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The following article is taken from an issue of the New
Brunswick Educational Administrator that was published
in the late eighties.
As such, it no longer describes the current situation in Quebec,
but it does provide an excellent example of the use of formula
funding for special-needs children. Bezeau, Lawrence M. (1989 09). "Special Education Provisions in Quebec Teacher Collective Agreements". New Brunswick Educational Administrator. 16: 3-8. |
Review of Class Size Research
General Provisions in the Collective Agreement
Class Sizes of Segregated Classes
Class Sizes of Integrated Classes
Conclusions
Bibliography
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New Brunswick legislation and government policy on special education has generated considerable discussion and debate in recent months. The time seems right to look at what our neighbours are doing in this area as a means of informing the debate. This article consists primarily of an examination of some of the detailed special education provisions contained in the provincially negotiated collective agreements that govern teachers in the Province of Quebec. This article relies on the agreement with the Provincial Association of Catholic Teachers (PACT), written in English. The majority of teachers in Quebec work under the agreement negotiated with the Centrale de l'enseignement du Québec. This agreement written in French contains special education provisions that do not differ significantly from those of the PACT agreement. The agreement negotiated with the Protestant association was not examined. It should be noted that these agreements have expired but are still in effect until new ones are negotiated, something not likely to occur before the provincial election.
The PACT agreement contains detailed class size limitations for classes at all levels and in many specific subject areas. These include maxima for segregated classes of exceptional children classified by type of exceptionality. For integrated classes, a weighting formula is used which reduces the maximum class size as a function of the number of exceptional children in the integrated classes and their type of exceptionality. Boards in Quebec are not absolutely bound by the maxima but are required to pay a penalty to any teacher whose class size exceeds the relevant maximum, according to an elaborate formula. This article examines the class size provisions on the assumption that their purpose is to determine the maximum class size rather than to calculate the pay penalty for classes over the maximum. Pay penalties are not considered in this article.
The discussion of collective agreement provisions in this article is designed to expose and clarify the mechanisms and the underlying logic rather than to present them using the precise vocabulary and organization of the agreement itself. Readers who are interested in precise wording should consult the actual agreements. The New Brunswick term exceptional pupil is used in this exposition. Pupils who are not exceptional pupils are here referred to as unexceptional, for want of a better term.
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Review of Class Size Research
Although somewhat equivocal, the research on class size supports the approach used in Quebec. Most class size research has used data aggregated to the class or school level and as such has been unable to address the question of differential effects of class size on different types of pupils. But the whole concept of special education relies on the classification of pupils as special or not or as exceptional or not. In looking at class size and special education it is essential to look at class size effects on individuals pupils rather than on aggregates of pupils.
In spite of the small number of studies conducted at the level of the individual pupil, the Illinois State Board of Education in a review of the class size literature ( Department of . . . ) was able to conclude that "Pupils with lower academic ability tend to benefit more from small classes than do students with average ability." (p. 6). This review was concerned only with the lower elementary grades although research from all levels was considered.
The truly ground-breaking research in this area was the series of production function studies conducted by Summers and Wolfe (1974) and Summers and Wolfe (1977). Their work was disaggregated to the level of the individual pupil and employed controls for a variety of inputs other than class size.
Their dependent variable was the difference between grade equivalent standardized achievement scores for grades three and six for a sample of grade six pupils. This gave them a value-added measure of output and permitted them to control for the achievement level at the beginning of the three year period.
Although class size had no significant effect at the class level, it did affect individual pupils. Pupils were classified into three groups; low, middle, and high achievers; according to their grade equivalent achievement at the beginning of the three-year period. Those at grade three scoring below 2.7 years were classified as low and those scoring above 3.9 years were classified as high. Summers and Wolfe found that low achievers did better in small classes (less than 28 pupils), that middle achievers did as well in small as in large classes, and that high achievers did more poorly in small classes (1977, p. 646). Children who face special difficulties in learning are more likely to benefit from the individualization that small classes permit. We can conclude from the Summers and Wolfe research that among exceptional pupils, as the term is used in New Brunswick, only the gifted are clearly unable to benefit from small classes.
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General Provisions in the Collective Agreement
In Quebec responsibility for special education policy-making is lodged at the board or commission level. Clause 8-9.03 requires that:
The board must adopt a policy on special education services for pupils with learning or emotional problems. The policy must establish the terms and conditions for the integration of pupils and the support services to be provided to these pupils.In addition clause 8-9.05(A) requires that this policy be implemented.
The pupils identified as having learning or emotional problems may be integrated totally or partially into regular groups or regrouped in special classes in accordance with the policy on the organization of special education services for pupils with learning or emotional problems.The above provision is reinforced by another clause dealing specifically with integration, clause 8-9.08.
The integration of pupils with learning or emotional problems shall only take place if the board has adopted a policy on special education services and the integration respects such a policy.These provisions together compel the board to determine its policy for dealing with exceptional children and to abide by that policy.
Two important committees have input into the special education policy-making process and into the placement of individual children. The first operates at the board level in accordance with clause 8-9.04.
The board and the union shall set up an advisory committee of teachers for pupils with learning or emotional problems. The committee's mandate shall be:At the school level, the principal sets up an ad hoc committee to deal with individual cases in that school. This committee includes among it members a representative of the school administration and one or more teachers. Any children in a school who are suspected by their teacher of having special learning or emotional problems are referred to the ad hoc committee through the school administration.
a) to give its view on the elaboration of a policy on the organization of special education services for pupils with learning or emotional problems;If the board does not accept recommendations made by the committee, it shall state its reasons to the committee in writing.
b) to make recommendations concerning the implementation of this policy;
c) to suggest the terms and conditions for integrating pupils and the support services to be given to these pupils.
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Class Sizes of Segregated Classes
The collective agreement defines two measures of class size on which its articles are based, maximum class size for single classes and maximum average class size for each school board. In each category of class, the single class maximum is higher than the maximum for the board average. At the primary or elementary level in schools with more than 99 students, classes with more than two grade levels are not allowed and for classes with two grade levels, the single class maximum size is reduced to the level of the maximum average class size.
Clause 8-8.03 quoted in Table One gives the maximum class size, for single classes and for board averages, for classes consisting entirely of unexceptional pupils and for segregated classes of exceptional pupils. It shows, for example, that at the primary or elementary level, no class can exceed 28 pupils and the average class size for a school board must not exceed 26 pupils. These maxima are reduced for classes of exceptional children. For example, segregated classes of multiply handicapped children cannot exceed 10 pupils and the board average for classes of this type cannot exceed 8 pupils. Similar provisions contained in the collective agreement for the pre-primary and secondary levels have been omitted from this discussion.
Clause 8-8.03 from the PACT Collective Agreement At the primary level, the maximum and the average number of pupils per group shall be: | |||
| AV | MX | ||
| A) | For the regular groups: | ||
| For the courses intended for the pupils of the primary level: | 26 | 28 | |
| B) | For the groups of pupils with learning or emotional problems: | ||
| 1) for the courses intended for special classes of pupils at the primary level identified as having minor learning disabilities (including pupils in readiness or waiting classes), severe learning disabilities or being educable mentally retarded: | 15 | 17 | |
| 2) for the courses intended for special classes of pupils at the primary level identified as trainable mentally retarded, having non-integrable motor disabilities, having slight or moderate cerebral palsy, suffering from physical disabilities, from non-medically controlled epilepsy or from socio-emotional disturbances: | 10 | 12 | |
| 3) for the courses intended for special classes of pupils at the primary level identified as multiply handicapped or having severe cerebral palsy: | 8 | 10 | |
| 4) for the courses intended for special classes of pupils at the primary level identified as deaf, hard of hearing, blind or partially sighted: | 5 | 7 | |
| 5) for the courses intended for special classes of pupils at the primary level identified as severely mentally retarded: | 4 | 6 | |
Several exceptions to the maxima are permitted by clause 8-8.01(E). The maxima do not apply to team teaching or conference courses. This clause also states that:. . . the maximum and average number shall not apply to a group of pupils in a special class identified as severely mentally retarded if the board provides visible support other than a teacher.
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Class Sizes of Integrated Classes
Clause 8-8.03 makes no provision for integrated classes, a matter which is dealt with elsewhere in the collective agreement, primarily in two appendices, XX and XXI. Class sizes for integrated classes are handled by a system of pupil weighting which uses integrated and segregated class size maxima as parameters in the weighting equation. Class sizes are based on weighted pupils rather than actual pupils. Unexceptional pupils receive a weighting of one whereas exceptional pupils receive a higher weighting according to the following formula:
We is the weighting factor for exceptionality e,
Mu is the maximum single class size for class type u (primary, for example) of unexceptional children, and
Me is the maximum single segregated class size for exceptional children of type e (severely mentally retarded, for example).
Several examples will clarify the use of this formula.
Take the case of one hard-of-hearing child being integrated into a class at the primary level. From Table One, the maximum class size for unexceptional children at the primary level is 28 (Item A) and the maximum class size for a segregated class of hard-of-hearing children is 7 (Item B4). The weighting factor is the quotient of 28 and 7, that is, 4. The weighting factor is multiplied by the number of children, one in this example, to give a product of 4. The maximum number of unexceptional children in the same class as the hard-of-hearing child will be 24, that is, 28 minus 4. The maximum class size is therefore 25, 24 unexceptional pupils and 1 hard-of-hearing pupil.
As a second example, assume that two pupils at the secondary level suffering from severe learning disabilities are being integrated into a general instruction course. At the secondary level the single class maximum for a general instruction course is 32 and for a segregated class with severe learning disabilities, 20. The weighting factor is therefore 32 divided by 20 or 1.6. This will be multiplied by the number of pupils (2) to give a total of 3.2 weighted pupils. The collective agreement requires that a non-integer number of weighted pupils be rounded to the nearest integer, in this case to 3. This class can have no more than 29 unexceptional pupils. The 2 learning disabled children count as 3 in determining the class size of 32, the maximum.
One obvious advantage of this type of formula is the absence of discontinuities at the boundaries. The formula produces a weighting of one for unexceptional children and a maximum class size just equal to the prescribed maximum for a class of unexceptional children. Also, when the number of exceptional children in an integrated class is increased to the point where there is no room for unexceptional children, the class size is equal to the maximum segregated class size for that type of exceptionality. In the first example above, if we put 7 hard-of-hearing pupils in a class then we will have 28 weighted pupils which leaves no room for unexceptional pupils. But 7 is exactly the single class maximum for a segregated class of hard-of-hearing pupils. In the second example above, 20 pupils with severe learning disabilities, the segregated class maximum, generate 32 weighted pupils (1.6×20) which is just equal to the maximum class size of unexceptional pupils. This weighting formula has these desirable characteristics for different class size maxima for both exceptional and unexceptional pupils.
Another desirable mathematical characteristic of the formula is that the choice of a class of unexceptional children and its class size as the base is an arbitrary one. We could have chosen a segregated class of exceptional children as the base and integrated unexceptional children into that class. This would produce weights of less than one for the unexceptional children but the resulting maximum class size for a given mix of children would be exactly the same. This characteristic takes on some importance in cases where segregated classes contain children with more than one type of exceptionality but no unexceptional children. In such a case we could arbitrarily choose any type as the basic type and integrate the other types into that class. The choice of basic type would not affect the outcome.
The formula and both examples above are based on the assumption that each integrated class contains one or more exceptional pupils with the same type of exceptionality. The collective agreement also allows for integrated classes with more than one type of exceptionality and provides a mathematical structure which is a logical extension of the formula for classes with two types of children. This approach will also work with classes with more than one type of exceptionality in which all children are exceptional.
In dealing with three or more types of children, it is necessary to designate a basic type to form the class into which the others are being integrated. The weighting given to pupils of that type will be one and the weighting given to pupils of each other type will be the maximum class size of the basic type divided by the maximum class size of that other type. The weighted total of children can be calculated by multiplying the number of children of each type by the weighting for that type and adding up these products. The maximum number of weighted children will be equal to the maximum class size of the basic type. This approach works even if there are no children of the basic type in the class.
Take as an example, a class of children at the primary level with minor learning disabilities into which 2 children with severe cerebral palsy and 1 severely mentally retarded child are to be integrated. From Table One, the class size maxima are 17, 10, and 6 respectively. Using unexceptional children as the base, we calculate weighting factors of 1.65 (28/17), 2.80 (28/10), and 4.67 (28/6). Into a class of 28 weighted pupils we introduce these 3 children who represent 10.27 weighted pupils (2.80+2.80+4.67). This leaves room for 17.73 weighted pupils which is equivalent to 10.7 (17.73/1.65) actual pupils with minor learning disabilities. After rounding we are left with a class of 14 children consisting of 2 children with severe cerebral palsy, 1 severely mentally retarded child, and 11 children with minor learning disabilities. We can check our arithmetic by calculating the number of weighted pupils represented by these 14 children. The calculation is (2.80×2) + (4.67×1) + (1.65×11) which yields 28.42. This rounds to 28, the maximum class size of a class of unexceptional children, the class size chosen as the base.
The choice of basic type is simply a choice of scale for the weights and the weighted pupils. Choosing unexceptional pupils as the basic type and giving them a weighting of one eliminates weights of less than one and makes the system more understandable. Exceptional children are assumed to require more teacher time or to otherwise make greater demands on the teacher and therefore to require a higher weighting than do unexceptional children. This is reflected in pupil weightings that exceed one.
An interesting aspect of this approach is that the minimum number of teachers required in a school will be a constant fraction of the number of weighted pupils and will not depend on whether or how they are integrated. Thus the system is fiscally neutral with respect to segregation and integration. Fiscal neutrality is highly desirable in that it permits the integration decision to be based on professional judgment rather than on financial incentives or disincentives that ignore both the welfare of the children in the school and the actual cost of the services being provided.
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Conclusions
The collective agreements that govern teachers in the Province of Quebec contain special education provisions that deal with the issue of segregation and integration in an internally consistent and fiscally neutral manner. Policy making in this area is lodged at the school board level with provision for teacher input into the policy making process.
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Bibliography
Department of Planning, Evaluation, and Research. (1985 01). Class Sizes for Kindergarten and Primary Grades: A Review of the Research. Springfield: Illinois State Department of Education.
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