Base 10 Ten Number System

INTRODUCTION

A teacher’s job is to ensure that all students are given the opportunity to be effectively taught. In order to achieve these objectives teachers need to obtain students’ prior knowledge and understanding to plan effectively. Throughout this report, the benefits and disadvantages of diagnostic interviews will be evaluated. It will also display how diagnostic interviews provide aid to a teachers’ professional judgment. In addition, the report will focus on the importance of understanding the place value and base ten number system. During the report, misconceptions will be revealed that students encounter with place value, and strategies introduced in which teachers can use to overcome these misconceptions. Discussion of students’

The base ten number system is the number system used by us in Australian, made up of 0 through 9. Place value position is determined by its value. The importance of understanding place value is that it gives knowledge of an amount to help make decisions in our everyday lives it relates to costs of things, distances and time. Firstly it needs to be understood the base ten number system of 0 through to 9, then understanding that after you reach ten it is regrouped and moves up to the next place value. Whilst learning the base ten number system it is important to also learn to subitize. Subitizing is the ability to recognise amounts quickly such as fingers and dots. “Subitizing is a fundamental skill in the development of number sense, supporting the develop of conservation, compensation, unitizing, counting on, composing and decomposing of numbers” (Silva, 2005, p. 5). The ability to group and quantify patterns quickly supports a child development with number sense. In addition, it is necessary to fully comprehend place value in order to perform “algorithms for addition, subtraction, multiplication, and division” (Reys et al., 2016, ch. 8.2). It is critical that students fully understand the meaning of a number to further develop their mathematics, and to overcome any misconceptions developed along the

Concrete models provide an opportunity for students to explore and gaining a true identity of number sense through patterning activities, classification, sorting and counting using a range of hands-on materials. An example is partitioning numbers in order to help students identify large numbers as numbers made of smaller components. This helps students to visualise numbers in their head making it easier to later calculate problems. Experiencing a range of concrete material activities is important in the development of students as prior knowledge differs in each student affecting the way in which they learn (Reys et al., 2016, ch. 8.2). Meaningful experiences can enhance learning by making the learning relevant to the students. For example making footprints and then building the feet together to form models helps create an abstract model, or the feet could be a variety of colours to represent a variety of values, or partitioned into different amounts to form the same number in a variety of ways. Number lines create place value thinking and promote skip counting and can be used very simply with a lot of numbers helping children to recognise patterns and also with very few numbers in order to developmental strategies. However starting with small and proportional