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Sunday, October 17, 2010

Teaching and Learning Fraction Concepts and Operations

The Institute of Education Studies (IES), part of the U.S. Department of Education, has recently released a research-based 90-page report titled, "Developing Effective Fractions Instruction for Kindergarten through 8th Grade." The report begins by detailing the poor level of understanding of fraction concepts and skills among U.S. students. For example data from international and national exams have shown that "50% of 8th-graders could not order three fractions from least to greatest...[and] fewer than 30% of 17-year-olds correctly translated 0.029 as 29/1000" (p. 6).

A panel of experts reviewed dozens of studies and identified five (5) recommendations for improving fraction instruction. From page 1 of the document:
  1. Build on students’ informal understanding of sharing and proportionality to develop initial fraction concepts.
  2. Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.
  3. Help students understand why procedures for computations with fractions make sense.
  4. Develop students’ conceptual understanding of strategies for solving ratio, rate, and proportion problems before exposing them to cross-multiplication as a procedure to use to solve such problems.
  5. Professional development programs should place a high priority on improving teachers’ understanding of fractions and of how to teach them.
This list fits well with the approaches I've found successful in my own classroom (previously) and in the experiences of my credential students in their classrooms. Learning to make sense of fraction concepts requires deliberate activities that allow for sense-making to occur.

Some resources to help you design such learning activities are:
Have fun with these! It is always great to see students "get it" when working with fractions.


  1. I failed to appreciate just how poor the comprehension level is on mathematical concepts such as fractions. That result from the IES report is surprising.

    Would you consider linking to my Math Concepts Explained website in your links section? It can be found at I would be happy to link back to your site. I am trying to increase the exposure of my site so that it can be found easier by students. Thanks.

  2. I absolutely adore reading your blog posts, the variety of writing is smashing.This blog as usual was educational.The information valuable and significant in this post.Thanks for sharing.....

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