According to the National Center for Education Evaluation (2010), a high number of U.S. students do not possess conceptual understanding of fractions even after they have had the opportunity to study about them for several years. Because these students lack this understanding they are limited in their ability to solve problems with fractions and to learn and apply mathematical procedures that include fractions. This is supported by Yanik, Helding, and Baek (2006) who report that students’ understanding of fractions reflect that most struggle with conceptualizing fractions, and that this is true not just nationally but also globally. According to Barnett-Clarke, Fisher, Marks and Ross (2010) teachers need to help students conceptualize fractions as an extension of the way in which we use whole numbers. They contend that measurement opportunities offer an effortless evolution from understanding whole numbers to understanding fractions. This leads educators to ask, what is the measurement model of fractions, what is it about measurement activities that serves as a conduit to rational numbers, and what elements must a quality measurement lesson include to help students see the relationship of whole numbers to rational numbers?
The measurement model of fractions as described by Lamon (2012) declares a fraction is usually the measure assigned to some interval or region. In a one dimensional interval the fraction measures length and a two dimensional interval the fraction measures area or volume. As imparted by Chapin and Johnson (2006), a rational number is the measure of some distance or region that is often referred to as some point on a number line and these points actually are a measure of distance. Lamon (1999) goes on to sa...
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...eachers of Mathematics, 335-339.
Moyer, P. S., & Mailley, E. (2004). Inchworm and a Half: Developing Fraction and Measurement Concepts Using Mathematical Representations. Teaching Children Mathematics, 244-252.
National Center for Education Evaluation. (2010). Developing Effective Fractions Instruction for Kindergarten Through 8th Grade. Washington D.C.: U.S. Department of Education.
Wong, M., & Evans, D. (2008). Fractions as Measures. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia (pp. 597-603). Brisbane: MERGA inc. 2008.
Yanik, H. B., Helding, B., & Back, J. M. (2006). Students' Difficulties in Understanding Fractions as Measures. 28th Annual meeting of the North American Chapter of the Internation Group for the Psychology of Mathematics Education (pp. 323-325). Merida, Mexico: Universidad Pedagogica Nacional.
Math is the study of patterns, with students learning to create, construct, and describe these patterns ranging from the most simple of forms to the very complex. Number sense grows from this patterning skill in the very young student as he/she explores ordering, counting, and sequencing of concrete and pictorial items. The skill of subitizing, the ability to recognize and discriminate small numbers of objects (Klein and Starkey 1988), is basic to the students’ development of number sense. In the article “Subitizing: What is it?
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.
The first standard in number and operations is Grade 3-5 g. develop and use strategies to estimate computations involving fractions and decimals in situations relevant to student’s experiences. The students had to estimate how many items and which items they could buy. They had to estimate the prices by using numbers with decimals and figuring out what the price was closer to in whole numbers. The second standard was h, use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. The visual models they used were the items and prices, it represented how decimals can be used in real life.
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.
Mathematical dialogue within the classroom has been argued to be effective and a ‘necessary’ tool for children’s development in terms of errors and misconceptions. It has been mentioned how dialogue can broaden the children’s perception of the topic, provides useful opportunities to develop meaningful understandings and proves a good assessment tool. The NNS (1999) states that better numeracy standards occur when children are expected to use correct mathematical vocabulary and explain mathematical ideas. In addition to this, teachers are expected
To investigate the notion of numeracy, I approach seven people to give their view of numeracy and how it relates to mathematics. The following is a discussion of two responses I receive from this short survey. I shall briefly discuss their views of numeracy and how it relates to mathematics in the light of the Australian Curriculum as well as the 21st Century Numeracy Model (Goos 2007). Note: see appendix 1 for their responses.
It contains exercises and mathematics problems designed for the instruction of math students or scribes. The papyrus includes problems with fractions, arithmetic, algebra, geometry and measurement (Allen, 2001, p.10). The Egyptian decomposed fractions into the sum of unit fractions – i.e. the reciprocals of whole numbers (Allen, 2001, p.9). The exact method for the decomposition into unit fractions “has been widely debated and no general method that works for all n has ever been discovered” (Abdulaziz, 2007).
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
I believe that learning mathematics in the early childhood environment encourages and promotes yet another perspective for children to establish and build upon their developing views and ideals about the world. Despite this belief, prior to undertaking this topic, I had very little understanding of how to recognise and encourage mathematical activities to children less than four years, aside from ‘basic’ number sense (such as counting) and spatial sense (like displaying knowledge of 2-D shapes) (MacMillan 2002). Despite enjoying mathematical activities during my early years at a Montessori primary school, like the participants within Holm & Kajander’s (2012) study, I have since developed a rather apprehensive attitude towards mathematics, and consequently, feel concerned about encouraging and implementing adequate mathematical learning experiences to children within the early childhood environment.
While numeracy and mathematics are often linked together in similar concepts, they are very different from one another. Mathematics is often the abstract use of numbers, letters in a functional way. While numeracy is basically the concept of applying mathematics in the real world and identifying when and where we are using mathematics. However, even though they do have differences there can be a similarity found, in the primary school mathematics curriculum (Siemon et al, 2015, p.172). Which are the skills we use to understand our number systems, and how numeracy includes the disposition think mathematically.
The early acquisition of mathematical concepts in children is essential for their overall cognitive development. It is imperative that educators focus on theoretical views to guide and plan the development of mathematical concepts in the early years. Early math concepts involve learning skills such as matching, ordering, sorting, classifying, sequencing and patterning. The early environment offers the foundation for children to develop an interest in numbers and their concepts. Children develop and construct their own meaning of numbers through active learning rather than teacher directed instruction.
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.
The prominence of numeracy is extremely evident in daily life and as teachers it is important to provide quality assistance to students with regards to the development of a child's numeracy skills. High-level numeracy ability does not exclusively signify an extensive view of complex mathematics, its meaning refers to using constructive mathematical ideas to “...make sense of the world.” (NSW Government, 2011). A high-level of numeracy is evident in our abilities to effectively draw upon mathematical ideas and critically evaluate it's use in real-life situations, such as finances, time management, building construction and food preparation, just to name a few (NSW Government, 2011). Effective teachings of numeracy in the 21st century has become a major topic of debate in recent years. The debate usually streams from parents desires for their child to succeed in school and not fall behind. Regardless of socio-economic background, parents want success for their children to prepare them for life in society and work (Groundwater-Smith, 2009). A student who only presents an extremely basic understanding of numeracy, such as small number counting and limited spatial and time awareness, is at risk of falling behind in the increasingly competitive and technologically focused job market of the 21st Century (Huetinck & Munshin, 2008). In the last decade, the Australian curriculum has witness an influx of new digital tools to assist mathematical teaching and learning. The common calculator, which is becoming increasing cheap and readily available, and its usage within the primary school curriculum is often put at the forefront of this debate (Groves, 1994). The argument against the usage of the calculator suggests that it makes students lazy ...
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
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