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Math Manipulatives
Math anxiety is a negative emotional reaction to mathematics that can be debilitating, It has been defined as a feeling of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in ordinary life and academic situations. Math anxiety often results in a lack of confidence in the subject, which impedes academic performance. It perilous hurdle for many children across all grade levels. Individuals with math anxiety often avoid studies in mathematics and therefore limit their career options (Hembree, 1990). Hence, interventions are imperative in order to prevent further affecting students success in both academic and life itself.
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Virtual manipulative tools are now also available for use in the classroom. It ranges from simple counting blocks to geoboards and tangram puzzles. Instead of reading about a math concept or working out a problem on paper, a student will work with a physical object to better understand what he/she is learning. The concrete representation is useful at all levels of math, from a preschooler using blocks to strengthen counting skills to an older student using fraction models to understand equivalent fractions.
Researchers have commenced that manipulatives are a powerful addition to mathematics instruction. Achievement in mathematics could be increased by the long-term use of manipulatives, as found by Meta-analyses by Suydam and Higgins (1977), Parham (1993), and Sowell (1989). The history of manipulatives for teaching mathematics extends at least two hundred years. More recent crucial influences have included Maria Montessori, Jean Piaget, Zoltan Dienes, and Jerome Bruner. Each of these pioneers and researchers has accentuated the importance of authentic learning experiences
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While children can remember, for short periods of time, information taught through books and lectures, deep understanding and the ability to apply learning to new situations requires conceptual understanding that is grounded in direct experience with concrete objects. The teacher has a critical role in helping students connect their manipulative experiences, through a selection of representations, to essential abstract mathematics. Together, outstanding teachers and regular experiences with hands-on learning can bestow students with powerful learning in
I visited Mrs. Cable’s kindergarten classroom at Conewago elementary school one afternoon and observed a math lesson. Mrs. Cable had an attention-grabbing lesson and did many great things in the thirty minutes I observed her. I have my own personal preferences, just like every teacher, and I do have a few things I would do differently. There are also many ways this observation can be related to the material discussed in First Year Seminar.
The Algebra II course was a college-prep lecture; they were at a higher level than a general class. With the title of the course, I expected to see well-behaved, attentive learners, who were interested in mathematics. When the apprentices did become disruptive or talkative, I expected that the teacher would discipline the students by sending them out into the hall or to the office, as occurred in my high school classes. I also expected to see a teacher that challenged the students’ knowledge of the subject, and pupils who gladly accepted that challenge. Finally, I anticipated the class lessons to go as follows: collect homework, class notes which are copied by the students, time set aside for the children to practice this work via worksheets and example problems, and then the assignment of homework for the next day. These expectations influenced the ways that I observed and reacted to Ms. Stone’s mathematics
...ts work on the lessons independently or with a preservice teacher by using manipulatives or other mathematical tools it will allow them to fully grasp the concept that is being taught so they can do well in the long run of learning more complex mathematics.
Mathematics education has undergone many changes over the last several years. Some of these changes include the key concepts all students must master and how they are taught. According to Jacob Vigdor, the concerns about students’ math achievements have always been apparent. A few reasons that are negatively impacting the productivity of students’ math achievements are historical events that influenced mathematics, how math is being taught, and differentiation of curriculum.
Larson et al. (2012) maintain that having a productive disposition is related to persevering to solve problems. Productive disposition is defined by Kilpatrick et al. (2001) as “habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy” (p. 5). Kilpatrick et al. report that students are excited about mathematics when they first come to school but that, unfortunately, our present school system is making most students lose this disposition. They call for teachers to change their practices to make mathematics more
Math manipulatives have been around for years, but are now becoming increasingly popular amongst educators. Math manipulatives include anything from buckets of pattern blocks, trays of tiles, and colored cubes to virtual manipulatives, or manipulatives colored and cut out by the students themselves. All of these materials can help assist in tangibly teaching children math concepts and by pulling math off the page and into the hands of students. For a child to be verbally and physically taught a math concept allows them to think, reason, and solve problems with the teacher's guidance as well as on their own. Manipulatives can be used in lower levels by children making up stories with numbers that use a certain number of blocks to learning decimal places and place value in older grade levels.
Manipulatives are “concrete objects that can be viewed and physically handled by students in order to demonstrate or model abstract concepts”. Wikipedia defines Manipulatives as an “object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name”. In 1951 Piaget’s work suggested “that children age seven to ten years old, work in primarily concrete ways and that the abstract notions of mathematics may only be accessible to them through embodiment in practical resources” (www.hand2mind). Manipulative materials are objects designed to represent explicitly and concretely math ideas that are abstract. They have both visual and tactile appeal and can be manipulated by learners through hands on
Sherley, B., Clark, M. & Higgins, J. (2008) School readiness: what do teachers expect of children in mathematics on school entry?, in Goos, M., Brown, R. & Makar, K. (eds.) Mathematics education research: navigating: proceedings of the 31st annual conference of the Mathematics Education Research Group of Australia, Brisbane, Qld: MERGA INC., pp.461-465.
Hatfield, Mary. “Use of Manipulative Devices: Elementary School Cooperating Teachers Report.” School Science and Mathematics. Volume 94, Issue 6. October 1994.
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
A large- scale study suggested that mathematic software increase students’ engagement and test scores. Barrow et al. (2009) tested a computer program designed to improve pre-algebra and algebra skills. They found that students learn through computer lab were scores 27% ahead students on traditional classroom. Similarly Rochelle et al. (2007) found that using Sim Calc Mathworlds improves student’s understanding of mathematics. Students who used Sim Calc had a better understanding than students who study in standard class. By use of autograph, students could gain a better understanding of what gradient are, what gradient look like and how gradient formed. Use autograph to create interval between two points and form a right-angle triangle where interval as the hypotenuse of the triangle could l...
Towers, J., Martin, L., & Pirie, S. (2000). Growing mathematical understanding: Layered observations. In M.L. Fernandez (Ed.), Proceedings of the Annual Meetings of North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ, 225-230.
Research has shown that ‘structured’ math lessons in early childhood are premature and can be detrimental to proper brain development for the young child, actually interfering with concept development (Gromicko, 2011). Children’s experiences in mathematics should reflect learning in a fun and natural way. The main focus of this essay is to show the effectiveness of applying learning theories by Piaget, Vygotsky and Bruner and their relation to the active learning of basic concepts in maths. The theories represent Piaget’s Cognitivism, Vygotsky’s Social Cognitive and Bruner’s Constructivism. Based on my research and analysis, comparisons will be made to the theories presented and their overall impact on promoting mathematical capabilities in children. (ECFS 2009: Unit 5)
Teaching young children is possibly one of the most challenging and difficult professions. No matter the subject, an educator must plan, prepare, organize, set up, and review everything that they are going to teach. “Students use mathematics textbooks to study and to do homework questions, while professors and teachers may use them to prepare classes and to teach” (Kajander & Lovric, 2009, p.173). Using textbooks can be a quicker and effective way to help ease the way some educators lesson plan; while teaching without textbooks may be a more difficult task but can be just as rewarding. There are advantages and disadvantages to both, but in the end both can be used in the classroom resulting in similar outcomes. Some of the best educators are
I would not say that I have a math phobia, because when I understand the math I am doing I really enjoy it. Math is like a puzzle and it is comforting to know that there is one right answer. In high school, however, I was not a fan of math. My math teachers were not the greatest and I had a lot of trouble grasping the concepts, which made me overly anxious for the tests. If my high school experience with math had been better then maybe I would have taken more math classes in college and would be more confident in my mathematical abilities.