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Previously Asked Question

What are some best practices in teaching number sense to elementary school students?

The Center’s website (www.centerforcsri.org) includes a link to our School Reform and Improvement Database with over 5,000 articles available. A search of your topic in our research database turned up the following document:
  • Adding It Up: Helping Children Learn Mathematics, 2001; The Strands of Mathematical Proficiency (Chapter 4)

    This chapter of Adding It Up, developed by the National Research Council’s Mathematics Learning Study Council, examines a framework of five strands or components for mathematical learning. The authors emphasize that the components are interwoven and interdependent in the development of mathematical proficiency. The five components are conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. The authors use National Assessment of Educational Progress (NAEP) data from 1973 to 1999 to analyze the mathematical proficiency of American students based on their framework.
    http://books.nap.edu/openbook.php?record_id=9822&page=115

This past fall, The Center produced a webcast on the topics of fractions. Some general strategies for mathematics instruction were discussed. This webcast can be accessed through The Center’s website at http://www.centerforcsri.org/webcasts/fractions/.

The U.S. Department of Education produced a report on the national Mathematics Advisory Panel in summer 2008. The Report included number sense as an important building block for learning higher mathematics.  brief summary of what The Report found regarding number sense is below:
  • U.S. Department of Education. (2008) The Final Report of the National mathematics Advisory Panel. Washington, DC. Available at http://www.ed.gov/MathPanel.

    The report defined number sense as entailing “an ability to immediately identify the numerical value associated with small quantities, a facility with basic counting skills, and a proficiency in approximating the magnitudes of small number of objects and simple numerical operations.” The report elaborated by defining a more advanced type of number sense as “a principled understanding of place value, of how whole numbers can be composed and decomposed, and of the meaning of the basic arithmetic operations of addition, subtraction, multiplication and division. It also requires understanding the commutative, associative and distributive properties and knowing how to apply these principles to solve problems."

The National Council of Teachers of Mathematics (NCTM) provides numerous resources and links to help school teachers and administrators with the latest research and math strategies. A search for developing number sense in students through the NCTM site turned up a variety of articles and resources. Listed below are a few of those resources:
  • In the article with link below, Developing Number Sense Through Mathematical Diary Writing, author Der-Ching Yang provided insights into the teaching of mathematics in Taiwan through his use of mathematical diaries as a strategy for developing number sense. The strategies are relevant to classrooms in the U.S.
    http://www.thefreelibrary.com/Developing+number+sense+through+mathematical+diary+writing:+Der-Ching...-a0164525592
  • The NCTM link below offers video clips to illustrate the range of understanding of numbers and their relationships for students in the early elementary grades. The video clips covered topics such as place value and number representations, grouping and the value of 10, and place value.
    http://illuminations.nctm.org/Reflections_preK-2.html
  • Bay, J. M. (2001). Developing number sense on the number line. Mathematics Teaching in the Middle School, 6(8).

    The author described the transformation she saw in her lessons and her students when she took a boring math problem off the pages of the worksheet and brought them to life with a brightly colored rope used as a number line. The activity she described can be used for any grade level. The author saw improvement in her students’ conceptual understanding and their enjoyment of the life-sized number line. This visual representation of a number line can be used to teach and understanding of small whole number sense for early elementary grades, large number sense for upper elementary, fractions and negative integers for upper elementary and middle school. As a visual tool, the life-sized number line was described as an “excellent visual tool” for comparing relative sizes of numbers and an effective linear-measurement model for looking at fractional amounts. There was little preparation involved and the class discussion generated was rich. The author found real gains in the students’ number sense. The author also suggested using it for a whole lesson or a warm-up exercise.
  • Schneider, S. & Thompson, C. S. (2000). Incredible equations develop incredible number sense. Teaching Children Mathematics, 7(3).

    The authors defined number sense as having a good understanding of number meanings and numerical relationships. When a student’s thinking about numbers is flexible they are able to think of a number in many different ways. For example, the number 13 can be 1 ten and 3 ones, 13 ones, 3 fours and 1 more, or as two nickels and three pennies. Furthermore, the student with good number sense knows how 13 compares in size with other numbers and the effects of operating on the number 13. The authors developed the number sense of their students further through the use of the Incredible Equations activity. Through provision of plenty of manipulatives and also a risk-free environment, students were able to create long equations and share them with the class. When students became stuck on any part of an equation, the teachers used it as a teachable moment and allowed students to make even more mathematical connections further promoting flexibility in their number sense. Students also had the opportunity to learn from each other. Some sample equations created by the students were:
    • 7500 – 7400 – 99 + 4 + 6 = 11
    • 8 x 8 – 65 + 11 + ½ + 7 - ½ + 5 = 22

A search of your topic on other search engines turned up the following article:
  • Carboni, L. W. (n.d.) Number sense every day. Retrieved on October 10, 2008, from http://www.learnnc.org/lp/pages/783

    Lisa Carboni of the University of North Carolina’s School of Education defined number sense as an intuitive feel for numbers and their relationships which develops when children solve problems for themselves. She went on to further specify that number sense includes the “meaning of a number, ways of representing numbers, relationships among numbers, the relative magnitude of numbers and skill in working with them”.

    Carboni refered to Trafton and Thiessen’s book Learning Through Problems: Number Sense and Computational Strategies. These authors described strategies commonly used by elementary age students to solve math problems. By listening to other students use these strategies and employing them themselves, children will become more comfortable and confident in their ability to work with numbers. These strategies plus others that Carboni herself listed include:
    • Partitioning numbers using tens and ones
    • Counting on or back from a number
    • Using “nice numbers”
    • Translating to a new problem
    • Graphic representations
    • Daily routines
    • Games

    The link to the site includes examples of ideas and activities you may find useful. Carboni concluded by emphasizing that number sense is not a set of distinct skills to be taught as a separate unit. Rather, it should be a part of children’s every day math lessons. This will foster better problem-solving skills.