JayChesser

     Chapter 9 focuses on developing measurement concepts.  Teachers should think about three areas when thinking about planning measurement instruction.  First, students must understand the attribute to be measured.  Second, that students should understand how filling, covering, matching, or making other comparisons of an attribute with measuring units produces a number called a measure.  Third, students will use common measuring tools with understanding and flexibility.    Students should also be exposed to informal units of measure as well as standard units.  Experimenting with informal units allows students to make comparisons and predictions.  The use of estimation is also encouraged because it helps students focus on the attribute being measured and the process required to measure it. 

     Chapter 10 is on algebraic reasoning.  The basis of algebraic reasoning begins in Kindergarten and should move from a very concrete toward symbolism and functions in the upper grades.  In the third grade, algebraic reasoning is still concrete, but extending into logical thinking and making predictions about patterns and relationships.  It is suggested by the authors that teachers should extend the task of repeating patterns by having students predict what element will be in the 15th or 17th position before starting.  Then have students extend the pattern to verify.  The use of grid configurations (3-square, 4-square, and 5-square wide) allows students to see what patterns develop with a recurring pattern.  "Grid Patterns" on page 292 addresses this type of extention.  Patterns with numbers can go beyond merely skip counting to more involved patterns such as double the previous number, or the next square  number (What's Next and Why).

     Chapter 11 addresses exploring data analysis.  Too often our students are presented with questions to answer and the data with which to answer them.  Although the questions may be of interest from the standpoint of data analysis, the questions are not necessarily of interest to our students.  "Students should be given opportunities to generate thier own questions, decide on appropriate data to help answer these questions, and determine methods of collecting the data." according to this chapter.  We tend to gather data simply to make a graph.  When students generate thier own questions to ask, the data that they collect has more value to them.  How they organize the data and represent it have more meaning.  As teachers, we spend too much time discussing the "how-tos" of graphing.  The issues of analysis and communication should be a teacher's goal.  Not how the graph was constructed.  "In the real world, technology will take care of details of graph construction."  As stated throughout the book, students should be able to express their thoughts about their graphs in writing.  Attention is given to several types of graphs that are used in the marketplace.  These graphs are located and discussed on pages 331 - 336.  In addition, time is spent discussing terms like mean, median,  and mode in relation to third through fifth grades.  These terms should be investigated by students through activities like "Leveling the Bars" and "The Mean Foot" (page 326).  For third grade students, it is suggested to start with the term "mean" or average.  After the ground work is laid for the mean, the other terms can be investigated.

     Chapter 12 emphasizes the reference to probability all around us.  We see probability in the weather forecast to medical research.  The overwhelming concept appears to be that chance has no memory.  It is important for students to understand this concept.  Saxon Math has a series of lessons dealing with probability ranging from impossible to certain.  Several activities in this book extend these concepts in Saxon Math to a different level.  I will probably take a few of the activities to enhance what Saxon does.