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Chapter five deals with building assessment into instruction. 

Standards-oriented instruction cannot occur without integrated 

assessment and good assessment cannot happen without good 

student-centred teaching. Assessment must be an integral 

component of instruction rather than something that occurs at the 

end of the unit. This chapter, then, is central to the foundational 

ideas of instruction. Assessment issues should be addressed at the 

same time as instructional issues. The purpose of assessment 

should be to monitor students’ progress, make instructional 

decisions, and to evaluate student achievement as well as 

instructional programs. Assessment opens up a dialogue with 

students, helping them see a vision of what excellence is about 

and how they can do better. The teacher’s task is to gather and 

make use of the information that comes from these tasks.

Chapter 6 focuses on Principles and Standards articulates 

the Council's belief that "mathematics can and must be 

learned by all students". Students with special needs 

benefit from others and support, including modeling by 

their classmates. Think aloud is an instructional strategy 

that involves the teacher demonstrating the steps to 

accomplish a task while verbalizing the thinking process 

and reasoning that accompany the steps. This also derives 

from the model in which expert learners share strategies 

with novice learners. Teacher need to learn how to keep 

standards high for the increasingly board diverse 

classroom that they will most certainly face. 

In chapter twenty it focuses in Geometric thinking. 

Geometry can be one of the most fun, exciting, engaging, 

profitable, and enticing areas of the curriculum. It is 

useful to think about geometry objectives in terms of two 

related framework: (1) spatial sense and geometric 

reasoning and (2) the specific geometric content found in 

your state. One aspect of the van Hiele theory that I have 

come to see as important in terms of daily instruction is 

the notion that the product of thought at one level 

becomes the object of thought at the next. The Standards 

authors organized geometry in four content areas which I 

think are quite useful. Therefore, following the discussion 

of the van Hiele theory are four sections containing 

activities for each of the four areas. This organization 

allows your teachers to easily find a content area and 

explore it across the van Hiele levels, or simply look at 

activities for a level of their interest.

Chapter nineteen focuses on the Measurement instruction has at least 

three distinct agendas. The first and most important is to help children 

understand what measurement is and how to go about doing it. This 

includes an understanding of the attribute that is being measured, how 

units are used in measuring, and an understanding of how measuring 

tools work. A second agenda is very much related to the first. It can be 

termed measurement sense; a familiarity of the most commonly used 

standard units, an ability to estimate with commonly used measures, 

and some flexibility with the use of related units. The third agenda is 

different from the first two: the development and use of a few standard 

formulas. Generally in the K-8 curriculum, these are area and volume 

formulas for common shapes. The text suggests an alternative to the 

traditional sequence of teaching time first to the hour, then the half 

hour, and so on. Instead, approximate clock reading for all times on the 

clock can be developed from the outset with a focus on the hour hand. 

The minute hand comes last as a refinement of the hour hand to tell 

more precisely how much after the hour it may be.

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