Evaluation of Mathematics MCQ Quiz - Objective Question with Answer for Evaluation of Mathematics - Download Free PDF

In the context of classroom assessment, especially during informal or formative evaluation, teachers often use observational tools to gain insight into students' behavior, learning processes, and interpersonal skills. One such tool is the anecdotal record, which captures qualitative, narrative data.

Key Points

•  When a teacher observes students during a group activity and writes short descriptions about how they interact, solve problems, and respond emotionally to peers, the focus is on capturing specific incidents and behaviors in a narrative, descriptive format.
• This type of note is non-quantitative and personalized, making it ideal for understanding student development and planning further support or instruction. Such documentation is called anecdotal records.

Hint

• Checklist: A yes/no or present/absent list used to note the occurrence of specific behaviors or skills. It doesn’t provide detailed descriptions.
• Portfolio: A collection of student work over time, showcasing learning progress.
• Rating scale: A quantitative tool where the teacher rates behavior or performance on a continuum (e.g., 1 to 5).

Hence, the correct answer is Anecdotal Records.

Remedial teaching is a targeted instructional approach designed to help students overcome specific learning difficulties. Its effectiveness depends on accurate diagnosis and appropriately tailored strategies to meet the unique needs of each learner.

Key Points

• Remedial teaching must be individualized because students have different types and causes of learning gaps. These differences can stem from conceptual misunderstandings, lack of practice, or emotional factors. Once a diagnosis reveals these issues, teaching strategies should be customized accordingly.
• The reason (R) supports the assertion by emphasizing that a uniform approach will not effectively address such varied needs. Since the reason provides a logical basis for the assertion, it correctly explains why remedial teaching should be tailored.

Hence, the correct answer is both A and R are true and R is the correct explanation of A.

Assessment in mathematics is not limited to formal tests. It can take many forms to understand how students learn and where they struggle. Diagnostic assessment is used to uncover students’ existing understanding, misconceptions, and learning gaps before or during instruction, allowing the teacher to adjust teaching strategies accordingly.

Key Points

• In the given scenario, the teacher asks students to visually represent 3/4, a common fraction, and then carefully examines these drawings.
• The goal is not to evaluate for marks but to gain insight into each student’s conceptual grasp of fractions how well they understand part-whole relationships, and whether they can translate a numerical fraction into a visual model.
• This kind of assessment helps in identifying specific misunderstandings, such as dividing the shape incorrectly or shading the wrong number of parts. Such analysis helps the teacher decide what kind of remedial or targeted support is needed, which is the core purpose of diagnostic assessment.

Hint

• Summative assessment measures learning at the end of a unit or term and is often graded. This is not the focus here.
• Norm-referenced assessment compares a student's performance to that of peers, typically through standardized testing.
• Formal written test involves structured, pen-and-paper tests with a fixed format and scoring, which is not part of the described activity.

Hence, the correct answer is diagnostic assessment.

Formative assessment is an ongoing process used by teachers during instruction to evaluate students’ understanding, skills, and needs. In mathematics education, it plays a crucial role in diagnosing learning gaps and guiding future teaching strategies.

Key Points

• Formative assessment is not about final grading but about informing both teaching and learning. When teachers use it effectively in mathematics, they can identify students’ misconceptions, errors, or incomplete understanding as they arise.
• This timely feedback enables teachers to adjust instruction and provide targeted support, helping learners grasp concepts before they fall behind. It creates a responsive learning environment where instruction is continuously adapted to meet learners’ needs.

Hint

• Using it only at the end of the term refers to summative assessment, not formative.
• Evaluating only memorization undermines the diagnostic and developmental purpose of formative assessment.
• Limiting assessment to summative forms ignores the real-time benefits formative assessment provides during learning.

Hence, the correct answer is Teachers can use formative assessment to detect errors and guide learners during instruction.

Assessment in mathematics should go beyond written tests to capture a holistic view of a student's understanding, skills, and attitudes. Continuous and Comprehensive Evaluation (CCE) is an approach that emphasizes regular, varied, and inclusive assessment methods to understand learners’ progress over time. 

Key Points

•  When a teacher uses tools like concept mapping, project work, oral questioning, and observation, they are actively engaging in continuous and comprehensive evaluation.
• These methods help assess not just factual knowledge, but also conceptual understanding, problem-solving ability, communication, and application in real-life contexts.
• Such varied techniques ensure that assessment is ongoing and covers multiple aspects of learning, not just limited to a final test.

Hint

• Norm-referenced testing is focused on comparing students’ performance with peers, which is not the goal here.
• Diagnostic evaluation is meant for identifying specific learning difficulties rather than supporting broad learning progress.
• Criterion-referenced assessment applies to checking if students meet specific objectives, but saying "only for written work" limits its scope and does not match the diverse tools mentioned in the question.

Hence, the correct answer is continuous and comprehensive evaluation.

Van Hiele Model of Geometric Thought in math education: the van Hiele model is a theory that describes how students learn geometry. 

Important Points

At Level 0 Visualization (Basic visualization or Recognition):

• At this level, pupils use visual perception and nonverbal thinking.
• They recognize geometric figures by their shape as “a whole” and compare the figures with their prototypes or everyday things (“it looks like a door”), categorize them (“it is / it is not a…”).
• They use simple language. 
• They do not identify the properties of geometric figures.
• Example: A child is not able to differentiate squares from rectangles and assigns both of them to the same category. According to Van Hiele's theory of geometric reasoning, the student is at Level 0 Visualization.

Additional Information

The van Hiele theory describes how young people learn geometry.
It postulates five levels of geometric thinking which are labeled visualization, analysis, abstraction, formal deduction, and rigor. Each level uses its own language and symbols. Students or pupils pass through the levels “step by step”

• Level 0 Visualization (Basic visualization or Recognition): At this level, pupils use visual perception and nonverbal thinking. They recognize geometric figures by their shape as “a whole” and compare the figures with their prototypes or everyday things (“it looks like a door”), categorize them (“it is / it is not a…”). They use simple language. They do not identify the properties of geometric figures. 
• Level 1 Analysis (Description): At this level pupils (students) start analyzing and naming properties of geometric figures. They do not see relationships between properties, they think all properties are important (= there is no difference between necessary and sufficient properties). They do not see a need for proof of facts discovered empirically. They can measure, fold and cut paper, use geometric software, etc.
• Level 2 Abstraction (Informal deduction or Ordering or Relational): At this level, pupils or students perceive relationships between properties and figures. They create meaningful definitions. They are able to give simple arguments to justify their reasoning. They can draw logical maps and diagrams. They use sketches, grid paper, geometric SW. 
• Level 3 Deduction (Formal deduction): At this level, students can give deductive geometric proofs. They are able to differentiate between necessary and sufficient conditions. They identify which properties are implied by others. They understand the role of definitions, theorems, axioms, and proofs. 
• Level 4 Rigor: At this level, students understand the way how mathematical systems are established. They are able to use all types of proofs. They comprehend Euclidean and non-Euclidean geometry. They are able to describe the effect of adding or removing an axiom on a given geometric system.

.Hence, we can conclude that the right answer to this question is the Visualisation level.  

Confusion PointsConcepts and procedures are dimensions of assessment of mathematical learning rather than Patterns and procedure.

Key Points

Dimensions of assessment of mathematical learning: To ensure a comprehensive assessment of mathematical learning following dimensions should be included:

• Concepts and procedures: Although a great deal is known from research about the nature and developmental trends of mathematical concepts and procedures. It is expected that every teacher while teaching mathematics in the classroom, should explore the nature of their student's development of the concepts and procedures.
• At the elementary stage, all the mathematical concepts and procedures can be included in ten broad areas:
  • Number (Real number system)
  • Number operations (Four processes)
  • Fractions (including decimals)
  • Space and spatial thinking
  • Measurement (both standard and non-standard measures)
  • Problem-solving
  • Patterns
  • Data handling
  • Basic algebraic processes (only in the upper primary stage)
  • Simple equations (only in the upper primary stage)

Hence, we conclude that Patterns and procedures are not a dimension of the assessment of mathematical learning.

According to the psychologist Jean Piaget, Conservation refers to a logical thinking ability that allows a person to determine that a certain quantity will remain the same despite adjustment of the container, shape, or apparent size. Note that:

• Conservation of mass/length: 7 years
• Conservation of weight: 9 years
• Conservation of volume: 11 years

Hence, Conservation of weight is grasped before conservation of volume but not before conservation of number.

Mathematics is not just the study of numbers and statistical data but also studies the different types of shapes, figures, and patterns.

• Van Heile's theory provides insight to the teacher about how students learn geometry at different levels.
• It helps in describing how the students learn at each level and pass to another level and shapes their learning of geometry at each level of learning.

Key Points Van Hiele levels are described below:

• Level 0: Visualization-The students can recognize shapes by their whole appearance that should just be like the exact shape. They can also compare the figures with their prototypes (exemplars) or everyday things but can not identify the properties of geometric figures. For example, they can compare the shape of a circle with bangles, coins, wheels, etc. but are unable to identify and describe the properties of a circle.
• Level 1: Analysis -They will learn the functions and parts of a figure. They can describe the properties of a figure and recognize the figures with the same properties. For example, they can identify the shapes and describe their properties such as a circle is a closed rounded figure with no corners.

It belongs to the upper level of elementary level classes.

• Level 2: Abstraction or informal deduction -The students will be able to understand the relationships between the properties of a figure. They can take part in informal deductive discussions and can discuss the different characteristics of figures. For example, the opposite sides of a parallelogram are parallel. The opposite sides of a square and rectangle are also parallel which means the square and rectangle are also a parallelogram.

It generally belongs to the upper elementary classes.

• Level 3: Deduction or formal deduction -At this level, the students become aware of the more complex geometrical concepts. They can prove an abstract statement on geometric properties to conclude. For example, they can prove that the square is a rectangle but a rectangle can not be a square.

It belongs to the higher level of classes where students usually combine a certain set of elements to prove any theorem to draw conclusions or do the evaluation.

• Level 4:Rigor -The last level of geometrical learning belongs to the senior secondary and university-level classes. The students are able to compare different geometrical results. For example, the sum of all three angles of a triangle is 180 degrees and is compared to the other properties or other results (to find exterior or interior angles of a triangle) related to the triangle to solve geometrical problems.

Hence, it is concluded that The above activity is appropriate for assessing the Visualization according to Van-Hiele.

Van Hiele Theory describes how people learn geometry. According to this theory, there are five levels of thinking in geometry. These are as follows:

Important Points

Five levels of thinking are as follow:

• Visualization Level 0: Describe and sort out shapes on the basis of appearance.
• Descriptive/Analytic/Analysis Level 1: Students start analyzing and naming the properties of geometrical figures.
• Abstract/Relational/Informal Deduction Level 2: Perceive the relationship between properties and figures and create meaningful definitions.
• Formal Deduction Level 3: At this level students can provide deductive geometrical proofs and are able to differentiate between necessary and sufficient conditions.
• Mathematical Rigor Level 4: This is the final step where geometry is understood as a mathematician.

Hence, Rigour represents the Last level of Van Hiele Theory.

Assessment is a key component of learning because it helps students learn. When students are able to see how they are doing in a class, they are able to determine whether or not they understand course material and the content of subject. 

• Assessment refers to an empirical formula that is used to define the programs and students learning improvement. It is the process of defining, collecting, analyzing, interpreting, and using information to increase students’ learning and development.
• The activity chosen for assessment should be different but of the same level and type as the activity usually carried out in the classroom.

Important Points Assessment methods: Methods will vary depending on the learning outcome(s) to be measured.

• Assessment approaches
  • Formative and summative 
  • Quantitative and Qualitative 
• Formative assessment: Formative Assessment is a tool used for continuous monitoring of the student’s progress, during the teaching-learning process in a non-threatening and supporting environment. 
• Summative assessment: The term ‘summative’ means summing up of all the available information regarding a program at its terminal point. In other words, summative assessment signifies all those tests that are taken at the end of the semester or the year after the completion of all units and lessons.

Hence we can conclude that Assessment is most closely related to Content of the subject.

Assessment is an ongoing and integral part of math instruction that enhances both teaching and learning math. Teachers give students opportunities to show what they know through varied and frequent assessments. Giving various types of mathematics assessments gives teachers a clearer picture of how their students are progressing. It also allows the teacher to adjust to the needs of different types of learners.

Important Points

Summative Assessment: In mathematics, summative evaluation only directly monitors the student's ability but does not pay attention to how the student uses knowledge to solve practical problems. 

• Summative Assessment is any method of evaluation performed at the end of a unit that allows a teacher to measure a student's understanding, typically against standardized criteria.
• The purpose of summative assessment is to gauge students' comprehension of the material presented at the end of a particular unit of work and is often measured with a grade or percentage, depending on the subject, so it is the term-end examination.
• One of the most common examples of summative assessment is the end-of-semester college examinations.
• The purpose of summative assessment is to gauge students' comprehension of the material presented at the end of a particular unit of work and is often measured with a grade or percentage, depending on the subject, It is used for grading, promotion, and placement.
• Assessment for the purpose of judging a student’s mastery of concepts is called summative assessment.
• Summative assessment is more product-oriented and assesses the final product, whereas formative assessment focuses on the process toward completing the product. Once the project is completed, no further revisions can be made, so summative assessment is product-oriented rather than process-oriented.​ ​​

Key PointsTools for summative assessment:  

• Examinations (major, high-stakes exams)
• Final examination (a truly summative assessment)
• Term-end exam 
• Semester exams 
• Performances Test
• Student evaluation of the course (teaching effectiveness) etc.​

Additional Information

• ​Formative assessment: Formative assessment provides feedback and information during the instructional process, while learning is taking place, and while learning is occurring.
• It focuses on diagnosing the strength and weaknesses of the children and formative assessment measures student progress but it can also assess your own progress as an instructor. 
• So focusing on diagnosing the strength and weaknesses of the children is a characteristic of formatives assessment, not summative assessment.​

​Tools for formative assessment: 

• Assignment
• Project-work
• Quiz
• Oral Question
• Journal entries etc.

Hence, we can conclude that the right answer to this question is It focuses on diagnosing the strength and weaknesses of the children.

Assessment is educational evaluation, the systematic way of collecting information and reading the work of class which is used to guide and improve students' performance in terms of learning and development. 

• There are different kinds of assessment tools to evaluate learners' performance during the learning process. Rubrics, rating scales, anecdotal records, portfolios, etc are the most common type of assessment tools.

Key Points

Rubric:

• A rubric is a scoring guide that includes a set of criteria to assess students’ work. It contains performance expectations for a piece of work. It is an assessment process based on performance that reflects process-content skills, working habits, and learning outcomes.
• It can be used for assessing any kind of performance because rubrics are very comprehensive in nature. Different components in the rubrics enable teachers to recognize the strength and weaknesses of learners formatively.
• It makes the expectations of the assessor clear to the students and also helps the students meet these expectations successfully. On the basis of the purpose of assessment, mainly two types of rubrics are used: Holistic rubrics and Analytical Rubrics.

From the above-mentioned points, we can conclude that a Rubric will be suitable to assess student's performance in this project.

Additional Information

• Checklist is used to evaluate the record opinions or judgments and to indicate the degree or amount. It consists of a list of items prepared by the teacher to study the relevant problems. The students just have to answer them in yes/no or tick mark the items to show the absence or presence of that specific item.
• Concepts maps include graphical and diagrammatical representations to illustrate the meaningful acquisition of various sub-topics of a concept. It helps the learners to draw an outline of the topic/concept or briefly explain the concept or to link any two concepts of any subject by summarizing it.   
• Paper - pencil test is related to the summative assessment which helps to measure, certify, and report the level of student learning at the end of the term.

Evaluation compromises of three steps -

Key Points

Tyler approach moved rationally and systematically through several related steps:

1. Begin with the behavioral objectives that have been previously determined.  
2. Identify the situations that will give the student the opportunity to express the behavior embodied in the objective.
3. Select, modify, or construct suitable evaluation instruments, and check the instruments for objectivity, reliability, and validity.
4. Use the instruments to obtain summarized or appraised results.
5. Compare the results obtained from several instruments before and after given periods in order to estimate the amount of change taking place.
6. Analyze the results in order to determine the strengths and weaknesses of the curriculum and to identify possible explanations about the reason for this particular pattern of strengths and weaknesses.
7. Use the results to make the necessary modifications in the curriculum. 

Hence, Based on Tyler's model which is on objectives the correct order of steps of evaluation in mathematics:

• Selection of objectives
• Identification of situations
• Selection of evaluation methods
• Constructions of evaluation devices
• Interpretations of evidences

Generally, the questions asked by the teacher during the teaching-learning process can be broadly classified into two types:

Open-ended questions

• These questions are also known as the divergent questions where the respondents are free to share, clarify and put their views. The students will elaborate their point of view and the teacher will be able to see the things from a student's perspective.
• These questions are generally framed in a single statement that requires a longer response.

​Close-ended questions

• These questions are also known as the convergent questions where the respondents answer in limited ways, like responding in ‘yes’ or ‘no’; underlining the replied among the predefined responses, putting the sign ‘correct’ or ‘incorrect’.
• They provide limited insight but can be easily used to analyze quantitative data.

​ Key Points

Thus, it is concluded that A and C are close-ended type questions whereas B and D are open-ended type questions.