1. Scholars have analyzed the findings of international studies of achievement to try to determine which, if any, aspects
of instruction are associated with national performance levels in math. Identify the major conclusions of these
analyses, and discuss the implications for improving mathematics performance in the United States.
ANSWER: Analyses of the studies suggest that characteristics such as class size, time allocated to
instruction, teachers’ experience or training, and amount of homework generally do not
accountforachievementscores.The“tellandshow”teachingapproachsoprevalent
in the United States and elsewhere also appears not to be correlated with math
performance. It may do little good, therefore, for the United States to try to raise
achievement by altering aspects of these characteristics. However, the analyses
indicate that, unlike in many other countries, the U.S. math curriculum is unfocused,
repetitive,incoherent,andnotverydemanding.Inaddition,itis“highlydifferentiated.”
That is, we tend to sort students into tracks that make higher math available only to
high-achieving students. The most productive route, then, to improving U.S.
performance may be to upgrade mathematics curricula and instruction so that all
students are challenged to perform at a higher level.
DIFFICULTY: Difficult
REFERENCES: 15-2k Achievement Levels of Elementary and Secondary Students
LEARNING OBJECTIVES: FOED.ORNS.17.15.02 – Describe how educational systems differ with respect to the
resources they devote to education, student-teacher and enrollment ratios, teaching
conditions reported by US teachers compared with teachers elsewhere, the extent of
centralization, vocational vs. academic education, enrollment in higher education, size of
the nonpublic sector, and achievement levels among students and young adults.
KEYWORDS: Bloom’s: Analyzing
2. Chapter 15 describes a number of characteristics of Japanese education that may account for the high achievement
levels among Japan’s youth, although we are not yet sure which of these characteristics are of crucial importance.
Which three of the characteristics do you believe are most significant to Japan’s high achievement levels? Describe
the characteristics and explain why you think they are important. Can or should the United States try to copy Japan
with regard to these characteristics? Be sure to give reasons for your position.
ANSWER: Students may identify any three characteristics (intense parental involvement, length of
school year, careful planning and delivery of a national curriculum, large amounts of
homework, less variability in achievement thanks to support for slower students,
emphasis on students’ character and sense of responsibility, educators’ sense of
KEYWORDS: Bloom’s: Analyzing