christian-bick/edugraph-knowledge · Datasets at Hugging Face

instruction stringlengths 19 448	output stringlengths 45 292
Represents numbers with an abacus.	{"Area": [], "Scope": ["Abacus"], "Ability": []}
A form of logical inference that starts with an observation or set of observations and then seeks to find the simplest and most likely explanation for the observations. It involves making an educated guess or hypothesis based on incomplete information. Abductive reasoning is often used in everyday life and in fields like science and detective work to generate possible explanations for phenomena.	{"Area": [], "Scope": [], "Ability": ["AbductiveReasoning"]}
Involves abstract concepts such as shapes or numbers.	{"Area": [], "Scope": ["AbstractionScope"], "Ability": []}
Using a wide range of words in speaking and writing. This involves actively employing diverse vocabulary to express ideas precisely and effectively.	{"Area": [], "Scope": [], "Ability": ["ActiveVocabulary"]}
The ability to adjust and modify ideas in response to new information or challenges. This involves being flexible and adaptable in one's thinking, and being willing to revise and refine ideas as needed.	{"Area": [], "Scope": [], "Ability": ["AdaptiveCreativity"]}
Counts manifested objects additively.	{"Area": [], "Scope": ["AdditiveCount"], "Ability": []}
The branch of mathematics that generalizes arithmetics and where letters represent unknown numbers, allowing us to explore patterns, solve equations, and model real-world situations.	{"Area": ["Algebra"], "Scope": [], "Ability": []}
Involves an analog clock.	{"Area": [], "Scope": ["AnalogClock"], "Ability": []}
A form of logical inference that involves identifying similarities between two or more situations or objects and then using those similarities to draw conclusions or make predictions about one of them. It relies on the idea that if two things are alike in some respects, they are likely to be alike in other respects as well. Analogical reasoning is often used in problem-solving, decision-making, and creative thinking.	{"Area": [], "Scope": [], "Ability": ["AnalogicalReasoning"]}
The branch of mathematics that deals with continuous change and investigates concepts like limits, continuity, derivatives, integrals, and infinite series to study functions, their properties, and their behavior.	{"Area": ["Analysis"], "Scope": [], "Ability": []}
The ability to examine information critically, break it down into its component parts, and identify patterns and relationships. It involves skills like critical thinking, problem-solving, and logical reasoning. Analytical capability allows individuals to evaluate information, draw inferences, and form their own conclusions.	{"Area": [], "Scope": [], "Ability": ["AnalyticalCapability"]}
Involves angle measurement.	{"Area": [], "Scope": ["AngleMeasurement"], "Ability": []}
Represents numbers with arabic numerals.	{"Area": [], "Scope": ["ArabicNumerals"], "Ability": []}
The branch of mathematics that deals with the properties and manipulation of numbers, including addition, subtraction, multiplication and division.	{"Area": ["Arithmetic"], "Scope": [], "Ability": []}
Articulation refers to the clarity and effectiveness with which someone expresses themselves.	{"Area": [], "Scope": [], "Ability": ["Articulation"]}
Understanding and appreciating artistic works, such as paintings, music, or literature. This involves analyzing the elements of art, such as form, style, and symbolism, to understand the artist's message and intent.	{"Area": [], "Scope": [], "Ability": ["ArtisticInterpretation"]}
The ability to identify and clearly state the fundamental assumptions or self-evident truths that serve as the foundation for a deductive system. This involves recognizing basic principles, defining key terms, and establishing the starting points for logical reasoning. Axiom definition is crucial for building a coherent and consistent framework for deductive reasoning, ensuring that all conclusions follow logically from the initial assumptions.	{"Area": [], "Scope": [], "Ability": ["AxiomDefinition"]}
Involves a balance scale.	{"Area": [], "Scope": ["BalanceScale"], "Ability": []}
Represents numbers in base 10 (decimal).	{"Area": [], "Scope": ["Base10"], "Ability": []}
Represents numbers in base 16 (hexadecimal).	{"Area": [], "Scope": ["Base16"], "Ability": []}
Represents numbers in base 2 (binary).	{"Area": [], "Scope": ["Base2"], "Ability": []}
Represents numbers in base 8 (octal).	{"Area": [], "Scope": ["Base8"], "Ability": []}
Base operations are the fundamental arithmetic actions performed on numbers that all other arithmetic operations are based one.	{"Area": ["BaseOperations"], "Scope": [], "Ability": []}
Represents numbers with a base ten blocks.	{"Area": [], "Scope": ["BaseTenBlocks"], "Ability": []}
Identifying prejudice or favoritism in information or arguments. This involves recognizing how personal opinions or perspectives can influence the way information is presented or interpreted.	{"Area": [], "Scope": [], "Ability": ["BiasDetection"]}
Identifying and avoiding biases in one's own thinking and communication. This involves being aware of personal prejudices and striving to present information objectively and fairly.	{"Area": [], "Scope": [], "Ability": ["BiasPrevention"]}
The branch of mathematics that provides tools for analyzing rates of change and accumulation. It deals with instantaneous rates of change that affect the slopes of curves, as well as with accumulation that affects areas under curves.	{"Area": ["Calculus"], "Scope": [], "Ability": []}
Represents functions and shapes in the cartesian coordinate system.	{"Area": [], "Scope": ["CartesianCoordinateSystem"], "Ability": []}
Involves distances expressed in centimeters.	{"Area": [], "Scope": ["CentimeterScale"], "Ability": []}
Circular shape drawing is the ability to create drawings or models of circular shapes.	{"Area": ["CircularShapeDrawing"], "Scope": [], "Ability": []}
The branch of mathematics that involves the development and application of mathematical methods and algorithms for solving problems using computers.	{"Area": ["ComputationalMathematics"], "Scope": [], "Ability": []}
Concept Classification The ability to organize and categorize concepts by identifying similarities, differences, and relationships between them. It involves grouping concepts based on shared attributes and creating hierarchical structures. Concept classification helps learners build mental frameworks and understand how knowledge is structured.	{"Area": [], "Scope": [], "Ability": ["ConceptClassification"]}
The ability to combine or integrate multiple concepts to create new or more complex concepts. It involves understanding how different concepts can be related and integrated to form a more comprehensive understanding. Concept composition allows learners to build upon existing knowledge and create new meanings.	{"Area": [], "Scope": [], "Ability": ["ConceptComposition"]}
The ability to infer or deduce new concepts from existing knowledge or information. It involves applying logical reasoning and making inferences to extend understanding beyond what is explicitly stated. Concept derivation allows learners to generate new insights and expand their knowledge base.	{"Area": [], "Scope": [], "Ability": ["ConceptDerivation"]}
The ability to identify common features or principles across different concepts and form broader understandings. It involves recognizing patterns, abstracting key ideas, and applying them to new situations. Concept generalization allows learners to transfer knowledge and make connections between different domains.	{"Area": [], "Scope": [], "Ability": ["ConceptGeneralization"]}
The ability to narrow down or refine a general concept to a more specific or concrete instance. It involves identifying distinguishing features, providing details, and applying the concept to a particular context. Concept specification allows learners to deepen their understanding and apply knowledge to specific situations.	{"Area": [], "Scope": [], "Ability": ["ConceptSpecification"]}
The ability to understand and apply big ideas, recognizing underlying patterns and connections between different concepts. It involves forming generalizations, creating mental models, and seeing the bigger picture. Conceptual thinking goes beyond memorizing facts and focuses on understanding the deeper meaning and relationships between ideas.	{"Area": [], "Scope": [], "Ability": ["ConceptualThinking"]}
Convergent Creativity: The ability to combine different ideas or perspectives to form a single, unified solution. This involves synthesizing information from various sources and finding common ground between different approaches.	{"Area": [], "Scope": [], "Ability": ["ConvergentCreativity"]}
Involves counting symbols.	{"Area": [], "Scope": ["CountingSymbols"], "Ability": []}
The ability to generate novel and valuable ideas. This involves thinking outside the box, exploring different perspectives, and coming up with original solutions to problems.	{"Area": [], "Scope": [], "Ability": ["CreativeCapability"]}
Time expressed in intervals of days.	{"Area": [], "Scope": ["DayIntervals"], "Ability": []}
Adding two or more decimals together. Example: 2.7 + 1.8 = 4.5	{"Area": ["DecimalAddition"], "Scope": [], "Ability": []}
Performing arithmetic operations on decimals (numbers represented with a decimal point).	{"Area": ["DecimalArithmetic"], "Scope": [], "Ability": []}
Dividing one decimal by another. Example: 6.3 / 2.1 = 3	{"Area": ["DecimalDivision"], "Scope": [], "Ability": []}
Raising a decimal to a power. Example: 1.2 ^ 2 = 1.44	{"Area": ["DecimalExponentiation"], "Scope": [], "Ability": []}
Finding the exponent to which a base (a decimal) must be raised to produce a given decimal.	{"Area": ["DecimalLogarithm"], "Scope": [], "Ability": []}
Multiplying two or more decimals. Example: 3.5 * 2.0 = 7.0	{"Area": ["DecimalMultiplication"], "Scope": [], "Ability": []}
Applying the decimal system of representing rational numbers using a base-ten place value system and a decimal point to separate whole and fractional parts.	{"Area": ["DecimalNotation"], "Scope": [], "Ability": []}
Finding the decimal that, when raised to a certain power, produces a given decimal. Example: The square root of 2.25 is 1.5	{"Area": ["DecimalRoot"], "Scope": [], "Ability": []}
Finding the difference between two decimals. Example: 5.8 - 2.3 = 3.5	{"Area": ["DecimalSubtraction"], "Scope": [], "Ability": []}
Reducing a quantity by a specific amount.	{"Area": ["Decrement"], "Scope": [], "Ability": []}
A type of reasoning where the conclusion is guaranteed to be true if the premises are true. It moves from general principles to specific conclusions, using logic and rules of inference to establish certainty. Deductive reasoning is often used in mathematics, logic, and other fields where absolute certainty is desired.	{"Area": [], "Scope": [], "Ability": ["DeductiveReasoning"]}
Counts manifested objects based on logical derivation of know facts.	{"Area": [], "Scope": ["DerivedCount"], "Ability": []}
Guiding and managing a conversation between two or more people. This involves ensuring that the conversation stays focused, productive, and respectful.	{"Area": [], "Scope": [], "Ability": ["DialogModeration"]}
Determining the difference in quantities of mathematical object, including numbers where difference represents the amount by which one quantity is greater or less than another.	{"Area": ["Difference"], "Scope": [], "Ability": []}
Digit notation uses symbols from 0 to 9 to represent any number.	{"Area": ["DigitNotation"], "Scope": [], "Ability": []}
Involves a digital clock.	{"Area": [], "Scope": ["DigitalClock"], "Ability": []}
Involves a digital scale.	{"Area": [], "Scope": ["DigitalScale"], "Ability": []}
Involves spatial dimensions with or without time or hyperdimensional concepts.	{"Area": [], "Scope": ["DimensionalAbstraction"], "Ability": []}
Comprehending the literal meaning of information. This involves understanding the explicit message conveyed by words, images, or other forms of communication.	{"Area": [], "Scope": [], "Ability": ["DirectUnderstanding"]}
The ability to generate a wide range of ideas or solutions. This involves brainstorming multiple possibilities and exploring different avenues before settling on a specific approach.	{"Area": [], "Scope": [], "Ability": ["DivergentCreativity"]}
The ability to accept and appreciate people from different backgrounds and cultures. This involves respecting and valuing diversity, and avoiding prejudice and discrimination.	{"Area": [], "Scope": [], "Ability": ["DiversityTolerance"]}
Elliptical shape drawing is the ability to create drawings or models of elliptical shapes.	{"Area": ["EllipticShapeDrawing"], "Scope": [], "Ability": []}
Recognizing and understanding the emotions expressed in communication. This involves interpreting the feelings conveyed through language, tone of voice, and nonverbal cues.	{"Area": [], "Scope": [], "Ability": ["EmotionExtraction"]}
The ability to understand, manage, and express one's own emotions effectively, as well as to understand and respond appropriately to the emotions of others.	{"Area": [], "Scope": [], "Ability": ["EmotionalCapability"]}
The ability to express emotions in creative and meaningful ways. This involves using art, music, writing, or other creative outlets to communicate feelings and connect with others on an emotional level.	{"Area": [], "Scope": [], "Ability": ["EmotionalCreativity"]}
Expressing emotions effectively in communication. This involves using language, tone of voice, and nonverbal cues to convey feelings and create an emotional connection with the audience.	{"Area": [], "Scope": [], "Ability": ["Emotionalization"]}
The ability to understand and share the feelings of others. This involves putting oneself in another person's shoes and imagining how they might be feeling in a given situation.	{"Area": [], "Scope": [], "Ability": ["Empathy"]}
Finding and fixing mistakes in written or spoken work. This involves carefully reviewing work for accuracy and making necessary corrections to improve clarity and understanding.	{"Area": [], "Scope": [], "Ability": ["ErrorCorrection"]}
Noticing mistakes or inconsistencies in information. This involves recognizing when something is incorrect, illogical, or doesn't fit with the overall context.	{"Area": [], "Scope": [], "Ability": ["ErrorDetection"]}
Carefully judging the quality, value, or significance of something. This involves assessing information or ideas based on criteria, evidence, and reasoning.	{"Area": [], "Scope": [], "Ability": ["Evaluation"]}
The act of conveying thoughts, feelings, or information. This involves encoding information into a form that can be understood by others. It can be verbal, nonverbal, or visual.	{"Area": [], "Scope": [], "Ability": ["Expression"]}
Taking out specific information or elements from a larger source. This involves identifying and isolating key details, facts, or ideas from a text, image, or other source of information.	{"Area": [], "Scope": [], "Ability": ["Extraction"]}
The act of making a process or activity easier for others. This involves guiding, supporting, and encouraging individuals or groups to achieve a common goal.	{"Area": [], "Scope": [], "Ability": ["Facilitation"]}
Adhering to formal rules and conventions in communication. This involves using appropriate language, structure, and style for specific contexts, such as academic writing or professional correspondence.	{"Area": [], "Scope": [], "Ability": ["Formalization"]}
Involves three spatial dimensions and time.	{"Area": [], "Scope": ["FourDimensional"], "Ability": []}
Adding two or more fractions, often requiring finding a common denominator. Example: 1/4 + 3/8 = 2/8 + 3/8 = 5/8	{"Area": ["FractionAddition"], "Scope": [], "Ability": []}
Performing arithmetic operations on fractions.	{"Area": ["FractionArithmetic"], "Scope": [], "Ability": []}
Dividing one fraction by another, which is equivalent to multiplying by the reciprocal of the second fraction. Example: (2/3) / (1/4) = (2/3) * (4/1) = 8/3	{"Area": ["FractionDivision"], "Scope": [], "Ability": []}
Raising a fraction to a power. Example: (1/2) ^ 3 = (1/2) * (1/2) * (1/2) = 1/8	{"Area": ["FractionExponentiation"], "Scope": [], "Ability": []}
Finding the exponent to which a base (a fraction) must be raised to produce a given fraction.	{"Area": ["FractionLogarithm"], "Scope": [], "Ability": []}
Multiplying two or more fractions by multiplying the numerators and the denominators. Example: (2/5) * (3/7) = 6/35	{"Area": ["FractionMultiplication"], "Scope": [], "Ability": []}
The system of symbols used to represent fractions, including the numerator and denominator.	{"Area": ["FractionNotation"], "Scope": [], "Ability": []}
Finding the fraction that, when raised to a certain power, produces a given fraction. Example: The square root of 9/16 is 3/4 because (3/4) ^ 2 = 9/16	{"Area": ["FractionRoot"], "Scope": [], "Ability": []}
Reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common factor. Example: 12/18 simplifies to 2/3 by dividing both by 6	{"Area": ["FractionSimplification"], "Scope": [], "Ability": []}
Finding the difference between two fractions, often requiring finding a common denominator. Example: 3/4 - 1/8 = 6/8 - 1/8 = 5/8	{"Area": ["FractionSubtraction"], "Scope": [], "Ability": []}
Represents geometric shapes with a geoboard.	{"Area": [], "Scope": ["Geoboard"], "Ability": []}
The branch of mathematics that studies shapes, the sizes, positions, and dimensions of things. It explores properties of points, lines, planes, and solids.	{"Area": ["Geometry"], "Scope": [], "Ability": []}
Involves a geometric representation.	{"Area": [], "Scope": ["GeometryRepresentation"], "Ability": []}
Expressing oneself through deliberate physical gestures and body language. This involves using hand movements, facial expressions, and body posture to convey meaning.	{"Area": [], "Scope": [], "Ability": ["GesticArticulation"]}
Understanding and interpreting body language and gestures. This involves paying attention to nonverbal cues, such as facial expressions, hand movements, and body posture, to understand the meaning behind them.	{"Area": [], "Scope": [], "Ability": ["GesticReception"]}
Using correct grammar in spoken and written communication. This involves applying grammatical rules accurately to ensure clear and understandable language.	{"Area": [], "Scope": [], "Ability": ["GrammaticalPrecision"]}
Facilitating interaction and collaboration within a group. This involves encouraging participation, managing group dynamics, and ensuring that the group stays on task and achieves its goals.	{"Area": [], "Scope": [], "Ability": ["GroupModeration"]}
Time expressed in intervals of hours in a day.	{"Area": [], "Scope": ["HourIntervals"], "Ability": []}
Understanding and appreciating humor. This involves recognizing the comedic elements in a joke, story, or situation, and understanding why it is funny.	{"Area": [], "Scope": [], "Ability": ["HumoristicInterpretation"]}
Involves more dimensions than three spatial dimensions and time.	{"Area": [], "Scope": ["HyperDimensional"], "Ability": []}
The ability to formulate testable explanations or predictions for observed phenomena. It involves identifying patterns, considering existing knowledge, and using creativity to propose possible answers to scientific questions. Hypothesis generation is a crucial step in the scientific process, guiding investigations and driving the search for new knowledge.	{"Area": [], "Scope": [], "Ability": ["HypothesisGeneration"]}
The process of evaluating a hypothesis through systematic observation, experimentation, and data analysis. It involves designing experiments to test predictions, collecting and analyzing data, and determining whether the evidence supports or refutes the hypothesis. Hypothesis validation is a cornerstone of scientific inquiry, ensuring that conclusions are based on rigorous evidence.	{"Area": [], "Scope": [], "Ability": ["HypothesisValidation"]}
Raising a quantity by a certain amount.	{"Area": ["Increment"], "Scope": [], "Ability": []}
A form of logical inference that involves drawing general conclusions from specific observations or examples. It moves from specific instances to broader generalizations. Inductive reasoning is often used in scientific inquiry to develop hypotheses and theories based on empirical evidence.	{"Area": [], "Scope": [], "Ability": ["InductiveReasoning"]}

Represents numbers with an abacus.

{"Area": [], "Scope": ["Abacus"], "Ability": []}

A form of logical inference that starts with an observation or set of observations and then seeks to find the simplest and most likely explanation for the observations. It involves making an educated guess or hypothesis based on incomplete information. Abductive reasoning is often used in everyday life and in fields like science and detective work to generate possible explanations for phenomena.

{"Area": [], "Scope": [], "Ability": ["AbductiveReasoning"]}

Involves abstract concepts such as shapes or numbers.

{"Area": [], "Scope": ["AbstractionScope"], "Ability": []}

Using a wide range of words in speaking and writing. This involves actively employing diverse vocabulary to express ideas precisely and effectively.

{"Area": [], "Scope": [], "Ability": ["ActiveVocabulary"]}

The ability to adjust and modify ideas in response to new information or challenges. This involves being flexible and adaptable in one's thinking, and being willing to revise and refine ideas as needed.

{"Area": [], "Scope": [], "Ability": ["AdaptiveCreativity"]}

Counts manifested objects additively.

{"Area": [], "Scope": ["AdditiveCount"], "Ability": []}

The branch of mathematics that generalizes arithmetics and where letters represent unknown numbers, allowing us to explore patterns, solve equations, and model real-world situations.

{"Area": ["Algebra"], "Scope": [], "Ability": []}

Involves an analog clock.

{"Area": [], "Scope": ["AnalogClock"], "Ability": []}

A form of logical inference that involves identifying similarities between two or more situations or objects and then using those similarities to draw conclusions or make predictions about one of them. It relies on the idea that if two things are alike in some respects, they are likely to be alike in other respects as well. Analogical reasoning is often used in problem-solving, decision-making, and creative thinking.

{"Area": [], "Scope": [], "Ability": ["AnalogicalReasoning"]}

The branch of mathematics that deals with continuous change and investigates concepts like limits, continuity, derivatives, integrals, and infinite series to study functions, their properties, and their behavior.

{"Area": ["Analysis"], "Scope": [], "Ability": []}

The ability to examine information critically, break it down into its component parts, and identify patterns and relationships. It involves skills like critical thinking, problem-solving, and logical reasoning. Analytical capability allows individuals to evaluate information, draw inferences, and form their own conclusions.

{"Area": [], "Scope": [], "Ability": ["AnalyticalCapability"]}

Involves angle measurement.

{"Area": [], "Scope": ["AngleMeasurement"], "Ability": []}

Represents numbers with arabic numerals.

{"Area": [], "Scope": ["ArabicNumerals"], "Ability": []}

The branch of mathematics that deals with the properties and manipulation of numbers, including addition, subtraction, multiplication and division.

{"Area": ["Arithmetic"], "Scope": [], "Ability": []}

Articulation refers to the clarity and effectiveness with which someone expresses themselves.

{"Area": [], "Scope": [], "Ability": ["Articulation"]}

Understanding and appreciating artistic works, such as paintings, music, or literature. This involves analyzing the elements of art, such as form, style, and symbolism, to understand the artist's message and intent.

{"Area": [], "Scope": [], "Ability": ["ArtisticInterpretation"]}

The ability to identify and clearly state the fundamental assumptions or self-evident truths that serve as the foundation for a deductive system. This involves recognizing basic principles, defining key terms, and establishing the starting points for logical reasoning. Axiom definition is crucial for building a coherent and consistent framework for deductive reasoning, ensuring that all conclusions follow logically from the initial assumptions.

{"Area": [], "Scope": [], "Ability": ["AxiomDefinition"]}

Involves a balance scale.

{"Area": [], "Scope": ["BalanceScale"], "Ability": []}

Represents numbers in base 10 (decimal).

{"Area": [], "Scope": ["Base10"], "Ability": []}

Represents numbers in base 16 (hexadecimal).

{"Area": [], "Scope": ["Base16"], "Ability": []}

Represents numbers in base 2 (binary).

{"Area": [], "Scope": ["Base2"], "Ability": []}

Represents numbers in base 8 (octal).

{"Area": [], "Scope": ["Base8"], "Ability": []}

Base operations are the fundamental arithmetic actions performed on numbers that all other arithmetic operations are based one.

{"Area": ["BaseOperations"], "Scope": [], "Ability": []}

Represents numbers with a base ten blocks.

{"Area": [], "Scope": ["BaseTenBlocks"], "Ability": []}

Identifying prejudice or favoritism in information or arguments. This involves recognizing how personal opinions or perspectives can influence the way information is presented or interpreted.

{"Area": [], "Scope": [], "Ability": ["BiasDetection"]}

Identifying and avoiding biases in one's own thinking and communication. This involves being aware of personal prejudices and striving to present information objectively and fairly.

{"Area": [], "Scope": [], "Ability": ["BiasPrevention"]}

The branch of mathematics that provides tools for analyzing rates of change and accumulation. It deals with instantaneous rates of change that affect the slopes of curves, as well as with accumulation that affects areas under curves.

{"Area": ["Calculus"], "Scope": [], "Ability": []}

Represents functions and shapes in the cartesian coordinate system.

{"Area": [], "Scope": ["CartesianCoordinateSystem"], "Ability": []}

Involves distances expressed in centimeters.

{"Area": [], "Scope": ["CentimeterScale"], "Ability": []}

Circular shape drawing is the ability to create drawings or models of circular shapes.

{"Area": ["CircularShapeDrawing"], "Scope": [], "Ability": []}

The branch of mathematics that involves the development and application of mathematical methods and algorithms for solving problems using computers.

{"Area": ["ComputationalMathematics"], "Scope": [], "Ability": []}

Concept Classification The ability to organize and categorize concepts by identifying similarities, differences, and relationships between them. It involves grouping concepts based on shared attributes and creating hierarchical structures. Concept classification helps learners build mental frameworks and understand how knowledge is structured.

{"Area": [], "Scope": [], "Ability": ["ConceptClassification"]}

The ability to combine or integrate multiple concepts to create new or more complex concepts. It involves understanding how different concepts can be related and integrated to form a more comprehensive understanding. Concept composition allows learners to build upon existing knowledge and create new meanings.

{"Area": [], "Scope": [], "Ability": ["ConceptComposition"]}

The ability to infer or deduce new concepts from existing knowledge or information. It involves applying logical reasoning and making inferences to extend understanding beyond what is explicitly stated. Concept derivation allows learners to generate new insights and expand their knowledge base.

{"Area": [], "Scope": [], "Ability": ["ConceptDerivation"]}

The ability to identify common features or principles across different concepts and form broader understandings. It involves recognizing patterns, abstracting key ideas, and applying them to new situations. Concept generalization allows learners to transfer knowledge and make connections between different domains.

{"Area": [], "Scope": [], "Ability": ["ConceptGeneralization"]}

The ability to narrow down or refine a general concept to a more specific or concrete instance. It involves identifying distinguishing features, providing details, and applying the concept to a particular context. Concept specification allows learners to deepen their understanding and apply knowledge to specific situations.

{"Area": [], "Scope": [], "Ability": ["ConceptSpecification"]}

The ability to understand and apply big ideas, recognizing underlying patterns and connections between different concepts. It involves forming generalizations, creating mental models, and seeing the bigger picture. Conceptual thinking goes beyond memorizing facts and focuses on understanding the deeper meaning and relationships between ideas.

{"Area": [], "Scope": [], "Ability": ["ConceptualThinking"]}

Convergent Creativity: The ability to combine different ideas or perspectives to form a single, unified solution. This involves synthesizing information from various sources and finding common ground between different approaches.

{"Area": [], "Scope": [], "Ability": ["ConvergentCreativity"]}

Involves counting symbols.

{"Area": [], "Scope": ["CountingSymbols"], "Ability": []}

The ability to generate novel and valuable ideas. This involves thinking outside the box, exploring different perspectives, and coming up with original solutions to problems.

{"Area": [], "Scope": [], "Ability": ["CreativeCapability"]}

Time expressed in intervals of days.

{"Area": [], "Scope": ["DayIntervals"], "Ability": []}

Adding two or more decimals together. Example: 2.7 + 1.8 = 4.5

{"Area": ["DecimalAddition"], "Scope": [], "Ability": []}

Performing arithmetic operations on decimals (numbers represented with a decimal point).

{"Area": ["DecimalArithmetic"], "Scope": [], "Ability": []}

Dividing one decimal by another. Example: 6.3 / 2.1 = 3

{"Area": ["DecimalDivision"], "Scope": [], "Ability": []}

Raising a decimal to a power. Example: 1.2 ^ 2 = 1.44

{"Area": ["DecimalExponentiation"], "Scope": [], "Ability": []}

Finding the exponent to which a base (a decimal) must be raised to produce a given decimal.

{"Area": ["DecimalLogarithm"], "Scope": [], "Ability": []}

Multiplying two or more decimals. Example: 3.5 * 2.0 = 7.0

{"Area": ["DecimalMultiplication"], "Scope": [], "Ability": []}

Applying the decimal system of representing rational numbers using a base-ten place value system and a decimal point to separate whole and fractional parts.

{"Area": ["DecimalNotation"], "Scope": [], "Ability": []}

Finding the decimal that, when raised to a certain power, produces a given decimal. Example: The square root of 2.25 is 1.5

{"Area": ["DecimalRoot"], "Scope": [], "Ability": []}

Finding the difference between two decimals. Example: 5.8 - 2.3 = 3.5

{"Area": ["DecimalSubtraction"], "Scope": [], "Ability": []}

Reducing a quantity by a specific amount.

{"Area": ["Decrement"], "Scope": [], "Ability": []}

A type of reasoning where the conclusion is guaranteed to be true if the premises are true. It moves from general principles to specific conclusions, using logic and rules of inference to establish certainty. Deductive reasoning is often used in mathematics, logic, and other fields where absolute certainty is desired.

{"Area": [], "Scope": [], "Ability": ["DeductiveReasoning"]}

Counts manifested objects based on logical derivation of know facts.

{"Area": [], "Scope": ["DerivedCount"], "Ability": []}

Guiding and managing a conversation between two or more people. This involves ensuring that the conversation stays focused, productive, and respectful.

{"Area": [], "Scope": [], "Ability": ["DialogModeration"]}

Determining the difference in quantities of mathematical object, including numbers where difference represents the amount by which one quantity is greater or less than another.

{"Area": ["Difference"], "Scope": [], "Ability": []}

Digit notation uses symbols from 0 to 9 to represent any number.

{"Area": ["DigitNotation"], "Scope": [], "Ability": []}

Involves a digital clock.

{"Area": [], "Scope": ["DigitalClock"], "Ability": []}

Involves a digital scale.

{"Area": [], "Scope": ["DigitalScale"], "Ability": []}

Involves spatial dimensions with or without time or hyperdimensional concepts.

{"Area": [], "Scope": ["DimensionalAbstraction"], "Ability": []}

Comprehending the literal meaning of information. This involves understanding the explicit message conveyed by words, images, or other forms of communication.

{"Area": [], "Scope": [], "Ability": ["DirectUnderstanding"]}

The ability to generate a wide range of ideas or solutions. This involves brainstorming multiple possibilities and exploring different avenues before settling on a specific approach.

{"Area": [], "Scope": [], "Ability": ["DivergentCreativity"]}

The ability to accept and appreciate people from different backgrounds and cultures. This involves respecting and valuing diversity, and avoiding prejudice and discrimination.

{"Area": [], "Scope": [], "Ability": ["DiversityTolerance"]}

Elliptical shape drawing is the ability to create drawings or models of elliptical shapes.

{"Area": ["EllipticShapeDrawing"], "Scope": [], "Ability": []}

Recognizing and understanding the emotions expressed in communication. This involves interpreting the feelings conveyed through language, tone of voice, and nonverbal cues.

{"Area": [], "Scope": [], "Ability": ["EmotionExtraction"]}

The ability to understand, manage, and express one's own emotions effectively, as well as to understand and respond appropriately to the emotions of others.

{"Area": [], "Scope": [], "Ability": ["EmotionalCapability"]}

The ability to express emotions in creative and meaningful ways. This involves using art, music, writing, or other creative outlets to communicate feelings and connect with others on an emotional level.

{"Area": [], "Scope": [], "Ability": ["EmotionalCreativity"]}

Expressing emotions effectively in communication. This involves using language, tone of voice, and nonverbal cues to convey feelings and create an emotional connection with the audience.

{"Area": [], "Scope": [], "Ability": ["Emotionalization"]}

The ability to understand and share the feelings of others. This involves putting oneself in another person's shoes and imagining how they might be feeling in a given situation.

{"Area": [], "Scope": [], "Ability": ["Empathy"]}

Finding and fixing mistakes in written or spoken work. This involves carefully reviewing work for accuracy and making necessary corrections to improve clarity and understanding.

{"Area": [], "Scope": [], "Ability": ["ErrorCorrection"]}

Noticing mistakes or inconsistencies in information. This involves recognizing when something is incorrect, illogical, or doesn't fit with the overall context.

{"Area": [], "Scope": [], "Ability": ["ErrorDetection"]}

Carefully judging the quality, value, or significance of something. This involves assessing information or ideas based on criteria, evidence, and reasoning.

{"Area": [], "Scope": [], "Ability": ["Evaluation"]}

The act of conveying thoughts, feelings, or information. This involves encoding information into a form that can be understood by others. It can be verbal, nonverbal, or visual.

{"Area": [], "Scope": [], "Ability": ["Expression"]}

Taking out specific information or elements from a larger source. This involves identifying and isolating key details, facts, or ideas from a text, image, or other source of information.

{"Area": [], "Scope": [], "Ability": ["Extraction"]}

The act of making a process or activity easier for others. This involves guiding, supporting, and encouraging individuals or groups to achieve a common goal.

{"Area": [], "Scope": [], "Ability": ["Facilitation"]}

Adhering to formal rules and conventions in communication. This involves using appropriate language, structure, and style for specific contexts, such as academic writing or professional correspondence.

{"Area": [], "Scope": [], "Ability": ["Formalization"]}

Involves three spatial dimensions and time.

{"Area": [], "Scope": ["FourDimensional"], "Ability": []}

Adding two or more fractions, often requiring finding a common denominator. Example: 1/4 + 3/8 = 2/8 + 3/8 = 5/8

{"Area": ["FractionAddition"], "Scope": [], "Ability": []}

Performing arithmetic operations on fractions.

{"Area": ["FractionArithmetic"], "Scope": [], "Ability": []}

Dividing one fraction by another, which is equivalent to multiplying by the reciprocal of the second fraction. Example: (2/3) / (1/4) = (2/3) * (4/1) = 8/3

{"Area": ["FractionDivision"], "Scope": [], "Ability": []}

Raising a fraction to a power. Example: (1/2) ^ 3 = (1/2) * (1/2) * (1/2) = 1/8

{"Area": ["FractionExponentiation"], "Scope": [], "Ability": []}

Finding the exponent to which a base (a fraction) must be raised to produce a given fraction.

{"Area": ["FractionLogarithm"], "Scope": [], "Ability": []}

Multiplying two or more fractions by multiplying the numerators and the denominators. Example: (2/5) * (3/7) = 6/35

{"Area": ["FractionMultiplication"], "Scope": [], "Ability": []}

The system of symbols used to represent fractions, including the numerator and denominator.

{"Area": ["FractionNotation"], "Scope": [], "Ability": []}

Finding the fraction that, when raised to a certain power, produces a given fraction. Example: The square root of 9/16 is 3/4 because (3/4) ^ 2 = 9/16

{"Area": ["FractionRoot"], "Scope": [], "Ability": []}

Reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common factor. Example: 12/18 simplifies to 2/3 by dividing both by 6

{"Area": ["FractionSimplification"], "Scope": [], "Ability": []}

Finding the difference between two fractions, often requiring finding a common denominator. Example: 3/4 - 1/8 = 6/8 - 1/8 = 5/8

{"Area": ["FractionSubtraction"], "Scope": [], "Ability": []}

Represents geometric shapes with a geoboard.

{"Area": [], "Scope": ["Geoboard"], "Ability": []}

The branch of mathematics that studies shapes, the sizes, positions, and dimensions of things. It explores properties of points, lines, planes, and solids.

{"Area": ["Geometry"], "Scope": [], "Ability": []}

Involves a geometric representation.

{"Area": [], "Scope": ["GeometryRepresentation"], "Ability": []}

Expressing oneself through deliberate physical gestures and body language. This involves using hand movements, facial expressions, and body posture to convey meaning.

{"Area": [], "Scope": [], "Ability": ["GesticArticulation"]}

Understanding and interpreting body language and gestures. This involves paying attention to nonverbal cues, such as facial expressions, hand movements, and body posture, to understand the meaning behind them.

{"Area": [], "Scope": [], "Ability": ["GesticReception"]}

Using correct grammar in spoken and written communication. This involves applying grammatical rules accurately to ensure clear and understandable language.

{"Area": [], "Scope": [], "Ability": ["GrammaticalPrecision"]}

Facilitating interaction and collaboration within a group. This involves encouraging participation, managing group dynamics, and ensuring that the group stays on task and achieves its goals.

{"Area": [], "Scope": [], "Ability": ["GroupModeration"]}

Time expressed in intervals of hours in a day.

{"Area": [], "Scope": ["HourIntervals"], "Ability": []}

Understanding and appreciating humor. This involves recognizing the comedic elements in a joke, story, or situation, and understanding why it is funny.

{"Area": [], "Scope": [], "Ability": ["HumoristicInterpretation"]}

Involves more dimensions than three spatial dimensions and time.

{"Area": [], "Scope": ["HyperDimensional"], "Ability": []}

The ability to formulate testable explanations or predictions for observed phenomena. It involves identifying patterns, considering existing knowledge, and using creativity to propose possible answers to scientific questions. Hypothesis generation is a crucial step in the scientific process, guiding investigations and driving the search for new knowledge.

{"Area": [], "Scope": [], "Ability": ["HypothesisGeneration"]}

The process of evaluating a hypothesis through systematic observation, experimentation, and data analysis. It involves designing experiments to test predictions, collecting and analyzing data, and determining whether the evidence supports or refutes the hypothesis. Hypothesis validation is a cornerstone of scientific inquiry, ensuring that conclusions are based on rigorous evidence.

{"Area": [], "Scope": [], "Ability": ["HypothesisValidation"]}

Raising a quantity by a certain amount.

{"Area": ["Increment"], "Scope": [], "Ability": []}

A form of logical inference that involves drawing general conclusions from specific observations or examples. It moves from specific instances to broader generalizations. Inductive reasoning is often used in scientific inquiry to develop hypotheses and theories based on empirical evidence.

{"Area": [], "Scope": [], "Ability": ["InductiveReasoning"]}