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MATHEMATICS, Arthur Benjamin - Secrets of mental math (Quick tricks, A…
MATHEMATICS
Arthur Benjamin - Secrets of mental math
Quick tricks
A little give and take
Products of misspent youth
New and improved products
Divide and conquer
Good enough
Math for the board
A memorable chapter
The tough stuff made easy
Presto-digit-ation
Epilogue by michael shermer
Gerard Kelly - Short-cut math
Fundamentals of short-cut methods
Addition
Subtraction
Multiplication
Division
Fractions, mixed numbers, and percentages
Acquisition of complex arithmetic skills and higher-order mathematics concepts
Insights from cognitive science on mathematical learning
Part 1. Complex arithmetic processing
The understanding of additive and multiplicative arithmetic concepts
Arithmetic word problem solving: the role of prior knowledge
Neurodevelopmental disorders as model systems for understanding typical and atypical mathematical development
Part 2: Rational number processing
The transition from natural to rational number knowledge
Fraction development in children: importance of building numerical magnitude understanding
Numbers as mathematical models: modeling relations and magnitudes with fractions and decimals
Part 3. Algebraic, Geometric, and Trigonometric concepts
Understanding children's difficulties with mathematical equivalence
Learning and solving more complex problems: the roles of working memory, updating, and prior skills for general mathematical archivement and algebra
Learning goemetry: the development of geometrical concepts and the role of cognitive process
The unit cirde as a grounded conceptual structure in precalculus trigonometry
Part 4. Instructional approaches
The power of comparison in mathematics instruction: experimental evidence from classrooms
Evidence for cognitive science principles that impact learning mathematics
Paul Carson - Become a math hacker