SULTANATE OF OMAN Ministry of Education Directorate General of Private Schools Department of Supervision & Evaluation Assessment Document for Mathematics For Bilingual Private Schools Grades (5-10) Trial Version 2012-2013 1
Contents Subject Page Introduction 3 General Note on Continuous Assessment 3 The Benefits of Continuous Assessment 3 The Relative Weight of the Continuous Assessment Tools 4 Tools for Continuous Assessment 5 Oral Work 5 Homework 5 Quiz 6 Project 12 Semester Exam 16 Student's Portfolio 17 Taxonomy 18 2
A. INTRODUCTION This Student Assessment Handbook is based on the official guidelines for assessment issued by the Directorate-General of Educational Evaluation (DGEE) of the Ministry of Education to provide information and guidance for teachers and supervisors on the assessment of students studying Mathematics in Grades (5-10). B. GENERAL NOTE ON CONTINUOUS ASSESSMENT Continuous Assessment Assessment that is conducted in schools, by teachersthroughout the school year, rather than just at the end. Provides a fairer, more balanced picture of student's attainment. Also, allows the inclusion of skills (e.g. communication) which are difficult (practically) to assess by means of formal testing. It can be used for both formative and summative purposes. Summative Assessment Assessment of student learning. Its purpose is to measure and report on standards of learning. Typically done by awarding marks and grades. Also, involves reporting to the Ministry and to parents. Formative Assessment Assessment for student's learning. Its purpose is to improve students' learning. Typically done by giving feedback through different tools such as of tests, quizzes, homework, oral work, projects, etc. C. THE BENEFITS OF CONTINUOUS ASSESSMENT The most important ways in which Continuous Assessment (CA) can be beneficial are: ó It encourages teachers to have good idea about the performance of all their students and to closely observe individual student s on-going progress and development. ó It, possibly, motivates students to work hard consistently, if they know that their everyday work in class contributes to their report card assessment. ó It is based on a positive view of assessment as a natural part of the teachinglearning process. ó It allows assessment of learning outcomes which are, for practical reasons, difficult to assess by means of formal testing. 3
ó It can provide a fairer, more balanced picture of student s achievement, especially for those who become nervous during formal tests. ó It provides information about student s learning at an early stage, making it possible for action to be taken promptly, while the academic year is still in progress. D. The Relative Weight of the Continuous Assessment Tools Name of the tool Grade (5-9) Continuous Assessment Tools Oral Work Quizzes Homework Total Project (10) (30) (10) Marks 3 3 4 10 10 10 3 3 4 10 60 40 Description of the tool Applied three times and the mark distributed according to conditions (page5) Three quizzes Three Homework (different topics) Final Exam To be done by MOE Name of the tool Grade 10 Continuous Assessment Tools Oral Work Quizzes Homework Total Final Exam (5) (30) (5) Marks 1 2 2 10 10 10 1 2 2 40 60 Description of the tool Applied three times and the mark distributed according to conditions (page5) Three quizzes Three Homework (different topics) To be done by School Remarks : 1. Marks must be recorded as a whole number with or without half only. 2. Rounding will be taken for Total of 100 only. 4
E. Tools & Techniques for Continuous Assessment This Section provides further information and explanation regarding the various tools and techniques, which can be used for assessment purposes in Mathematics during the semester: Continuous Assessment Tools Oral Work Homework Quiz Project* Semester Exam *Only for Grades (5-9) i. Oral work : is applied through the teaching and learning process, and through the responses to verbal discussion about an issue or a topic. It is applied usually between two or more persons (between teacher and student or between a group of students or between student and classmate). Taking into account the following conditions: It should measure the learning outcomes or objectives of Mathematics Scope & Sequence NOT of the curriculum. It may include oral short questions that require specific answers. It should be accompanied to the daily teaching practices (during the lessons). It could be as asking the students questions or giving idea. It should target each time a specific level/group of students. ii. Homework: tasks assigned to students by their teachers to be done in their spare time at school or home. The teacher should take into account the suitability of the level of each student. It must be corrected by the teacher and feedback should be given to student. The three times should be planned for at the beginning of the year so that printed papers should be shown as evidences. More homework of course should be given approximately daily. 5
iii. Quiz: during the semester applied at the end portion of the content. The following criteria must be taken into consideration while preparing Quizzes: 1. There will be three Quizzes in each semester for Grades (5-10); each one worth 10 marks. 2. The teacher must inform students of the date of the test. 3. The Quiz must be short lasting (no more than 20 minutes). 4. The Quiz must be set according to the approved objectives of Mathematics Scope & Sequence. 5. Each Quiz must cover different topics (to ensure that each course topic is tested over time). The coverage must be assigned according to the determined specifications. See table on page7. 6. The question paper and its answer key must be prepared for each Quiz. 7. Marks must be as a whole number with or without half only (5 and 5.5 but 5.25 is not accepted). 8. Quiz must consist of two parts: (40% Multiple-choice items and 60% Extended response items). a. Question 1: (MCQ) consists of 4 items each worth one mark. b. Question 2: (ERQ) consists of minimum two parts worth 6 marks. 9. The level/type of the given questions must be divided into varient learning levels/types (30% Knowledge, 50% applying, 20% Reasoning) these level domains will be in details in the following tables: 6
Grade ( ) QUIZ#( ) 2012/2013 Table 1 Weight according to (Number-Average) of (Pages Goals Periods) No. of MCQ Topic periods *** Weight Mark 1 2 3 4 ERQ 40% 60% TOTAL 100% 10 4 6 *** Not necessary Number of periods, you may consider No. of periods, pages or goals or average of two or three of them. Grade ( ) QUIZ # ( ) 2012/2013 Table 2 Learning Levels Questions Contents Answer Partial Degree Knowledge Applications 30% 50% Reasoning 20 % Question Mark MCQ Q.1 Q.2 ERQ Q.3 1) 1 2) 1 4 3) 1 4) 1 1) 2) 3) 6 1) 2) 3) TOTAL 10 3 5 2 10 7
Example Grade ( 6 ) QUIZ#( 3 ) 2012/2013 Table 1 Weight according to (Number) of (Pages) Topic # Weight Mark MCQ ERQ 40% 60% 1 Decimals 5 35.7% 4 3 1 2 Comparing and ordering D. 2 14% 1.5-1.5 3 Add. & Sub. of Decimals 3 21% 2-2 4 Multiplication of Decimals 2 14% 1.5-1.5 5 Division of Decimals 2 14% 1 1 - TOTAL 14 100% 10 4 6 Grade ( 6 ) QUIZ#( 3 ) 2012/2013 Table 2 Questions Contents Answer MCQ Q.1 ERQ Q.2 Q.3 8 Partial Degree Learning Levels Knowledge Application Reasoning 30% 50% 20% 1) Decimals C 1 - - 2) Decimals A 1 - - 3) Decimals D 1 - - 4) Division of decimals A 1 - - 1) Order of decimals 6.9623;8.1375;8.138 1.5 - - 2) Multiplication of decimals 4.89 12 978 + 4890 5868 1.5 - - Question Mark 3) Decimals 0.9642 1 - - 1) a) Addition of 2.85 decimals + 3.2 1 - - 6.05 b) Subtraction of 10.00 2 decimals 6.05 1 - - 3.95 TOTAL 10 3 5 2 10 4 4
Ministry of Education Directorate General of Private School..Private School Mathematics Quiz #(3) First Term 2012-2013 Name:. Class : 6 \... Date: \.\201 10 Question one: Circle the letter of the correct answer: (1) "Ninety four and seven hundredths" is : a) 49.07 b) 49.7 c) 94.07 d) 94.7 (2) The place value of 2 in 0.2417 is : a) tenths b) hundredths c) thousandths d) ten-thousandths (3) 7 + 0.03 + 0.0007 = a) 7.37 b) 7.307 c) 7.037 d) 7.0307 (4) Dana bought a package of 4 clips for 2.2 R.O.How much did each clip cost? a) 0.55 b) 5.05 c) 5.5 d) 55 (4 Marks) Question Two: Solve the following questions (show all the required work): 1) Write the decimals in order from least to greatest. 8.1375 ; 8.138 ; 6.9623 2) Find 12 4.89 (1.5 Mark) (1.5 Mark) 9
3) What is the greatest decimal number less than 1 that you can write using the digits 0, 2, 4, 6 and 9 only once? (1 Mark) Question Three: Solve the following questions (show all the required work): 1) Mr. Sami has 10 Riyals.He gave his son Tareq 2.85 Riyals and his daughter Muna 3.2 Riyals. a) How much totally money did Mr. Sami give to Tareq and Muna? b) How much money is left with Mr. Sami? (1 Mark) (1 Mark) - End of the quiz 10
iv. Project: School Project is an assessment tool that depends on investigation and practical skills to reach scientific results & explanations can be done by one student or more. We can define that the project passes through some steps: 1. Select a title 2. Determining a plan 3. Find tools/ways 4. Project Execution 5. Evaluating results 6. Writing reports 7. Exposing project The following criteria should be taken into consideration while preparing the project: Assessed once a semester. Achieve the learning outcomes and related to the real life situations. Suitable to students mental abilities. Suitable to parents abilities especially in the financial side. The teacher may offer the students some topics and they may select from them. The project has to be as an application. Suitable time must be taken into account. Can be done under more than one subject if integration is there. Safety rules and criteria must be followed. Good to give clear instructions to help students. Steps of scientific research must be generally accordingly with student level. An unified sheet for each project to be marked equally with the same criteria. Criteria must be written to be shown when required. Should be done under the Supervision of the teacher. It can be done by one or a group of ( 2 5 ) students with clear specified role for each. Teacher discusses with students the project because the oral evaluation gives a clear picture of the effort that suits the student and his/her participation in group work. 11
More than one student can choose the same project topic but with different data and handling for each student. The student should write a brief report, taking into account the following points: - Title of the project - Aim or purpose - Apparatus and Materials - Procedures - Answering questions (Observations & Results) 12
Suggested Student's Form for Mathematics Project Student's name:.. Class:.. Project's Title: Purpose /Aim: Apparatus and Materials: 1-2- 3-4- Procedure: 1-.. 2-.. 3-.. 4-.. 5-.. (3 marks) Calculation & modeling: to be attached to the report. (4 marks) Answer the following questions: Q#(1) :..... Q#(2) :..... Q#(3) :..... 13 (3 marks)
Project marking criteria: planning (writing Aim, Materials & Procedure) Description Good & clear planning. Clear planning but it needs some modification. There is some planning but it isn t clear. Marks 3 2 1 Application Work based on precise, good & clear evidences. 4 (mathematical processes) & Clear work but isn t based on precise modeling 2-3 evidences. report & answering questions Total Unclear & imprecise work, with weak evidences. Good & clear report, excellent answering with logically reasons. Unclear report in some parts, good answering with some logically reasons. Unclear report, poor answering & no logically reasons. 1 3 2 1 10 Marks 14
v. Semester Exam: Formal exams administered at the end of each semester. Semester exam is valued at 40% for Grade(5-9) and at 60% for Grade10 The marks for the year will be : 1. For grade (5-9) the summation of (60% + 40%) = 100%. 2. For grade 10 the summation of (40% + 60%) = 100%. Student achievement to be reported as a letter-grade and marks. The following table shows the breakdown of percentage marks and corresponding letter-grades: Mark Range Letter-Grade Descriptor 90% - 100% A Excellent 80% - 89% B Very good 65% - 79% C Good 50% - 64% D Satisfactory 49% or less E Needs further support General specifications for both END-OF-semester EXAMS: Time: (2) hours for Grades (5-9) and (2 ) hours for Grade 10. Preparation: o For Grades (5-9) : By Directorate General of Private School. o For Grade 10 : By school. Match with learning taxonomy cognitive domain (knowing, applying, and reasoning). Instructions will be given before the question. Responses to questions must be in the Exam papers. Total score is 40 marks for Grades (5-9) and 60 marks for Grade 10. Contents: o 40% as Multiple-choice items o 60% as Extended response items 15
Grades 5-9 10 Q1 (MCQ) 16 mrk (8 items) 24 mrk (12 items) Q2 Q3 Q4 Total 12 mrk 12 mrk - 40 mrk 12 mrk 12 mrk 12 mrk 60 mrk The exam paper must meet the following ratios: Level Knowing Application Knowing Total Percentage 30% 50% 20% 100% Hence tables that show the specifications of the semester one exam and semester two exam according to the weight of topics will be sent to schools later from D.G. Privet School. vi. Student's Portfolio: The educational supervisors will moderate continuous assessment marks awarded by schools. - A portfolio for each student must be allocated and kept with the teacher. - A portfolio for each student has to contain evidences for the given mark for each assessment tool except for the oral work. - A portfolio for each student must contain students' works (3 Quizzes, 3 Homework, 1 project) in each semester. - Works must be marked by the teacher. - Scores must be recorded in the assessment's form once works are marked. 16
Taxonomy (Cognitive Domains): Knowing: Facility in using mathematics, or reasoning about mathematical situations, depends on mathematical knowledge and familiarity with mathematical concepts. The more relevant knowledge a student is able to recall and the wider the range of concepts he or she has understood, the greater the potential for engaging in a wide range of problemsolving situations and for developing mathematical understanding. Without access to a knowledge base that enables easy recall of the language and basic facts and conventions of number, symbolic representation, and spatial relations, students would find purposeful mathematical thinking impossible. Facts en compass the factual knowledge that provides the basic language of mathematics, and the essential mathematical facts and properties that form the foundation for mathematical thought. Procedures form a bridge between more basic knowledge and the use of mathematics for solving routine problems, especially those encountered by many people in their daily lives. In essence a fluent use of procedures entails recall of sets of actions and how to carry them out. Students need to be efficient and accurate in using a variety of computational procedures and tools. They need to see that particular procedures can be used to solve entire classes of problems, not just individual problems. Knowledge of concepts enables students to make connections between elements of knowledge that, at best, would otherwise be retained as isolated facts. It allows them to make extensions beyond their existing knowledge, judge the validity of mathematical statements and methods, and create mathematical representations. 17
Recall Recall definitions; terminology; number properties; geometric properties; and notation (e.g., a b = ab, a + a + a = 3a). Example : The area of a square with a side of (b ) cm : 2 A) 2 b B) b C) b 2 D) b + 2 Recognize Recognize mathematical objects, e.g., shapes, numbers, expressions, and quantities. Recognize mathematical entities that are mathematically equivalent (e.g., equivalent familiar fractions, decimals and percents; different orientations of simple geometric figures). Example : What of these shapes is called a triangle? A) B) C) D) Compute Carry out algorithmic procedures for +,,,, or a combina on of these with whole numbers, fractions, decimals and integers. Approximate numbers to estimate computations. Carry out routine algebraic procedures. What is the value of : 2a + 4a 3a? A) a B) 2a C) 3a D) 4a 18
Retrieve Retrieve information from graphs, tables, or other sources; read simple scales Which of these classes has the biggest number of girls? 25 20 15 10 5 0 Class A Class B Class C Class D Boys Girls A) Class A B)Class B C) Class C D) Class D Measure Use measuring instruments; choose appropriate units of measurement. Which of these is the best for measuring a distance between two cities in two different countries? A) mm B) cm C) m D)km Classify/O rder Classify/group objects, shapes, numbers, and expressions according to common properties; make correct decisions about class membership; and order numbers and objects by attributes. Example : Which of these is not a rational number? A) 3.5 B) 5 C)- D) 4 19
Applying: The applying domain involves the application of mathematical tools in a range of contexts. The facts, concepts, and procedures will often be very familiar to the student, with the problems being routine ones. In some items aligned with this domain, students need to apply mathematical knowledge of facts, skills, and procedures or understanding of mathematical concepts to create representations. Representation of ideas forms the core of mathematical thinking and communication, and the ability to create equivalent representations is fundamental to success in the subject. Problem solving is central to the applying domain, but the problem settings are more routine than those aligned with the reasoning domain, being rooted firmly in the implemented curriculum. The routine problems will typically have been standard in classroom exercises designed to provide practice in particular methods or techniques. Some of these problems will have been in words that set the problem situation in a quasi-real context. Though they range in difficulty, each of these types of textbook problems is expected to be sufficiently familiar to students that they will essentially involve selecting and applying learned facts, concepts, and procedures. Problems may be set in real-life situations, or may be concerned with purely mathematical questions involving, for example, numeric or algebraic expressions, functions, equations, geometric figures, or statistical data sets. Therefore, problem solving is included not only in the applying domain, with emphasis on the more familiar and routine tasks, but also in the reasoning domain. 20
Select Select an efficient/appropriate operation, method, or strategy for solving problems where there is a known procedure, algorithm, or method of solution. If Ali is older than Ahmed who is younger than Salem. The ages of Ali, Ahmed, and Salem are x, y and z, respectively. What of these is untrue? A) y < x B) y < z C) y > z D) x > y Represent Display mathematical information and data in diagrams, tables, charts, or graphs, and generate equivalent representations for a given mathematical entity or relationship. In the following table, what is the value of A - B? X 2 0 2 Y = 3x - A 4-2 B A) -2 B) 0 C) 2 D)3 Model Generate an appropriate model, such as an equation, geometric figure, or diagram for solving a routine problem. In the following table, what of the following is true? X -1 0 1 y 1 2 5 A) Y = 3x +2 B) Y = 2x + 3 C) Y = 2x +2 D) Y = x + 5 21
Implement Solve Routine Problems Implement a set of mathematical instructions (e.g., draw shapes and diagrams to given specifications). Draw a right triangle that its smaller sides length are ; 3cm, 4 cm Solve standard problems similar to those encountered in class. The problems can be in familiar contexts or purely mathematical. If 3a 4b = c, 6a + 4b = 2c, then c = A) 2b B) 3a C) 2a D) 3b Reasoning: Reasoning mathematically involves the capacity for logical, systematic thinking. It includes intuitive and inductive reasoning based on patterns and regularities that can be used to arrive at solutions to non-routine problems. Non-routine problems are problems that are very likely to be unfamiliar to students. They make cognitive demands over and above those needed for solution of routine problems, even when the knowledge and skills required for their solution have been learned. Non-routine problems may be purely mathematical or may have real-life settings. Both types of items involve transfer of knowledge and skills to new situations, and interactions among reasoning skills are usually a feature. Problems requiring reasoning may do so in different ways, because of the novelty of the context or the complexity of the situation, or because any solution to the problem must involve several steps, perhaps drawing on knowledge and understanding from different areas of mathematics. Even though of the many behaviors listed within the reasoning domain are those that may be drawn on in thinking about and solving novel or complex problems, each by itself represents a valuable outcome of mathematics education, with the potential to influence learners thinking more generally. For example, reasoning involves the ability to observe and make conjectures. It also involves making logical deductions based on specific assumptions and rules, and justifying results. 22
Determine, describe, or use relationships between variables or objects in mathematical situations, and make valid inferences from given information. Analyze Find the domain of = Generalize / Specialize Extend the domain to which the result of mathematical thinking and problem solving is applicable by restating results in more general and more widely applicable terms. If =, =, write in terms of a and b. Integrate/ Synthesize Make connections between different elements of knowledge and related representations, and make linkages between related mathematical ideas. Combine mathematical facts, concepts, and procedures to establish results, and combine results to produce a further result. Find the diameter of the triangle : 3 2 Provide a justification by reference to known mathematical results or properties. Prove that there is no biggest integer : Justify Solution; Suppose ; N is the biggest number N + 1 is integer since the sum of two integers is an integer But N + 1 > N So there is no integer. 23
Solve Nonroutine Problems Solve problems set in mathematical or real life contexts where students are unlikely to have encountered closely similar items, and apply mathematical facts, concepts, and procedures in unfamiliar or complex contexts. Solve ; = 1, x > 0. End of the Document 24