MAVA Math: Number Sense

An Important Message To Teachers, Parents, and Students: What is number sense? Number sense is basic insight into the structure and use of numbers. For example, a student without number sense will do long division to find 600 divided by 4. A student with number sense will say that half of 600 is 300, and half of 300 is 150, saving energy and time. Or, a person without number sense will subtract across many places. Someone with number sense will add back rather than subtract to obtain the answer faster. Number sense does not replace or precede basic arithmetic algorithms. However, one who truly understands the basic algorithms knows how and when to alter them. Number sense is to math as common sense is to life. What is the difference among number sense, mental math, and quick math? All are related. Mental math implies that students do problems solely after hearing them. Quick math implies that students do problems primarily for the sake of speed. Number sense implies that students may see and/or hear problems; understanding is paramount to tricks. Moreover, with a number sense approach, students may minimally write work. Why are problems in this book in horizontal rather than vertical form? Vertical form lends itself to using standard arithmetic algorithms. Horizontal form lends itself to using number sense. Why should students not show full work for the problems? Everyone teaching and doing math needs to understand the wide range of math problems. Some, done by professional mathematicians, may require dozens of pages of work. At the other extreme, some should be done completely mentally. Problems commonly seen in textbooks for grades one through twelve require a few digits of writing up to a few inches. Students should not show full work for the problems in this book. Full work counteracts the development of number sense. How does a student learn to do the problems without full work? MAVA Math: Number Sense Solutions provides not only answers but also helpful ideas between the two columns of problems. Apply methods from the examples shown to the other problems. What is the grade level of this book? While this book aims at grades one through five, some children may begin earlier. Also, children in middle school lacking number sense may find this book useful. What are the two numbers at the top left corner of each page following the topic identifier? The number to the left of the dash indicates the school grade; the number to the right of the dash provides a possible sequencing within each grade. How firm are the two numbers at the top left corner of each page? Both numbers are approximations because students’ abilities and schools’ curricula vary. The school grade number corresponds to material in basal texts by national publishers. Still, a given skill may appear in many grades: initially as introduction, the next year as review, and the following year as mastery. Moreover, children at the start of a grade are different students than at the end of the same grade. Does a child need to develop number sense given the availability of calculators? Thankfully, for children who do not develop number sense, calculators are available in later life. However, no adult should close a door on a child in any subject. Math is one of the two most basic skills in life (language the other) and is essential for so many careers. Overdependence on a calculator cripples a child’s numeric thinking. What is the best order of topics to follow? Math does not have one correct order in which to study topics. Students learn math best by studying arithmetic and geometry in parallel with complementary strands of number theory, probability, and statistics. With topics in alphabetical order, students or teachers may find problems that meet a specific need or supplement school lessons. Still, some topics have an inherent order as LCM before fraction addition with different denominators. Why do some topics have so many more pages than other topics? Math for first graders begins with place value, addition, and subtraction. These topics, needing deep and careful study, lend themselves to the growth of number sense. For older elementary children, multiplication, for example, offers vast richness for the development of number sense, while a topic such as probability requires a middle school student to study its subtleties. Are these topics and questions all that exist for number sense development? No, these topics and problems are a representative sample within a framework of 298 pages of math. One can always think of additional valuable exercises. Also, at the middle school level, more sophisticated concepts are appropriate for number sense development. Should a topic without pages for a grade level not be studied at all in that grade? A void of pages for a topic in a grade does not imply that the topic is inappropriate at that grade. Some topics at a certain grade lend themselves better to a different style of math book. For example, a first grader could draw lines of symmetry through shapes or locate figures in the positive-positive quadrant of the coordinate plane. Check www.mavabooks.com for other style textbooks. What is the significance of the ordering of pages within a topic? With addition, for example, pages could be organized by regrouping: all problems with no regrouping followed by all with regrouping. Alternatively, as this book does, pages could be organized by number of digits: all one-digit problems, followed by all 2-digit and 3-digit problems. Arguments could be made for either case. Teachers, students, and parents should use pages in any order that suits their specific needs. Please read the "Free Preview" for MAVA Math: Number Sense Solutions for the continuation of this Q&A.