Operational symbols and notations are often mistaken for numbers in the problem. Geometry may be equally perplexing. Frustration and confusion plague this student. It is exclusively bound to the symbolic representation of ideas. Most of the difficulties seen in mathematics result from underdevelopment of the language of mathematics. Teaching of the linguistic elements of math language is sorely neglected. The syntax, terminology, and the translation from English to math language, and from math language to English must be directly and deliberately taught!
Historically, mathematicians have operated as if math was an exclusive club, whose members speak a secret language. They taught math in a rigid, complicated manner, and were proud of it. Egotistically satisfying their "fewer the better attitude," they happily weeded out underachievers. Every math concept has 3 components. The first is the linguistic, composed of the words the specific terminology , arranged in definite ways to convey meaning the syntax , and the rules of translation from English into math, and from math into English.
The second component is conceptual, or the mathematical idea or mental image that is formed by combining the elements of a class, into the notion of one object or thought. Third, is the procedural skill component of problem solving, which schools focus on almost exclusively. Sharma offers examples of poor math language development: Students are frequently taught the concept of "least common multiple", without sufficient linguistic analysis of the words definitions and how their order or arrangement syntax affects their meaning.
This can be demonstrated by asking students to define the terminology. Several incorrect answers will be generated. This proves that students have memorized the term without understanding it linguistically. Teachers do a great disservice to students by treating math as a collection of recipes, procedures, methods, and formulas to be memorized. The new term must be related or made analogous to a familiar situation in the English language. Students must be taught the relationship to the whole, of each word in the term, just as students of English are taught that a "boy" is a noun that denotes a particular "class.
Adding another adjective, like "handsome," further restricts, narrows, or defines the boy's place in the class of all boys. This can be graphically illustrated: Sharma The language of mathematics has a rigid syntax, easily misinterpreted during translation.
For example, "94 take away 7, " might be written correctly, in the exact stated order, as " Some students are linguistically handicapped by teachers, parents, and textbooks that use "command specific" terminology to solicit certain actions. For example, most children are told with informal language to "multiply, "add, "subtract," and "divide. To eliminate this problem, matter-of-factly interchange the formal and informal terms in regular discourse.
Seek to extend the expressive language set of the student to include as many synonyms as possible. Use at least two terms for every function.
Sharma For example say, "You are to multiply 7 and 3. You are to find the product of 7 and 3. The product of 7 times 3 is The dynamics of language translation must also be directly taught. Two different skills are required. Students are usually taught to translate English expressions into mathematical expressions.
But first they should be taught to translate mathematical language into English expression. Instead of story problems, Sharma advocates giving the child mathematical expressions to be translated into a story in English.
How many more candy bars did I get last Halloween than this Halloween? Now, to facilitate the child's discovery of extraneous information, ask them to add the dates to each Halloween event in the story. The child may respond, "On October 31, , I got 7 big candy bars. But on October 31, , I only got 4.
How many more candy bars did I get in than I got in ? Why not? The child will respond, "Because I just added the dates in there. The number of candy bars did not change. A student can go quite far on either extreme of the continuum.
A quantitative personality can accomplish a lot being strong in mathematical procedures. Qualitative personalities are able to solve a wide range of problems intuitively and holistically. But an excellent mathematician must have command of both learning styles. According to Paiget , , children learn primarily by manipulating objects until the age of If children are not taught math with hands-on methods, between years 1 and12, their ability to acquire math knowledge is disturbed at the point when hands-on explorations were abandoned in favor of abstractions.
This clearly sets them up for mathematical disabilities in the next developmental period of formal propositional operations. The best teaching methods are diagnostic and prescriptive. They take all of the above mentioned factors into consideration. The teacher recognizes that she is teaching to students who span the continuum of quantitative and qualitative learning styles, and supplies plenty of presentation methods and learning activities to stimulate each type of math learning personality.
Without becoming overwhelmed with the prospect of addressing each child's needs individually, the continuum can be easily covered by following the researched and proven method below. After determining that your students have all of pre-requisite skills and levels of cognitive understanding, introduce the new concept in the following sequence:.
Introduce the general principle, truth, or law that other truths hinge on. Let the students use investigations with concrete materials to discover proofs of these truths. Give many specific examples of these truths using the concrete materials. Have students talk about their discoveries about how the concept works.
Then show how these individual experiences can be integrated into a general principle or rule that pertains equally to each example. Reemphasize the general law, rule, principle, or truth that other mathematical truths hinge on. Then show how several specific examples obey the general rule. Have students state the rule and offer specific examples that obey it.
Have students explain the linguistic elements of the concept. Every student with a normal IQ, can learn to communicate mathematically, if taught appropriately. Curricula in the pre-school and early elementary years should focus on the development of the 7 prerequisite math-readiness skills.
Teachers and students need to be aware of, and able to accommodate, the different learning styles or "math learning personalities" and the corresponding teaching methods that address each style. Mathematics must be taught as a mandatory second language. The specific language of mathematics should be deliberately taught each year of the Kindergarten through 12th grade scholastic program, just as reading and English are taught.
It must be communicated to parents, teachers, and students, that competency in the language of mathematics, is just as socially and economically essential as excellent reading and writing skills. Proven programs of prevention, systematic evaluation, identification of learning difficulties, early intervention, and remediation in mathematics must be implemented immediately, to reverse dismal achievement statistics, and secure better educational and economic outcomes for America's students.
The United States government has lofty goals for math achievement. The U. Department of Education's math priority reads: "All students will master challenging mathematics, including the foundations of algebra and geometry, by the end of 8th grade.
But compared to other countries, after 4th grade, American students fall behind because the curricula continues to emphasize fractions, decimals, and whole number operations,.
Progress facilitated by professionals will not be realized until the concerns of math teachers and special educators, converge. Typically, math educators are concerned with how best to teach concepts. Special educators are concerned with communicating the abilities and limitations of students.
Each is working in isolation on the problem of math learning. A change needs to take place. The teacher needs to focus more on the abilities and learning styles of the child, and the special educator needs to focus more on achieving the content of the mathematics curriculum. Government statistics report that math education translates into educational and economic opportunities. Taking tough math courses is more predictive of college attendance than is family background or income.
Winters Technical careers require high levels of math competence. According to the Department. Progress is imminent. The government has teamed up with major mathematics organizations to develop voluntary standards and a framework for the careful preparation of math teachers.
Many organizations, like the Public Broadcast System, businesses-education partnerships, and math and science mentoring programs, are finding creative ways to engage student interest in math, and demonstrate real applications of math in daily life.
Blaine, Worthen R. Sanders, and Jody L. Booth, Wayne, Gregory G. Colomb, and Joseph M. The Craft of Research. Chicago: University of Chicago Press. Progress of Dr.
Ladislav Kosc's Work on Dyscalculia. Funk and Wagnalls. Standard Desk Dictionary. Snyder, Thomas D. Program Analyst, Claire M. Department of Education. Tutor training modules were used to train tutors on how to assist potential tutees in understanding a lesson. The tutors used supplemental online course instruction to assist students in each tutorial session. Research questions were the following: 1. After completing the tutorials, how much did the students feel the tutorial program improved their academic success?
The peer tutoring program increased grades for half of the 25 tutees. Tutees reported their confidence and willingness to ask for help improved. But on October 31, , I only got 4. How many more candy bars did I get in than I got in ? Why not? The child will respond, "Because I just added the dates in there. The number of candy bars did not change. A student can go quite far on either extreme of the continuum.
A quantitative personality can accomplish a lot being strong in mathematical procedures. Qualitative personalities are able to solve a wide range of problems intuitively and holistically. But an excellent mathematician must have command of both learning styles. According to Paiget , , children learn primarily by manipulating objects until the age of If children are not taught math with hands-on methods, between years 1 and12, their ability to acquire math knowledge is disturbed at the point when hands-on explorations were abandoned in favor of abstractions.
This clearly sets them up for mathematical disabilities in the next developmental period of formal propositional operations. The best teaching methods are diagnostic and prescriptive. They take all of the above mentioned factors into consideration. The teacher recognizes that she is teaching to students who span the continuum of quantitative and qualitative learning styles, and supplies plenty of presentation methods and learning activities to stimulate each type of math learning personality.
Without becoming overwhelmed with the prospect of addressing each child's needs individually, the continuum can be easily covered by following the researched and proven method below. After determining that your students have all of pre-requisite skills and levels of cognitive understanding, introduce the new concept in the following sequence:.
Introduce the general principle, truth, or law that other truths hinge on. Let the students use investigations with concrete materials to discover proofs of these truths.
Give many specific examples of these truths using the concrete materials. Have students talk about their discoveries about how the concept works. Then show how these individual experiences can be integrated into a general principle or rule that pertains equally to each example.
Reemphasize the general law, rule, principle, or truth that other mathematical truths hinge on. Then show how several specific examples obey the general rule. Have students state the rule and offer specific examples that obey it. Have students explain the linguistic elements of the concept.
Every student with a normal IQ, can learn to communicate mathematically, if taught appropriately. Curricula in the pre-school and early elementary years should focus on the development of the 7 prerequisite math-readiness skills. Teachers and students need to be aware of, and able to accommodate, the different learning styles or "math learning personalities" and the corresponding teaching methods that address each style.
Mathematics must be taught as a mandatory second language. The specific language of mathematics should be deliberately taught each year of the Kindergarten through 12th grade scholastic program, just as reading and English are taught.
It must be communicated to parents, teachers, and students, that competency in the language of mathematics, is just as socially and economically essential as excellent reading and writing skills. Proven programs of prevention, systematic evaluation, identification of learning difficulties, early intervention, and remediation in mathematics must be implemented immediately, to reverse dismal achievement statistics, and secure better educational and economic outcomes for America's students.
The United States government has lofty goals for math achievement. The U. Department of Education's math priority reads: "All students will master challenging mathematics, including the foundations of algebra and geometry, by the end of 8th grade.
But compared to other countries, after 4th grade, American students fall behind because the curricula continues to emphasize fractions, decimals, and whole number operations,.
Progress facilitated by professionals will not be realized until the concerns of math teachers and special educators, converge. Typically, math educators are concerned with how best to teach concepts. Special educators are concerned with communicating the abilities and limitations of students.
Each is working in isolation on the problem of math learning. A change needs to take place. The teacher needs to focus more on the abilities and learning styles of the child, and the special educator needs to focus more on achieving the content of the mathematics curriculum. Government statistics report that math education translates into educational and economic opportunities. Taking tough math courses is more predictive of college attendance than is family background or income.
Winters Technical careers require high levels of math competence. According to the Department. Progress is imminent. The government has teamed up with major mathematics organizations to develop voluntary standards and a framework for the careful preparation of math teachers.
Many organizations, like the Public Broadcast System, businesses-education partnerships, and math and science mentoring programs, are finding creative ways to engage student interest in math, and demonstrate real applications of math in daily life.
Blaine, Worthen R. Sanders, and Jody L. Booth, Wayne, Gregory G. Colomb, and Joseph M. The Craft of Research. Chicago: University of Chicago Press. Progress of Dr. Ladislav Kosc's Work on Dyscalculia.
Funk and Wagnalls. Standard Desk Dictionary. Snyder, Thomas D. Program Analyst, Claire M. Department of Education. National Center for Education Statistics. Washington, DC. Sharma, Mahesh Educational Methods Unit. Sharma, Mahesh. Tobias, Sheila. Over-coming Math Anxiety. Turabian, Kate Secretary Riley.
Mathematics Equals Opportunity October January 9. Winters, Kirk. ED Initiatives. Washington, D. Search this site. Evaluating Math Special Ed Programs. Sharma Sharma believes that teacher trainers are not bringing all the known aspects of math learning into the teacher preparation curriculum.
Sharma In the end, teachers teach as they were taught. Teachers need to realize that if students are experiencing difficulty, they should ask themselves the following questions: 1. Sharma Recent studies show that student achievement is strongly influenced by teacher levels of expertise.
Sharma For example, most studies show that girls do better than boys in math until the age of Sharma Boys and girls are given ample opportunities to play with blocks, Legos, board games, and various materials requiring fine-motor coordination. CTLM , 53 Even the most "mathematically gifted" individual can be hindered by inadequate math education. CTLM , 6. CTLM , A dyscalculia diagnosis in pre-school age children can be made when a child cannot "perform simple quantitative operations" that should be "routine at his age.
Sharma [1. Sharma Differences in cognitive ability affect the students' ability, facility, and understanding, and point to the difficulties they will have with specific math concepts. Sharma For example, a child with a low level of cognition, is not capable of the higher order thinking required for basic math concepts.
Students will invariably have Sharma An example of an advanced level of cognition, is a student who uses knowledge of multiplication facts to solve a problem using a least common multiple.
Sharma [2. Sharma Quantitative learners, like to deal exclusively with entities that have determinable magnitudes, like length, size, volume, or number. They prefer Sharma , 22 Quantitative students learn math best with a highly structured, continuous linear focus. Sharma Qualitative learners approach math tasks holistically, and intuitively, that is, with a natural understanding that is not the result of conscious attention or reasoning.
Sharma , 22 Qualitative learners dislike the procedural aspects of math, and have difficulty following sequential procedures, or algorithms. Eventually, the qualitative student may show Sharma , 22 Qualitative students learn best with continuous visual-spatial materials. Sharma By the age of 12, the academically neglected child has developed anxiety, insecurity, incompetency, and a strong dislike for mathematics because his experiences with it have been hit or miss.
Sharma [3. Seven Prerequisite Math Skills.
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