i. Numbers and Operations are the center of the Strand Model, and have the following elements:
a) one-to-one correspondence is primarily developed through repeated experience, rather than direct instruction.
b) counting, which develops from rote counting into rational counting as children learn that each object must have a counting word and that the words must come in a particular order.
(1) Counting for 3 and 4 year olds should emphasize small numbers of objects used in regular activities.
(2) Counting for 5 and 6 year olds should involve larger numbers, recording and comparison of numbers and counting by multiples.
c) Concepts of number develop rapidly over the preschool period so that five year olds should be able to correctly categorize values 1 through 9.
d) Concepts of place value may not be appropriate until second grade, when children begin dealing with two-digit arithmetic. Manipulatives and concrete demonstrations greatly facilitate acquisition of this concept.
e) Arithmetic principles should be introduced to young children with small whole numbers.
(1) 3 and 4 year olds begin developing simple mathematical concepts through manipulation of objects.
(2) Formal instruction should follow the development of reversibility, generally when children are 5 or six.
(3) 7 and 8 year olds can begin formal instruction in multiplication and division.
(4) Symbols, such as those for fractions, should not be introduced until the concept is understood. Discussion of fractions should begin with oral representations, rather than written symbols.
ii. Seriation tasks are inherent in most play, but seriation skills are limited in young children.
a) Four-year-old children generally compare only pairs of items at a time in academic tasks, but may seriate several items in real-world contexts.
b) Five-year-olds can seriate three or more items, and the number increases and children's skills develop.
c) By seven children can find missing objects in a series and match series of different objects.
iii. Measurement tasks cannot exceed children's conservation skills.
a) Three-year-olds can measure single items or compare pairs of objects, using terms like larger and more.
b) Five-year-olds can begin to use standard measures and compare measurements of different objects, although they may not understand stable linear orders.
c) Seven-year-olds can more accurately measure, and perhaps remeasure, quantities. iv. Time is often emphasized in early childhood programs, but is often not understood until age ten. Concrete measures, such as failing sand, are more appropriate than clocks for preschoolers.
v. The money system is confusing to preschoolers who believe that bigger indicates more, and is frequently not useful knowledge for young children. Underlying concepts of buying and spending are more important than knowledge of specific currency.
vi. Geometry for young children should focus on understanding of shapes and volume. Manipulation of shapes, such as blocks, is key for understanding these principles at any age. Older children should apply principles to reallife problems.
vii. Algebra deals with patterns ( the organization of information), and functions (patterns resulting from actions on objects or numbers). Five-year-olds can begin to explore patterns and functions in real-life settings by charting observations, and older children can create function tables.
viii. Data analysis can easily incorporate concepts of probability.
a) Three-year-olds can observe food choices and weather patterns.
b) Five-year-olds can graph similar information, with more possible choices.
c) Seven-year-olds can handle more complex mathematical tasks and graphs.
D) Process Strands provide a framework in which content can be embedded.
i. Problem solving should be used in childrenŐs activities throughout the day.
ii. The Reasoning and proof strand draws attention to Logical thinking, which is practiced in any situation that requires children to classify or organize materials and use logical language (e.g. if/then, because, all vs. some).
a) Activities for five and six year olds should focus on classifications, particularly shared or overlapping classifications.
b) Activities for seven and eight year olds should focus on set comparisons and the use of arithmetic to record information.
iii. Communication requires children to organize their thinking. Early mathematical communication may be nonverbal. Older children can use graphs or models.
iv. Connections should be made between math and other subjects.
v. Representational skills allow children to record information for preservation and discussion.
6. Materials for Instruction
A) Blocks, cubes, beans and buttons are useful in making math concepts concrete. However, rods of varying lengths are less useful for young children who do not understand seriation. For similar reasons, counting lines are inappropriate while pie sections are useful. Concrete materials are always better than paper and pencil worksheets for young children.
B) Calculators are fun and engaging parts of the classroom, but do not replace logical mathematical skills. Computers, however, can offer children the opportunity to manipulate objects and explore mathematical principles.