Mathematics : Mathematical Problem Solving

From birth, it is important for practitioners to support the early years’ mathematical development. Children learn emergent maths which is a “term used to describe children construct mathematics from birth” (Geist, 2010). The Early Years Statuary Frameworks (EYFS) (Department of Education) states that maths is one of the specific areas.

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

Problem Solving, Numeracy and Reasoning: Helping to expand their knowledge of problem solving using stories, games, role play, singing and games. Making the child feel easy talking about and understanding the language of reasoning and problem solving.

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,

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.

Mathematical activities at Ysgol Dolafon are delivered in accordance with pupil’s individual needs and great deal of emphasis is given to continuity of learning. Ample opportunity is provided for pupils to discuss their understanding of concepts as they progress and teachers are aware of the importance of eliminating any gaps in the children’s mathematical knowledge. The Welsh Assembly Government guideline for Mathematical Development maintains that: ‘It is crucial that gaps in children’s mathematical learning are avoided, so that children do not miss out on essential elements in their understanding of mathematical concepts’ (WAG 2008) and Ysgol Dolafon fully agrees with that statement.

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,

Ollerton, M. (2010) ‘Using problem-solving approaches to learn mathematics’ in Thompson, I. (ed.) Issues in Teaching Numeracy in Primary Schools (2nd edn), Maidenhead, Open University Press

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).

Multiplicative thinking is imperative to a child’s understanding of important mathematical concepts and is seen as the ‘big idea’ in number that links multiple key ideas and strategies (Vergnaud, as cited in Siemon, 2011). Commonly, children have a procedural based view of multiplicative thinking which can hinder progress, as opposed to a more conceptual view which is a far better learning framework (Hurst & Hurrell, 2016). If teachers are to maximise a child’s learning, they must acknowledge this and help children maintain a conceptual understanding of multiplicative thinking and emphasise this much more so than procedural rules. Several key ideas and strategies underpin the success of multiplicative thinking and a greater conceptual understanding.

In “Teaching Kids Why Math Matters” Donaldson said, “A person 's success in life depends on how well she can solve problems. No matter what her career or life situation, she’ll find satisfaction

Maths is ubiquitous in our lives, but depending on the learning received as a child it could inspire or frighten. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Solso (2009) explains that math has the ability to confuse, frighten, and frustrate learners of all ages; Math also has the ability to inspire, encourage and achieve. Almost all daily activities include some form of mathematical procedure, whether people are aware of it or not. Possessing a solid learning foundation for math is vital to ensure a lifelong understanding of math. This essay will discuss why it is crucial to develop in children the ability to tackle problems with initiative and confidence (Anghileri, 2006, p. 2) and why mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri).

Mathematics has always been a difficult subject for students. Many children have developed phobias and barriers towards mathematics, which prevail into adulthood, thus limiting their potential. This limitation implies problems of learning, resulting in the child a sense of inferiority.

Mathematics is a type of reasoning. Thinking mathematically includes thinking in a rational way, developing and checking conjectures, understanding things, and forming and validating judgments, reasoning, and conclusions. We show mathematical habits when we acknowledge and explain patterns, build physical and theoretical models of sensations, develop sign systems to assist us stand for, control, and review concepts, and create treatments to address issues (Battista, 1999).

It is important to teach or at least try to teach students problem solving related to math. Problem solving plays a big part in the math process. Teaching problem solving is beneficial to students because helps the students find solutions when struggling. It helps math to be more interesting and less stressful. Students see math with less negative reaction and more hope. Problem solving helps and improves student’s ability to think, solve, and find solutions. It is important for students to have the ability to have problem solving skills and this is what it teaches the students. Ultimately, problem solving helps students focus increase and learn what works best for them.