CHAPTER NINETEEN
EVALUATION IN MATHEMATICS EDUCATION
19.1 Objectives
By the end of this chapter, you should be able to:
i. Define Measurement and Evaluation
ii. State the types of Measurement and Evaluation
iii. To distinguish between Measurement and Evaluation.
iv. Purpose of Measurement and Evaluation
19.2 Introduction
You are introduced to certain key ideas in this chapter that are connected to determining whether or not goals have been attained. The chapter essentially walks you through what measuring and assessment entail in math instruction. Additionally, their kinds are covered. You should be aware of the subtle differences between these ideas and their respective purposes.
19.3 Measurement
Measuring is the act of assigning numbers to things, quantities, or events in accordance with a well-defined rule or standard in order to ascertain their value, height, and volume. In other words, measuring is the systematic method of determining the presence of a property. Physical measurement and psychological measurement are the two forms of measurement. Sometimes, physical measurement is referred to as empirical measurement. It refers to the use of measuring instruments, such as tapes, rulers, thermometers, clocks, speedometers, etc., to estimate the size of anything, particularly in reference to a recognized standard. While psychological measuring (educational measurement) entails the use of educational instruments such as tests, interviews, examinations, and observations, this is done to assess intangible characteristics such as intelligence, aptitude, and other quantitative factors.
19.4 Measurement Levels
There are several degrees of measurement based on what is to be measured, the equipment to be used, the characteristic being measured, and the desired level of precision. There are four scales of measurement: nominal scale, ordinal scale, interval scale, and ratio scale.
Nominal Scale: This scale is designed for identifying purposes only and only allows classification into classes or categories. Measurements based on this scale include classifying individuals by gender (male, female), tribe (Nupe, Gwari, Kambari), religion (Muslim, Christianity), and marital status (single, married). Their categories have no associated magnitude, and these scales reflect the lowest level of measurement. For example, the course codes MAT124 and MAT225 cannot be combined or subtracted to make sense when using this scale of measurement.
Ordinal Scale: measuring on this scale permits classifying and ranking and bears the "order" quality. On this scale, the assignment of rankings (or places) to students based on their test scores is an example of measuring. Other variables employed on this scale include merit, reward, rating, etc. This scale allows for the correlation or comparison of variables. In other words, the student ranked first performed better than the student ranked second. However, no mathematical operations other than comparison are possible in this scale. You cannot say position 3rd plus 2nd or position 3rd minus 2nd, nor are the gaps between distinct ranks or positions always equal.
• Interval: this scale is classifiable, uniformly spaced, and possesses the quality of order. Examples of measurements on this scale are examination scores or grades. The difference in performance between scores 40 and 45 will be equivalent to the difference in performance between scores 10 and 15. Test (examination) scores, the degree of temperature, and all psychological measurements employ interval scales of measurement as independent variables. This scale is used for all mathematical operations except division, as interval scale has no zero value. For instance, if a student receives a score of 0% on an exam, this cannot be construed as a sign of ignorance or lack of intelligence; 0% is not absolute. In other words, it does not correlate to a lack of the attribute in its entirety.
Ratio Scale: this scale possesses all the characteristics of the interval scale, including the ability to be classified, ranked, uniformly spaced, and the presence of a natural zero. On this scale, 0 represents the lack of the attribute being assessed. For example, if the length of an item is 0 centimeters, that thing does not exist. Time, weight, height, distance, etc., are variables that employ ratio scales of measurement. This scale permits all mathematical operations, and the physical sciences employ this degree of measurement. The ratio scale is the most polished, exact, or accurate of the scales, followed by the interval scale and the ordinal scale in that order. The nominal scale has the lowest degree of precision. The first three levels of measurement in mathematical education are nominal, ordinal, and interval.
Attempt 1
1. What exactly is measurement?
2. Mention the two fundamental types of measurement.
3. What are the four measuring scale levels?
4. Which of these has the only ordering property?
5. Describe the characteristics of the interval and ratio scales
6. Provide two measurement examples for each of the four scales.
19.5 Measurement Inaccuracies
The definition of measurement error is the difference between the real or actual value and the measured value. The inaccuracy may originate from several sources and is often characterized as follows:
These varieties are:
1. Gross Errors
Systematic Errors 2.
3. Random Errors
19.5.1 Gross Errors
This error is caused by human error, such as when the individual operating the instrument takes the erroneous reading or records inaccurate data. This blunder falls under the category of human error and is characterized as a big error. The major mistake can only be prevented by attentive reading.
19.5.2 Synchronous Errors
These mistakes are inherent to instruments due to their mechanical design. They may be the result of production calibration or device usage. These inaccuracies may result in an erroneous reading that is too low or too high. Additionally, the issue might be caused by operator error. Good equipment utilized in an uneducated manner provide a tremendous outcome. For instance, improper usage of the instrument may result in the inability to modify the zero of the instrument, inadequate initial adjustment, and excessive resistance. These faulty procedures may not cause irreparable harm to the instrument yet may nonetheless result in mistakes.
19.5.3 Random Errors
This sort of inaccuracy is referred to as random error, and it is generated by rapid changes in the meteorological conditions. These forms of mistake exist after systematic error has been eliminated. Hence such type of error is also called residual error.
19.6 Evaluation
Evaluation may be considered an inherent component of every educational activity plan, regardless of the duration of the teaching. The evaluation procedure is ongoing throughout the duration of education. It is also regarded as the last action that concludes the teaching-learning process, regardless of whether the instruction lasted a year, a semester, a teaching unit, or a single period. The analysis of these definitions reveals that assessment as an important component of the teaching-learning process consists of three parts. Which are.
1. Identifying and describing the desired results
2. Creating or selecting tests and other assessment instruments related to the targeted aims.
3. Using the evaluation data to improve learning and teaching.
When discussing evaluation in the mathematics classroom, we attempt to determine the quantity and quality of students' mathematical comprehension and success based on clearly specified goals. However, emphasis is placed on making instructional objectives explicit and quantifiable.
19.7 Types of Assessment
There are four forms of evaluation: placement, formative, diagnostic, and summative.
19.7.1 Placement Evaluation
This is the evaluation performed in order to categorize pupils into the right category. Before allocating students to the sciences, arts, commerce, and technical tracks, several schools provide tests to determine their performance. This form of evaluation is conducted by the teacher to determine the entrance behavior of each pupil.
19.7.2 Formative Assessment
Formative assessment is an evaluation aimed to aid both the teacher and student in identifying parts where the student failed to learn. It offers feedback to the instructor and student to help them address problem areas. This is accomplished by weekly tests, final exams, etc. As an effective mathematics instructor, you must always assign homework or classwork after each lesson in order to receive feedback on your teaching.
19.7.3 Diagnostic Assessment
This kind of assessment is meant to be used after formative evaluation. You employed formative assessment as a math teacher to pinpoint your pupils' areas of weakness, and you subsequently used remedial strategies to address recurrent problems. You will now create a type of diagnostic exam that is used in classroom education to ascertain the underlying reason why pupils continue to have learning challenges. These diagnostic tests might be in the form of a performance test, a self-rating, an interview, an observation, etc.
19.7.4 Summative Assessment
This is the form of assessment that is created and conducted at the conclusion of a period of instruction or a course of study. It is termed a summary because its purpose is to establish the extent to which the educational aim has been met. It is also designed to assign students course grades and certificates. The awards for educational certificates, such as NCE. Diplomas, degrees, WAEC, and NECO, among others, are awarded through a final test, which is an example of summative assessment. This will determine the degree to which the program's broad objectives have been met. It focuses on the objectives, development, and results of the teaching-learning process.
19.8 Functions of Assessment
The purpose of evaluation in mathematics education may be categorized into four major categories, which are as follows.
i. Instructional capabilities
ii. Administrative functions, iii. Counseling functions, and iv. Research functions.
19.8.1 Educative Functions
These functions pertain to the ways in which evaluations assist in enhancing the quality of classroom activities. Instructional functions are comprised of all evaluation functions that can lead to enhanced teaching and learning in the classroom and result in highly effective instruction. The particular instructional roles of educational evaluation include.
i. Good study habits: regular evaluation or testing causes pupils to often update their schoolwork. And this promotes healthy study habits in the student's thinking.
ii. Motivation: evaluation enhances students' motivation anytime they get feedback on performance that motivates them to work more, regardless of whether the input is good or negative. If the evaluation is favorable, the kids are happy and will work diligently to maintain their performance. If the grade is unfavorable, the student will be motivated to improve their performance.
Evaluation offers information to the instructor regarding the students' entering habits. Any effective classroom instruction must document students' prior knowledge or lack thereof at the outset of the course.
iii. Determining the extent to which objectives have been realized: Evaluation helps to offer information that assists the instructor in determining the extent to which the educational objectives have been attained. At the conclusion of the lesson, information indicating the extent to which the instructional objectives have been met is made available.
feedback on instructors' and students' areas of weakness and strength
Evaluation gives teachers and students with information on their weaknesses and strengths. Students will determine where their strengths and weaknesses lie. On the other hand, the instructor will see which educational strategies are effective and which are not.
19.8.2 Administrative Capabilities
Evaluations have the following particular administrative purposes in mathematical education and education in general:
Students are classified based on their talents and interests using evaluation data. This information helps us determine what sort of course a student should take, whether he or she should enroll in teacher education, secondary education, or technical education.
Placement of students: the information offered by evaluation aids in placing students at a point or grade in a course that is most suited to their individual qualities. It also involves placing the student in the most suitable career. An example of placement would be placing a gifted kid in a scientific class rather than an arts class.
Selection: a specialized administrative function of evaluation that aids in selecting individuals and curricular materials that fulfill the institution's best interests. The school chooses whether a new set of curricular materials (textbooks, equipment, and supplies) will be selected to promote the institution's goal accomplishment based on assessment comments.
Certification: the data collected during assessment served as the foundation for providing certificates to students who successfully completed a program.
19.8.3 Guidance Functions
Evaluation in mathematics and education fulfills the following particular guiding roles:
i. Diagnosis of student learning challenges: the information produced by evaluation aids in the diagnosis of students learning difficulties. This information is to guarantee the right educational growth of the student through programme of remediation.
ii. Solving societal and individual issues. The evaluation results will help the school counselor to assist kids in resolving their social and personal issues. Numerous kids have multiple social and personal issues, such as family issues, peer group conflicts, and adjustment issues, among others. The school counselor will be able to support the student in coping with this sickness if the evaluation yields appropriate information.
iii. Occupational career: an additional specialized counseling role offered by educational evaluation is supporting the student in making an appropriate and effective vocational selection. It is vitally important to find a career that matches one's aptitude, interests, and skills.
19.8.4 Research Capabilities
Evaluation in mathematics and education serves several important research purposes, including:
i. Effectiveness of educational techniques requires study to determine which instructional approach is more successful. Evaluation gives the evidence required for appropriate conclusion formation.
ii. Effectiveness of instructional materials: Research undertaken in the domain of instructional material effectiveness will aid in determining which materials will be effective in achieving certain educational objectives in mathematics. This research is made possible through evaluation.
iii. New curriculum effectiveness: research assistance in determining the efficacy of a new curriculum prior to its implementation in a school system. The evaluation information aids in generating judgments on the efficacy of the new curriculum.
iv. characteristics and influencing elements of the learners Through research, we have been able to comprehend the characteristics of the learner as well as other factors that influence learning.
Activity
1. Provide an explanation of educational measurement and evaluation
2. Acknowledge measurement errors
3. Mention the four levels of measurement.
4. Explain the meaning of summative evaluation
5. Give two examples of the kind of evaluation
6. State the four major functions of evaluation in mathematics education
7. What specific guidance functions does evaluation serve in mathematics education
8. State the specific research function which evaluation serves in mathematics education
19.9 Summary
In this chapter, the following points shave been highlighted.
§ Measurement is the systematic process for finding the extent to which an characteristic is present in an object in numerical terms; evaluation has to do with making valid judgment or decision based on the information obtained through evaluation.
§ Measurement is of two kinds, physical and psychological. Physical is carryout by the use of measurement instruments, such as clock, thermometer, calendar, etc. Educational measurement is carryout through test, interview, etc.
§ Errors in measurement and its classification gross, systematic, random were presented and discussed.
§ We spoke about four different measuring scales. These are the ratio scale, which contains absolute zero and is particularly utilized in the physical sciences, the ordinal scale, which uses rank order, the interval scale, which uses equal intervals and equal amounts but without absolute zero, and the nominal scale, which involves easy identification.
§ Evaluation can be classified into placement, formative diagnosis and summative
§ Evaluation in education serves four major functions-instructional, administrative, guidance and research functions.
References
Maruf,O.I & Aliyu, Z.,(2013). Measurement and evaluation in education. Printed by: Stevano Printing Press