LHightower

Chapter 9  is about deveoping measurement concepts. Estimation of measurements is something students need to experience. It is also important that students practice using various units, sometimes even creating their own units. Everyday objects can be very helpful in measuring area, i.e. beans, color tiles, pennies. Using these objects can lead into measurement using standard units.

Algebraic reasoning is covered in Chapter 10. Patterns, symbols,  and number relationships are the basis of algebra. Students need to see that algebraic variables are just other ways to represent numbers.

Chapter 5 focuses on basic concepts of fractions:1.You can have fractions of an object or a set. 2.The more fraction parts, the smaller the parts. 3.The denominator of a fraction is a divisor and the numerator tells how many fractional parts you're working with. 4.Equivalent fractions are different ways of looking at the same amount. Many hands-on activities are listed to teach these concepts.

Computation of fractions is the main focus of Chapter 6. It is very important that students do more than just memorize the rules of computation.  They need to truly understand  the operations and what they mean. Many opportunities for "informal exploration" of these operations are described in this chapter.

Chapter 7 stresses "friendly fractions to decimals". Students need to see that decimals are simply another way of writing fracions. Those who have never grasped place value will, of course, have a very difficult time understanding decimals. Base ten blocks can be a valuable tool when teaching decimals. Ordering decimals and computation of decimals are included in this chapter, as well as the teaching of percents.

Geometric concepts are the emphasis of Chapter 8. We need to provide students with many experiences to develop their spatial sense. Transformation of shapes is a concept often ignored. It includes the study of translations, reflections, and rotations. The research of two Dutch educators is introduced in this chapter (the van Hiele levels of geometric thought). There are five levels, which the authors summarize. Geoboards and pattern blocks are essential manipulatives when teaching geometry.

Chapters 1-4 of Teaching Student Centered Mathematics had an overwhelming amount of material.  It stresses a very non-traditional method of teaching math that requires teachers to look at math instruction in a totally new light.  Four basic components  are as follows:1)Children learn constructively. 2)We need to teach math as a means to solve problems, not just to find answers. 3)Lessons need to be carefully planned, not just by following a textbook. 4)Teachers need to constantly assess where their students are.  The book talked about the importance of students interacting with one another as they try to solve problems. Every student has the ability to make sense of math, even though they will do that in different ways and at different rates. 

The second chapter of the book was a collection of activities to teach number sense. Relating multiplication and division to repeated addition and subtraction was one of the big ideas discussed. Other big ideas were place value structure and  characteristics of whole numbers.

Chapter 3 discussed different strategies to help children master their basic facts. Number relationships help students remember facts. To master subtraction facts, children need to "think addition". (Rather thank thinking 13 minus 6, a child should think of addtion facts: what number added to 6 makes 13?)  Children need to understand that all the facts are related.  They should always be thinking about ways to figure out new facts from those they already know. One interesting statement that stood out was that calculators should be out on students' desks every day.  The authors believe that rather than interfering with students learning their facts, use of calculators may actually help them learn basic facts more quickly.

The last chapter in this week's assignment taught strategies for whole number computation. Teachers should not be so adamant that students use traditional algorithms for computation.  Invented strategies are usually understood better by the students who create them. Flexible methods often require a better understanding  of operations.