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close this bookImproving Student Achievement in Mathematics (IAE - IBE - UNESCO, 2000, 48 p.)
View the document(introduction...)
View the documentThe International Academy of Education
View the documentPreface
View the documentIntroduction
View the document1. Opportunity to learn
View the document2. Focus on meaning
View the document3. Learning new concepts and skills while solving problems
View the document4. Opportunities for both invention and practice
View the document5. Openness to student solution methods and student interaction
View the document6. Small-group learning
View the document7. Whole-class discussion
View the document8. Number sense
View the document9. Concrete materials
View the document10. Students’ use of calculators
View the documentConclusions
View the documentAdditional resources
View the documentReferences
View the documentThe International Bureau of Education-IBE

1. Opportunity to learn

The extent of the students’ opportunity to learn mathematics content bears directly and decisively on student mathematics achievement.

Research findings

The term ‘opportunity to learn’ (OTL) refers to what is studied or embodied in the tasks that students perform. In mathematics, OTL includes the scope of the mathematics presented, how the mathematics is taught, and the match between students’ entry skills and new material.

The strong relationship between OTL and student performance in mathematics has been documented in many research studies. The concept was studied in the First International Mathematics Study (Hus, where teachers were asked to rate the extent of student exposure to particular mathematical concepts and skills. Strong correlations were found between student OTL scores and mean student achievement scores in mathematics, with high OTL scores associated with high achievement. The link between student mathematics achievement and opportunity to learn was also found in subsequent international studies, such as the Second International Mathematics Study (McKnight et al.) and the Third International Mathematics and Science Study (TIMSS) (Schmidt, McKnight & Raizen).

As might be expected, there is also a positive relationship between total time allocated to mathematics and general mathematics achievement. Suarez et al., in a review of research on instructional time, found strong support for the link between allocated instructional time and student performance. Internationally, Keeves found a significant relationship across Australian states between achievement in mathematics and total curriculum time spent on mathematics.

In spite of these research findings, many students still spend only minimal amounts of time in the mathematics class. For instance, Grouws and Smith, in an analysis of data from the 1996 National Assessment of Educational Progress (NAEP) mathematics study, found that 20% of eighth-grade students had thirty minutes or less for mathematics instruction each day.

Research has also found a strong relationship between mathematics-course taking at the secondary school level and student achievement. Reports from the NAEP in mathematics showed that ‘the number of advanced mathematics courses taken was the most powerful predictor of students’ mathematics performance after adjusting for variations in home background’.

Textbooks are also related to student OTL, because many textbooks do not contain much content that is new to students. The lack of attention to new material and heavy emphasis on review in many textbooks are of particular concern at the elementary school and middle-school levels. Flanders examined several textbook series and found that fewer than 50% of the pages in textbooks for grades two through eight contained any material new to students. In a review of a dozen middle-grade mathematics textbook series, Kulm, Morris and Grier found that most traditional textbook series lack many of the content recommendations made in recent standards documents.

United States data from TIMSS showed important differences in the content taught to students in different mathematics classes or tracks. For example, students in remedial classes, typical eighth-grade classes and pre-algebra classes were exposed to very different mathematics contents, and their achievement levels varied accordingly. The achievement tests used in international studies and in NAEP assessments measure important mathematical outcomes and have commonly provided a broad and representative coverage of mathematics. Moreover, the tests have generally served to measure what even the most able students know and do not know. Consequently, they provide reasonable outcome measures for research that examines the importance of opportunity to learn as a factor in student mathematics achievement.

In the classroom

The findings about the relationship between opportunity to learn and student achievement have important implications for teachers. In particular, it seems prudent to allocate sufficient time for mathematics instruction at every grade level. Short class periods in mathematics, instituted for whatever practical or philosophical reason, should be seriously questioned. Of special concern are the 30-35 minute class periods for mathematics being implemented in some middle schools.

Textbooks that devote major attention to review and that address little new content each year should be avoided, or their use should be heavily supplemented in appropriate ways. Teachers should use textbooks as just one instructional tool among many, rather than feel duty-bound to go through the textbook on a one-section-per-day basis.

Teachers must ensure that students are given the opportunity to learn important content and skills. If students are to compete effectively in a global, technologically oriented society, they must be taught the mathematical skills needed to do so. Thus, if problem solving is essential, explicit attention must be given to it on a regular and sustained basis. If we expect students to develop number sense, it is important to attend to mental computation and estimation as part of the curriculum. If proportional reasoning and deductive reasoning are important, attention must be given to them in the curriculum implemented in the classroom.

It is important to note that opportunity to learn is related to equity issues. Some educational practices differentially affect particular groups of students’ opportunity to learn. For example, a recent American Association of University Women study showed that boys’ and girls’ use of technology is markedly different. Girls take fewer computer science and computer design courses than do boys. Furthermore, boys often use computers to programme and solve problems, whereas girls tend to use the computer primarily as a word processor. This suggests that, as technology is used in the mathematics classroom, teachers must assign tasks and responsibilities to students in such a way that both boys and girls have active learning experiences with the technological tools employed.

OTL is also affected when low-achieving students are tracked into special ‘basic skills’ curricula, oriented towards developing procedural skills, with little opportunity to develop problem solving and higher-order thinking abilities. The impoverished curriculum frequently provided to these students is an especially serious problem because the ideas and concepts frequently untaught or de-emphasized are the very ones needed in everyday life and in the workplace.

References:

American Association of University Women, 1998; Atanda, 1999; Flanders, 1987; Grouws & Smith, in press; Hawkins, Stancavage & Dossey, 1998; Hus 1967; Keeves, 1976, 1994; Kulm, Morris & Grier, 1999; McKnight et al., 1987; Mullis, Jenkins & Johnson, 1994; National Center for Education Statistics, 1996, 1997, 1998; Schmidt, McKnight & Raizen, 1997; Secada, 1992; Suarez et al., 1991.