BACK TO THE MATH HOMEPAGE

1960, Reprint of 1955 edition with minor revisions.

The mathematical emphasis of this document was on basic daily computations and number sense. For grades 1 to 6 Arithmetic is divided into four sections. The four headings are Our Number System, The Fundamental Operations, Measurement, and Problems.

Measurement involved computations using imperial units of measure.

Philosophical Basis

"The aim of the course in Arithmetic for the elementary grades is to help the child to understand the value of number in the ordinary affairs of life, to provide him with training in the use of number for his own practical purposes, and to form the foundation upon which his subsequent mathematical experience will be built." (p. 94)

This document's primary emphasis, as it pertains to Mathematics, is on the four fundamental computational operations, addition, subtraction, multiplication and division. The expectation is that children will be able to correctly complete their Arithmetic problems with a high degree of accuracy and skill.

"It is highly important that children be trained from the beginning to be satisfied only with accurate work. To this end, a thorough mastery of the 'combinations' and of the fundamental processes is essential." (p. 95)

"A large proportion of the practice in arithmetic should be 'mental' i.e., done without a pencil." (p.95)

"In all written work, exactness, neatness, and orderliness must be insisted upon. Children should not be allowed to make their calculations in slovenly fashion on 'scribbling' paper, which is thrown away, and then record the results in neat 'statements,'for inspection." (p.95)

Selection of Topics by the Teacher
Individual teachers have the responsibility to select what to teach so that it is relevant to the individual students in their own community. Except ". . .  in Arithmetic, which is definitely sequential . . ." (p.11)
"The elementary school has no business with uniform standards of attainment. Its business is to see that children grow in body and mind at their natural rate, neither faster or slower, and if it performs its business properly, there will be as much variety of attainment as there is of intellectual ability." (p.11)

This document refers to Mathematics instead of simply Arithmetic as the course of study. Mathematics is subdivided into three strands. These are Arithmetic, Measurement, and Geometry. The only addition to that of the Little Grey Book is in Geometry. A significant change in the content of Mathematics comes with the use of the metric system and the SI units in measurement.

"By the end of the Junior Division, the program will have provided the child with the opportunity to develop competence in the areas of Arithmetic, Measurement and Geometry." (p17)

Philosophical Basis of Education in the Primary and Junior Divisions

The basic underlying principal of this document is that for the child to make sense of the world around him then he must explore and play with his world. In this exploration of the relationships of the world around him, the child develops his own understanding of the world.

Children learn and grow at different rates and the educational process should be designed to accommodate the individual child's own stage of development.

"Implicit in the philosophy of this document is the idea of acceptance- the acceptance by the school of all children with their wide variations in ability, physique and understanding." (P.10)

A main shift from Arithmetic in the Little Grey Book takes place here in the understanding of how students make connections about the world around them. In contrast to The Little Grey Book, where  rote memorization and repeated drill of basic facts was used to instill understanding of numbers, this document emphasizes the need for children to experience math in a concrete way before moving to a more abstract understanding of concepts.

" Children who have had many opportunities to build and talk about models begin to make accurate drawings and plans much sooner than do children who have not had these experiences, Speech, play, models and drawings are essential forms of communication. Discussion helps children to discover contradictions or lack of accuracy in their pictures, sketches and other representations of reality. Observation and discussion reveal to the teacher the stage of development of eack child an provide clues for planning appropriate activities and experiences." (p. 66)

"Of equal significance are the opportunities [provided] for children to work mathematically from experiences with real things, to create their own quantitative abstractions from reality." (p.66)

Selection of Topics by the Teacher
"Individual teachers have the responsibility of selecting strategies, resources and activities appropriate to the needs of individual children, who should then be involved in setting short-term objectives, in devising ways and means of accomplishing tasks, and choosing activities." (p. 3)
Guidelines not detailed courses of study because curriculum must be related to the needs of the individual students. (p. 2)

The Common Curriculum: Policies and Outcomes Grades 1-9 (1995)

There are five key elements of the Common Curriculum. These are a focus on Learning Outcomes, All Students, Integrated Learning, Excellence and Equity, Accountability and Standards and lastly a focus on Collaboration.

The Common Curriculum: Provincial Standards, Mathematics, Grades 1-9

The Key Components of Mathematics Learning
-communication
-reasoning
-problem solving
-connections to events in every day life
-technology plays an increasing role as a tool to attain the outcomes.

Key Vocabulary from the document as it pertains to Mathematics.

1 Outcome - Understanding that a student should have and operations they should be able to perform at a particular point.
2 Strand - a particular vein of Mathematics. There are six outlined ( see below)
3 Standards of Performance - A 4 level range of achievement of the Outcomes
4 Outcomes Based Education - Stresses process over product - Content becomes a tool for attaining Outcomes.
5 Performance Assessment - Observing and assessing students as they use math to solve problems.

Six Strands of Mathematics

1 Number sense and Numeration
2 Geometry and Spatial Sense
3 Measurement
4 Patterning and Algebra
5 Data Management and Probability
6 Problem Solving and Inquiry

The Provincial Standards Mathematics, Grades 1-9, 1995 describe three aspects of mathematics. The first is what we want students to know. The second deals with their skills and this is what we want students to do. The third aspect deals with what we want our students to be like. We want them to develop a positive attitude toward Mathematics.  "The Provincial Standards represents a clear call to teach a different brand of Mathematics, and to teach and assess it differently." (p.1 OMCA Linking Assessment and Instruction in Mathematics: Connecting to the Ontario Provincial Standards)

"The purpose of the Ontario Curriculum, has been developed to provide a rigorous and challenging curriculum. The required knowledge  and skills for each grade set high standards and identify what parents and the public can expect children to learn  in schools of Ontario." (p. 3)

This document follows a more traditional approach to Mathematics and shifts an increased set of expectations into  lower grades. There is an increased emphasis on the mastery of  basic number facts and on paper and pencil skills in mathematical operations.

This document is organized with specific expectations for each grade from grade 1 to 8.  Within each grade there are 5 Strands, similar to those in the Common Curriculum with the exception that Problem Solving and Inquiry have been incorporated in all of the five strands.

The Ontario Curriculum has two main elements. These are expectations and achievement levels. "The expectations identified for each grade  describe the knowledge  and skills that students are expected to develop  and to demonstrate in their class work, on tests, and in various other activities on which their achievement is assessed." (p. 4)
" The achievement levels are brief descriptions of four possible  levels of student achievement. These descriptions along with more traditional letter grades and percentage  marks, are among  a number tools that teachers will use to assess students' learning." (p.5)