CONSTRUCTION OF ACHIEVEMENT TEST
GENERAL STEPS
1. Identify and define the learning outcomes to be measured
2. Prepare test specifications
3. Construct relevant test items
4. Review and edit the items
5. Arrange the items in the test
6. Prepare directions
Steps 1
1. Identify and define learning objective
2. State the general objectives
3. Develop 5 to 15 general objectives
4. State the specific objectives
5. For each G.O., develop 3-5 specific objectives
Steps 2
Preparing test specifications
1. Select the specific outcomes to be tested
2. Outline the subject matter by listing topic and subtopic areas in the lesson plan.
3. Make a two-way table of specifications.
Step3
1. Selection the type of test items to use
2. Selection type items
3. Matching items to specific objectives
4. For each S.O write one or more related items
STATISTICAL MEASURES
THE MEAN AND THE MEDIAN
The two most common measures of central tendency are the median and the mean, which can be illustrated with an example. Suppose we draw a sample of five women and measure their weights. They weigh 100 pounds, 100 pounds, 130 pounds, 140 pounds, and 150 pounds.
To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values. Thus, in the sample of five women, the median value would be 130 pounds; since 130 pounds is the middle weight.
The mean of a sample or a population is computed by adding all of the observations and dividing by the number of observations. Returning to the example of the five women, the mean weight would equal (100 + 100 + 130 + 140 + 150)/5 = 620/5 = 124 pounds. In the general case, the mean can be calculated, using one of the following equations:
Population mean = μ = ΣX / N
Sample mean = x = Σx / n
where ΣX is the sum of all the population observations, N is the number of population observations, Σx is the sum of all the sample observations, and n is the number of sample observations. When statisticians talk about the mean of a population, they use the Greek letter μ to refer to the mean score. When they talk about the mean of a sample, statisticians use the symbol x to refer to the mean score.
THE MEAN VS THE MEDIAN
As measures of central tendency, the mean and the median each have advantages and disadvantages. Some pros and cons of each measure are summarized below.
The median may be a better indicator of the most typical value if a set of scores has an outlier. An outlier is an extreme value that differs greatly from other values.
However, when the sample size is large and does not include outliers, the mean score usually provides a better measure of central tendency.
THE RANGE
The range is the difference between the largest and smallest values in a set of values.
For example, consider the following numbers: 1, 3, 4, 5, 5, 6, 7, 11. For this set of numbers, the range would be 11 - 1 or 10.
THE VARIANCE
In a population, variance is the average squared deviation from the population mean, as defined by the following formula:
σ2 = Σ ( Xi - μ )2 / N
where σ2 is the population variance, μ is the population mean, Xi is the ith element from the population, and N is the number of elements in the population.
The variance of a sample, is defined by slightly different formula, and uses a slightly different notation:
s2 = Σ ( xi - x )2 / ( n - 1 )
where s2 is the sample variance, x is the sample mean, xi is the ith element from the sample, and n is the number of elements in the sample. Using this formula, the sample variance can be considered an unbiased estimate of the true population variance. Therefore, if you need to estimate an unknown population variance, based on data from a sample, this is the formula to use.
THE STANDARD DEVIATION
The standard deviation is the square root of the variance. Thus, the standard deviation of a population is:
σ = sqrt [ σ2 ] = sqrt [ Σ ( Xi - μ )2 / N ]
where σ is the population standard deviation, σ2 is the population variance, μ is the population mean, Xi is the ith element from the population, and N is the number of elements in the population.
And the standard deviation of a sample is:
s = sqrt [ s2 ] = sqrt [ Σ ( xi - x )2 / ( n - 1 ) ]
where s is the sample standard deviation, s2 is the sample variance, x is the sample mean, xi is the ith element from the sample, and n is the number of elements in the sample.
QUARTILES
Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively.
Note the relationship between quartiles and percentiles. Q1 corresponds to P25, Q2 corresponds to P50, Q3 corresponds to P75. Q2 is the median value in the set.
DIAGNOSTIC TESTING AND REMEDIAL TEACHING IN MATHEMATICS
DIAGNOSTIC TEST IN MATHEMATICS
The diagnostic in mathematics comprises of module tests which are primarily criterion-referenced based, as opposed to norm-referenced. Diagnostic reading and spelling tests are norm-referenced, tests. There is no test, however there is a set range of tests for particular age/year levels. In particular, junior primary teachers may need to gauge the reading competency of their group and decide whether to have all the students complete the sections as they are read out.
The main role as a teacher is to promote quality learning among the students. This is possible only when you act as a guide and the students actively participate in the process of learning. During the teaching-learning process, you have to locate and identify the areas where the learner commits mistakes. It is the crucial stage of the teaching-learning process where you have to DIAGNOSE and prepare instructional material for REMEDIAL TEACHING to ensure the desired quality of learning.
At this stage the role of a teacher is just like a doctor’s. The doctor takes all the steps necessary to diagnose the disease by performing different tests and then prescribes medicines for the particular disease. In the case of education the process of Diagnostic Testing is the STEP and REMEDIAL TEACHING is the PRESCRIPTION. Hence diagnostic testing and remedial teaching are very essential for ensuring effective learning and in improving the quality of education.
In general, after completing a particular unit/topic you conduct a test to assess the achievements of learners.
After evaluation you draw some conclusions and you find that some of the students have fared very well and a particular group of students have achieved below your expectations. Now you will have to find out the causes for this low achievement or slow learning. There would be certain reasons for this low achievement. Now it is very essential to find out the particular area where the difficulty lies or the particular concept where the learner commits errors. To locate and identify the areas of learning difficulties leads to Diagnostic Testing. After identifying the areas where the error lies, you have to find out the reasons due to which the particular child/group of students have not responded well. At this stage you have to play the role of a doctor. If a patient visits the doctor’s clinic he suggests different tests relevant to the symptoms observed by him. After getting reports he is in a position to identify and diagnose the disease and then prescribe the medicine for it.
Likewise, as a teacher, you have to first identify and locate the area where the error lies. The process adopted for this purpose in educational situations is known as Diagnostic Testing. We may say that Diagnostic Testing implies a detailed study of learning difficulties. In diagnostic testing the following points must be kept in mind:
i) Who are the pupils who need help?
ii) Where are the errors located ?
iii) Why did the error occur ?
STEPS AND STAGES IN DIAGNOSTIC TESTING
The essential steps in educational diagnosis are:
i) Identifying the students who are having trouble or need help.
ii) Locating the errors or learning difficulties.
iii) Discovering the causal factors of slow learning.
i) Identifying the students who are having trouble or need help
First, one must know the learners who require help. For this you can administer a general chievement test based on the topics already taught. After evaluation you will be in a position to make lists of students who are below average, average or above average. Next, one has to locate the area where the error occurs in order to have a deeper insight into the pupils’ difficulties.
ii) Locating the errors or learning difficulties
After identifying the students who need help and visualising the necessity of additional instructional material to improve the quality of learning, your main role is to find out the area where the learner commits mistakes or which is the area where learning difficulties lie.
iii) Discovering the causal factors of slow learning
In some cases of learning difficulties, the causal factors are relatively simple. A student may be inattentive during teaching-learning or may be committing errors due to insufficient practice or irregular attendance. Sometimes the cause is ill-health or faulty work habits etc. It has also been observed sometimes that the basic cause of low achievement is a feeling of helplessness or
the complexity of the subject-matter which perhaps is much above the level of their comprehension.
REMEDIAL TEACHING
While diagnosis is the process of investigating the learners’ difficulties and the reasons for this, its follow up leads to actions that may help children make up their deficiencies. This step is generally termed Remedial Teaching. So you have to be skilled in preparing or arranging for such materials which may be used to undertake corrective instruction and thus enhancing the quality of learning.
Selection of Materials
The following points should be kept in mind while selecting appropriate instructional material:
i) The corrective material should be designed to correct the students’ individual difficulties.
ii) You have to analyze the work of slow learners by means of observation, interview and Diagnostic Testing. A careful consideration of the three may help decide what kind of corrective material is to be designed and whether material will be adequate to correct the specific difficulties of learners.
iii) The corrective material should be graded, self-directive and should permit students to work independently. Written directions, which accompany the material, should be easily readable and comprehensible by the students.
iv) The corrective material must permit individuals to progress according to their
pace.
v) The material should encourage systematic recording of evidence of pupils’
progress.
Enough practice should be provided to pupils on similar questions until they attain
mastery. While selecting and implementing the instructional material the most important thing is the individual need of the student in a particular area. You have to give differential treatment. Different methodologies have to be adopted for different kinds of students. Other modes of interaction such as learner-learner interaction and learner-material interaction may also be utilized, besides the traditional teacher-learner interaction, using appropriate instructional material.
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