Manipulatives in a math classroom can be used to help a student become more engaged in what they are learning. In mathematics, manipulatives are defined as an object that is designed so that the learner can perceive the mathematical concept by “manipulating” it. In this article, I learned about the various manipulatives teachers and students traditionally use such as concrete manipulatives, while in contemporary classrooms teachers and students also used pictorial as well as virtual manipulatives. The National Council of Teachers of Mathematics encourages the teachers and the students to use a variety of representations during mathematic instruction. This article addresses examples of the various types of manipulatives, the theoretical foundations to use manipulatives in mathematics classrooms, and struggles while using manipulatives.
One key point from the article that I found interesting was that, through multiple representations the curriculum can be presented in mathematics by physical, pictorial, or virtual
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Since the early 1900s, it has been considered essential for teachers and students to use manipulatives during elementary math teaching and learning. Some states such as California has mandated the use of manipulatives for teaching. Furthermore, the article mentions how there is theoretical support for the use of manipulatives from well-known theorists such as, Piaget, Dienes, and Bruner who all strongly support the use of physical manipulatives. Another key point from the article was that there are also studies that do not support the use of manipulatives due to various reasons. The most interesting point to me is that some students are not making connections between multiple representations. Nevertheless, some students have too much fun with the manipulative presented and it is mistaken as a toy rather than a beneficial
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.
Kieren, T., Gordon-Calvert, L., Reid, D. & Simmt, E. (1995). An enactivist research approach to mathematical activity: Understanding, reasoning, and beliefs. Paper presented at the meeting of the Ame rican Educational Research Association, San Francisco.
...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.
All children learn differently and teachers, especially those who teach mathematics, have to accommodate for all children’s different capacities for learning information. When teaching mathematics, a teacher has to be able to use various methods of presenting the information in order to help the students understand the concepts they are being taught.
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
...ett, S. (2008) . Young children’s access to powerful mathematical ideas, in English, Lyn D (ed), Handbook of international research in mathematics education, 2nd edn, New York, NY: Routledge, pp. 75-108.
...atics in six countries, Mathematics Teaching in the 21st Century, Center for Research in Mathematics and Science Education, Michigan State University.
Ward (2005) explores writing and reading as the major literary mediums for learning mathematics, in order for students to be well equipped for things they may see in the real world. The most recent trends in education have teachers and curriculum writers stressed about finding new ways to tie in current events and real-world situations to the subjects being taught in the classroom. Wohlhuter & Quintero (2003) discuss how simply “listening” to mathematics in the classroom has no effect on success in student academics. It’s important to implement mathematical literacy at a very young age. A case study in the article by authors Wohlhuter & Quintero explores a program where mathematics and literacy were implemented together for children all the way through eight years of age. Preservice teachers entered a one week program where lessons were taught to them as if they were teaching the age group it was directed towards. When asked for a definition of mathematics, preservice teachers gave answers such as: something related to numbers, calculations, and estimations. However, no one emphasized how math is in fact extremely dependable on problem-solving, explanations, and logic. All these things have literacy already incorporated into them. According to Wohlhuter and Quintero (2003), the major takeaways from this program, when tested, were that “sorting blocks, dividing a candy bar equally, drawing pictures, or reading cereal boxes, young children are experienced mathematicians, readers, and writers when they enter kindergarten.” These skills are in fact what they need to succeed in the real-world. These strategies have shown to lead to higher success rates for students even after they graduate
Using manipulatives in the classroom is an amazing way for kids to not only explain, but also show their thinking and cognitive skills. Throughout my observation of this assignment there were several manipulatives used in the centers as well as lesson plans at the schools I observed at. Manipulative play is easy to set up and can happen indoors or out. The definition of a manipulative would be physical objects that are used as teaching tools to engage students in the hands-on learning. They can be used to introduce, practice, or remediate a concept. It is highly important that schools and childcare centers incorporate this type of learning into their programs. A manipulative may be as simple as grains of rice or as sophisticated as a model of our solar system or even blocks for math. Concrete models can also be very beneficial to a child’s understanding when using manipulatives, due to the fact that help with real situations they may possibly encounter. The manipulatives I saw in the classrooms would be blocks, bears, straws, a rug chart, as well as colored sticks. Majority of these items were used for either counting or sorting. According to Caston Cain, “All aspects of manipulatives practice fine motor skills from picking up pieces to stacking, snapping together and even taking
What is math? If you had asked me that question at the beginning of the semester, then my answer would have been something like: “math is about numbers, letters, and equations.” Now, however, thirteen weeks later, I have come to realize a new definition of what math is. Math includes numbers, letters, and equations, but it is also so much more than that—math is a way of thinking, a method of solving problems and explaining arguments, a foundation upon which modern society is built, a structure that nature is patterned by…and math is everywhere.
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.
Her paper, “Dance and mathematics: Engaging senses in learning,” shows that math concepts can be understood clearer if you experience them with your body, which is attained through using dance to teach these math concepts. Watson expresses ideas such as “using physical imagination to explore shapes from the inside [being] used for geometrical education with students” (17). This idea, along with others, brings out the fact that Watson has numerous specifics when it comes to evidence that dance is effective in creating an easier mathematics learning system for students, which proves that there is a definite connection between the two subjects. However, for my argument, I still do not have evidence that this relationship can be put in reverse. She does not touch upon the proposal that mathematical concepts can be used to aid in making dance education simpler, so I proceeded my research to find supplementary evidence of this
...nd dynamic changes in the competitive nature of the job market, it is evident to myself that being eloquent in all aspects of numeracy tools and knowledge is imperative in the 21st Century. The calculator is one such tool for children which supports mental computation to check answers to develop independent learning, as discussed earlier. It also fits into the pre-operation developmental stage of a child to enhance their symbolic thinking, similar to that of an adults scheme of thinking, as opposed reliance on senses alone. The interviews further grounded my reasoning around my argument and allowed me to not only gain an insight to how those similar to me think and those not so similar. This investigation has strengthened my argument that the use of calculators in the primary school classroom, if used appropriately, are an invaluable tool for teaching and learning.
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.
Allowing children to learn mathematics through all facets of development – physical, intellectual, emotional and social - will maximize their exposure to mathematical concepts and problem solving. Additionally, mathematics needs to be integrated into the entire curriculum in a coherent manner that takes into account the relationships and sequences of major mathematical ideas. The curriculum should be developmentally appropriate to the