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

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.

When assessing students' understanding of data and statistics, it's important to focus on skills that go beyond memorization and test-taking. Understanding data involves more than just knowing formulas; it requires the ability to interpret, analyze, and use data in meaningful ways. These skills are essential for making sense of the world around us, whether it's interpreting survey results, analyzing trends, or drawing conclusions from data.

Key Points

• Ability to collect and organize data efficiently (a): This skill is essential for setting up the foundation of any statistical analysis. Being able to collect data accurately and organize it in a clear manner is the first step in making sense of it.
• Ability to interpret and analyze data from charts and graphs (c): This skill is fundamental in data and statistics. Charts, graphs, and tables are often used to display data, and being able to interpret these visuals is key to understanding what the data is saying. This involves drawing conclusions and making inferences based on the information presented in these visuals.

 Hint

• Memorizing statistical formulas without understanding (b) or simply answering textbook questions without using data (d) are not effective indicators of true understanding.
• These activities might help with basic recall but fail to measure a student’s ability to apply statistical concepts in real-world situations or interpret data meaningfully.

Hence, the correct answer is (a) and (c).

In the teaching-learning process, assessing students involves not just evaluating academic knowledge but also observing their behavior, participation, and interpersonal skills, especially during group activities.

Key Points

•  To observe and note students’ participation, cooperation, and communication during group activities, a tool is needed that allows for ongoing observation and detailed recording of student behavior.
• Anecdotal records serve this purpose best. They involve brief, narrative descriptions of significant incidents or behaviors observed by the teacher.
• This tool helps in documenting how students interact with peers, contribute to group tasks, and communicate ideas.
• It captures specific examples of social and emotional skills in action, making it highly effective for monitoring student development in group settings.

Hint

•  A question paper is used to assess cognitive skills and subject knowledge, typically through written responses, and does not capture behavioral observations.
• A rubric is a scoring guide used to assess performance based on a set of criteria, which can be effective in structured assessments but may not capture spontaneous or unexpected behaviors during group activities.
• A report card provides a summary of student performance, often at the end of a term, and is not used for ongoing observation or noting specific behaviors during classroom interactions.

Hence, the correct answer is Anecdotal Record.

Assessment is a continuous process in education that helps track and improve student learning. It plays a crucial role in shaping both teaching strategies and student outcomes.

Key Points

•  Assessment as learning emphasizes the role of the student in the assessment process. In this approach, students are encouraged to reflect on their understanding and take responsibility for their learning.
• They assess their own progress and set goals to improve. This kind of assessment is integrated into daily classroom activities and helps students become independent learners.
• By engaging in self-assessment, students develop critical thinking and metacognitive skills, which ultimately lead to deeper learning and improvement. This makes assessment a learning active and learner-centered process closely connected with reflection and self-monitoring.

Hint

• Summative assessment is mainly used to evaluate student learning at the end of a unit or term and does not typically inform day-to-day teaching strategies. 
• Formative assessment is directly related to the teaching-learning process. It is used throughout the learning period to monitor student progress and to make immediate instructional adjustments, so saying it is unrelated to the teaching-learning process is inaccurate.
• Assessment for learning is not confined to the end of an academic session. It is an ongoing process that takes place during the learning to provide feedback and guide instruction, helping both students and teachers.

Hence, the correct answer is Assessment as learning involves students actively reflecting on their own learning.

At the secondary level, assessment serves multiple functions beyond just grading. It becomes a tool for measuring conceptual understanding, identifying learning gaps, and ensuring alignment with curriculum objectives. However, it should not limit students to rigid procedures or serve solely for competitive filtering.

Key Points

• Understanding the specific learning needs of each student helps teachers differentiate instruction and offer targeted support, which is critical at this stage.
• Evaluating how well the goals of the mathematics curriculum are being met ensures that teaching practices are aligned with educational standards and learning outcomes.
• These two points reflect the formative and summative purposes of assessment in a balanced way.

Hint

• Checking whether students have mastered a fixed method limits creativity and critical thinking, which are essential at the secondary level where flexible problem-solving should be encouraged.
• Shortlisting students for competitive exams is not a core purpose of classroom assessment it is an external application and not aligned with inclusive, learner-centric education.

Hence, the correct answer is (A) and (B).

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.