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Math research reveals early-learning needs

Basic arithmetic and focus on numbers is crucial to student success

Researchers identified key variables for success in elementary math and beyond.

Numbers, counting, and low-level arithmetic are three basic competencies that are vital to later success in math, and students should have these key math skills in first grade in order to be successful in math in fifth grade, according to a long-term study released by psychologists at the University of Missouri (UM).

“Math is critical for success in many fields, and the United States is not doing a great job of teaching math,” David Geary, UM’s Curator’s Professor of Psychological Sciences, who led the research team, said in a statement. “In order to improve basic instruction, we have to know what to instruct.”

Researchers monitored 177 elementary students from 12 different elementary schools from kindergarten to fifth grade, and intend to continue monitoring them through high school. Students who understood the number line and some basic math facts in the beginning of first grade showed faster growth in math skills over the next five years.

“It is important that children understand the meaning of Arabic numerals, that is, the quantities they represent and be able to quickly translate quantities into numerals and numerals into quantities. [The study] also highlights the importance of knowing basic facts and the number line,” Geary said.

Teachers and parents can incorporate the results of this study into their math instruction to build long-term math skills and success in math.

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Comments:

  1. perumula

    July 26, 2011 at 8:25 pm

    I suggest that everyone reading this article also watch and listen to Salman Khan’s Google Author’s presentation: http://www.youtube.com/watch?v=PhO2gshIVuE He makes a powerful case for online learning and watching the nitty-gritty than can hold kids back until they get over a hump.

  2. perumula

    July 26, 2011 at 8:25 pm

    I suggest that everyone reading this article also watch and listen to Salman Khan’s Google Author’s presentation: http://www.youtube.com/watch?v=PhO2gshIVuE He makes a powerful case for online learning and watching the nitty-gritty than can hold kids back until they get over a hump.

  3. mikegold600

    July 27, 2011 at 5:02 pm

    I’m afraid that there are way too many unexamined assumptions informing this research for its results to lead to the conclusions that Professor Geary wishes everyone to make. For one thing, he assumes that the key place to start is with numbers and counting. However, there is a very successful early elementary mathematics curriculum developed by Elkonnin and Davydov in the Soviet Union, versions of which are still used in Russia today, which grounds mathematics not in counting but in measurement and comparison, something that does NOT require that very young students come to school with a mastery of counting or that they be drilled in counting, the number line, etc., from day one in school. Indeed, the late John van de Walle, one of this country’s leading experts on K-8 mathematics methods, warned repeatedly of the dangers associated with the premature use of the number line to model mathematical ideas.

    I am increasingly suspicious of the motives behind Professor Geary’s research and the “obvious” implications of his results. Like many people with a dog in the fight when it comes to the “best” way to teach mathematics to children, Professor Geary seems to have had a conclusion in mind before he posed his question, and unsurprisingly, he conducted his inquiries with the assumption that the outcome he wanted was in fact “The Truth.” Such research borders on propaganda more than scientific inquiry. It is unsurprising given the US approach to teaching mathematics in the upper grades that kids who are less facile with counting would fare less well in school mathematics. That hardly demonstrates that kids who are less facile in counting when they start school are in fact less well-prepared or less able to learn mathematics.

  4. mikegold600

    July 27, 2011 at 5:02 pm

    I’m afraid that there are way too many unexamined assumptions informing this research for its results to lead to the conclusions that Professor Geary wishes everyone to make. For one thing, he assumes that the key place to start is with numbers and counting. However, there is a very successful early elementary mathematics curriculum developed by Elkonnin and Davydov in the Soviet Union, versions of which are still used in Russia today, which grounds mathematics not in counting but in measurement and comparison, something that does NOT require that very young students come to school with a mastery of counting or that they be drilled in counting, the number line, etc., from day one in school. Indeed, the late John van de Walle, one of this country’s leading experts on K-8 mathematics methods, warned repeatedly of the dangers associated with the premature use of the number line to model mathematical ideas.

    I am increasingly suspicious of the motives behind Professor Geary’s research and the “obvious” implications of his results. Like many people with a dog in the fight when it comes to the “best” way to teach mathematics to children, Professor Geary seems to have had a conclusion in mind before he posed his question, and unsurprisingly, he conducted his inquiries with the assumption that the outcome he wanted was in fact “The Truth.” Such research borders on propaganda more than scientific inquiry. It is unsurprising given the US approach to teaching mathematics in the upper grades that kids who are less facile with counting would fare less well in school mathematics. That hardly demonstrates that kids who are less facile in counting when they start school are in fact less well-prepared or less able to learn mathematics.

  5. mikegold600

    July 27, 2011 at 5:09 pm

    @perumula: I’m curious as to why comments on the video you link to have been disabled. Fear of uncomfortable questions? I always find it troubling when a site won’t allow comments, particularly when there is money and politics involved. Khan has money from Gates, Google, Microsoft (double dipping?), etc. Not that he’s a bad guy (or a good one), but why are the money people lining up behind this, I can’t help but wondering.

    The introduction of Khan as the Linus Torvald (sp.?) of education is just a little bit nauseating.

  6. mikegold600

    July 27, 2011 at 5:09 pm

    @perumula: I’m curious as to why comments on the video you link to have been disabled. Fear of uncomfortable questions? I always find it troubling when a site won’t allow comments, particularly when there is money and politics involved. Khan has money from Gates, Google, Microsoft (double dipping?), etc. Not that he’s a bad guy (or a good one), but why are the money people lining up behind this, I can’t help but wondering.

    The introduction of Khan as the Linus Torvald (sp.?) of education is just a little bit nauseating.

  7. edukare

    July 27, 2011 at 5:52 pm

    I am glad to know that research is being done to support what I learned in teaching elementary students for 32 years.
    The foundations in math are as important to future success as the foundations in reading. I always have felt that basic numeration concepts, such as knowledge of numbers, counting and arithmetic were prerequisite skills for later work in math. Without those foundational skills, kids just don’t do well and begin to either hate math or be afraid of it.

  8. edukare

    July 27, 2011 at 5:52 pm

    I am glad to know that research is being done to support what I learned in teaching elementary students for 32 years.
    The foundations in math are as important to future success as the foundations in reading. I always have felt that basic numeration concepts, such as knowledge of numbers, counting and arithmetic were prerequisite skills for later work in math. Without those foundational skills, kids just don’t do well and begin to either hate math or be afraid of it.

  9. kaybutler

    July 31, 2011 at 11:46 pm

    I have told many of my students and their parents, “If you think you are ‘not good in math,’ it’s probably because you did learn or understand some of the basics.” How can students “estimate” in high school if they are not good at the basic facts needed for mental math (addition, subtraction, multiplication, division)? If students did not have enough experiences to understand fractions and why the “‘rules’ for fractions” work, they will have difficulty with rational expressions and functions in Algebra. For each secondary topic taught, there are usually mutliple basic understandings needed for mastery. So, if students don’t master the basics, they will struggle with mathematics for years to come! I try to identify holes and fill them in whenever possible, but with 25-40 students in a class, it’s difficult to meet all of the individual needs of my students since their experiences are so varied. However, I continue to try to bring them from where they are individually to where they need to be collectively! :)

  10. kaybutler

    July 31, 2011 at 11:46 pm

    I have told many of my students and their parents, “If you think you are ‘not good in math,’ it’s probably because you did learn or understand some of the basics.” How can students “estimate” in high school if they are not good at the basic facts needed for mental math (addition, subtraction, multiplication, division)? If students did not have enough experiences to understand fractions and why the “‘rules’ for fractions” work, they will have difficulty with rational expressions and functions in Algebra. For each secondary topic taught, there are usually mutliple basic understandings needed for mastery. So, if students don’t master the basics, they will struggle with mathematics for years to come! I try to identify holes and fill them in whenever possible, but with 25-40 students in a class, it’s difficult to meet all of the individual needs of my students since their experiences are so varied. However, I continue to try to bring them from where they are individually to where they need to be collectively! :)

  11. kathydunn

    August 10, 2011 at 10:58 pm

    Just look at the teaching of math as the teaching of history since cave man days. One of my favorite cartoons is a cave man outside of his cave and counting on his fingers while saying “One, two, many!”

    My 4th graders loved caveman math as we progressed from learning/reviewing numbers to long division during 4th grade. I firmly believe that teaching any subject is first of all salesmanship followed by the sharing the relevance of the subject so the students understand why it is important whether the subject be math, science, reading, or sociology. By the way, long division is only about 500+/- years old so we have come a long way since caveman days.