My Teaching Ideas and Theory Applications

This paper will demonstrate the pre-service teachers’ understanding of mathematical practices as part of the Common Core State Standards in Mathematics. It will address two specific standards for Mathematical Practices, describing the essence of both and providing a description of how teachers facilitate these practices and how students are engaged in the practices.

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

My passion for mathematics was fixed at the age of ten, on the morning that my mathematics teacher told I would be sitting the Junior Maths Challenge, 'as practice for when you are older'. As I nervously started to answer the questions, a whole world began to open before me. I revelled in the problem solving, answering questions of a nature I had not seen before. My teachers were delighted when I emerged from the exam hungry for more. Since then I have consistently demonstrated my aptitude, achieving gold awards through to senior level, and scoring highly in the European Kangaroo.

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.

Essential aspects that underpin the professional and dedicated educator include the revising of knowledge and experience, reflection, and an effort in understanding their students. Within mathematics, these skills are informed by the curriculum chosen, the students involved, and the pedagogy that is selected, that create the professional judgement cycle (as seen in Appendix One) (Department of Education and Training Western Australia [DETWA], 2013a). The more teachers understand about their students, the more they can adapt the learning environment to cater for these different learning approaches (Burns, 2010).

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,

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

- The Math area in the classroom is composed of concrete materials for learning numbers and quantities. Children gain a strong foundation in the basic concepts, and can move on to more complex mathematical procedures and concepts as they are able—at their own pace.

In this class educators read, researched, and possibly changed their thinking on the following three theories: behaviorism, cognitivism, and constructivism. Throughout these theories educators must include the social cognitive theory. This paper will discuss each theory as to an educator’s thoughts and how they are applied throughout daily teaching in the classroom.

Many educators will argue what makes an effective teacher and how that correlates with the function of the classroom. When we talked about how to be an effective teacher we discussed three components, teaching through problem-solving and selecting appropriate tasks, creating appropriate environments and using appropriate interventions. In my field experience, I was able to observe these three effective mathematics teaching components and understand how they apply to the classroom. After leaning about these components, I was then able to use them in my personal experience and see how they

In today’s society mathematics is a vital part of day-to-day life. No matter what a person is doing at home or at the workplace, he/she is constantly using different mathematics skills to simply function. Then what does this mean for mathematics education? When someone needs to utilize a skill every day then he/she needs a strong background in the skill. Therefore, today’s students need more than a just a working knowledge of mathematics or enough knowledge to pass a test. Today’s students need to understand how mathematics works and how to utilize mathematics skills in the best way possible.

Social constructivism’s origins are largely attributed to Lev Vygotsky (1978). Vygotsky believed that social constructivism is the idea that learning occurs when people are socially active; in other words, learning is created through our interaction with others. In a constructivist style classroom, the focus shifts from the teacher teaching the students to the students teaching each other and having more control over what they learn by asking questions and coming up with their own conclusion on things (2016). This style of teaching can be very successful when the teacher provides enough scaffolding. In a typical classroom, you have a teacher standing in the front of the room lecturing to students while they sit and take notes on the information being given so they can spit it back up for a test they will have at the end of the unit. In the constructivist style classroom, the students are pushed to be more active and engaged in their learning process (Education Theory). The teacher creates an environment where students are urged to speak up and share what they think and have the class run more on a student run process. The teacher’s role in this style is not to sit and lecture information but rather engage students actively to find this information on their own and discover it so that it creates more meaning and provides a better understanding. The main goal in this type of learning environment is problem solving. This style of teaching promotes self-guidance and can even

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).

Constructivism is connected to the theories of Piaget and Vygotsky. Piaget believed that cognitive development occurred in four stages that have distinct developmental characteristics.  He theorised that all information is organised into ‘schemas’, and this refers to the manner in which a child organisesand stores information and knowledge received. As new information is received, it is either incorporated into existing schemas (assimilation) or new schemas (accommodation) are created (McDevitt & Ormrod, 2010).  Vygotsky’s theories compliment those of Piaget and place a greater importance on social interaction as he considered cognitive development predominately was achievedthrough social interaction.  Vygotsky believed that learning could be accelerated with the assistance of a more advanced peer or teacher.  This concept is referred to as the zone of proximal development (ZPD) and works in conjunction with the theory of ‘scaffolding’, where a teacher provides support to student and as proficiency increases the scaffolding is decreased (Marsh, 2008). Evidence of scaffolding is seen throughout the Maths video as Ms Poole provides an outline of the lesson and the goals to allow students to establish a focus.

This units has improved my mathematical competency and my disposition towards mathematics. I now feel a lot more confident in many specific mathematical areas and in mathematics in general. Also, I am much more aware of the progress in my mathematical understanding as I have identified my current strengths and weakness as well as created solid plans to improve the weaker areas. A negative disposition or anxiety towards mathematics, can hinder improvement. Students who are anxious, bored, fearful, or simply believe that mathematics is unimportant, are likely to avoid the study of mathematics (Metje, Frank, & Croft, 2007). This then becomes the real challenge of mathematics classes as the main emphasis is diverted from teaching the mathematics content to giving the students confidence in their mathematical skills. A reoccurring notion throughout this unit is the ‘big ideas’ of mathematics. A big Idea is an idea that is central to the learning of mathematics and a statement that links numerous mathematical understandings into a coherent whole (Charles, 2005). Charles (2005) believes that these big Ideas should be the “foundation for one’s mathematics content knowledge, for one’s teaching practices, and for the mathematics curriculum”. This is because grounding one’s mathematics content knowledge on these big ideas establishes a robust, in depth and advanced understanding of mathematics.