Numeracy in primary schools
Numeracy is very important in primary schools today, with mental
calculations being a central part of the mathematics curriculum. These
mental methods of calculation should be encouraged from an early age,
mathematics is used in our everyday lives without many of us
realising; checking our change at the shops and leaving the house in
order to arrive at school on time.
It is advised that Numeracy lessons start with a 5-10 minute starter
of oral or mental calculation work, working as a whole class to
rehearse, sharpen and develop the children’s skills. Various ways can
be used to sharpen these skills including counting in steps of
different sizes, practising mental calculations and the rapid recall
of number facts; this can be done through playing interactive number
games ‘a number one less than a multiple of 5’ etc.
Mental calculations are introduced to children in the autumn term of
year 1 at a basic level of addition and subtraction. In key stage 2
these mental calculations have become more complex; children include
multiplication and division according to the National Numeracy
Strategy.
However, these mental calculation strategies are not as straight
forward as just asking the class a question in order to get a
response, individualisation or ‘over-differentiation’ in the teaching
of mental mathematics has been hailed as a major barrier to the
effective learning. It is clear from this statement from Professor
David Reynolds that individualisation is indeed an obstacle:
“We’re clear about what went wrong. Methods of teaching introduced in
the 70’s and 80’s, had deleterious effects on maths in particular. All
the research agrees that the one thing that badly affects p...
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...physical development it is up to teachers to help
and differentiate class work to coincide with the children’s
development.
However an alternative to Piaget's’ view of cognitive development was
provided by the Russian literary critic and psychologist Vygotsky. He
distinguished between lower functions of human psychology like
recognizing and sensation, and higher functions like thinking and
understanding. According to Vygotsky ‘What a child can do in
cooperation today, he can do alone tomorrow’. He talks about the Zone
of Proximal Development, which is their level of actual development of
their level of potential development, what they can do with help of an
instructor. The ZPD is an indicator of the teachability of the child.
Vygotsky suggested it gave a better measure of a child’s capacity than
any test of current ability, such as an intelligence test.
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.
Place value and the base ten number system are two extremely important areas in mathematics. Without an in-depth understanding of these areas students may struggle in later mathematics. Using an effective diagnostic assessment, such as the place value assessment interview, teachers are able to highlight students understanding and misconceptions. By highlighting these areas teachers can form a plan using the many effective tasks and resources available to build a more robust understanding. A one-on-one session with Joe, a Year 5 student, was conducted with the place value assessment interview. From the outlined areas of understanding and misconception a serious of six tutorial lessons were planned. The lessons were designed using
This project aims to examine if children have rules for making plurals. For example, if a child says that the plural of book is books. Does he really know that he has to add the allomorph /-s/ to the singular to make the plural? Or does he memorize the plural form independently from the singular?
Methods and approaches to teaching have been greatly influenced by the research of Jean Piaget and Lev Vygotsky. Both have contributed to the field of education by offering explanations for children's cognitive learning styles and abilities. While Piaget and Vygotsky may differ on how they view cognitive development in children, both offer educators good suggestions on how to teach certain material in a developmentally appropriate manner.
Common Core is a set of high-quality academic standards in Math, English, Language Arts, and Literacy (“Common Core”). The standards outline what every student should be able to interpret by the end of the grade (“Common Core”). The standards are supposed to allow students to be ready when they graduate from high school regardless of where they are taught (“Common Core”). Forty-two states, the District of Columbia, four territories, and the Department of Defense Education Activity have adopted and fully believe that Common Core is necessary (“Common Core”). However I do not agree with the Common Core Curriculum in any way. I believe that every child learns in a different way and at a different pace. If we continue to hold children
Piaget versus Vygotsky: Similarities and Differences This paper explores the ideas of Jean Piaget and Lev Vygotsky. Exploring their philosophies and how they impact us today. The two scholarly articles show similarities and differences in their works and explore what they each mean. Jean Piaget and Lev Vygotsky are two of the most influential philosophers in the field of cognitive development.
“The Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects (“the Standards”) are the culmination of an extended, broad-based effort to fulfill the charge issued by the states to create the next generation of K–12 standards in order to help ensure that all students are college and career ready in literacy no later than the end of high school.” http://ccss.lausd.net/content/science. The reason for the change is due to the fact that the state standards were too vague and too long to drive instruction.
Macmillan, A. (2009). Numeracy in early childhood: Shared contexts for teaching and learning. Melbourne, Victoria: Oxford.
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
For Vygotsky, children are seen as active beings on their development through social interactions with parents, teachers, and other adults, as well as by participating in their cultural activities. The interactions they have with other individuals and their culture opens their minds to new information and helps develop skills not previously attained. To further understand cognitive development in Piaget and Vygotsky’s theory, we must first look at the processes involved.
Problem solving within mathematics is important as children need to apply and transfer their learning of how to solve calculations into everyday situations. Enabling children to deduce what algorithm is required in a given situation is important as the way in which a problem is approached (NCTM, 1989) is an essential skill, in addition to arriving at a correct answer. Furthermore the NCTM (1980) recognised that teaching problem solving to children develops their skills and knowledge that are used in everyday life whereby the inquiring mind, tenacity and receptiveness to problems are developed.
Jean Piaget, Lev Vygotsky, and John Dewey have written extensively on educational theories. Their work as a collective focuses on three specific issues that are of concern in the text; the characteristics of the learner, the curricular content, and the instructional strategies which are used as a structures for learning. Classroom environments based on their work are referred to as constructivism. The theory of cognitive development is described as how children create their own knowledge. The first three stages of cognitive development are referred to as sensorimotor, preoperational, and concrete operations; these stages describe the development of children from birth to age eight. During these first stages of development it is said that children
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.
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