FRHD 2040 Chapter Notes - Chapter 11: Problem Solving, Data Analysis
1 Jun 2018
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CHAPTER 11
Defining Mathematics
• The science of numbers and their operations, interrelations, combinations, generalizations, and
abstractions, and of space configurations and their structure, measurement, transformations,
and generalizations
Learning Mathematics
• The physical world
o Hot, cold, rough, smooth
• The social world
o Language, religion, superstition
• The construction of mental relationships
o Counting, seriation, numeration, conversation
o Piaget: logicomathematical learning
▪ Creating categories and hierarchies of objects without regard to their physical
properties
▪ Simple abstraction
• Ignoring other properties and only focus on one
▪ Reflective abstraction
• Learner manipulates objects and then reflects on the results
Teaching Mathematics
• Standards for mathematics education
o Content standards
▪ Number and operations
▪ Geometry and spatial sense
▪ Measurement
▪ Patterns, functions, and algebra
▪ Data analysis, statistics, probability
o Process standards
▪ Problem solving
▪ Reasoning and proof
▪ Communication
▪ Connections
▪ Representation
• The strand model
o Conceptualizing important elements of mathematics instruction
o Content standards
▪ Used to solve problems in all strands
o Process standards
▪ Surround the content strand because good instruction embeds the content
within the framework created by the process strands
o The content strands
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Defining mathematics: the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions, and of space configurations and their structure, measurement, transformations, and generalizations. Ignoring other properties and only focus on one: reflective abstraction. Learner manipulates objects and then reflects on the results. Logical connections among mathematics and the other subject areas in the curriculum: representations, skill of finding ne(cid:449) (cid:449)ays to illustrate one"s understanding in, process skill instruction communication. Intended to be used in a natural, integrated fashion: not expected to plan a lesson around these. Materials for mathematic instruction: manipulatives, mathematic concepts are presented accurately, materials do not distract from the concept to be learned, calculators and computers, let children explore calculators. Integrating mathematics into the curriculum: mathematics and play, goals of math games, paly according to the rules, understand numbers can be represented in many ways, count in various ways, compare quantities, take others" perspecti(cid:448)es, strategies for game playing.
