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Opportunity to Learn (OTL)

One of the fundamental concepts in the ME.ET study is opportunity to learn. Our main question is about understanding what students seeking elementary certification are offered in their undergraduate mathematics classes. Of course, the study has focused more narrowly, concentrating on the first mathematics class these students are required to take, across eighty institutions in three states.

Within this sample, we are investigating opportunity to learn in three ways:

  • What is offered in the textbook that is used in each class and what parts of the textbook are used (e.g., what chapters are "covered")?
  • What does the instructor report he or she taught and how is time in the class allocated across selected topics? What are the instructor's cognitive goals for the students?
  • What do applicable local, state and national policies suggest are appropriate goals for these students, and what do those goals indicate normatively about opportunity to learn? These policies include high stakes tests required for teacher certification, which offer a concrete example of what students are expected to learn.

OTL has a history as a construct in research on mathematics education, having been used to understand and account for differences in achievement on international assessments of K-12 students (see references below). The idea has been that, to understand test scores across different populations, it is important to know what the curriculum offers. OTL measures have become increasingly sophisticated over time, starting as a simple yes/no dichotomy (Did the student study this topic?) and moving to a continuum that considers not only whether the topic is taught but also for how long and in what depth a student engages with the topic (engaged time). Some work on OTL has attempted to estimate how long it takes a student of a given age to learn a specific topic. This would yield a complete "equation" for opportunity to learn.

OTL = (Engaged Time) / (Time needed to learn)

In our study, we use a simpler version of OTL, investigating through the instructor survey how much time is spent on a topic and what the instructor's goals are for that topic. Combined with textbook analyses, and a report fromt he instructor about what parts of the textbook are used, we expect to be able to look at similarities and differences across the classes in the study and perhaps gain a better understanding of the mathematical education of prospective elementary teachers.


Floden, R. E. (2002). The measurement of opportunity to learn. In Board on International Comparative Studies in Education, A. C. Porter & A. Gamoran (Eds.), Methodological advances in cross-national surveys of educational achievement . Washington, DC: National Academy Press.

McDonnell, L. M. (1995). Opportunity to learn as a research concept and a policy instrument. Educational Evaluation and Policy Analysis, 17 (3), 305-322.

Porter, A. (1995). The uses and misuses of opportunity-to-learn standards. Research News and Comment, January-February , 21-27.

Wang, J. (1998). Opportunity to learn: The impacts and policy implications. Hierarchical linear model of analysis. Educational Evaluation & Policy Analysis, 20 (3), 137-156.

This material is based upon work supported by the National Science Foundation under Grant No. 0447611, with additional support from the College of Education at Michigan State University and the Center for Proficiency in Teaching Mathematics (CPTM) at the University of Michigan

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