"Bear in mind that the wonderful things you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labor in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honor it, add to it, and one day faithfully hand it to your children. Thus do we mortals achieve immortality in the permanent things which we create in common." - Albert Einstein

Thursday, December 12, 2013

How A Young Child Understands Numbers Is Key to Success in Math

Renovating a basement can be challenging especially without the help of an architect or a room designer. Take, for example, a wall for a future wet bar. The overall width of the wall matters needs to match the desired wall cabinets. One possible configuration is shown below in which a wine shelf is sandwiched between two cabinets.

If the wall is 48 inches wide, this dictates what the sum of the widths of the two side cabinets plus the width of the wine rack should be. If the wine rack is y inches wide, then the width of the side cabinets, defined as x inches, must obey the following equation:

48 = 2x + y

Thus, a wine rack that is 24 inches wide requires side cabinets that are 12 inches wide. On the other hand, if the wine shelf is only 18 inches wide then each cabinet can take 15 inches from the wall space. Some may say that this is algebra. But without doubt, being able to do this is a good sign of being functionally numerate (a condition in math analogous to reading's functionally literate). With the recent Program for International Student Assessment (PISA) results suggesting that math instruction is not working as well as it should be in the United States, it is only natural to hear numerous opinions on what has gone wrong and what needs to be done. It is during these times that one must remain focused on evidence since opinions can easily sound attractive, but in reality, are really void of substance.

One important correlation that is obvious in the most recent PISA test is between the math scores and early childhood education. This does not mean however that preschoolers should be taught elementary mathematics. In order to perhaps understand the connection, one may look at what adults who are successful in math knew before they entered kindergarten. This requires a good longitudinal study that involves decades. One recent study makes the reasonable assumption that the mathematical skills and knowledge at the end of elementary school may already predict math proficiency in the adult years. This then requires less years for a longitudinal study to be completed, six to seven years. The study, published in PLOS ONE, is entitled "Adolescents’ Functional Numeracy Is Predicted by Their School Entry Number System Knowledge". The title provides the major finding of the study: What children in kindergarten know about numbers affects how they perform in math in their teenage years. Here, it is important to take note of what number system knowledge means so that it is clear what children need before starting formal schooling. The number system knowledge found to correlate with later performance in math consists of the following:
  • understanding of the relative magnitude of numerals
  • the ordering of these numbers
  • the ability to combine and decompose them into smaller and larger numerals
  • to use this knowledge to solve arithmetic problems
With regard to preschool, the first two are probably most relevant. The last two are usually addressed in kindergarten and first grade. The first two, having a sense of what numbers mean, can easily be integrated into play. The study notes as well that the reason why number knowledge correlates with math achievement at the end of sixth grade is its strong correlation with functional numeracy. Last but not least, the study also finds:
...growth in number system knowledge is less important for predicting functional numeracy than is school entry number system knowledge. Children scoring in the bottom quartile on the numeracy measure in seventh grade started school behind their peers in number system knowledge and showed less rapid growth from first to second grade, but typical growth thereafter....
The above is significant. It points to where the problem begins. Furthermore, it tells us exactly where it needs to be addressed. The authors conclude:
...the implication is that interventions to improve children’s early understanding of the relations among numerals need to be implemented before the start of schooling or in first grade....
This helps explain why countries with high quality preschool education does better in PISA....

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