Wednesday, February 20, 2013

Math Mania

Mathematics - "the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalization" --- Miriam Webster Online Dictionary

Arithmetic - "a branch of mathematics that deals usually with the non negative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them" --- Miriam Webster's Online Dictionary

My brain is on math overload!!  I've been studying "best practices" for math lately and there's a ton of information out there.  Traditional math, new math, reform math, living goes on and on.  Math has become a controversial subject and has brought about much debate triggering the "math wars".   I've been studying the history of math in an attempt to figure out the differences in it as I make curriculum decisions for our family in the upcoming school year.   I plan to do a series of posts regarding my findings and how it relates to various curricula.

Let's start with the history of mathematics....

Traditional Math was the predominant method of mathematics education in the United States in the early-to-mid 20th century in which students were given instruction in standard arithmetic methods (algorithms) to perform a task in a standard sequence  Traditional Math uses step by step procedures for calculations, much of which can be done with computers and technology today.

Topics and methods in traditional math include elementary arithmetic, addition, carry, subtraction, multiplication, multiplication table, division, long division, arithmetic with fractions, lowest common denominator, arithmetic mean, volume, etc.  Critics of traditional math argue that it relies too heavily on rote memorization and repetition failing to promote conceptual understanding. 

New Math came about during the 1960's.  It was a dramatic change in the way mathematics was taught primarily in American grade schools. The name is commonly given to a set of teaching practices introduced in the U.S. shortly after the Sputnik crisis in order to boost science education and mathematical skill so that the intellectual threat of Soviet engineers and highly skilled mathematicians could be met.  New math was based on set theory, which is a branch of mathematics based on sets.  I can't begin to understand the language and aspired concepts of new math, nor do I have the time or energy to study it.  For further interest, you can read more about it here

Reform Math or Standards Based Mathematics came about in the early 1980s, particularly in North America, as educators reacted to the "new math" of the 1960s and 1970s. The work of Piaget and other developmental psychologists shifted the focus of educators from mathematics content to how children best learn mathematics.  It became more about child development rather than step by step memorization.

Reform Math is based on principles explained in 1989 by the National Council of Teachers of Mathematics (NCTM).  The NCTM produced a document attempting to set forth a vision for K-12 mathematics education in the U.S. and Canada.  Their recommendations were adopted by many education agencies, from local to federal levels through the 1990s. The standards were revised in 2000 and these updated standards continue to serve as the basis for many states' mathematics standards, and for many federally funded textbook projects.

Reform mathematics curricula challenges students to make sense of new mathematical ideas through exploration, projects, and real life scenarios.  Although Reform Math has been very controversial.  Some opponents refer to it as "fuzzy math".  Reform texts emphasize written and verbal communication, working in cooperative groups, making connections between concepts, and connections between representations.  Research has shown that children make fewer mistakes with calculations and remember algorithms longer when they understand the concepts underlying the methods they use.

I think there are parts of Reform Math that are beneficial and parts that are a little fuzzy.  I think it depends more on the teacher and how well they understand math and can relay their understanding to the students.  I feel very strongly about students learning their math facts inside and out with whatever method works.  Whether that be through exploration or memorization, math facts are an essential base for all other math concepts.  Maria Miller, author or Math Mammoth, wrote this blog post back in 2006 regarding Reform Math and the importance of balance.

Stay tuned for how this relates to our current math curriculum options.....'s the link for Part 2 and Part 3, as well as some thoughts on math and the Common Core State Standards.


  1. I have to wonder what is different between the methods of today and the generally successful methods of the one room schoolhouse days. Any thoughts? And if those methods are different from what we find effective today is that because our children are blessed with different methods or because our children have been handicapped by the media driven society to have less focus and ability to learn? Weird thoughts, but that's what I'm wondering.

  2. That's an interesting thought Tristan and I have often wondered similar things. You know in our local public school, the math curricula was changed to reform math over 10 years ago and it is still controversial there today. (Though they have started to supplement with traditional math :) Parents always want to know why fix it if it's not broken? The answer I so often heard from school officials was "best practice" and times have changed so drastically because of technology that we can't predict what types of jobs we'll be training our kids for because they don't even exist yet. So in essence, are we preparing them for the unknown?.....that's just weird, isn't it?!? I also had teachers tell me that it wasn't necessary for our children to learn rote math facts because in this day and age everyone has a calculator or carries some sort of electronic device to figure for them. I advised that I didn't have a cell phone, never have, and that I don't carry a calculator in my back pocket when I go to the grocery store. You should have seen the look I

    Don't get me wrong, technology is great when it works, but I personally don't care to be dumbed down to technological dependence.

    I see the benefit of reform math in getting kids to understand the how as well as the why. I just don't care to get wrapped up in fads and trends. My goal in all this research is to find a balanced approach that promotes math proficiency and understanding. I want our kids to be challenged, yet maintain that love of learning. I want the best of both worlds ;-)

    Thanks for sharing your thoughts,