M. Burgess & J. Cummins
The objectives of this curriculum unit are:
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A. Students will be able to use mathematical concepts to help clarify their beliefs to effect solutions to issues, and improve verbal skills.
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B. Students will be able to use the steps common to the scientific method as an aid in the development of cognitive skills.
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C. Students will be presented with opportunities to refine those skills relevant to the promotion of leadership skills and to be a productive member of a team.
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D. Students will be aided in the development of a data base that will serve them well regardless of their future educational or career goals.
Rationale
We often hear one person or group criticize another for being narrow minded, intellectually limited. The complaint in general stems from observations or interactions that leads one to [assume] that such persons are victims of inadequate cognitive skill development, or that their actions are based upon a very limited data base.
By data base we mean the information available to aid one in the recognition, construction, and implementation of a solution in regard to a problematic situation. Problem solving is predicated upon making the right connections among several factors. Steinberg, in describing the difference between the types of thinking employed by children, and that employed by adolescents, cites the use of the “scientific method” in problem solving situations (reasoning that systematically tests and then accepts or rejects hypotheses) as a key characteristic of the adolescent age group. The data base that one has at ones’ disposal and the skills necessary to obtain needed information are directly related to one’s ability to actually test an hypothesis. Consequently, ones ability in employing said method will be adversely affected if the data base is limited and those skills which co-vary with this entity (grasping, interpretation, computation, transformation, integration, etc.) are equally limited.
Under such conditions cognitive skill development does not receive needed stimulation, and as a result can be effectively arrested. No one is born with an adequate data base and the related skills that co-vary to the extent that one can function in this modern communication orientated world of ours. The needed base of information and related skills have to be acquired and then reinforced.
In our system (U.S.A.) of education the *integrationist mentality is most often visible in the elementary/grade school and in institutions of higher learning especially at the graduate level.
In graduate circles collaboration is a given. Individuals with extensive data bases and particular skills form teams (research, study, activist, etc.) to obtain object-goals. In such situations relationships between distinct variables are investigated, and integrated. Relative stability of the group during the course of the project is a key characteristic of this particular approach. In elementary/grade school the shared structures and object-goals are also stressed, in modified form of course. The classroom unit is a stabilized unit, the group is not in a constant state of change. Relationships between distinct variables are investigated and integrated. Emphasis is placed on group dynamics, one’s relationship within the group, and the formation of teams within the group.
I
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Children come here . . . let us form our circle—Teacher holds up a piece of paper. “What color is this paper?” . . . (class) “Red”—“Watch me cut this shape . . . —Teacher performs operation—“What shape is this . . . (class) . . . ”Triangle”—”What color triangle is this?” . . . (class) “Red triangle”—“Let’s count the sides” . . . (c1ass) . . . ”1, 2, 3..
(Observation of a Day Care class—age range 3 to 4 years of age)
*By “integration” and “integrationist” we refer to the ability to synthesize the relationship between two or more distinct variables.
In this activity a number of objectives are addressed: (a) group participation, (b) mathematical skill development, (c) recognition (color, shape), (d) integration.
II
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Four little frogs jumping on a bed
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One fell off and bumped his little head
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Momma frog called the doctor and the doctor said,
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“No more frogs jumping on the bed”
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Three little frogs jumping on the bed . . .
(observations of same class)
The songs promotes
mathematical
skill development and the type of symbolism that serves as the basis for any
English
Lesson. Jumping on a bed can be dangerous. Issues relevant to
Social
Studies/History
are also present. For example: a. Rules—No more jumping on the bed, and (b) Civil disobedience—The frogs continue to jump.
Another key objective at this level of educational instruction focuses on students remaining attentive during the delivery of instructions and showing respect for the rights of others (raising hands, etc.). This objective, however, is not projected as the key determiner of success at this level. Lessons and activities are designed with an awareness of the needs of the child (freedom of expression, movement, choice) versus that of society (order, submission to a controlling entity). Thus the children come to expect that others will recognize their viability as a social entity with the related rights and privileges. As they proceed through the ranks they are reluctant to relinquish that which they were helped to realize.
The structure common to middle and high school classes is the separation of academic disciplines. Five or six subject classes constitutes a standard academic load. The base class (homeroom generally) from Period I until the end of the academic day is repeatedly altered. It is not uncommon especially in a large comprehensive high school for students to encounter a high percentage of new students with each successive class. Except for chance meetings in the hall, cafe, or an extra curricula activity, many students will not see each other until the next—academic class—day.
Consequently, the concept of a base group is largely symbolic.* If we consider the forces which beset a typical student attempting to negotiate middle and high school as it is presently structured we find what we have chosen to label the “multiple force phenomena.” The multiple-force phenomena relates to the transition from elementary/grade school to the higher levels (middle, high school) which is characterized by the activation of multiple forces.
Examples of Multiple Force Phenomena:
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A. Multiple disciplines: Five or six academic classes. B. Multiple Approaches: Methods and approaches used by instructors will probably vary, with a maximum total of 6.
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C. Multiple Personalities: Each teacher is a distinct personality.
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D. Multiple base group: Seldom do entire classes move together as a unit from class to class.
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E. Multiple time frames: Classes range from 43 to 47 minutes and movement is predicated on the bell—regardless of how involved a lesson may be.
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F. Multiple assignments: Assignments, homework, etc., are in general issued without regard for what may be happening in other disciplines.
If we were to compare the elementary/grade school experience to that of the middle/high experience the resulting equations would be characterized by an increase in coefficient of change from Step I to Step II.
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*(1) If the family unit or community is in a state of flux and does not promote relatedness in regard to key variables the likelihood of stability in regard to a base group is further diminished.
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(2) The average time period per class falls within the range of 43 to 57 minutes. Non-Instructional class time (attendance, collecting homework, announcements, etc.) can easily consume 5 to 10% of the allotted class time. With the recent push for standardization of instruction (cost effective—purchase of instructional materials, testing—national, state, city wide) many teachers have had to react to the pressures of covering pre-determined parameters of information or to “teach the test.”
Key: y = 6, X = Number from 1 to 6, A, B, C, D, E, F (defined above) minus the multiple.
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Step I: X, A + B + C + D + EX + FX = Elementary/grade school.
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Step II: Ay + X, B + Cy + X,D + Ey + XF = Middle/High school
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For many students, especially urban students, the elevation from step I to step II is the beginning of the end of success in school. The number of variables exceed their capacity for integration. They quite simply cannot pull it together.
The individual for whom this structure has been devised is at a stage in the life cycle characterized by extensive physical, emotional and cognitive changes. It is also a time when the adolescence is being re-defined as a social entity. Students who possess adequate to superior verbal skills and are products of base groups (family, community) that define relatedness of variables are in a better position to counter-act the demands of school than those whose strengths lie in the non-verbal skill field, and who are not products of base groups that define relatedness of variables. Given the design of the middle/high school units in regard to the dissemination of instructions selected students non-verbal, are programmed for teacher/students, student/student, and school/student mis-communication.
A commonly referred characteristic of many urban students is that they are “street wise.” Street wise connotates that one has refined problem solving skills in relation to a data base that has been nurtured by a particular environment. The particular environment* in addition provides the key reinforcers for language, attitude and behavior. These reinforcers are gradually strengthened if alternative keys are not available or competitive. Thus what may appear to be a lack of desire or capability to improve language, behavior, attitude, may well be an inability to utilize the available vehicle(s) for skill development. The church social organizations, family, and school are examples of vehicles for skill development.
Even when the deciphering and/or utilization of the vehicle for skill development is effected, without adequate
*Particular environment denotes an environment that is limited in regard to society as a whole. 0ne’s neighborhood, the inner city, rural communities and suburban communities are examples of particular environments. Key reinforcers development appears to reach a point of diminishing return, and is then effectively arrested. Another point to consider is that quite possibly many urban students reject improved verbal skill development because such improvement will not necessarily aid them in negotiating the particular environment which has ascended to the position of primary impact. With out reinforcements from a competitive environment there is no impetus to resist the shaping pressures within the particular environment. Thus behaviors related to skill development can heighten said pressures and court strong negative reactions from peers.
“you talk funny man—you sound like a . . . boy..You ain’t down—you ain’t one of the home boys . . . Hey, he . . . the man . . . check them out”
Such a reaction can activate behaviors which translate into harassment, isolation, or violence. These reactions can be endured; however, this is unlikely unless strong key reinforcers of the deviant behavior(s) (new) are in place and functioning.
It is with these concerns in mind that we began to re-think approaches in regard to education in general, and the urban situation in particular. The relocation of the target population, the urban verbally deficient student, to a new physical environment is not to be considered. Resources cannot sustain such a proposition. The cultivation of a competitive environment has merit, and is the underlying theme of this curriculum unit.
Movement in the direction of competitive environment which can rival the “particular environment” of the student and lessen the effects of the multiple force phenomena is based upon an approach to education that is geared toward integration. It may not be possible to decrease the number of variables, however, they can be aligned in a manner whereby they not only began to co-vary, but the co-variation is pronounced, and easily identified as such.
Example:
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A. Disciplines should actively seek to reinforce a Mathematical base in all classes. To integrate other disciplines (Science in History).
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B. The method or instructional process which defines the approach in each class should move in the direction of utilization of the Scientific Method.
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C. There should be a common base of information incorporated by all classes (Life skills, common word list, and knowledge of mathematical symbols.
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D. That each class should incorporate skill development as it relates to leadership and functioning as a member of a team.
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E. Immediate connection of instructions and how instructions can be used in the environment.
The key reinforcers for students which will enable him/her to withstand the pressures of the particular environment have got to come from within.
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Step I: The genesis of their inward motivation lies with the belief that school is an entity that can be successful negotiated.
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Step II: That there are rewards associated with school that are not materialistic or related to high visibility.
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Step III: That one is not alone. That there is strength in numbers.
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These steps provide the foundation for the needed ideological relocation given that a physical relocation is not a feasible alternative. An ideological relocation that promotes skill development, with appropriate reinforcers that define the parameters of an ideological base group. The succeeding pages of this unit will present strategies and lesson plans which support such an approach to education.
Strategies/Lessons
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I. Unit Objectives: Students will be able to use mathematical concepts to help clarify their beliefs, effect solutions, and improve verbal skills.
There is no escaping the numbers; or the related concepts. They are a part of every aspect of life, and should be integrated within the curriculum of every discipline. One need not be a math major to effect implementation. Key Areas are recognition, computation, application and related vocabulary. Introduction can start with a related lesson.
Example:
The Language of Standard Measures/English. A Short History of Standard Measures/History.
Subtle incorporation, however, is the long range objective. In discussions or explanations at the board one can use symbols (=,$gt, $lt). (Example, The Army of the North was$gt the Army of the South) One can give students a list of symbols and encourage them to use them in situations where they are being asked to take notes.
Another tactic is to have students read tables, graphs and then convert this information into a percentage, computation. One can then encourage them to use this information to make a statement or develop a position with an essay or position paper. Simple interpretation of symbols or formulas can aid students in the development of improved writing skills (ex. a + b = c, A plus B is equal to C) The use of Math related terms (ascending, descending, ratio, etc.) should be emphasized whenever possible or relevant. It is important not to over extend in regard to the ability level of the students. A moderate but consistent pace of incorporation works best.
Social
Studies
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I. Objectives:
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Primary Student will be able to transform information from one form to another.
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Secondary (a) Student will be able to write simple and compound sentences
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(b) Student will exhibit knowledge of basic mathematical concepts and formulas
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(c) Student will be able to follow directions, written, and oral.
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Motivation Based on some pre-determined criteria arrange
class
in a bar graph. Explain the function of a bar graph. Point out to student the particular information that they are comparing.
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Activity Teacher should
define
and give
examples
of the following terms:.
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Minority, Pre-registration, Absentee Ballot, Candidate, Majority, Plurality, Coalition
Students should be required to record this information and have it available as they proceed with the assignment.
