Being Fluent In Number Sense

Every day, mathematics is used in our lives. From playing sports or games to cooking, these activities require the use of mathematical concepts. For young children, mathematical learning opportunities are all around them. Knaus (2013) states that ‘Young children are naturally curious and eager to learn about their surroundings and the world they live in’ (pg.1). Children, young and old, and even adults, learn when they explore, play and investigate. By being actively involved, engaging in activities that are rich, meaningful, self-directed and offer problem solving opportunities, children given the chance to make connections with their world experiences (Yelland, Butler & Diezmann, 1999). As an educator of young children,

This interview also showed me that not every child will be able to understand mathematical problems the same. Certain students may require more attention and extra help and it is very important not to let that child get behind. Especially in Elementary school, everything the children learn will be needed for the future lessons because math problems continue to get more complex and require previous

Numeracy development is important for all children as maths is an important part of everyday life. The way in which maths is taught has changed greatly over the years. When I was at school we were taught one method to reach one answer. Now, particularly in early primary phase, children are taught different methods to reach an answer, which includes different methods of working out and which also develops their investigation skills. For example, by the time children reach year six, the different methods they would have been taught for addition would be number lines,

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.

Van de Walle, J, Karp, K. S. & Bay-Williams, J. M. (2015). Elementary and Middle School Mathematics Teaching Developmentally. (9th ed.). England: Pearson Education Limited.

Their 2000 publication, the Principles and Standards for School Mathematics, is still prevalent. This document, setting forth ten guidelines for improving math education, refined, extended, and replaced NCTM’s earlier recommendations. Not only does the Principles and Standards for School Mathematics address five important content areas, it also establishes five important mathematical processes deemed necessary in quality education, like problem solving, reasoning and proof, communication, representation, and connections. When it comes to making connections, NCTM further asserts that instructional programs from prekindergarten through grade 12 should enable all students

The National curriculum states that in Mathematics teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is

When the practitioners are planning, they can also ensure that they involve all children no matter what the mathematical ability to allow group learning and supporting one another which Vygotsky (Richard Culatta, 2015) says is how children learn best. Practitioners should plan for an enabling environment that promotes maths by surrounding the children in mathematical concepts and language, to support emergent maths. Practitioners should praise children. Practitioners should support all children’s development to ensure children and school ready and they are developing their emergent

Children at this age also have different skills related to numeracy. Fostering numeracy skills in early childhood education not only predicts for later Math achievement but also for greater literacy skills (NAEYC, 2009). Since mathematical concepts are often intertwined with so many areas such as science, literacy, dramatic play, block building, and more, math learning centers offering interdisciplinary materials and activities ensure that young children grow to understand and appreciate the real life applications of mathematical concepts (Fu, 2010).

Algebra is a critical aspect of mathematics which provides the means to calculate unknown values. According to Bednarz, Kieran and Lee (as cited in Chick & Harris, 2007), there are three basic concepts of simple algebra: the generalisation of patterns, the understanding of numerical laws and functional situations. The understanding of these concepts by children will have an enormous bearing on their future mathematical capacity. However, conveying these algebraic concepts to children can be difficult due to the abstract symbolic nature of the math that will initially be foreign to the children. Furthermore, each child’s ability to recall learned numerical laws is vital to their proficiency in problem solving and mathematical confidence. It is obvious that teaching algebra is not a simple task. Therefore, the importance of quality early exposure to fundamental algebraic concepts is of significant importance to allow all

Imagine being given a math problem, such as, 7+7. Most people would do simple mental math to get the solution fourteen. However, in American education millions of kids are required to fathom these problems with a concept known as “number bonds,” and restricting children to one way of solving is profoundly hampering innovativeness in American children (Garelick). Not only has this change in education caused anxiety in children of all ages, but also in their parents who struggle in assisting their children with their school work because they find the new concepts perplexing and divergent from the way they were instructed as children.

Constructs in fractions extend many of the principles encountered in multiplicative thinking. It has been observed language and a variety of models improve understanding of these constructs (Reys et al, 2012). Therefore, these models should be scaffolded to develop student skills and knowledge for manipulating fractions with operations. The underpinning principle is the part-whole construct (Charalambous & Pitta-Pantazi, 2005). The subconstructs for fractions that build on this construct are quotient, ratio, measure and operator (Charalamous & Pitta-Pantazi, 2005; Clarke, Roche & Mitchell, 2008). As with multiplicative thinking there is a loose sequence to learning these constructs which overlaps. Their instruction during the primary years is important because a fifth-grader’s fractional knowledge can predict later outcomes in mathematics (Dooren & Vershaffel, 2015).

Mathematics, like every creation of man, have evolved without really knowing how far you can get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate. Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes.

A common and innocent mistake to avoid—that instructors, teachers, schools and textbooks do all over the world—is the separation of teachings of division and fractions. Fractions are usually taught at a much later time than division, and introduced as a completely new topic. However, the teaching of division

Using fractions or decimals instead of integers is a simple way to differentiate in the classroom. Students who find the current topic dull and