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# Quantitative Aspects

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OBJECTIVES: (1) To be familiar with the different statistical tools needed in educational planning;
(2) To know the computation techniques and formulas used in educational planning; and
(3) To be aware about the criteria used for rating students and teachers performance TOPICS:
(1) Basic Statistics Needed in Planning
(2) Computation Techniques
(3) Performance Indicators TYPES OF STATISTICAL DATA
NEEDED IN EDUCATIONAL PLANNING STATISTICS is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including planning of data collection in terms of the design of surveys and experiments.
A Statistician is someone who is particularly well versed in the ways of thinking necessary for the successful application of statistical analysis. Such people have often gained the experience through working in any of a wide number of fields. A. Demographic Statistics
Demography is the statistical study of human populations.
“Demo” means “the people” and “graphy” means “measurement”.
• Total Population by sex and age
• Population Projection
• Population by Educational Attainment (literacy)
• Natality, Mortality and Migration B. Labor Force Statistics
The labor force participation rate is the ratio between the labor force and the overall size of their cohort (national population of the same age range).
• Economically active population, by industry and educational attainment
• Projection of the Labor Force
• Economically active population by occupation, sex and age C. Economic and Financial Statistics
• Gross National Product
• Total Public Expenditure by authority and purpose D. Statistics on Educational Institutions
• Institutions by level and type of education
• Institutions by Region
• Number of Schools of the First and Second Year Levels of Education by number of grades, number of teachers and number of pupils enrolled E. Teachers and Other Educational Personnel
• Number of Teachers by Sex and Age
• Teachers by Qualification and Length of Service
• Number of Teachers lost to the Educational System each year for various reasons
• Teachers by Subjects
• Full-time and Part-time Teachers, Hours of Teaching
• Number of Non-Teaching Staff, Inspectors, Administrative, Health and Other Auxiliary Personnel F. Classes
• Number of Classes by Grade
• Number of Classes by Size G. Pupils / Students
• Number of Pupils by age, sex and grade
• Pupils at the First and Second Levels of Education leaving school each year
• Pupils repeating grades each year
• Pupils at the Second Level of Education by Branch of Study
• Students at the Third Level of Education by Field of Study
• Graduates at the Third Level of Education by Field of Study, Level and Type of Degree or Diploma
• First time students at the Third Level of Education by Field of Study
• Number of Pupils by Region
• Pupils in non-co-educational schools
• Full-time and Part-time Pupils
• Pupils by Socio-economic Origin
• Pupils by Domicile
• Average Daily Attendance of pupils at the first and second levels of education
• Students abroad, by country, field and duration of study H. School Building and Equipment
• School buildings by type of construction, qualitative standards and size
• Classrooms and Special Rooms
• School buildings, classrooms and special rooms completed each year, and their capital costs I. Educational Testing and Vocational Guidance
• Evaluation of pupil's achievement
• Mental measurement of pupils
• Measurement of pupils' aptitudes and interests J. Health and Feeding of Pupils
• School health services
• School feeding programmes K. Out-of-school Education
• Facilities for out-of-school education, by type of organization
• Staff engaged in out-of-school education, by sex and qualification
• Persons availing themselves of facilities for out-of-school education, by sex, age and level of educational attainment L. Cost of Education
• Recurring expenditure on education by public authorities
• Capital expenditure on education
• Loans, repayment and interest charges, related to educational expenditure
• Private expenditure for education COMPUTATIONAL TECHNIQUES
IN EDUCATIONAL PLANNING Our current educational model is based on the compartmentalization of knowledge. This has been a powerful tool, but in today’s world more and more knowledge is spilling over the boundaries of the compartments we have constructed, for example across the boundaries between biology, chemistry, and physics. For all people, understanding the world as interlocked complex system (social systems, job markets, financial markets, political systems, schools, ecological systems, universities, etc.) is critical for making decisions in their lives as individuals and as citizens.
Based on UNESCO (United Nations Educational, Scientific and Cultural Organization) format, the DepEd at one time prepared the following guidelines: In this preparation of an educational analysis of a given district, division, or region, all available data will be evaluated in terms of the existing educational policies and national standards. In doing this, educational planners will need computational techniques to obtain a clear picture and meaning of every available data. Some computational techniques are presented and illustrated by the DepEd. A. Growth Rates
Elementary school enrollment in Bautista District (Province of Pangasinan) in SY 1976-1977 is 2861. In 1977-1978 it has increase to 2874. What is the growth rate? Rate of Growth = 2874 - 2861 x 100 2861 = 13 x 100 2861 = 0.45% If we want to compare enrolment over a period longer than 1 year, the above simple formula is not sufficient For example, in SY 1965-1966 elementary grades enrolment is 2345 in Bautista District. The growth of enrolment over the period 1964-1966 to1977-1978 is Using the formula r = Eb-Eo x 100 tEo where:
Eo = enrolment from previous data available (e.g. 2345)
Eb = recent enrolment data available (e.g. 2874)
t = number of school years between Eb and Eo
r = rate of growth therefore:
Rate of Growth = 2874 - 2345 x 100
13 (2345)
= 529 x 100 3185
= 166 x 100
= 16.6 or 17% However, the term “16.6 or 17% over 13 years” is not very meaningful, because it is not easily comparable. If for another district or region we find as rate of growth “3 over 12 years” it is impossible to say immediately whether this represents a faster or slower growth rate. To enable this comparison, we calculate the “average annual rate of growth”. For the calculation of this average annual rate of growth two methods can be used:
(1) Calculating the growth rate of each year in the period and thereafter deriving the arithmetic mean of these growth rates.
(2) Using the formula En = Eo (1 + 1) ⁿ Example: Basilan Elementary School 1973-1974 12703
1974-1975 14807
1975-1976 20109 Method (1)
a. Growth from 1973-1974 to 1974-1975 16.56%
b. Growth from 1974-1975 to 1975-1976 35.8%
c. Average annual growth rate 16.56 + 35.8 = 26.18% 2 Method (2)
En = enrolment
Eo = enrolment in the first year of the period
i = average annual rate of growth n = number of years in the period Using the given example: Enrolment 1975-1976 = Enrolment 1973-1974

Or 20109 = 20109 (1 + i) ² The problem is solved along the following steps: a. 20109 = (1 + i) ² Dividing gives a result b. 1.583 = (1 + i) ² this equation can be solved by the use of logarithms:
c. log 1.583 = log ( 1 + i) ² because log = b log a, this gives:
d. log 1.583 = 2 log ( 1 + i) looking log 1.583 in the logarithms table (logarithms on base 10) gives:
e. 0.19948 = 2 log ( 1 + i)
f. 0.19948 = log ( 1 + i) Dividing gives the result
g. 0.09974 = log ( 1 + i) Looking uo the antilog of 0.0974 gives the value of ( 1 + i)
h. 1.25817 = ( 1 + i) or
i. i = 0.25817 0r 25.82% It can be seen that the both methods give almost the same results and it would be seen that the first method is simpler, but that is only because our example is so simply chosen. If the period would be longer, the number of annual rates to be calculated would become quite large and for those who can handle the logarithms calculations, the second method should be preferred. B. Extrapolation

Extrapolation id the process of estimating beyond the original observation interval. The value of a variable on the basis of its relationship with the another variable. It is similar to interpolation, which produces estimates between observation, but, extrapolation is a subject to greater uncertainty and a higher risk of producing meaningless results

The average annual rate of growth can be used to extrapolations or projections: Example:
Given the following elementary school figures:

SY 1973-1974 12703
SY 1978-1979 31356 The average rate of growth is 19.81% per year over the period 1973-1974 to 1978-1979. When asked “What will be the elementary school enrolment in school year 1983-1984?” The most straightforward approach is to assume that the enrolment will continue to increase with 19.81% per year. The same formula as for the average annual rate of growth can be used
En = Eo (1 + i) ⁿ In our simple example En now represents enrolment in school year 1983-1984 and Eo as the base year for our projections.
Enrolment in SY 1983-1984 = Enrolment in SY (1978-1979) (1 – 1981) a. 1983-1984 = 31356 ( 1 + 1981 ) changing on to logarithms
b. 1983 – 1984 = log 31356 + log ( 1 + 0.1981)
c. 1983 – 1984 = log 31356 + 5xlog ( 1 + 0.1981) looking up the values of logarithms in the table gives
d. 1983 – 1984 = 4.4963 + 5x (0.0785)
e. 1983 – 1984 = 4.4963 + (0.3925)
f. 1983 – 1984 = 4.888 looking up the antilog 4.888 we find
g. 1983 – 1984 = 77268 C. Interpolation

Interpolation is a method of constructing new data points within the range of a discrete set of known data

Usually Census data are available at 5 year intervals. We need interpolation to estimate data (data in between census periods). In the following example, we want to estimate the population of the province of Pangasinan in 1279. Population of Pangasinan in 1975 : 1,520,085
Projected population in 1980 : 1,666,817 For planning purposes we may want to know the 1979 population. The approach is as follows: a. Over the period 1975 – 1980, the average annual growth of population is 1.86%
b. Using the formula
Population in 1979 = Population in 1975 ( 1 + .0186)
1979 = 1,520,084 ( 1 + 0.0816)
c. Population in 1979 = 1,636,379 PUPIL – TEACHER RATIO Definition : Pupil-Teacher Ratio = Enrolment at a certain level in a given year
Number of teachers at the same level in the same year Example:
Pupil-teacher ratio at the elementary level of education
District Bautista, 1975:
Enrolment at the elementary level: 2846
Teachers at the elementary level: 129 Pupil-Teacher Ratio = 2846
129
= 22 ILLITERACY RATIO Definition : Illiteracy Ratio = Number of persons illiterate in an age-group x 100
Total Population in the age group Example:
Illiteracy Ratio : Province of La Union 1970:
Number of persons illiterate in age groups 6 years old and over: 34,575 Illiteracy Ratio: 34,575 x 100
305,946
= .113 x 100
= 11.3% 1. Participation Rate or Net Enrollment Rate (PR or NER)
The percentage of 10-12y/o in the Middle School to the population of the same age range
= No. of 10-12 years old enrolled in SY 2011-2012 x 100
Population of 10-12 age grouped, 2011

2. Gross Environment Ratio (GER)
The percentage of the age-group population 10-12y/o in the middle school
= Total middle school enrolment in SY 2011-2012 x 100
Population (10-12 years old) in 2011

3. Retention Rate (RR)
The percentagePercentage of enrollment in any school year that continues to be in school the ff. year
= Enrolment in Grade 7-8 SY 2011-2012 x 100
Enrolment in Grade 6-7 SY 2011-2012

4. Transition Rate (TR)
The percentage of student who graduated from one level of education and moved on to the higher level
= No. of students enrolled in Grade 6 in SY 2011-2012 x 100

5. Cohort Survival Rate (CSR)
The percentage of enrollment of a certain cohort (group) of students in the beginning grade at a certain level of education who reached the final grade of the required number of years for the level
= Enrolment in Grade 8 in SY 2011-2012 x 100
Enrolment in Grade 6 in SY 2010-2011

6. Drop-out Rate (DR)
The percentage of students who left school during the school year to the total number of students enrolled during the previous year.
= No. of Drop-out in Grade 6-8 in SY 2011-2012 x 100
Total enrollment in the middle school SY 2010-2011

7. Repetition Rate (RR)
The percentage of students who enrolled in the same grade more than once in a year to the total number of students who enrolled in the same grade during the previous school year
= No. of students who repeated Grade 6 in SY (2011-2012) x 100
No. of students enrolled in Grade 6 in SY 2009-2010

The percentage of graduates of a certain level of education in a given school year to the total enrollment in the terminal year of the same level
No. of Grade 8 enrolled in SY 2011-2012

9. Completion Rate (CR)
The percentage of students completed (graduated) the particular cycle of education to those enrolled in the first year of the cycle
= No. of graduates in the middle school ( Grade 8) SY 2011-2012 x 100
No. of students enrolled in Grade 6 in SY 2009-2010

10. Student-Teacher Ratio (STR)
The proportion of the students enrolled in a certain level at a given school year to the number of teachers teaching them. On the average, the number of students to a classroom teacher
= Enrollent in the middle schools (Grade 6-8)
No. of teachers in the middle school (Grade 6-8)

11. Class-Classroom Ratio (CCR)
The relative value of the number of classes to the number of classrooms
= No. of Classes in the Middle School (Grade 6-8)
No. of Classrooms used/available

12. Student-Textbook Ratio (STR)
The proportion of enrollment at a certain level in a given school year to the number of usable textbooks available at the same level in the same school year. On the average, it is the number of textbooks for every students.
= Enrolment in the Middle School (Grade 6-8)
Total number of available usable Textbooks

13. Per Student Cost (PCS)
The ratio of the total education expenditures to the total enrollment in a given school year.
= Total Expenditures (salaries + other school operating expenses) for Middle School in SY 2011-2012 x 100
No. of students enrolled in Middle School in SY 2009-2010 PERFORMANCE INDICATORS
Performance Appraisal System for Teachers (PAST)

A performance indicator or key performance indicator (KPI) is a type of performance measurement.[1] An organization may use KPIs to evaluate its success, or to evaluate the success of a particular activity in which it is engaged. Sometimes success is defined in terms of making progress toward strategic goals,[2] but often success is simply the repeated, periodic achievement of some level of operational goal (e.g. zero defects, 10/10 customer satisfaction, etc.). Accordingly, choosing the right KPIs relies upon a good understanding of what is important to the organization. 'What is important' often depends on the department measuring the performance - e.g. the KPIs useful to finance will be quite different than the KPIs assigned to sales. Since there is a need to well understand what is important (to an organization), various techniques to assess the present state of the business, and its key activities, are associated with the selection of performance indicators. These assessments often lead to the identification of potential improvements, so performance indicators are routinely associated with 'performance improvement' initiatives. A very common way to choose KPIs is to apply a management framework such as the balanced scorecard. The term “performance appraisal” is the one being employed to describe the processes being undertaken in Victorian schools at the present time. The terms “evaluation” and “appraisal” are used almost interchangeably in much of the literature dealing with the topic, however the term “appraisal” appears to be preferred to designate procedures currently being trialed and implemented in Victoria. The term “evaluation” seems to imply some kind of hierarchical intervention, whereas “appraisal” appears to denote to a greater degree, professional dialogue between colleagues perhaps between peers. Ingvarson and Chadbourne (1994) make a distinction between the two as follows: EVALUATION is “summative assessment for determining whether teachers move from one position to another within a career path,” and APPRAISAL is “formative assessment for improving the performance of teachers within their current position, and for accountability.” (Enclosure to DepEd Order No. 94, s. 2010) GUIDELINES ON THE COMPUTATION AND USE OF THE
DIFFERENT PERFORMANCE INDICATORS
AND OTHER BEIS (Basic education Information System) RELATED DATA 1. Participation Rate or Net Enrolment Rate
a. This indicator makes use of data gathered from the population census undertaken by the National Statistics Office (NSO). Data is disaggregated at the provincial and city levels.
b. While NSO available population data disaggregated down to the barangay level, the computation of this indicator at the school level is not allowed because of the issue on catchment area. A barangay may have more than one school in its catchment area and if participation rate is computed at the school level, the resulting data will not be accurate because the schools will be using the same population data of the barangay. Henceforth, participation rate shall not be computed at the school level.
c. Only the data generated from BEIS shall be used as official Participation Rate. 2. Simple Drop-out Rate and School Leavers Rate
a. Currently, there are two types of drop-out data generated by BEIS, the simple drop-out rate which calculates the percentage of pupils/students who do not finish a particular grade/year level within the school year and school leavers rate which covers both pupils/students who do not finish a particular grade/year level as well as those who finish but fail to enroll in the next grade/year level. School Leavers Rate, is theoretically more comprehensive than Simple Drop-Out Rate but becomes unreliable in areas with substantial migration.
b. Simple drop-out rate is useful at the school level. For purposes of showing the magnitude of drop-outs at the national and sub-national levels, the school leavers rate is the more appropriate indicator to be used. 3. Computation of Performance Indicators
a. data on performance indicators at the Division and Regional Levels are requested by local officials and stakeholders even before the official data generated by the Central Office is released.
b. The Division and Regional Planning Units can compute their respective indicators using the data from the School Statistics Module (SSM) for the public schools. The data generated will serve as preliminary data until such time that the private schools and SUCs laboratory schools data are available and will be used to produce the official performance indicators of DepEd. 4. Use of Enrolment Data
a. Enrolment data at various levels (school, division, and regional) are useful to monitor enrolment trends and growth rates for a period of time.
b. Enrolment data should be shared with the local government units and other stakeholders who have the need for such data.

What to Rate? This Performance Appraisal System for Teachers (PAST) is a self-rating tool. It is composed of three major components (with weight assignments) as follows: I - Instructional Competence (70%)
A. Lesson Planning and Delivery (45% for Teachers, 40% for Master Teachers)
B. Technical Assistance - Master Teachers only (15%)
C. Learners Achievement (20% for Teachers, 10% for Master Teachers)
D. School, Home and Community Involvement (5%) II - Professional and Personal Characteristics (20%)
1. Decisiveness
2. Honesty/Integrity
3. Dedication/Commitment
4. Initiative/Resourcefulness
5. Courtesy
6. Human Relations
8. Stress Tolerance
9. Fairness/Justice
10. Proper Attire/Good Grooming III - Punctuality and Attendance (10%) PLUS FACTORS (5 for each indicator but not exceed 2 points for the total) For Teachers:
1. Rendered any of the following technical assistance
1.1 provide assistance to co-teachers in improving their teaching competence
1.2 assisted school administrators in planning and managing in-service training
1.3 served as consultant in the preparation of supplementary instructional materials
1.4 served as demonstration teacher on innovative teaching techniques, classroom management
2. Conducted action research whose findings and recommendations have been adopted by the school
3. Subject area coordinator/chairman in district/division
4. Teacher-In-Charge of school for lone rating period For Master Teachers
1. Published at least one (1) article in professional magazine and periodicals related to their field of specialization and useful effective teaching
2. Served as resource person/consultant in district/division/regional/national level
3. Conducted action research(es), the findings/results of which can be utilized in the improvement of instruction in the district
4. Designed evaluation and monitoring program for district/division Summary of Ratings Teacher Master Teacher
I. Instructional Competence (70%)
A. Lesson Planning and Delivery 45% 40%
B. Technical Assistance - 15%
C. Learners Achievement 20% 10%
D. School, Home and Community Involvement 5% 5%
II. Professional and Personal Characteristics (20%) 20% 20%
III. Punctuality and Attendance (10%) 10% 10%
____________________ ____________________
100% 100% CONCLUSION: The utilization of these data for educational planning falls within the scope of educational planning itself. It is evident, however, that the statistical analyst can do more than furnish descriptive statistics about the educational system. Statistical analysis, through the inter-relationships of the various data enumerated, can focus upon certain strengths and/or weaknesses in the educational system. The analyst can also demonstrate trends and changes observed till the present and, within limitations, project future tendencies. Further, together with the educational planner, he can apply various hypotheses and project the quantitative consequences of such hypotheses and/or assumptions. Some of the inter-relationships that serve the educational planner are very basic. Demographic and pupil statistics, for example, relate the application of formal education to the age-group "eligible" and thus be essential in determining the quantitative status of education in relation to the potential demand for education. The relationship between the labor force and the various types of education throws light upon the ability of the educational system to supply the human resources necessary. In conjunction with economic and financial statistics the direct role of education in economic development might be studied. Statistics of teachers and pupils together with educational testing data help measure the efficiency of the school system itself. Costs and economic data show the investment in education related to the economic capacity of the society and can help set a target for future educational investment. These are but a few of the numerous possibilities for fruitful statistical analysis for educational planning. Thus, although many of these statistics are not "educational statistics" in the narrow sense, it is to be remembered that the process of educational planning does not operate in an "educational vacuum" and the statistics needed must likewise include information concerning the relevant factors influencing and influenced by the basis for and the results of educational planning.

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