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Math Facts

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Submitted By Dqureshi001
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“Memorizing math facts is the most important step to understanding math. Math facts are the building blocks to all other math concepts and memorizing makes them readily available” (EHow Contributor, 2011). To clarify, a math fact is basic base-10 calculation of single digit numbers. Examples of basic math facts include addition and multiplication problems such as 1 + 1, 4 + 5, 3 x 5 and their opposites, 2 – 1, 9 – 4, 15/5(Marques, 2010 and Yermish, 2011). Typically, these facts are memorized at grade levels deemed appropriate to a student’s readiness – usually second or third grade for addition and subtraction and fourth grade for multiplication and division.
If a child can say the answer to a math fact problem within a couple of seconds, this is considered mastery of the fact (Marques, 2010). Automaticity – the point at which something is automatic- is the goal when referring to math facts. Students are expected to be able to recall facts without spending time thinking about them, counting on their fingers, using manipulatives, etc (Yermish, 2011). .
In order to become a fluent reader, a person must memorize the sounds that letters make and the sounds that those letters make when combined with other letters. Knowing math facts, combinations of numbers, is just as critical to becoming fluent in math. Numbers facts are to math as the alphabet is to reading, without them a person cannot fully succeed. (Yermish, 2011 and Marquez, 2010). A “known” fact is one that is “answered automatically and correctly without counting” (Greenwald, 2011).
In order for a child to achieve academically, the child must master basic facts. A child's progress with problem-solving, algebra and higher-order math concepts is negatively impacted by a lack of fact fluency. As a result, a child's overall self confidence and general academic performance will decline (Groves, 2011).
In the 1990’s, math curriculum reforms were introduced which replaced rote memorization with what is referred to as integrative math teaching. “This involves teaching many different concepts at the same time instead of sequentially, and using manipulatives in place of numbers to illustrate mathematical concepts long after number sense should have been mastered” (Groves, 2011). This switch in theory, caused serious controversy among mathematicians and math educators. If children have not yet mastered basic math facts, how can they be expected to master advanced concepts? Researchers believe that it is just too much too soon for young children (Groves, 2011). Tom Loveless says “Youngsters who have not mastered whole number arithmetic by the end of 4th grade are at risk of later becoming remedial students in mathematics.” Furthermore, he “urges that every student in the nation should receive a thorough grounding in arithmetic” (Loveless, 2011).
The push to master facts by a certain age and prior to moving on to more complex math is most controversial with parents and teachers of gifted students. These students are often thought to be bored by simple, basic math concepts. Although “some of the very highest areas of math do not require automaticity of basic math facts, they do require automaticity of the skills that fall somewhere in between them and single-digit addition, and that those skills are very difficult to master and to automatize when the basic stuff isn't firmly in place” (Yermish, 2011). Is it possible for students to advance without being secure? Math is cumulative, and, as a result, weaknesses in arithmetic will effect the learning of all future math. Most people believe that learning math facts is boring. This is not a reason to skip learning them. This becomes a challenge for teachers. They must find a way to make intrinsically boring material interesting enough that students will see the relevance and show a desire to master it because it is important.

Is Technology the Downfall of Math Education
In their article, "The Arithmetic Gap", Tom Loveless and John Coughlan, state that while math achievement seems to be increasing (according to the National Assessment of Educational Progress – NAEP) computational skills are decreasing. They blame the decline on the introduction of calculators in elementary classrooms. When 4th graders who should be able to add, subtract, multiply and divide single digit numbers (and perhaps even some simple two-digit numbers) mentally choose to rely on a calculator given to them by their teacher, their scores tend to be lower than those who do not. Like others, Coughlan and Loveless go on to blame the math “reform” standards and the curricula introduced by National Council of Teachers of Mathematics (NCTM) in the early 90’s (Loveless and Coughlan, 2004). Critics claim that the reform efforts put little emphasis on learning basic mathematics and algorithms and, instead, encouraged reliance on calculators, student-directed activities and discovery learning processes. In contrast, those who favored the reform efforts claim traditionalists put too much emphasis on rote memorization and algorithms to the detriment of understanding and reasonableness (Loveless, 2011).
In response to the criticism, the NCTM issued new Curriculum Focal Points (CFP’s) which were released in September 2006. The purpose of the CFP’s is to inform teachers about the most important concepts to be taught and learned at each grade level. The CFP’s state that “second graders should be able to quickly recall basic addition and subtraction facts and fourth graders must have quick recall of multiplication and division facts” (www.nctm.org, 2011).
Memorizing math facts is not a new concept. It is something children have been doing for years. Most people can recall countless timed fact sheets, flashcards and various other dittos. However, with all of the new, readily available technology, people often ask why time should be wasted memorizing information. “Math Facts ARE important for children to learn without the aid of electronics. Not only will it help them solve more complex math problems more quickly, but it will expand their number sense as well” (Marquez, 2010). “Number lines, charts, counters, and calculators are great tools to introduce addition, subtraction, and multiplication, but the bottom line is that fluency and knowing the correct answers to math facts is essential! If children do not memorize the math facts, they will always struggle with math” (Greenwald, 2011).
Facts as the Foundation for Higher-Level Math
Math fluency, as recognized by automaticity, is the foundation for future math learnings. “When children have automatic recall of facts, they can quickly retrieve answers from memory without having to rely on counting procedures, such as counting on fingers”(Spear-Swerling, 2006). When children lack automaticity, the time spent laboring over more basic tasks causes “brain drain” and prevents them from moving on. “Knowing their facts prepares children for more difficult math classes, such as algebra and calculus, by allowing them to focus their memory power on learning the more complex skills, instead of struggling through the facts” (Stern, 2010).
When students fail to memorize their facts, “they usually hit the wall some time in middle school or in algebra I, where you have to use these math facts rapidly on the fly”(Yermish, 2011). Calculators are not effective when factoring quadratic equations. How does a calculator help you to determine what two numbers multiply to one number yet add up to another? Automaticity of facts frees up working memory to work higher skills being learned in the current grade/course. “It's like a dyslexic kid who can't keep track of the flow of ideas in a long article because he's spending too much brain power (and hence time) on reading individual words” (Yermish, 2011). Regardless of the amount of time (which is thought to be very little) it takes to use a calculator, those few seconds cause a child to lose track of thought. Though useful, calculators cannot replace the best, most effective tool children have, their brains. Children do not always carry calculators with them, yet knowing how to calculate mentally allows them to answer questions no matter where they are and to determine reasonableness of estimates. Calculators do not make mistakes, but people do when they use them. If a child does not know his/her facts, then he/she will not be able to determine when a calculator use error has been made.
“Skills such as adding and subtracting larger numbers, telling time, counting money, measurement, long multiplication and division are just a few of the concepts that a child will encounter” where automaticity of facts will assist (Marquez, 2010). When a student gets lost in calculations there is little time to learn the processes. Knowing facts allows children to determine number relationships and number sense which helps with estimating skills. Such skills are used on a daily basis. Shopping is one time where these skills come in handy. Knowledge of math facts proves to be a more effective tool than a calculator.
Math Anxiety
The amount of time lost on basic calculations when a child has failed to memorize basic math facts takes away from the time needed to complete tasks. When faced with longer tests and assignments, a child may be unable to complete them due to the lost time. Upper grade courses come with more challenging work and longer tests/tasks. Incomplete work results in lower grades and eventually lower self-esteem. The impact will go beyond just math courses. A loss in self confidence also leads to a loss of interest in courses/school and results in mental blocks (Marquez, 2010).
Math fact memorization causes a tremendous amount of anxiety with elementary sudents. Like the old adage, if you don’t use it you’ll lose it, some believe that learning math facts can be done through something similar to osmosis. They believe that if you use them, you will eventually commit them to memory. This idea is in sharp contrast to skill and drill. However, there is something in between where exposure and drill meet in a way that seems less threatening to a child. When presented in such a manner, children can learn and will enjoy it.
Conclusion
Robert Mahoney poses an interesting question regarding procedural knowledge versus declarative knowledge. He shares a scenario in which someone has a broken down vehicle and is choosing a mechanic. He asks whether the person would choose a mechanic with all of the latest technology at his disposal to diagnose the issue or if they would choose a mechanic with experience who uses technology as a tool, not as the method. Mahoney recommends the experienced mechanic. He refers to calculators as “knowledge at your fingertips” but warns that they do not help with assessing reasonableness. Furthermore, cautions that calculators help to find a possible answer but offer no assistance with learning a concept (Mahoney and Knowles, 2010).
Automaticity of math facts is beneficial to all mathematics learning. Fortunately, there are ways to help students learn basic facts without skill and drill. Explicit strategy instruction is more effective than encouraging strict rote memorization (Woodward, 2006). Yet, many educators are unsure of how to help students master facts. Too many educators still have misconceptions of how students learn facts and how they commit them to long-term memory (Baroody, 1985).
Some people argue that students no longer need to learn how to compute now that calculators are widely available. “While facility at one-digit computation is far from the primary aim of elementary school mathematics, it is an important skill that provides the foundation for many other topics”(Burton and Knifong, 1982).

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