Mathematics as a Science of Patterns Flashcards
The word Mathematics comes from the Greek _______, which, in the Greek language, means “that which is learnt,” or “lesson” in modern Greek
mathema
The word Mathematics comes from the Greek mathema, which, in the Greek language, means “______” or “_______” in modern Greek
“that which is learnt,” or “lesson”
8 characteristics of Mathematics
- classification
- logical sequence
- structure
- precision and accuracy
- abstractness
- symbolism
- applicability
- generalization
Characteristic of mathematics: generates relations through which objects are grouped according to similarities and differences.
Classification
Characteristic of Mathematics: each step can be derived logically from the preceding steps
logical sequence
Characteristics of Mathematics: mathematical object that is related to the given set that gives additional meaning or significance.
Structure
Characteristics of Mathematics: ______ is how close a measured value is to the actual (true) value. While, ____ is how close the measured values are to each other
Accuracy, Precision
Characteristic of Mathematics: is the process of extracting the underlying essence of a mathematical concept by taking away any dependence on real-world objects.
Abstractness
Characteristic of Mathematics: is used by mathematicians to communicate mathematical ideas instead of words.
Symbolism
Characteristic of Mathematics: mathematics can be used in all field of human endeavor
Applicability
Characteristic of Mathematics: is the process of “finding and singling out (of properties) in a whole class of similar objects.”
Generalization
6 natures of mathematics?
- A science of measures
- intellectual game
- the art of drawing conclusions
- a tool subject
- a system of logical procedures
- an intuitive method
Nature of Mathematics: It is an activity that involves interaction with a concrete system with the aim of representing aspects of that system in abstract terms if “concrete” implies “real”
a science of measures
Nature of Mathematics: are games of skill that require significant intelligence and cognitive effort. Games and mathematics both require a strong dose of patience, restraint, and concentration
Intellectual game
Nature of Mathematics: Making sense of mathematics using logical thinking is foundation of reasoning and proof standard
The art of drawing conclusions
Nature of Mathematics: In many fields of human activity, mathematics is a highly powerful instrument of investigation.
a tool subject
Nature of Mathematics: Problem-solving is an important component of mathematics. Problem-solving is also a skill which can enhance logical reasoning
A system of logical procedures
Nature of Mathematics: Mathematics have traditionally regarded intuition as a way of understanding proofs and conceptualizing problems. The ability to see what is reasonable or not, and the ability to put all these together.
An intuitive method
- Is a repeated arrangement of numbers, shapes, colors, and the like.
- Also known as sequence.
- Logical connections to form generalizations.
- Predictions.
pattern
4 commonly used patterns in Mathematics?
- number patterns
- logic patterns
- word patterns
- symbol patterns
- Pattern in which a number of lists follow a certain sequence.
- Also known as the sequences of series in numbers.
- Helps make a generalization of how the numbers are arranged in a sequence.
Number pattern
3 common number sequence pattern?
- Arithmetic sequence
- geometric sequence
- Fibonacci numbers
is a sequence of numbers such that the difference between the consecutive terms is constant.
Arithmetic sequence
is a sequence of non zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Geometric sequence
A sequence of numbers such that each number is the sum of the two preceding ones, starting from 0 and 1.
Fibonacci numbers
- Is a set of numbers, words, objects etc., following in a sequence with a relation between two consecutive sets.
- Deals with the characteristics or order of various objects.
- Appears in a sequence while some possess similar attributes
Logic pattern
3 steps to construct or solve logic pattern?
- Find the rule of the pattern.
- Understand the nature of the sequence; and
- Analyze the difference between the two successive terms.
- Helps make sense of language and serve as strategy for spelling.
- Used in decoding.
- Includes vowel pairs, cvc silent e, rcontrolled vowels, consonant blends, and consonant digraphs.
Word pattern
- word with a group of two or three consonants each make its own sound.
- ex: grow, blend, sleeve, stair, sweet, free, blood, clothes
consonant blends
- words with two or three letters that comes together to create a single sound.
- ex: cheat, shop, sheep, brush, shirt, shade
consonant diagraphs
- a spelling pattern in which two or more adjoining letters represent a single vowel
- ex: sound, school, clean, each, feet, moon, cheese
vowel diagraphs
- vowels that glide in the middle.
- ex: boil, now, soil, brown, cloud, rain, meat, bout, cow
Vowel diphthongs
