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.
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ReplyDeleteThe Teaching of Fractions should also be guided by the National Council of Teachers of Mathematics (NCTM)
DeleteMathematics teachers are guided by principles that are outlined by the National Council of Teachers of Mathematics (NCTM). These principles are there to ensure a high quality of education in numeracy is delivered to students and the processes are there as a guide in teaching the subject. The processes include communication, representation, problem-solving, connections and reasoning and proof. These processes can be included in the teaching of Fractions as educators must ensure that proper communication occurs and children develop problem solving skills. Conceptual and relational understanding in Mathematics bring together these processes as conceptual knowledge allows students to gain a proper representation of the content being taught and the students are able to make connections with higher order questions because of a well taught concept. One of the processes reasoning and proof can be directly related to relational understanding as students through relational understanding know what to do and why and this can be translated to students being able to reason out problems and prove why a specific approach was taken.
Teaching Fractions conceptually and relationally would allow for greater success in the classroom. Students would benefit from lessons that would stay in their long term memory and they would understand specifically why a task or procedure is being done and not just go on with the notion that one must learn the rules and follow them with no questions asked. With relational understanding students have fun learning and as they also create their own knowledge they build confidence in themselves and so the famous “mathematics anxiety” that students face can be diminished as success surges. It is essential that teachers adopt these approaches to teaching Mathematics to ensure that significant learning occurs in the classroom and Fractions will no longer be seen as a challenge.
References:
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Common Fraction Scope and Sequence
ReplyDeleteCLASS CONCEPT COM/
ORDERING EQUALIVANCE ADD SUB MULIT DIV MENTAL/P.SOL
Infants 1
Infants 2 half -quarter*no symbols
Std 1 half (1/2)-quarter (1/4)-third (1/3)-fifth (1/5)-tenth(1/10
Std 2 Introduce set model-half (1/2)-quarter (1/4)-third (1/3 Comparing 2 fractions ordering Equivalent fractions Like denominators(oral) Like denominators
Standard 3 to Standard 5
Concepts – improper fractions mixed numbers (3-5)
Comparisons – Conversions of improper fractions to mixed numbers (3-5)
Equivalence - Introduce common multiples (3-5)
Standard 3 - Addition like and unlike denominators Standard 4 & 5 mixed numbers.
Standard 3 – Subtraction like and unlike denominators Standard 4 & 5 mixed numbers Standard 3 - mental oral problems
Standard 4 - Multiplication Fraction by whole numbers written problems.
Standard 5 - Two proper fractions, two improper fractions, two mixed numbers and numbers by a fraction.
Standard 4 - Division whole numbers by fractions
Standard 5 -Fraction by fraction and fraction by a whole numbers.
This proceeded table care to show what level and what topics are given to our students to learn the dynamics of fractions, how it is gradually introduced to them.
In the teaching of fractions, teachers need to understand what fractions are and what children should come to understand about them. Children must understand various aspects about fraction concepts and relationships before beginning fraction computation. A key element of all instruction is to make sure that students understand the concept and many do so by visualizing these concepts and relationships. Teachers should thus be able to draw from the experiences of the students when teaching, so that the students can relate and connect with the concepts that are being taught; in this case fraction. In Trinidad, many teachers teach the concept of fractions without putting thought into it or putting much effort into the students grasping this concept fully. Several recommendations that can be made to the teaching of fractions, which include:
ReplyDelete• When deciding on a method of how to teaching fractions, we need to use fractional analogies that the student will immediately recognize.
• Use visual models or manipulatives during the teaching of fractions. In that way fractions become something concrete to the students, and not just a number on top of another without a meaning.
• Ensure those fractions are thought with simplification slowly and thoroughly.
• Explain the numerator and the denominator until every student understands. Students will never understand how to add or subtract a fraction until they truly understand the concept of a fraction.
Fractions are an important part of the mathematics curriculum. Understanding fraction concepts, comparison, ordering, number sense and equivalence lays the foundation for later work with fraction computation and prepares children for using mathematics in their everyday lives.
Group Members: C. Bisram, R. Simbhoo, E. Sucre, K. Khan, C. Ramdhanee
Reference:
Cathcart, G. W., Pothier, Y.M., Vance, J.H & Bezuk, N.S (2011). Learning Mthematics In Elementary and Middle Schools: A Learner Centred Approach (5th Edition). Boston: Prentice-Hall Inc
Group members: Rishmattie Maharaj, Christine Jianath, Angalie Maraj, Maya Dass
ReplyDeleteTeaching the concepts of fractions is one of the main challenges in teaching mathematics at school. One reason for that is how to engage students in activities that involve such concepts in their everyday life. They construct knowledge about fractions from experiences at home, sports games etc. students then come to school with this “constructed” knowledge which then interacts with the “instructed” knowledge offered by the mathematics curriculum and teachers (Smith, 2002). When students are exposed to fundamental fraction concepts early in the elementary grades, their understanding of fractions develops and changes (Saxe et al, 2005). It is our job as teachers to help students to make the connection between their constructed knowledge and their instructed knowledge as well as the new powerful ideas that we expect them to learn and master.
Reference
Hart, K. (1981). Fractions, Children understanding of mathematics: 11-16. CSMS 1981, (pp 66-81).
In Trinidad and Tobago the teaching of fractions affects the Learning of fractions which can be one of the most difficult tasks for children. My group members and I agree totally with the notion that teachers in Trinidad and Tobago teach the concept of fractions in a way that promotes procedural knowledge and deprive students of learning conceptually. One of students’ problems is that they don’t view fractions as numbers at all, but as “meaningless symbols that need to be manipulated in arbitrary ways to produce answers that satisfy a teacher,”
ReplyDeleteAnother common problem is that teachers in Trinidad and Tobago too often focus on the learning outcomes and not on the learning process. This is why students frequently misunderstand concepts. The difficulty children have with fractions should not be surprising considering the complexity of the concepts involved and the lack of emphasis placed on teaching each concept in a way that students can understand. Clearly, the way fractions are taught must be improved. Because of the complexity of fraction concepts, more time should be allocated in the curriculum for developing students' understanding of fractions. But just more time is not sufficient to improve understanding; the emphasis of instruction should also shift from the development of algorithms for performing operations on fractions to the development of a quantitative understanding of fractions.