Hye, we meet again!! During my third workshop with Dr. Ann, we have been introduced to the concept of algebra. Algebra could be generally defined as a branch of mathematics dealing with relation, utilizing letters and and represent certain numbers or values. In relation to algebra topic, our attention was been drawn to the topic of ' pattern' and ' function'. These topics will be further explored in this entry in relation to provide a meaningful and hands on learning experience.
PATTERN
- Warren and Cooper (2006) classify two types of predominant pattern that a child explored in the early years, which is repeating pattern and growing pattern. Warren and Cooper (2006) put forward the notion that the learning of these patterns indirectly helps to children to develop their understanding of functional thinking, that is relationship between two data sets, at an early age.
- In teaching repeating patterns to the students, Papik ( 2007) recommended that children recognize and identify the repeating patterns better if they were immersed in meaningful experience.Those meaningful experience serves as a direction to the teaching and learning of patterns and algebra in the first years of schooling.
- Repeating patterns is a sequence or set which is repeated over and over. Liljedahl (2004) defines repeating pattern as a cyclic structure which is generated by repeated application of a smaller potion of the pattern itself. For example AB is a repeating unit of a pattern containing ABABABAB.
* Useful tips : In teaching repeating patterns to the children,teachers need to make sure that the children are able to recognize the core of the pattern.
In giving out a meaningful learning experience to the children which introduce and extends the understanding of repeating pattern, teacher can conduct the series of activities as below.
1) Recognize the pattern - at this stage, children needs to recognize the core of the pattern. Children needs to master this skill beforehand as the skill will be required in the next stage. The teacher can starts the lesson giving out an example of a repeating pattern.Taking example of repeating pattern of ABABABAB, this pattern will be displayed to the class ( see picture below). In getting the students to understand the concept of 'core', teachers can scaffold the learning process by giving out questions like
" What is being repeated in this pattern?"
" It is AB? Yes, AB is being repeated."
" Thus, what do we call AB? Yes, AB is the core of this pattern which eventually repeats itself, thus forming this pattern."
Warren and Copper advocates that patterns which is presented in a variety of different modes such as geometric shape appears to be more effective as it enhances the potential for generalizing the core of a pattern regardless of the mode. Taking that as a consideration, the teacher uses unfix cubes to represent ABABAB pattern horizontally. However, at the later stage where the students are required to copy and create the pattern, the students need to do it vertically in a tower pattern.
" It is AB? Yes, AB is being repeated."
" Thus, what do we call AB? Yes, AB is the core of this pattern which eventually repeats itself, thus forming this pattern."
Warren and Copper advocates that patterns which is presented in a variety of different modes such as geometric shape appears to be more effective as it enhances the potential for generalizing the core of a pattern regardless of the mode. Taking that as a consideration, the teacher uses unfix cubes to represent ABABAB pattern horizontally. However, at the later stage where the students are required to copy and create the pattern, the students need to do it vertically in a tower pattern.
2) Copy a pattern - at this stage,teacher sets the students to re-create the patter. In doing so, teacher can sets the students in pairs, get the students to talk to each other regarding the pattern that has been shown to them at the beginning of the lesson. It is important for the children to verbalize and describing the pattern to each other. Then, the teacher explains that they need to create the exact pattern except that they will do it vertically, in a tower form, until the 4th term only.
3) Extend a pattern- students should be able to continue a pre- established rule, in this context would be the rule of copying and re create the pattern which have been shown to them at the beginning of the lesson.
4)Create a pattern- using the unfix cubes of different colours which each represent the unit A and B, students need to create the pattern instructed by the teacher. It is important for the teacher to put forward the notion of maintaining a consistent rule in creating the pattern.
5)Translate a pattern- at this stage, justification of the student's pattern will be evaluated. In order to assess whether the students understand the concept of repeating patter, students should be encouraged to justify their pattern and the strategy used to solve the task. For example, the teacher can post questions for instance
Student's task : copy ABABAB pattern using the unfix cubes, forming a vertical tower pattern until the 4th term
3) Extend a pattern- students should be able to continue a pre- established rule, in this context would be the rule of copying and re create the pattern which have been shown to them at the beginning of the lesson.
4)Create a pattern- using the unfix cubes of different colours which each represent the unit A and B, students need to create the pattern instructed by the teacher. It is important for the teacher to put forward the notion of maintaining a consistent rule in creating the pattern.
5)Translate a pattern- at this stage, justification of the student's pattern will be evaluated. In order to assess whether the students understand the concept of repeating patter, students should be encouraged to justify their pattern and the strategy used to solve the task. For example, the teacher can post questions for instance
Teacher : What is the unit being repeated in this pattern?
Student : AB is repeated in the pattern.
Teacher: How do you know when you stop? How do you know not to put the cube
together anymore? ( pointing at the student's tower pattern)
Student : Because we need to put the AB cube four times only. This is
the first,( pointing to the AB cube at the tower ), this is the second, third and the fourth. When it comes to fourth term, we need to stop building the tower.
Student : AB is repeated in the pattern.
Teacher: How do you know when you stop? How do you know not to put the cube
together anymore? ( pointing at the student's tower pattern)
Student : Because we need to put the AB cube four times only. This is
the first,( pointing to the AB cube at the tower ), this is the second, third and the fourth. When it comes to fourth term, we need to stop building the tower.
The questions posted eventually develops the student's higher order thinking and reasoning skills. In fact, it serves as a evident which clearly demonstrate the student's understanding of concept of repeating pattern and concept of number of repetition as well.
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