RRR 1

Chapters 5 & 6

Review

Chapter five contains the type of information that is impossible to ignore, difficult to skim, but simple to employ.  The selection begins with four major thinking processes: observing and inferring, comparing, classifying, and sequencing.  The explanation of each process is followed by suggestions for activities.  Next, three ideas for developing and practicing skills are listed: Carroll, tree, and Venn Diagrams.  The chapter also covers topics such as estimating and assessing the learning of math skills. 

Chapter six explains how to attach meaning to numbers with concepts including conservation, zero, and grouping.  The next section of the chapter explains that only after the student understands the significance of the numbers and can explain it orally, should the teacher have the students work with written numbers.

Reflect

These chapters are very interesting and even more so, very useful.  I like that the book includes activities for the teacher to use.  As a new teacher, I don’t feel there are enough suggestions for teachers to use in the context of complex subjects like math.  More importantly, I like the manner in which the book explains how students begin to grasp an understanding of mathematical concepts.  It was not until chapter six that I realized that chapter five was not emphasizing working with written numerals.  Of course, the examples and activities all used pictograms and symbols, but I did not connect that with the absence of written numbers.  It is fascinating, and, I believe, an overlooked phenomenon that students do need to comprehend the value and relationship of numbers before they can move on to the next step of doing problems on paper.

Respond

Although I am a new teacher, I have bee a substitute teacher and tutor and seen countless examples of what students, grades K-8, are working on for their math classes.  Almost without exception, I find the work dull and tedious.  A common example can be illustrated by the 1^st grader who has four worksheets of math problems to do for homework in one night.  The student’s understanding of numbers is so underdeveloped that he has to use counters and, even then, has trouble grasping the relationships.  The worksheets are usually so repetitive the students does half of one sheet, and then plays a searching game of his own where, instead of doing the math, he matches the numbers in the problem with another elsewhere on the worksheet, then copying his answer.  Perhaps this repetition does eventually drill the meaning into the student’s mind, but in a callous and deadening manner. 

Carry this poor learning environment into the later grades, and you find the same thing occurring.  Boring homework, repetitive exercises and math without a connection to the greater environment all furthers the distaste most students find for math.  My only criticism of chapters five and six is that there are not that many activities for the upper grades.  Perhaps this is because the concepts being discussed should be gained in the primary grades, but I do believe activities for older students could help to support previously learned ideas, or perhaps even teach concepts the students never had access to. 

Michael Beyer