KBKilpatrick

Chapter 9 deals with early fraction concepts.  Fractions present a considerable challenge for elementary and even middle school students.  This chapter explores a complete conceptual development for beginning at grade 1 or 2, with most of the concepts for 3rd grade.  These concepts range from the understanding of the fractional part of the whole, models for fractions, fraction symbols, fraction number sense, and equivalent-fraction concepts. 

Chapter 10 begins to touch on algebraic reasoning.  Today we hear and read about algebraic reasoning and thinking.  This includes students uses algebra patterns, representations, and functions.  These concepts should begin in Kindergarten and continue through the years.  This chapter focuses on the content of algebra: pattern and regularity, representation and symbolism, and relationships and functions.

Chapter 11 talks about helping children use data.  Data in the form of graphs is important in the way we receive information in everyday life.  Students must begin be grasping how information is categorized and presented in several graphical forms.  The focus of our teaching should be for our students to be able to use information from graphs to answer questions. 

Chapter 12 deals with early experiences and with probability concepts.  Simply telling children how probability works is completely useless.  Instruction at this level should confront students with the outcomes of simple games and experiments with discussion of the reasons for these outcomes. 

Chapter 5 dealt with base-ten concepts and place value.  A students concept of place value developes over the K-6 span, grades K-3 being the most important years in this time.  In years K and 1 they count and recognize patterns to 100.  They also begin to place items in groups of ten as a unit.  Second graders begin to connect these patterns to our base ten number system, and third graders carry this over to 3 and 4 digits.  Children also start working to put numbers together and take them apart in many different ways to solve different types of addition and subtraction problems.  Children should be allowed to use their experiences with computation to grow understanding of place value as well as firm up computation.  These concepts should be taught together not separately. 

Chapter 6 touches on strategies for whole- number computation.  One way of working a math problem should not be the goal for mastery of computational skills.  Mastery of computational skills is very important, however growth of many skills that will serve in the real world should be the goal. 

Chapter 7 geometric concepts and thinking is the focus here.  Not all people think about geometric ideas in the same manner.  It is beneficial to think of objectives in terms of two separate but related terms:  spatial reasoning, or spatial sense.  Spatial sense is an idea or intuition about shapes and their relationships.  Spatial reasoning deals with the way children think and reason about a shape in space.  This chapter talks about how to teach children in both areas at all different levels. 

Chapter 8 discusses measurement.  Before anything is measured meaningfully, it is important to understand the attribute to be measured.  Children must tie measurement and estimation to a personal understanding with the unit being used to measure. 

Chapter 1 can be summerized by a single statement.  Students can develop understanding of math and math concepts themselves.  This, inturn, developes confidence by being engaged in doing the mathematics.  Teaching math effectively is to meet them on their level so new ideas are created so that students can make connections in mathematics.  This combines an understanding of how children learn, learning through problem solving, and assessing through daily basis. 

Chapter 2 deals with developing early number concepts and number sense.  Numbers are complex concept for childern to grasp.  A firm grasp of numbers and concepts covers many ideas and skills.  Children come to school with many concepts and ideas about numbers.  These ideas should be built on as children work to develope new ideas.  Developing these concepts takes time and experience and grows the further concepts to come in later school years. 

Chapter 3 discusses children connecting different meanings, interpretations, and relationships to the four operations of addition, subtraction, multiplication, and division so students can use these operations in real-world settings.  Operation sense is the focus of this chapter and how to develope this concept.  This is a firm grasp of the operations and the meanings they take on real life.

Chapter 4 touches on basic facts in addition (subtraction) and multiplication (division).  These are problems where both addends and both factors are less than 10.  Mastering a basic fact means that a child can give a response to a problem in about three seconds without resorting to counting or other less efficient means of calculation.  Children, all children, can develop these tools to help them master these basic facts.