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Teaching Student Centered Mathematics Grades 3-5

Chapters 9-12

Chapter 9 focuses on developing measurement concepts. The author states that there are three areas to think about when planning measurement instruction. First, students will understand the attribute to be measured. Second, students will 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.

It is also pointed out that students should be exposed to informal units of measure as well as standard units. Experimenting with informal units allows student to make comparisons and predictions about such attributes as length or area. The use of estimation is also encouraged because it helps students focus on the attribute being measured and the measuring process. For example, have students measure a length with one unit, then provide them with a different unit and see if they can predict the measure of the same length with the new unit.

Chapter 10 centers around algebraic reasoning. It focuses on the content of algebra and discusses the areas of pattern and regularity, representation and symbolism, and relationships and functions.

There were several activities involving repeating and growing patterns that I would like to try in the classroom. The activities on p. 294, "Extend and Explain" and "Predict How Many" involve the use of manipulatives to extend patterns, but at the same time require students to explain each step.

Chapter 11 address exploring data analysis. Most of the time we give students questions and data to work with instead of letting students generate their own questions and data. If students can develop questions that are of interest to them, then they will be more interested in the gathering and organizing of the data to answer their questions. As part of their analysis of graphing procedures, students should be given the opportunity to express their thoughts about their graphs in writing.

The author also explores teaching students about the mean. Activities such as the ones outlined on p. 326 are a good way to begin developing this concept in third grade.

Chapter 12 explores the concept of probability. One of the first "big ideas" that the author states, is that probability has no memory. Students must realize that the outcome of prior trials have no impact on the next.

Activities are developed to help students understand the concept of the extremes of chance situations, ranging from impossible to certain and understanding frequency of outcomes of an event. I thought it was interesting that several of the activities were very similar to some that third grade does through the Saxon Math lessons. Some were taken to another level and gave some ideas that I'll try with my class.

 

Teaching Student-Centered Mathmatics grades 3-5

Chapters 5-8

Chapter 5 examines the development of fraction concepts. As students develop their understanding, the use of models as manipulatives is very important and should not be limited to use only in the lower grades. The models help students understand ideas that are often confusing. The author maps out three types of models, which are, region or area models, length models, and set models.

On page 138, there is an activity to help students understand if a fraction is more, less, or equal to a whole. This is an extremely difficult concept for most students to grasp, but  by using  pattern blocks, rods, or multiples, student can see relationships.

Chapter 6 continues the study of fractions as used in computation. It is stessed that students must have a good understanding of basic fractions before performing operations with fractions. For example, for addition and subtraction the student must understand that the numerator tells the number of parts and the denominator tells the type of part.

I was always taught and told to teach that to add and subtract fractions with unlike denominators, you must find a common denominator. The activity on page 164, shows just the opposite. By using inventive strategies students can add and subtract unlike fractions that are easily related, such as, halves, fourths, and eights.

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.

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 thatn 1. By using 10x10 squares students can create fractions to represent numbers such as .65. When they color in the 65 out of 100 squares, they can then begin to see the relationship of decimals and fractions, and begin to compare the value. With questions such as is this decimal greater that 1/2?

Another activity, is to use the 10x10 grid again, but this time, dividing the grid into a fractional part. In the book they used 1/4. 25 squares are colored. Then the student changes the 25 squares into ten strips and 5 squares which represent 2/10 and 5/100, or 25/100.

Chapter 8 deals with geometric thinking and geometric concepts. Much attention is given to the Van Hiele levels which describe how we think and what types of geometric ideas we think. The chapter is logically organized to follow activities through these five levels of thinking.

Teaching Student-Centered Mathmatics grades 3-5

Chapters 1-4

The idea of using problem-based lessons in math intrigued me when I heard about it during a recent math in-service. Giving students the opportunity to investigate, experiment, and constuct their own way of arriving at a solution has to develop a deeper understanding of math concepts.
 
This book gives many ideas to foster flexible as well as reflective thinking in children. I found the activity introduced on page 12,  Learning Through Problem Solving: A Student-Centered Approach,  offered a way of working with multiplication that I had never thought about. The figure on page 18 really made me think when I looked at all the different and inventive ways students could approach a problem solving situation.

Chapter 3, p. 88-96, caused me to rethink the traditional methods of teaching multiplication and division, for example timed tests, which the author feels have little value in the learning of multiplication facts. There are some excellent ideas presented, some that I already use, but taken a step farther. One of these is the use of arrays not only to introduce the concept of multication, but as needed to help understand any unknown facts.