According to MOE Curriculum guide and a detailed recommendation for classroom implementation

According to the Ministry of Education in Trinidad and Tobago, their curriculum guide states that;

Numeracy refers to the ability and competence to apply mathematical concepts (ideas) and skills (processes) to effectively engage in and manage diverse situations in real life. It facilitates the development of higher-order thinking skills that equip students with a solid foundation for the problem-solving challenges of the future.

They also state that “fraction is used to describe equal parts of a whole or equal parts of a collection of objects. It is a number (e.g. ¼ is a number on a number line). After teaching fractions they want to ensure that students would be able to explain the ways fractions are used outside of school.

Our Group Determined,

Students can be introduced to fractions informally by the use of discrete objects,

such as pencils, pies, chairs, etc. If the whole is a collection of 4 pencils, then one

pencil is 1/4 of the whole. If the whole is 5 chairs, then one chair is 1/5 of the whole, etc.

This is an appropriate way to introduce students to the so-called unit fractions,1/2, 1/3 ,1/4 , . . .

The pros and cons of using discrete objects to model fractions are clear. It is simple, but it limits students to thinking only about \how many" but not “how much". Thus if the whole is 4 pencils, we can introduce the fractions 2/4 and 3/4 by counting the number of pencils, but it would be unnatural to use this method to introduce the whole.

Evaluate the teaching of fractions by Teachers in Trinidad. Propose Recommendations for Teaching Fractions to aid Students' understanding

The national assessment of educational progress reports that fractions are "exceedingly difficult for children to master" (NAEP, 2001).

Teachers in the teaching of fractions often employ direct teaching strategy that promotes procedural knowledge and down plays conceptual understanding of concepts. In Trinidad, our group determined that some reasons for this type of teaching were time constraints, teachers’ beliefs and style(lazy teacher syndrome J) and examination oriented culture for SEA, National Test etc. There is a wide curriculum gap between the expectation of the syllabus and what actually happens in the classroom.

The following are recommendations proposed to the teaching of fractions at Ordinary level:

1) Staff development workshops and seminars to equip teachers with skills which will enable them to employ child centred teaching strategies that may result in the conceptual understanding of concepts.

2) If teachers make sure they provide a sound definition of a fraction and provide additional time for student exploration with fractions they may find that their students perform better.

3) Teachers should encourage students to generate their own examples as this will help them understand concepts better.

4) It is important for teachers to prove increased time on the topic to give students enough time to conceptualize the concepts.

5) Assessment should be school based on the process of teaching rather than the outcome of teaching, for example, the assessment criteria of the national syllabus should not be centred on public examinations but should incorporate a component of continuous assessment to encourage teachers to use appropriate teaching strategies to meet the curriculum goals of relevant teaching.

How do you use Fractions in your everyday life? How can you get your students to understand that they use fractions in their everyday life?

Our group recognized that we use fractions in our everyday life via many avenues, however we will only post one to allow others the opportunity to post different ways. When sharing our pack of skittles in class, we actually count how many are in the pack and determine how much each person gets to ensure an equal share...(I of course get the uneven number if there are any :)

To help students recognize that they use fractions in there everyday life we  would verbalize our "sharing/dividing" stories and have them do the same giving them the opportunity to recognize the pattern of how often they use this concept without even being aware of it.

Many people use fractions in one way or another in everyday life. For example, when a person wakes up and allocates the time to spend on each item of the daily chores, the time spent x on one of the items is part of the twenty-four hours in a day. One may further come into contact with fractions on checking time. In the majority of cases many people including students do this without realizing that they are coming into contact with fractions (Burns, 1992).

Fractions are central to peoples’ everyday lives (Burns, 1992). People need to have a deep understanding of fractions for them to be able to apply them in their day-to-day activities. Researchers have established that many students have considerable difficulty in understanding fractions (Behr et al., 1992). The sources of the students’ problems of understanding fractions may be categorized into two major related groups. These are the formal teaching strategies and informal learning of fractions concept as argued by Behr and others (1992) Informal learning starts at an early stage before pupils go to school and continues during formal learning. This implies that prior knowledge on a particular concept like fractions is so vital in the learning process. Students’ prior knowledge is a combination of different life experiences they have encountered in their day to day lives that require them to use knowledge of fractions. If students fail to realize their informal encounter with fractions in their daily activities, the formal learning of such concept remains abstract and irrelevant.

Students’ learning depends on the teaching strategy. When students are taught concepts by rules, they are not afforded the opportunity to construct a conceptual foundation for understanding.

Hierarchy of Skills for Teaching Fractions

This is the Hierarchy of Skills for teaching fractions given by Mr. David Ali. The questions I pose to everyone are:

1.       1. Were you as a student taught following this format when you were in school?

2.       2.  Do you believe that teachers are aware of this system when it pertains to teaching fractions in their classroom?

3.       3. Do you think children will understand fractions better if they are taught following this hierarchy of skill?

Our group concluded that we were only sometimes taught using these levels, however due to the time constraints of the lessons teachers were often in a rush to “complete the syllabus” instead of allowing students the opportunity to grasp understanding. We also believe that teachers are aware of the hierarchy of skills but due to the large content and level scope they often bypass it to accomplish the task of completing a packed syllabus in such a short time. Honestly we also believe that teaching following accomplishment of these different levels will ensure that students learn and UNDERSTAND the content of fractions better.

Hierarchy of Skill for fractions.

 Develop an understanding of fractions using area models.

·         Identify wholes and parts of wholes.

·         Differentiate between equal and unequal parts of the whole.

Become aware of the names associated with fractions to tenths using area models.

·         Explore the relationship among concrete (area model), pictorial and symbolic representations of fractions up to tenths.

Demonstrate an understanding of equivalent fractions.

·         Compare and order fractions by direct comparison.

·         Explore equivalent forms of fractions with denominators up to ten.

·         Compare and order fractions using the concept of equivalence

Extend the concept of fractions to include multiple representations, equivalence, ordering and simple computation.

·         Explore fractions using area, linear and set models.

·         Recognize and generate equivalent fractions using a variety of models.

·         Use the algorithm for finding equivalent fractions.

·         Compare and order proper fractions with unlike denominators using equivalent forms.

·         Distinguish between proper, improper and mixed number and convert from one form to another.

·         Add and subtract proper fractions with same denominators.

Demonstrate an understanding of solving problems involving fractions and the four operations.

·         Add a fraction to a whole number.

·         Subtract a fraction from a whole number.

·         Add and subtract fractions involving same denominator and one denominator a multiple of the other.

·         Multiply fractions by whole numbers.

·         Calculate the whole given a part as a unit fraction.

·         Divide whole numbers by fractions.

·         Solve real-life problems involving fractions and using the algorithms developed.

Demonstrate an understanding of adding and subtracting fractions and mixed numbers, concretely, pictorially and symbolically.

·         Develop and apply algorithms to add and subtract fractions and mixed numbers.

·         Solve problems involving addition and subtraction of fractions including mixed numbers.

Demonstrate an understanding of multiplying a fraction by a whole number, multiplying fractions and mixed numbers concretely, pictorially and symbolically.

·         Develop and apply algorithms to multiply:

ü  a fraction by a whole number

ü  fraction by fraction

ü  mixed numbers

Demonstrate an understanding of dividing whole numbers by fractions, fractions by whole numbers and fractions concretely, pictorially and symbolically.

·         Solve problems involving the multiplication of:

ü  a fraction by a whole number

ü  fraction by fraction

ü  mixed numbers

·         Develop and apply algorithms to divide:

ü  a whole number by a fraction

ü  a fraction by a whole number

ü  A fraction by fraction.

·         Solve problems involving the division of:

ü  a whole number by a fraction

ü  a fraction by a whole number

ü  A fraction by a fraction.

WELCOME TO MATH 2003
The challenges of Teaching and Learning Fractions at the Early Level.