Assessing Fraction Knowledge(THIS IS PART OF A MATHEMATICS UNIT IN A BACHELOR OF EDUCATION DEGREE) - Coursework Example

Running Head: ASSESSING FRACTION KNOWLEDGE Name Course Instructor Date Table of Contents Table of Contents 2 Introduction 3 Background 3 Definition of fractional sense 3 Explain and discuss where fraction sense sits within mathematics education 4 Completion of tasks 4 Diagnostic Assessment 4 The students 5 Planning 5 Results 5 Discussion 6 Teaching fractions 6 What needs to be considered when teaching fractions? 6 What are effective teaching strategies to help children understand fractions? 7 What your lesson plan will address. 7 Lesson plan 7 Conclusion 9 References 9 Assessing Fraction Knowledge in Children Introduction In the past few years, the assessment of young children especially in mathematical learning has become increasingly essential. Because of a consensus that exists among practitioners and researchers that early childhood at the year between 2 and 4 of school is an essential period for school readiness, educators of these children believes that learning of mathematics in the form of fraction is very essential (Wright & Stafford, 2000). It is evident that when there are such consensus testing of mathematical fraction in young children becomes a frequent and often occurrence. The importance of this paper is to widely give an understanding why there is difficulty in teaching is finding out what children know or understand about an aspect of mathematics. As a result, this will give a clear idea of where to start teaching new material can be established. Background According to Wright & Stafford (2000), in their lives, children are known to develop mathematical competence early. Scholars and researchers have not been able to understand about how this whole concept occurs but assume that this competence develops in the course informal mathematical children experiences. In the past, it has been attributed that teachers, parents and scholars have not been able to see involvement in mathematics without any kind of close observation thus loosing on the opportunity to build on learning opportunities among children in their tender age (Wright & Stafford, 2000). Definition of fractional sense In order to understand fractional sense, it is essential to first understand what a fraction is. In mathematical concept, a fraction is defined as a ratio of two numbers other than zero. It can further be defined as a subdivision of whole. Sophian (2004) asserts that, fractions are divided in three senses. The first sense is that involving a component of a mixture which is separated by way of fractional process it is classified under nouns that denotes substances. The second sense entails a small section of item that forms a whole piece and that which is classified under nouns that denote manmade objects. Finally, the third sense entails quotient of two rational numbers and is classified under nouns that denotes units of measures and quantities (Sophian, 2004). Explain and discuss where fraction sense sits within mathematics education Today, due to increase in technology there is variation in where fractional sense sits within mathematics education. Sophian (2004) asserts that, technology is playing a major role in enhancing the in understanding fractions. Introducing children to technology enhances learning more through demonstration different fraction in terms of shapes, color and patterns. Use of several representations creates ability on young students to translate various representational models and fractional constructs. Further, educators need to provide necessary experiences as a way of enhancing student informal understanding of fractional concepts (Sophian, 2004). Completion of tasks In order to understand on the research topic, it was necessary to conduct some tasks so as to get first hand information. Two children one at the school age of four and the other six were used as samples. The three tasks involved entailed; asking them which fraction was bigger different fraction were used so as children could pick which was bigger, broken egg where children were ask if eggs were put in a basket and some broke how many were left after the broken ones were removed from the basket and finally, to get a third of something using different representation in the forms of balls, patterns and objects. Both the children have to participate in the three tasks with minimal assistance from their parents. Diagnostic Assessment Diagnostics assessment is usually designed to assists educators in finding out what children know and do not know about fractions. Diagnostic assessment should be carried out in all stages of understanding learning mathematics by young children (Hannula, 2005). These assessments are carried out in the form of interviews where Performa sheets should be used in assisting to record what is said during interview, close observation and questionnaire for parents. By using different assessment methods, it is evident that early childhood educators will be able to build up comprehensive idea on what students know or do not know about mathematics especially fractions. The students The two students that were picked one were at four and the other six year in school. The three year old was a girl who had only attended day care for several months whereas the four year old was a boy who had started attending junior school. Choosing these two students were essential so as to know if there exists variation when focusing on age groups and understanding fractions. The students were not be taught about the tasks but rather they were to follow example where the interviewer was to record the results. Planning According to Hannula (2005), planning was very essential so that to have proper grounds for discussion, analysis and finding regarding students understanding of mathematical fractions. The background of each child was noted down and paper and pens provided to each child.. Planning was in the form of: Choosing a task Introducing the task to the children Using the task with students Analyze the children sample Lesson plan for student learning Results The exercise with the two children proved to be a success at the end. The exercise was conducted with minimal assistance from the interviewer. In task1, the younger child, at year 2 demonstrated little knowledge in identifying which fraction was bigger. On the other hand the older one in year four had correct answers in this task. In task two and three, both children got the answers correct. Discussion It is evident that students tend to grasp concepts in fractions easily when taught using manipulative objects, images, objects and pictures. Use of such materials enable the students to see how the fractions are created hence encouraging them to form visual images in the mind and even try to find the answers mentally. At lower levels of primary, children have basic knowledge about fractions like it was demonstrated by the year two student. This is important because as they progress further to upper classes, they can understand complex fractional operations. It is therefore advisable for mathematics teachers to apply the strategy of teaching fractions by use of visual objects especially at lower classes instead of use of rules which prove to be difficult for students to memorize (Treacy and Cairnduff, 2009). Teaching fractions Fractions form an integral part of the mathematics curriculum hence should be introduced to children right from kindergarten. It cannot be overemphasized that fractions are used in almost all scenarios in life therefore all the concepts involved should be well understood by students. Concepts of simple fractions should begin to be taught to children in the lower classes of primary school. Acquisition of such knowledge goes a long in helping children to build on other skills such as in measurements and in telling time. There are many benefits of teaching fraction during early stages of life for example students can conduct simple measurements such as measuring the correct proportion of sugar when making cookies even during their juniors grade (Treacy and Cairnduff, 2009). What needs to be considered when teaching fractions? Sophian (2004) asserts that when teaching fractions in classroom, it is essential for student to have a deep understanding of the basic concepts that are being taught. Although fractions are taught as separate topics in the course of learning, they also form a crucial part of other areas in the mathematics curriculum. Therefore, it is vital for mathematic teachers to teach fractions in conjunction with other topics in the syllabus if full learning potential is to be realized. Any mathematics concept is well understood if intertwined with other concepts. It is also important for the teacher to know the age group of the students he/she is teaching. This is because students tend to understand fractions differently at different levels of life. For instance, at the primary level, students especially those at the lower levels tend to compare issues with real life scenarios hence it would be best if teachers taught fractions using visual models. What are effective teaching strategies to help children understand fractions? The most reasonable way of teaching fractions is by use of visual fractions whereby simple fractions are performed by use of images and pictures without necessarily using any specific rule. Although text books show fraction pictures, they are not enough and it is more appropriate for the teacher to draw pictures of fractions on the black or white board. Another way to make children find fractions interesting is to use delicacies such as Hershey’s milk chocolate and pizzas then instructing them to divide it into given fractions after which they will get to enjoy the chocolate. Use of computers and calculators is another way of making fractions an interesting unit (Hannula, 2005). What your lesson plan will address. My lesson plan will first address the objectives of the lesson to include what the students must achieve by the end of the lesson. The next part of the lesson plan will be the subject matter to include the references used, material, skills and the concepts used. The last part will be the procedure to be followed to carry out the activities. Lesson plan I. Objectives Identify simple fractions. Shade the given figure according to the fractions given. Appreciate the work of each other in terms of beauty and neatness II. Subject Matter: Topic: Simple Fractions Materials: A basket of eggs, cut pieces of card with varying shapes and colored balls. Skills: Identify fractions, Coloring, appreciate the beauty of one’s work. Concepts: Fractions III. Procedure: Task 1: To identify which fraction is bigger. 1/4 or 1/2 1/3 or 1/2 Task 2 Teacher’s Activities Pupils’ Activities Teacher: Class, what are these Eggs These are broken and unbroken boiled eggs. Do you also eat eggs? Yes/No Madam I know you are hungry, so we’ll take a bite. Come to the front and identify the fraction of broken eggs A part of a whole is called_______ A fraction So what is the fraction of broken eggs in the basket? 2/5 Good Task 3: To arrange the ball in way that demonstrates a third. Conclusion Fractions form an important part of everyday life; therefore they should be taught in way that can be understood by students with different understanding capabilities. Children should be exposed to fractions right from their lower levels of education such they will have no difficulties in other units in mathematics that utilize the fraction principles. The exercise demonstrated that that fractions can be understood very easily if taught properly. References Hannula, M. (2005). Spontaneous focusing on numerosity in the development of early mathematical skills. Turku, Finland: University of Turku Press. Sophian, C. (2004). Mathematics for the future: Developing a Head Start curriculum to support mathematics learning. Early Childhood Research Quarterly, 19, 59-81. Treacy, K. and Cairnduff, J. (2009). Revealing What Students Think: Diagnostic Tasks for Fractional Numbers. Perth: Steps Professional Development. Wright, R. & Stafford, A. (2000). Early Numeracy: Assessment for Teaching and Intervention. London: Paul Chapman Read More

Completion of tasks In order to understand on the research topic, it was necessary to conduct some tasks so as to get first hand information. Two children one at the school age of four and the other six were used as samples. The three tasks involved entailed; asking them which fraction was bigger different fraction were used so as children could pick which was bigger, broken egg where children were ask if eggs were put in a basket and some broke how many were left after the broken ones were removed from the basket and finally, to get a third of something using different representation in the forms of balls, patterns and objects.

Both the children have to participate in the three tasks with minimal assistance from their parents. Diagnostic Assessment Diagnostics assessment is usually designed to assists educators in finding out what children know and do not know about fractions. Diagnostic assessment should be carried out in all stages of understanding learning mathematics by young children (Hannula, 2005). These assessments are carried out in the form of interviews where Performa sheets should be used in assisting to record what is said during interview, close observation and questionnaire for parents.

By using different assessment methods, it is evident that early childhood educators will be able to build up comprehensive idea on what students know or do not know about mathematics especially fractions. The students The two students that were picked one were at four and the other six year in school. The three year old was a girl who had only attended day care for several months whereas the four year old was a boy who had started attending junior school. Choosing these two students were essential so as to know if there exists variation when focusing on age groups and understanding fractions.

The students were not be taught about the tasks but rather they were to follow example where the interviewer was to record the results. Planning According to Hannula (2005), planning was very essential so that to have proper grounds for discussion, analysis and finding regarding students understanding of mathematical fractions. The background of each child was noted down and paper and pens provided to each child.. Planning was in the form of: Choosing a task Introducing the task to the children Using the task with students Analyze the children sample Lesson plan for student learning Results The exercise with the two children proved to be a success at the end.

The exercise was conducted with minimal assistance from the interviewer. In task1, the younger child, at year 2 demonstrated little knowledge in identifying which fraction was bigger. On the other hand the older one in year four had correct answers in this task. In task two and three, both children got the answers correct. Discussion It is evident that students tend to grasp concepts in fractions easily when taught using manipulative objects, images, objects and pictures. Use of such materials enable the students to see how the fractions are created hence encouraging them to form visual images in the mind and even try to find the answers mentally.

At lower levels of primary, children have basic knowledge about fractions like it was demonstrated by the year two student. This is important because as they progress further to upper classes, they can understand complex fractional operations. It is therefore advisable for mathematics teachers to apply the strategy of teaching fractions by use of visual objects especially at lower classes instead of use of rules which prove to be difficult for students to memorize (Treacy and Cairnduff, 2009).

Teaching fractions Fractions form an integral part of the mathematics curriculum hence should be introduced to children right from kindergarten. It cannot be overemphasized that fractions are used in almost all scenarios in life therefore all the concepts involved should be well understood by students. Concepts of simple fractions should begin to be taught to children in the lower classes of primary school.

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