Resources
‘Mathematical resources’ can be expressed as materials such as manipulative (structured and unstructured), and images that could support mathematical learning when utilised (Drews 2007). Manipulative is a type of resource that supports learning in mathematical lessons. Jarvin et al. (2009) identified manipulative’s as being “concrete objects used to help students understand abstract concepts.” There are two types, structured and unstructured manipulative (Bottle 2005). Structured apparatus such as Dienes, primarily focus on a particular conceptual structure (i.e. helps in understanding the place value system). Unstructured apparatus such as Multilink cubes have no explicit focus on a concept, therefore, can be used in many ways (i.e.
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Bruner (cited in Taylor, 2014) believes that learning occurs through three phases, with the Enactive and Iconic phase linking to the use of resources to support the learning of mathematical concepts. The Enactive phase involves manipulating concrete objects while the iconic phase involves concepts represented through images (Hannum, 2015). Similarly, Piaget emphasised the importance that a student needs to manipulate physical objects to understand abstract concepts (Drews, …show more content…
Furthermore, research conducted by Sowell (cited in Bolden et al. 2012) found that when using resources to represent a concept, students did not benefit in their learning of mathematics as there is no real mathematics conveyed in the resource. Therefore, McNeil (2007) concludes; we should not make assumptions that students can understand the mathematical concept through manipulating
The students are building on the knowledge they have gather from their daily routine, and are able to more easily grasp the concept of place value. Furthermore, in Piaget theory “children need many objects to explore so that they can later incorporate these into their symbolic thinking” (Gordon, & Browne, 2010, p. 106). The teacher gave students a variety of materials to understand the lesson in a pleasurable way. Equally important, the students’ scheduling was derived from Piaget as the students had “plenty of time to explore” (Gordon, & Browne, 2010, p.
Steen, Lynn Arthur . "Integrating School Science and Mathematics: Fad or Folly?." St. Olaf College. (1999): n. page. Web. 12 Dec. 2013..
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).
Brooks, J.G. &Brooks, M.G. (1995). Constructing Knowledge in the Classroom. Retrieved September 13, 2002 for Internet. http://www.sedl.org/scimath/compass/v01n03/1.html.
The second part of this memo contains a rhetorical analysis of a journal article written by Linda Darling-Hammond. Interview The following information was conducted in an interview with Diana Regalado De Santiago, who works at Montwood High School as a mathematics teacher. In the interview, Regalado De Santiago discusses how presenting material to her students in a manner where the student actually learns is a pivotal form of communication in the field (Personal Communication, September 8, 2016).
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
...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.
Countless time teachers encounter students that struggle with mathematical concepts trough elementary grades. Often, the struggle stems from the inability to comprehend the mathematical concept of place value. “Understanding our place value system is an essential foundation for all computations with whole numbers” (Burns, 2010, p. 20). Students that recognize the composition of the numbers have more flexibility in mathematical computation. “Not only does the base-ten system allow us to express arbitrarily large numbers and arbitrarily small numbers, but it also enables us to quickly compare numbers and assess the ballpark size of a number” (Beckmann, 2014a, p. 1). Addressing student misconceptions should be part of every lesson. If a student perpetuates place value misconceptions they will not be able to fully recognize and explain other mathematical ideas. In this paper, I will analyze some misconceptions relating place value and suggest some strategies to help students understand the concept of place value.
Wu, Y. (2008). Experimental Study on Effect of Different Mathematical Teaching Methodologies on Students’ Performance. Journal of Mathematics Studies. Vol 1(1) 164-171.
Vygotsky’s theory mainly looks at ‘zone of proximal development’ (Coffey, 2012). According to Coffey, 2012, ‘zone of proximal development’ refers to the gap between what a learner has already learnt and what he or she can achieve from the support given. Bruner’s theory further supports Vygotsky’s theory, by stating that learning is an active process where children build upon their previous knowledge (Charlesworth & Lind, 2003). (Charlesworth & Lind, 2003) explains that Bruner;s theory is comprised of three learning stages:enactive, iconic and symbolic. In each of these learning stages, the primary focus is that of building up children;s previous knowledge, which indeed links to Vygotsky 's understandings of the ‘zone of proximal development’ which is similar in the way that children learn upon using their prior knowledge. Both of these theories look at the notion of building upon children;s prior knowledge and this is demonstrated in today’s teaching. It is seen in today 's classrooms during maths classes where children are assessed on their maths skills and from this data the required amount of support so the zone of proximal development is utilised and then when math learning occurs it is being built upon to create new maths knowledge or strengthen their skill set. Hence, as maths is a skill set that cannot be just understood by direct instruction from the
However, one must remember that art is by no means the same as mathematics. “It employs virtually none of the resources implicit in the term pure mathematics.” Many people object that art has nothing to do with mathematics; that mathematics is unemotional and injurious to art, which is purely a matter of feeling. In The Introduction to the Visual Mind: Art and Mathematics, Max Bill refutes this argument by stati...
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
Mathematics teachers teach their students a wide range of content strands – geometry, algebra, statistics, and trigonometry – while also teaching their students mathematical skills – logical thinking, formal process, numerical reasoning, and problem solving. In teaching my students, I need to aspire to Skemp’s (1976) description of a “relational understanding” of mathematics (p. 4). Skemp describes two types of understanding: relational understanding and instrumental understanding. In an instrumental understanding, students know how to follow steps and sequential procedures without a true understanding of the mathematical reasons for the processe...
Some children find that mathematics is too abstract and does not connect to their daily life. They may find mathematics boring and irrelevant. Children who are forced to learn mathematics through rote memorization might find that they do not understand mathematical concepts and are unable to solve problems at a higher level as their foundation and grasp of basic math concepts are weak. Children who are forced to sit still and learn math by doing many worksheets may develop math anxiety and an aversion to numbers.
Throughout out this semester, I’ve had the opportunity to gain a better understanding when it comes to teaching Mathematics in the classroom. During the course of this semester, EDEL 440 has showed my classmates and myself the appropriate ways mathematics can be taught in an elementary classroom and how the students in the classroom may retrieve the information. During my years of school, mathematics has been my favorite subject. Over the years, math has challenged me on so many different levels. Having the opportunity to see the appropriate ways math should be taught in an Elementary classroom has giving me a