Measurement and Statistics for Teachers

Malcolm L. Van Blerkom

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781315464756
• Edition: 2
• Topic: Education
• Subtopic: Education General

Measurement and Statistics for Teachers deftly combines descriptive statistics and measurement in the classroom into a student-friendly, practical volume. Based on a course taught by the author for the past 25 years, this book offers to undergraduate education students a clear account of the basic issues in measurement and details best practices for administering performance assessments, interpreting test scores, and evaluating student writing. This second edition includes updated pedagogical features, timely discussions of student assessment, state standards (including NCLB), and an expanded focus that incorporates the needs of Early Childhood, Elementary, and Secondary teachers.

Part I

Measurement

Section I

Basic Issues of Measurement

This book is divided into two parts and five sections. Part I Section I includes four chapters that will introduce you to basic measurement principles. Chapter 1 will introduce you to the various roles that measurement plays in the classroom, to basic terminology, to the difference between formal and informal assessment, to the ways that you can use assessment in the classroom, and finally to the difference between maximal performance and typical performance measures. Chapter 2 will introduce you to various approaches that you can use to interpret test scores, how to choose a particular approach, and finally to the desired characteristics of both criterion-referenced and norm-referenced tests. Chapter 3 will introduce you to the use of standards, goals, and objectives as an approach to help you decide what to teach and what to assess. You will learn about several approaches to how to prepare objectives and how to use them in the classroom. In Chapter 4 you will learn about reliability, both from a theoretical perspective and a practical classroom perspective. In addition, you will learn how to interpret reliabilities and how to make your classroom assessment techniques more reliable. Finally, in Chapter 5 you will be introduced to validity, how you can go about getting evidence of validity, and how reliability and validity are related to one another.

1

Introduction to Measurement

Introduction

In this chapter, we will begin to look at the various ways that we use measurement in the classroom. We will differentiate among the terms assessment, measurement, and evaluation as well as differentiate between formal and informal assessment. We will look at the various roles of assessment including preliminary, diagnostic, formative, and summative assessment. We will also differentiate between maximum and typical performance measures. Finally, we will examine a brief overview of the remaining chapters on measurement.

The Role of Measurement

Measurement plays many different roles in our lives. During the past week, I’ve had to rely on measurement in many different ways. The other day, while at the grocery store, I had to locate a can of diced tomatoes that was 14.5 ounces for a recipe for Spanish rice. Each morning I rely on my alarm clock to wake me at 6:30 AM. I’ve recently watched the price of a gallon of gasoline rise and fall. When a student asked me for a recommendation, I reviewed his performance in my class by checking my grade book, paying special attention to his test scores. These examples represent only a few of the many of ways that I use measurement on a daily basis.

You will also use measurement a great deal in your classrooms. You may give students diagnostic tests to assess how well they are reading, spelling, writing, counting, and so on. You will give tests to assess how well your students have learned and mastered the material that you have been teaching. You’ll use informal assessment on a daily basis to judge how well your lessons are progressing—to find out if your students appear to be comprehending your instruction. You will collect homework to assess if your students are actually able to apply the new skills that they have been learning. As you will see, measurement will play many different roles in your classrooms.

In the five chapters of Part II we will discuss statistics. That discussion is designed primarily to give you sufficient background to be able to examine and comprehend the many measurement concepts that we will be discussing in the remaining 16 chapters. Those statistical concepts that will be most often used in the discussions of measurement include the mean, the standard deviation, the variance, correlation, and z-scores. You will see how we use these and other statistical concepts to build good measurement practices.

Assessment, Measurement, and Evaluation

There are many different terms that describe the processes that we use to judge student performance. The three terms most commonly used are assessment, measurement, and evaluation. Although I will provide you with specific definitions for each term, I must warn you that there is no international law or agreement on how these terms must be used. I have seen many instances where these three terms are freely used interchangeably as if they all meant exactly the same thing. However, I’ll give you specific definitions for each according to the ways that each term is used most frequently in education.

Assessment

The most general term is assessment. Assessment is a very general term that describes the many techniques that we use to measure and judge student behavior and performance. Although in some professional circles the term assessment sometimes means something more specific, in relation to the classroom, it is typically a very general, a very generic term. When in doubt about how to label a technique, the safest label to use would be assessment.

Measurement

Over the years, I have seen many definitions of measurement. However, here is the one that I find the most useful. Measurement is the process of assigning meaningful numbers (or labels) to persons or objects based on the degree to which they possess some characteristic.

Let’s look at some examples and start with how we could take measurements of an object. What are some characteristics of a classroom to which we could assign meaningful numbers or labels? The first thing that we generally think of is the classroom’s dimensions, especially its length and width. A second important characteristic is the classroom’s seating capacity. Some classrooms may be designed to hold 20 students, whereas others could accommodate 35 to 40 students. This becomes important when we are assigning classes to certain rooms. Still another characteristic that I find important is board space. I tend to use the board a great deal, especially in some classes, and want classrooms with plenty of board space (perhaps measured in square feet). What about the room number? For example, let’s say that we are in room 231. Is the room number a form of measurement? It may be! The room number is frequently used as a substitute for a name and can be considered measurement at the nominal (naming) level (see Part II Chapter 18). If room numbers are assigned to rooms randomly and don’t assist a stranger in finding the room, then I would argue that in that case the room number was not a form of measurement. In that case the room number was not very meaningful. However, if room numbers are assigned in some logical order (as they are in most buildings) and they assist a stranger in finding the room, then I would argue that they are measurement, if only at its least sophisticated level. In this case the room number has some meaning and tells you something about the classroom—where it is located.

For another example, let’s use a student. What are some characteristics of a student that can be described with meaningful numbers or labels? Of course, many of the student’s various physical characteristics such as height, weight, and age can all be described with meaningful numbers. Even describing other characteristics such as gender are frequently considered meaningful at the nominal level. Other characteristics to which we can ascribe meaningful numbers would include the student’s score on the last social studies quiz, the student’s score on an I.Q. test, or her score on the standardized math achievement test. There are many student characteristics that we can measure in a meaningful way.

Measurement is primarily a mechanical process. When we score a test, count up the number of points that the student earned, and record that number, we are using measurement.

Evaluation

The third term is evaluation. Evaluation involves the use of measurement to make decisions about or to determine the worth of a person or object. Evaluation is frequently the step that follows measurement. Let’s say that Dana earned 87 on a 100-point science test. When we scored Dana’s test and determined that she earned 87 out of 100 points we were using measurement. It was a mechanical process. If we then decide that Dana’s test score of 87 translates to a letter grade of B, we are now using evaluation. Deciding on a grade was dependent on a judgment of worth. A letter grade is typically a statement of worth—A is excellent, B is good, C is average, and so on. So, scoring a test is measurement, but assigning a grade is evaluation.

Evaluation comes in many forms. One obvious form is the use of letter grades. However, we sometimes run courses on a pass/fail basis. If your mean test score is 75% or higher, you pass. If it is below 75% you fail. At other times, teachers may prepare a narrative statement concerning how well the student is performing and use terms like “making satisfactory progress,” or “still needs more work in this area.” These are also forms of evaluation.

Definitions

Assessment is a very general term that describes the many techniques that we use to measure and judge student behavior and performance.

Measurement is the process of assigning meaningful numbers (or labels) to persons or objects based on the degree to which they possess some characteristic.

Evaluation involves the use of measurement to make decisions about or to determine the worth of a person or object.

There are several measurement issues that would be helpful to address in this chapter. First, we will differentiate between formal and informal assessment. Then we will look at the various ways that we use assessment in the classroom. Finally, we will differentiate between maximum and typical performance measures.

Formal vs. Informal Assessment

Generally, when you think about assessment in the classroom, I would guess that tests and quizzes are probably the first things that come to mind. Tests, both standardized and teacher-made; quizzes; and other similar devices are referred to as formal assessment devices. With formal assessment, you, the teacher, are able to complete the assessment in a relatively standardized manner and are able to control many aspects of the process. With formal assessment, all students are given the same questions to answer, typically have exactly the same amount of time to respond, and complete the device in a relatively consistent fashion. Formal assessment is important in the classroom; however, it is not the only type of assessment that we use.

A much more common type of assessment is what we refer to as informal assessment. It involves the many observations that we make about students and the many questions that we ask students throughout the day. It may involve having a young student read aloud and attempting to note and remember which reading processes are still giving...

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Contents
• Preface
• Acknowledgments
• Part I Measurement
• Part II Descriptive Statistics
• Appendix
• References
• Index