ARITHMETIC INSIGHTS

By SARAH HERNANDEZ

CONTENTS PART ONE: ELEMENTS WHAT IS MATHEMATICS? THE THREE MATHEMATICAL WAYS OF ECONOMY THE SECRET OF MATHEMATICAL BEAUTY LAYER UPON LAYER WHOLE NUMBERS MEANING AND CALCULATION THE DECIMAL SYSTEM WHAT IS LEARNED? PART TWO: THE ROAD TO ABSTRACTION — PRINCIPLES OF TEACHING CONVEYING ABSTRACTIONS DIVERSITY AND FIXATION WHY TEACHING IS DI?CULT MEDIATION MAGIC WORDS THE CALCULATOR AND OTHER AIDS THE COURAGE FOR SIMPLICITY PART THREE: ARITHMETIC FROM FIRST TO SIXTH GRADES A MEANING THE MEANING OF ADDITION THE MEANING OF SUBTRACTION THE ESSENCE OF MULTIPLICATION THE TWO MEANINGS OF DIVISION MEANING AND WORD PROBLEMS B CALCULATION THE CALCULATION OF ADDITION SUBTRACTION: LOAN OR REORGANIZE? THE CALCULATION OF MULTIPLICATION VERTICAL MULTIPLICATION MEMORIZE OR CALCULATE ANEW? CALCULATION OF DIVISION BEGINS ON THE LEFT C FRACTIONS DIVISION AND FRACTIONS FRACTIONS TURN DIVISION INTO MULTIPLICATION A CONVERSATION ON DIVISION BY FRACTIONS SOLVED EXERCISES ON FRACTIONS THE COMMON DENOMINATOR THE LEAST COMMON DENOMINATOR MIXED NUMBERS D DECIMALS DECIMAL FRACTIONS CALCULATION IN DECIMAL FRACTIONS PERCENTAGES — A UNIVERSAL LANGUAGE FOR FRACTIONS E RATIOS PROPORTIONALITY MORE RATIO PROBLEMS