- Standardized and other formal assessments
(http://www.cmec.ca/pcap/indexe.stm). They are not intended to provide individual feedback to students are
similar in purpose to the NAEP tests administered in the United States.
International comparisons
Along with the increasing globalization has come an interest with international comparisons in educational
achievement and practices and more than 40 countries participate in two major testing initiatives. The Trends in
International Mathematics and Science Study (TIMSS) have assessed students in fourth and eighth grades four
times through 2007. The Programme for International Assessment (PISA) have assessed 15-year-olds in reading,
mathematical and science literacy in more than forty countries on three times since 2000. The items on both series
of tests include multiple choice, short answer and constructed response formats and are translated into more than
30 languages.
Policy makers are often interested in the comparison of average students’ scores across countries. For example,
in eighth grade science on the 2003 TIMMS students from Canada, United States, Hong Kong, and Australia scored
significantly higher than the international average whereas students from Egypt, Indonesia, and the Philippines
scored significantly below the international average (TIMMS 2003). On the mathematics test in the 2003 PISA, 15-
year-old students from Hong Kong, China and Finland scored higher than students from Canada and New Zealand
who in turn scored higher than the students from United States and Spain, who in turn scored higher than the
student from Mexico and Brazil (OECD, 2004).
Both series of tests also collect survey data from students, teachers or school principals allowing for information
about instructional practices and student characteristics. For example, teachers from the Philippines report
spending almost twice as much time teaching science to fourth graders than in the United States (Martin, Mullis,
Gonzalez, & Chrostowski, (2004). Student reports from PISA indicate that there is considerable cross-country
variation in how much students feel anxiety when doing mathematics. Students in France, Italy, Japan, Korea
report feeling the most anxious whereas students in Denmark, Finland and Netherlands and Sweden feel the least
anxious (OECD 2004).
Understanding test results...........................................................................................................................
In order to understand test results from standardized tests it is important to be familiar with a variety of terms
and concepts that are fundamental to “measurement theory”, the academic study of measurement and assessment.
Two major areas in measurement theory, reliability and validity, were discussed in the previous chapter; in this
chapter we focus on concepts and terms associated with test scores.
The basics
Frequency distributions
A frequency distribution is a listing of the number of students who obtained each score on a test. If 31 students
take a test, and the scores range from 11 to 30 then the frequency distribution might look like Table 44. We also
show the same set of scores on a histogram or bar graph inExhibit 20. The horizontal (or x axis) represents the
score on the test and the vertical axis (y axis) represents the number or frequency of students. Plotting a frequency
distribution helps us see what scores are typical and how much variability there are in the scores. We describe more
precise ways of determining typical scores and variability next.