21 33 45 57 69 81 93 10 22 34 46 58 70 82 94 11 23 35 47 59 71 83 95 12 24 36 48 60 72 84 96 13 25 37 49 61 73 85 97 14 26 38 50 62 74 86 98 15 27 39 51 63 75 87 99 16 28 40 52 64 76 88 100 17 29 41 53 65 77 89 18 30 42 54 66 78 90 19 31 43 55 67 79 91 20 32 44 56 68 80 92 B. Work Sample 2: Skip Counting by 2 C. Lesson Plan: Place value Read More