Feb 09, · As state testing regimes were first being implemented, they noted that because prior student academic achievement and students’ social class are still the strongest predictors of how well a given school will do on academic achievement measures, “focusing state policy on student performance might simply concentrate high-achieving students in Academic and Financial Aid Warning, and Academic and Financial Aid Probation statuses provide an opportunity for students to improve academic performance and meet overall requirements for degree completion. Students placed on one of these statuses should meet with their Academic Advisor to discuss course scheduling and to plan for remediation California State University, Long Beach (CSULB, Long Beach State, Cal State Long Beach, LBSU, or Beach) is a public university in Long Beach, blogger.com acre campus is the second largest of the school California State University system (CSU) and one of the largest universities in the state of California by enrollment, its student body numbering 39, for the
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Author: Rotigel, J. Today, as usual, Mrs. Johnson began her 3rd-grade math class by reading aloud a thinking puzzle: Charlie, the dog, was tied to a 2-meter rope. His favorite ball was lying in the grass at least 10 yards away from him. He managed to grasp the ball easily. How did he manage dissertation and connecticut academic performance and students achievement do this?
While his classmates were pondering the problem, Nathan had already formulated the answer. Surprising even Mrs. Johnson, Nathan immediately found the lateral dissertation and connecticut academic performance and students achievement puzzle required little effort and absolutely no math, dissertation and connecticut academic performance and students achievement.
While other students were converting meters to yards, moving decimal points, and drawing pictures, Nathan realized that the other end of the rope was not attached to anything; the dog merely had a 2-meter rope tied to his collar, but was not tethered at all. Nevertheless, most teachers have had similar experiences with children who are talented in mathematics and strong in logical reasoning.
Unfortunately, many programs for gifted children are inadequate and poorly designed Heid,leaving classroom teachers to struggle to meet the needs of gifted children effectively. What resources are available for these students? What assessment tools are appropriate? Do these children need acceleration or enrichment? This article will address these and other questions in an attempt to shed some light on the difficult issues of challenging and nurturing children who demonstrate talent in the field of mathematics.
Whether math problems require computation skills, problem-solving strategies, inferential thinking skills, or deductive reasoning, mathematically talented students are often able to discern answers with unusual speed and accuracy. Mathematically gifted students are able to see relationships among dissertation and connecticut academic performance and students achievement, concepts, and ideas without the intervention of formal instruction specifically geared to that particular content Heid, Due to their intuitive understanding of mathematical function and processes, dissertation and connecticut academic performance and students achievement, they may skip over steps and be unable to explain how they arrived at the correct answer to a problem Greenes, For example, Mariah, an energetic, 6th-grade prealgebra student, often seems disinterested during her hourlong math class, as she doodles and appears to be preoccupied.
After all, she can solve these linear algebraic equations in just one step. Mariah views practicing step-by-step processes as a waste of time when solutions can be found by just looking at the problem. Students who are talented in mathematics often demonstrate an uneven pattern of mathematical understanding and development, since some are much stronger in concept development than they are in computation Rotigel, ; Sheffield, Since these children often prefer to learn all they can about a particular mathematical idea before leaving it for new concepts, a more expansive approach to mathematics based upon student interest may avoid the frustration that occurs when the regular classroom schedule demands that it is time to move on to another topic.
A more linear approach to mathematics is often a better dissertation and connecticut academic performance and students achievement for gifted children instead of the spiral curricula often found in textbook series and followed by classroom teachers. For example, when the topic of decimals is introduced, children with mathematical talent can be allowed to delve much further into the topic, learning practical applications for decimals and the connections between decimals and other mathematical topics.
Bailey, a mathematically precocious 5-year-old, dissertation and connecticut academic performance and students achievement, understands that numbers have patterns and relationships to real life. While watching a series of movie previews at the local theater, she can skillfully decide which new releases will occur before or after she turns 6 simply by noting their release dates in the upcoming year.
Parents of preschoolers may report that their child demonstrates an unusual interest in mathematical concepts and particularly enjoys games involving numbers.
At an early age, some gifted students note relationships between products and prices in the grocery store, the passage of time, changes in weather temperatures, and measurements of distances. By the time these emergent mathematical geniuses arrive for their first formal math lessons in kindergarten, they may have already established their own unique theories of number sense, sequences and patterns, problem solving, and computational strategies.
Formal instruction in elementary school classrooms often lacks challenge for the gifted learner dissertation and connecticut academic performance and students achievement courses in regular classrooms sometimes have a relatively narrow range of topics, minimal investigation of concepts, repeated drill and practice, and yearly repetition.
The basic mathematical concepts that are presented in kindergarten and 1st grade can be a particular problem for children who have already mastered number recognition, one-to-one correspondence, and counting. Students gifted in mathematical thinking and problem solving need greater depth and breadth of topics and openended opportunities for solving more complex problems Sheffield, Misunderstandings regarding the nature of giftedness and talent abound, and busy teachers and administrators are sometimes at a loss to know how to nurture and challenge children whose abilities belie their age-based grade-level placement.
However, according to the Principles and Standards for School Mathematics National Council of Teachers of Mathematics,p. All too often, the regular curriculum is insufficient in depth, breadth, and pace to meet the needs of the gifted child Wolfle, Most educational settings do not adequately address and meet the needs of gifted students, and most teachers make only a few minor modifications to the curriculum when attempting to teach them Archambault et al.
Planning for 12 years of mathematics instruction for all students has sent many administrators and district curriculum specialists scrambling for the latest research on best practices, dissertation and connecticut academic performance and students achievement, and the notion of meeting the needs of mathematically advanced students adds complexity to the task.
The dilemma of choosing between acceleration to an advanced math class placement and providing planned enrichment activities within the regular classroom setting plagues math coordinators, curriculum specialists, superintendents, and parents. According to the Principles and Standards for School Mathematics NCTM,p.
Grade-level achievement test results can be somewhat helpful, for if a student scores extremely well, it may indicate that mathematics is an area of strength for him or her. If a child scores at or above the 95th percentile on a grade-level achievement test, it is possible that the test did not have enough items of appropriate difficulty for the child, thus the score may not indicate his or her true level of understanding.
In this case, dissertation and connecticut academic performance and students achievement, it may be necessary to administer an above-level test that will contain more items of higher difficulty. The EXPLORE American College Testing Program, was developed for 8th-grade students and therefore contains a sufficient number of higher level items to allow students to demonstrate their proficiency more fully. According to ACT, the EXPLORE is directly related to student educational progress and includes a large number of complex problem-solving items and fewer measures of narrow skills.
Many of the regional talent searches around the country offer EXPLORE testing in mathematics, as well as other subject areas. No evaluation should be based simply on standardized testing, however, dissertation and connecticut academic performance and students achievement.
Teacher observations, classroom-based assessment, daily performance, and social and emotional needs must be included in the evaluation. It is important that data be gathered and analyzed by a multidisciplinary team of educators who are able to make and carry out educational recommendations for the student. An investigation of repeated topics, overlapping concepts, and ineffective activities could identify weaknesses in the math program.
For example, dissertation and connecticut academic performance and students achievement, ratios and proportions could be coupled with simple fractional portions of sets.
Some measurement or temperature concepts could be integrated into other curricular areas like science, thus allowing for more enrichment lessons in visual logic, inferential thinking, and deductive reasoning. According to VanTassel-Baska befficient use of time is an important consideration in the development of talent.
Once a sufficient foundation of information is gathered, an individualized plan can be established for each mathematically gifted student. It then becomes the responsibility of classroom teachers to implement the program.
The plan may include enrichment experiences; differentiation of instruction, including pretesting and compacting the curriculum; flexible cluster grouping by topic or mathematics achievement; grade skipping in math; mentoring; and increased use of technology.
The decision regarding which level of intervention is necessary should be based upon the evaluation. Highly gifted students may require more intense modification such as grade skipping in mathematics.
Daily ongoing assessment, teacher observations, achievement tests, and above-level testing can all be helpful in determining the type of program that will best meet the needs of each gifted child. For example, a lesson on calculating the area of polygons might dissertation and connecticut academic performance and students achievement just the basic formula for most students, dissertation and connecticut academic performance and students achievement, but should provide various real-world applications of calculating area for gifted learners.
The increased complexity of the problems should require higher order thinking skills and provide opportunities for open-ended responses. Effective differentiation of instruction is very different from the unfortunate practice of simply assigning 20 problems to the gifted child while the remainder of the class is given only The task of differentiating each lesson requires accessing additional resources, planning for small-group interaction, and perhaps even modifying lessons during delivery Tomlinson, In most instructional settings, the mathematical understanding and performance of the students is diverse, so classroom teachers plan their instruction with a myriad of learners and learning styles as the focus.
Using a pretesting component in the math program allows for the identification of attained skills, strategies, and achieved concepts prior to the beginning of a new unit. For the gifted population, this helps eliminate the repetition from year to year in the mathematics curriculum. This process provides the foundation for effective differentiation of instruction, as each student should receive instruction based upon his or her identified instructional level Howley, As noted by Winebrennergifted students whose programs have been compacted can spend time working on their differentiated activities while their classmates are preparing dissertation and connecticut academic performance and students achievement state assessments.
It is certainly possible to meet the needs of some gifted students simply by enriching and modifying the existing mathematics curriculum. Enrichment is designed to expose students to a variety of topics related to those of the regular education program and to allow for further investigation of them. In cases where math students are grouped according to their understanding of mathematical concepts and ideas, teachers can cover concepts at an appropriate pace for the group.
Pretesting and compacting of the curriculum are helpful here, as they allow the group of mathematically talented students to be appropriately challenged. In addition, a classroom of homogeneously grouped gifted students would enable a teacher to apply the Enrichment Triad Model Renzulli, For example, once students have mastered basic algebraic concepts, additional learning opportunities would be provided in the area of divergent thinking, individual projects, and group activities that would connect those algebraic concepts with real-world events and scenarios.
Since many mathematically talented students have already mastered the basic skills, the enrichment activities and advanced projects their teachers have planned may not provide sufficient challenge. Indeed, for many talented youngsters, some degree of acceleration is needed based on their demonstrated achievement and ability. Gifted students may have already acquired the content and concepts presented in these classes, so acceleration to a math class at a higher grade level may be the most viable option.
Acceleration may be the only way to accomplish this. Classroom experience and research demonstrate that, even though they may be younger, children who are exceptionally talented in mathematics will learn material much more quickly and with fewer repetitions than the regular curriculum allows Sowell, Thus, the repetitions of a spiral curriculum become redundant and mundane to a gifted math student.
On the other hand, gifted students in accelerated classes have opportunities to work with advanced concepts, in-depth topic investigations, and problems with real-world applicability. Many advances in technology can assist the classroom teacher in meeting the learning needs of dissertation and connecticut academic performance and students achievement math students by providing opportunities to explore complex problems and mathematical ideas NCTM,p.
Readily accessible classroom computers, supervised access to the Internet, and appropriate software programs offer opportunities for gifted students to advance at their own rate.
Teachers sometimes experience frustration when gifted children can arrive at correct answers through nontraditional methodologies or when some of their questions are far beyond the scope of the lesson at hand. Since gifted students can often interpret, predict, and analyze mathematical situations and problems better and faster than their teachers, a significantly different instructional approach may be necessary. Unfortunately, inexperienced or untrained teachers sometimes make provisions for the gifted by assigning them enrichment worksheets, independent projects, or reports on famous mathematicians.
Being sensitive and aware of the unique characteristics of gifted students enables teachers to set more realistic expectations in the classroom.
Teachers need to be confident in their own mathematical knowledge and teaching abilities in order to accept the divergent thinking abilities of their gifted students. When gifted students are able to arrive at the correct answer by following an unmarked thinking path, teachers should acknowledge this creative, divergent problem-solving strategy and not reprimand the student through missed points or a lowered grade because of not following more traditional techniques.
Teachers should adapt the content where appropriate, condense the concepts where applicable, alter the pace of content acquisition, and allow for open-ended, multiple solutions to problems. Meeting the needs of each learner is the goal of every teacher, and each grade level has its own unique challenges. Being aware and sensitive to the unique characteristics of gifted learners will assist teachers in providing a myriad of opportunities for growth in mathematical reasoning and problem solving.
The authors would like to thank Michael Bosse and Jacquie Gentile for their helpful comments on an earlier version of this paper, dissertation and connecticut academic performance and students achievement. American College Testing Program ACT. EXPLORE technical manual. Iowa City, IA: Author. Archambault, F. Regular classroom practices with gifted students: Results of a national survey of classroom teachers.
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Feb 09, · As state testing regimes were first being implemented, they noted that because prior student academic achievement and students’ social class are still the strongest predictors of how well a given school will do on academic achievement measures, “focusing state policy on student performance might simply concentrate high-achieving students in We value excellent academic writing and strive to provide outstanding essay writing service each and every time you place an order. We write essays, research papers, term papers, course works, reviews, theses and more, so our primary mission is to help you succeed academically Jul 20, · Enrichment is designed to expose students to a variety of topics related to those of the regular education program and to allow for further investigation of them. In cases where math students are grouped according to their understanding of mathematical concepts and ideas, teachers can cover concepts at an appropriate pace for the group
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