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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.
Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.
One of the most influential of Piaget’s findings was his theory on the developmental stages of children’s cognition. The developmental stages consist of periods of months or years in which development occurs (Ojose, 2008). There are four Stages of Cognitive Development, the sensorimotor stage, the pre-operational stage, the concrete operational stage, and the formal operations stage. This theory has shaped the way many educators have shaped their lesson plans for years, for example, According to Bobby Ojose (2008), Piaget’s “work on children’s quantitative development has provided mathematic educators with crucial insights into how children learn mathematical concepts and ideas” (p. 26).
The modern mathematical mind of a high school student is an abyss due to the colorless lectures constantly repeating. Recently, the updated education system, Common Core Math, was implemented across the United States. Common Core Mathematics is a set of standards that focuses on a set of math skills and concepts to prepare students for mathematics in college, career, and in life. Although there has been a continuous dispute on how to instruct math, there are multiple methods for a teacher to teach mathematics. For example, some teachers stress memorization and exact answers, while others teach math with meaning and approximation. An adequate math pedagogy is perfectly between the two methods; a method where students can mentally solve a simple
Jones, Rebecca. “Solving Problems in Math and Science Education.” The American School Board Journal. 185.7 (1998): 16-20.
My students we be able to do math confidently and enjoy the subject. Every student is going to be strong in different areas of math and that’s okay. I need to express to students that we are all different and think different in other subjects. I believe students struggle with math because they feel discouraged math has this reputation for being disliked.
They saw the difficulties that students were facing with understanding geometry, therefore, conducted research with the goal of understanding the children’s levels of geometric thinking. The Van Hieles knew that students needed to have more experience in thinking at lower levels and fully understanding the concepts in order to later be able to write geometric proofs [5]. They developed a model that takes the learner through five levels of understanding, which are not age-dependent but are more related to the experiences of the students. The levels are sequential, therefore, students need to pass through the levels 0 through 4 in order as their understanding increases. Instruction level must not be higher than the level of the student because it will inhibit the student from learning [6].
Wu, Y. (2008). Experimental Study on Effect of Different Mathematical Teaching Methodologies on Students’ Performance. Journal of Mathematics Studies. Vol 1(1) 164-171.
4.Leder, Gilah C. Mathematics Achievement and Fear of Success. Journal for Research in Mathematics, 13(1982), 124-135.
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.
While I was waiting for students to solve the problem I notice that almost half of the group used the unifix cubes in order to figure out the answer. The unifix cubes were necessary for the students because they were able to see the problem by having a hands-on material. Students were able to group blocks, deduct blocks, and count all the blocks that they had in their stack in order to
Kirova, A., & Bhargava, A. (2002). Learning to guide preschool children's mathematical understanding: A teacher's professional growth. 4 (1), Retrieved from http://ecrp.uiuc.edu/v4n1/kirova.html
...S. and Stepelman, J. (2010). Teaching Secondary Mathematics: Techniques and Enrichment Units. 8th Ed. Merrill Prentice Hall. Upper Saddle River, NJ.
A somewhat underused strategy for teaching mathematics is that of guided discovery. With this strategy, the student arrives at an understanding of a new mathematical concept on his or her own. An activity is given in which "students sequentially uncover layers of mathematical information one step at a time and learn new mathematics" (Gerver & Sgroi, 2003). This way, instead of simply being told the procedure for solving a problem, the student can develop the steps mainly on his own with only a little guidance from the teacher.
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...