JayChesser

     Chapter 5 deals with developing Fraction Concepts.  Manipulatives are strongly advised.  Three types of models are discussed:  region/area models, length models, and set models.  Activities like 5.1 and 5.2 may be helpful.  Students have difficulty when models show fractional parts that are not equal.  Working through these activities allows students to see the difference and have a chance to vocalize or write an explanation of how the parts are equal or are not equal.

     Chapter 6 is on Fraction Computation.  The development of fraction concepts should follow the same path as the development of whole numbers.  Manipulatives to explore and answer simple contextual tasks is paramount.  Just as a number represents a quantity or value, fractions likewise must be constructed and understood by the learner.  Rules should be abandoned until students can bridge the gap between concept and application of the rules.  Begin simple and build from there.  The concepts of multiplying and dividing fractions again begins with informal exploration beginning with simple contextual tasks.  Relating multiplying fractions to whole number multiplication helps students.  Traditional algorithms are not to be taught initially.  Time must be allocated for invented strategies by students.  The most important thing for the teacher to remember is that the strategy must be constructed by the student and that the student must be able to explain his/her strategies and answers.

     Chapter 7 explores the use of Decimals and Percentages.  It begins by discussing ways to help students gain a better understanding of decimals by developing a conceptual understanding between fractions and decimals.  It is suggested that students should discover the relationship between decimals and fractions by reviewing the base-ten system and ultimately learning that this system can be extended to include numbers less than one.  By using the 10 x 10 squares, students can create fractions to represent numbers such as .65.  Students color 65 out of the 100 squares to begin to see the relationship of decimals and fractions, and begin to compare the value.  Teachers should ask questions like "Is this decimal greater than 1/2?"  Students should be allowed to verbalize their answers to ensure concept comprehension.

     Chapter 8 deals with Geometric Thinking and Geometric Concepts.  Students score lower than other countries in the area of geometry.  Because of this, schools are embracing the works of Pierre van Hiele and Dina van Hiele-Geldof.  They believe that students go through five different levels (0 - 4) as they progress through geometric thinking and concepts.  The levels are not age dependent in the sense of developmental stages of Piaget.  Their belief is that geometric experience is the greatest single factor influencing advancement through the levels.  The Hieles believe that the more students play around with the ideas in their suggested activities, the more relationships they will discover.  Teachers are not to tell students about their explorations, but rather facilitate the study.  Teachers should challenge students with questions and allow the students to explain in thier own words what they are doing.  By listening to their answers, teachers can assess student understanding of geometry.

     I think the chapters in this section of reading are very helpful in teaching our third graders.  Content of the activities can be enhanced to challenge students.  So the activities reach all students!