My Philosophy of a Constructivist Mathematics Education

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,

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.

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.

A classroom with a critical and creative thinking environment provides opportunities for higher-level thinking within authentic and meaningful contexts, complex problem solving, open-ended responses, and cooperation and interaction. Many students see math as right or wrong and they don’t question or explore more. As a future math teacher, I want students to learn to question, be critical, and be creative. I want my future students to feel engage in exploration and investigation. I want to equip my students with higher levels of thinking and engagement and make mathematics more relevant and meaningful.

A student has the ability to learn without a teacher. However, the Law of the Teaching Process creates the background for a teacher to guide a student on the path to more knowledge. A teacher should establish a safe environment that encourages thinking to help students learn “the unknown by the way of the known” (84). Acquiring their knowledge and increasing their mental power correlates to the aims of a teacher as they guide students. While a teacher is to be passionate in laying out knowledge, the really work of an education, acquiring knowledge, is the work of the student. A student learns by discovery and information stores as the student interprets the new information.

The great challenge for constructivism is that the world in which students and teachers interact is not utopian. Students come to class with predetermined ideas about a course, or with personal needs that distract from attention from the classroom experience. Some students are not willing or able to interact with peers due to emotional issues, thus

Constructivism in the classroom usually means students are engaged in activities like experiments, or real-world problem solving to increase knowledge, followed by a reflection of how their understanding of the concept has changed (Brooks, Ed.D, n.d.). Cognitivism methods of instruction are commonly integrated with the levels found in Bloom’s Taxonomy: knowledge, comprehension, application, analysis, synthesis and evaluation (Bloom, 1956). The instructor must understand the prerequisite knowledge possessed by the student, and the student is encouraged to use appropriate strategies to help make the learning meaningful.

Based on several studies, one of the best ways to understand mathematical ideas and apply these ideas is through the use of manipulatives. Students explore these manipulatives, however, it is important that they make their own observations. The teacher then should model and show how to use the materials and explain the link of these materials to the mathematical concept being taught. Schweyer (2000) stated that students learn best when they are active participants in the learning process where they are given the opportunity to explore, assimilate knowledge and discuss their discoveries.

students eyes to a world of mathematics that they never before could have even began to

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.

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.

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).

Furthermore, as I read the assigned articles and viewed videos, I realized that my teachers obviously, followed Piaget’s, Vygotsky. Dewey, and Bruner constructivist view because they used the theory of assimilation and accommodation, e.g., the learning of a new experience and changing of a person’s worldview. I also discovered after deep reflection on this week’s assignment, how much of an impact my teachers had on my teaching style. Before retiring, I taught based on what my students needed. Therefore, much of my teaching mixed the theories of, Constructivism, Social Constructivism and Cognitive-Behavioral depending on the student.

There are five identified central tenets of constructivism as a teaching philosophy: Constructivist teachers seek and value students’ points of view. This concept is similar to the reflective action process we call withitness, in which teachers attempt to perceive students’ needs and respond to them appropriately; Constructivist teachers challenge students to see different points of view and thereby construct new knowledge. Learning occurs when teachers ask students what they think they know about a subject and why they think they know it; Constructivist teachers recognize that curricula must have meaning for students. When students see the relevance of curricula, their interest in learning grows; Constructivist teachers create lessons that tackle big ideas, not small bits of information. By seeing the whole first, students are able to determine how the parts fit together; Constructivist teachers assess student learning in daily classroom activities, not through the use of separate testing or evaluation events. Students

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.