Overview
Mathematical concepts and models help us to understand, analyse, and
communicate both qualitative and quantitative ideas about our environment. They
help us to make sense of the world around us and encourage the development of
thinking and investigative skills. Mathematics skills help us to solve everyday
problems, and they contribute to self-reliance, responsible consumerism, and
effective management of financial resources. For these reasons, the development
of mathematics skills is a high priority for all students.
Students must understand and appreciate the relationship between the
mathematics they learn in school and the events and activities of daily life.
This understanding is so crucial to students' success that it should be the
primary focus of program development. Students must come to understand and use,
both in and outside the classroom, the concepts of shape, size, number,
distance, scale, time, and money.
The mathematics program should actively involve students in the learning
process by providing them with opportunities to handle materials, ask
questions, and make decisions. In order to ensure comprehension, teachers must
take a systematic approach, developing a concept by moving from the concrete to
the abstract. Such an approach might involve the following sequence of
activities:
- an activity in which students actively participate;
- presentation of pictures or objects that illustrate or represent the
concept;
- use of language to explain the concept clearly and consistently;
- introduction of written symbols that represent the concept;
- application of the concept in a variety of real-life situations.
It is important to recognize that some students will require extended
opportunities to work at the concrete or pictorial level.
Mathematics instruction focuses on three major areas: arithmetic,
measurement, and geometry. The depth and scope of programming in these areas
will depend on individual needs and abilities, but the primary goal for all
students is the development of problem-solving abilities.
Students can use computers for individualized mathematics learning and
practice. Computers also provide opportunities for peer interaction.
It is important to focus on the skills that students require to function
more independently at school, at home, and in the community. Teachers should
also concern themselves with skills that will be needed in the next
educational, work, or living environment.
The Planning Cycle
Assessment and Development
In the first two phases of the planning cycle, educators need to:
- observe students in a variety of school and community settings to
determine both the skills that they have acquired and those that they need to
acquire;
- assess students' ability to recognize, select, and use relevant
information to solve personal problems.
Implementation and Evaluation
In the last two phases of the planning cycle, educators need to:
- provide students with a balanced program that comprises elements of
arithmetic, measurement, and geometry;
- provide opportunities for students to use their skills to solve problems in
a variety of community settings;
- provide opportunities for peer tutoring;
- provide memory aids (e.g., pocket-sized reference charts of basic
arithmetic facts, multiplication tables, measurement conversions,
money-equivalency statements) whenever possible;
- ensure that students are well versed in the use of the calculator;
- provide many, varied opportunities for students to practise and apply the
skills they learn, both at school and in the community;
- evaluate achievement in terms of the student's ability to solve practical
problems.
Resources
Ontario. Ministry of Education. The Formative Years: Provincial
Curriculum Policy for the Primary and junior Divisions of the Public and
Separate Schools of Ontario. Toronto: Ministry of Education, Ontario, 1975.
_____. From Counting to Calculation. Support Document to The
Formative Years. Toronto: Ministry of Education, Ontario, 1976.
_____. Mathematics, Intermediate and Senior Divisions, Part 1: Grades 9
and 10, Basic Level, and Grades 11 and 12, Basic Level. Curriculum
Guideline. Toronto: Ministry of Education, Ontario, 1985.
_____. Ontario Schools, Intermediate and Senior Divisions (Grades
7-12/OACs): Program and Diploma Requirements. Rev. ed. Toronto: Ministry of
Education, Ontario, 1989.
Case Study - Elementary Level
Student Profile Clare is a playful, active six-year-old with
Down syndrome. She is fitted with two hearing aids and wears glasses. Although
her speech is unclear to people who have had no contact with her, her language
skills are sufficient to enable her to communicate her needs effectively. Clare
is toilet trained and feeds and dresses herself with minimal help. Her
gross-motor skills are somewhat underdeveloped, but she has no difficulty in
getting around the school and playground. Clare shows a particular interest in
cutting and pasting activities and can assemble an eight-piece inset puzzle.
She can count orally to 5, although she does not yet have an understanding of
the concept of sets.
Learning Environment Clare attends a regular Grade 1 program
and is provided with adult support for about 30 per cent of the time she is in
school. An itinerant teacher visits her once a week and assists the teacher in
modifying the regular program to suit Clare's needs and in monitoring her
educational plan.
Expected Learning Outcome Clare is expected to develop an
understanding of early mathematical concepts.
Student Program Clare is being provided with opportunities to:
- - -
- explore many aspects of pouring and comparing through sand and water play;
- enrich her vocabulary of words for mathematical concepts (e.g., shape,
size, volume);
- develop an understanding of the use of money by handling money that is
brought to school for class trips or to make purchases;
- develop a sense of the sequence of activities and anticipate the next event
by learning to follow school routines and recognize calendar events and
seasonal changes;
- use numbers in such activities as stating her age, address, and telephone
number;
- improve her perception of her body's size and position through physical
activity;
- learn to discriminate, classify, and order objects at a very elementary
level through activities involving blocks, pegs, beads, and interlocking cubes;
- improve her fine motor skills by manipulating materials;
- develop an understanding of more formal mathematical concepts (e.g., the
number concepts from 1 to 3).
Case Study - Secondary Level
Student Profile Michael is a co-operative, soft-spoken, well
mannered eighteen-year-old. He communicates effectively with others and can
follow single-step instructions. He relates well to adults and peers and is
well liked by his classmates. He has basic reading skills (e.g., he can read
and follow his timetable). He writes his name, address, and telephone number
and looks up baseball and hockey scores in the newspaper. He can count and
sequence numbers to 100 and uses a calculator to solve problems involving
addition, subtraction, and multiplication. He can tell time to the
quarter-hour. He is usually accurate in identifying the date and is beginning
to keep an appointment book. He approaches tasks carefully and completes
assigned work on time.
Learning Environment Michael attends semestered classes at his
community secondary school. He is integrated for mathematics and physical
education but completes other academic tasks in the resource room. Michael has
the ability to be independently employed. He has already participated in two
in-school work experience programs. His teacher has arranged for him to work at
a company that assembles electronic parts for computers.
Expected Learning Outcomes Michael is expected to:
- learn to assemble electronic units and then package them in sets of 100;
- improve the numeracy and social skills that he will require for his
personal needs and for independent employment.
Student Program Michael is being provided with opportunities
to:
- calculate his salary, given his hourly rate and the number of hours that he
will be working, and discuss how he will budget this amount;
- apply the banking skills he has learned in class (e.g., by making deposits
and withdrawals);
- solve problems that will help him learn how to package electronic parts in
units of 100;
- tell time to the minute so that he does not exceed the time allowed for
morning, lunch, and afternoon breaks;
- determine the number of hours he will work and thus the amount of leisure
or school time that he will have;
- become familiar with the kinds of deductions that will be made to his
earnings;
- increase his understanding of terms related to employment (e.g.,
deductions, income tax, gross and net income );
- devise a budget based on his actual earned income;
- learn to relate effectively to supervisors in the work setting;
- increase his feelings of self-worth as he successfully completes his
employment experience;
- express his feelings about satisfying and unsatisfying aspects of the job
and discuss any difficulties he has had at work, in preparation for future
decision making regarding employment.
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