10 Myths about Math Education,

And Why You Shouldn’t believe


This 2005 article by Karen Budd, Elizabeth Carson, Barry Garelick, David Klein, R. James Milgram, Ralph A. Raimi, Martha Schwartz, Sandra Stotsky, Vern Williams, and W. Stephen Wilson casts aside the often repeated and much revered myths math educators like to claim about constructivist math.   There is no evidence to support any of these myths.  None.


    here to read the entire article.

  • Myth #1: Only what students discover for themselves is truly learned.
  • Myth #2: Children develop a deeper understanding of mathematics and a greater sense of ownership when they are expected to invent and use their own methods for performing the basic arithmetical operations, rather than study, understand and practice the standard algorithms.
  • Myth #3: There are two separate and distinct ways to teach mathematics. The NCTM backed approach deepens conceptual understanding through a problem solving approach. The other teaches only arithmetic skills through drill and kill. Children don’t need to spend long hours practicing and reviewing basic arithmetical operations. It’s the concept that’s important.
  • Myth #4: The math programs based on NCTM standards are better for children with learning disabilities than other approaches.
  • Myth #5: Urban teachers like using math programs based on NCTM standards.
  • Myth #6: Calculator use has been shown to enhance cognitive gains in areas that include number sense, conceptual development, and visualization.
  • Myth #7: The reason other countries do better on international math tests like TIMSS and PISA is that those countries select test takers only from a group of the top performers.
  • Myth #8: Math concepts are best understood and mastered when presented “in context”
  • Myth #9: NCTM math reform reflects the programs and practices in higher performing nations.
  • Myth #10: Research shows NCTM programs are effective.

3 Responses to “10 Myths about Math Education,”

  1. Barry Garelick Says:

    For more information about discovery learning and the appropriate and inappropriate ways to apply it, see my article on the subject at Third Education Group Review:

  2. shana donohue Says:

    What a great set of myths! So you mean it’s actually OK to have kids memorize their multiplication tables? (sarcasm) I am horrified that my 11th graders stumble on “6 times 4”, “3 times 7”. etc. It makes trinomial factoring SUPER fun.

    I invented a tool you may find interesting. My kids also stumble on adding with negatives (“-12 + 5”, for example) and instead of getting into absolute value every time, I invented a ruler that does it for them. My hope is that after a bit they will gain a better sense of how negative numbers work with positves. I hope you check it out…

  3. Richard Phelps Says:

    The web address for Barry Garelick’s article on Discovery Learning in Response no. 1 above has moved. It can now be found here:


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