Developing minds of tomorrow: exploring students' strategies involved in the generalization of linear patterns (original) (raw)
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The Seventh Grade Students’ Generalization Strategies of Patterns
Journal of Education and Learning (EduLearn)
This article describes a generalization strategy on pictorial visual patterns. This explorative descriptive study involves 60 students of 7 Grade Student of private junior high school in Tuban East Java Indonesia. Data obtained through the pattern generalization task. The type of pattern used in this research is pictorial sequences with two non-consecutive terms. Selection of a pictorial sequences with two non-consecutive pattern to focus students' attention on visual stimuli. Based on the students answers of pattern generalization task, there are 33 students who answered correctly and 27 students answered wrong. From the correct answer, there are six different general formula representations. The visualization strategy used by the students begins by splitting the image into smaller elements. The way students break down into smaller elements is also diverse. Students divide the image in the form of V (2 matchsticks), U shape (3 matchsticks), square shape (4 matchsticks) and lastly divide in a unit additive consisting of 7 matchsticks.
Exploring and Fostering Second Graders' Mathematical Patterning
A teaching experiment on patterning was conducted with grade two pupils using pattering activities to identify their abilities and difficulties, and to develop their thinking as much as possible. Thus, the objective was to explore and foster pupils' mathematical patterning: creating and extending patterns, identifying units of repeat and its length, and predicting terms of given patterns. The teaching experiment was conducted at Dona Berber Primary School found in Bahir Dar City Administration. Twenty-five students (from seven to thirteen years of age) who got parental permission to come to school in the opposite school shifts were taken as participants of the study. These pupils sat in groups of five and each group was provided with matchsticks, beads with different sizes, bottle tops, and counters with different shapes and colors. The teaching experiment was conducted in two periods each lasting two and half an hour. Data were gathered using task-based group interviews, field notes, observations, and pupils' sample works that were captured through mobile camera. Although students indicated that they had learned patterning in their previous grade, they constructed only constant patterns. However, after provided with an analogy for repeating patterns, they created many and even complex repeating patterns. They could easily extend given patterns and determine the unit of repeat and its length. However, predicting terms was difficult for them except for patterns with length of core unit two.
The Thinking Process of Students Using Trial and Error Strategies in Generalizing Linear Patterns
Numerical: Jurnal Matematika dan Pendidikan Matematika, 2020
Patterns generalization learning at the junior high school is more emphasis on the generalization of linear patterns. One problem in generalizing linear patterns is that students do not know the process of using trial and error strategies to generalize linear patterns. For this reason, the purpose of this study was to analyze the thought processes of 2 junior high school students who succeeded in generalizing linear patterns using trial and error strategies. The results show that there are two trial and error strategies that can be used to generalize linear patterns, namely: (1) Trial and error strategy by looking at the relationship of quantity consists of three steps. The first step is called relating, namely, the subject connects between the first term, the term in question, and difference. The second step is called searching, where the subject finds similarities by using addition and subtraction operations to obtain the nth term formula. The third step is called extending; the s...
Developing the Mind of Tomorrow
The study investigates students' strategies involved in the generalization of "linear patterns". The study followed the qualitative research approach by conducting task-based interviews with twenty-nine primary second grade students from different high, intermediate and low ability levels. Results of the study presented several strategies involved in the generalization of the patterns including visual, auditory, mental, finger counting, verbal counting, and traditional (paper and pencil) strategies. The findings revealed that the type of the assigned pattern (simple or complex) and the type of the structure of the pattern itself (increasing or decreasing) play a big role for students' strategies involved to either discover the rule of the pattern or to extend it. However, students in early ages could master several skills and choose appropriate procedures to deal with patterns, which indicate that they could develop their algebraic thinking from early stages. Findings of the study also revealed that using different senses, using the idea of coins, using the numbers line, recognizing musical sounds, using concrete materials like fingers, applying different visual and mental strategies, and even applying traditional calculations could help students to work with "linear patterns". It is recommended that teachers introduce different strategies and procedures in teaching patterns to meet the needs of students as different learners, give them the opportunities to develop their thinking strategies and explore their thoughts. More research is recommended to explore students' strategies involved in the generalization of different kinds of patters at different stages.
– Algebra is generally considered as manipulating symbols, while algebraic thin king is about generalization. Patterns can be used for generalizat ion to develop early graders' algebraic thinking. In the generalization of pattern context, the purpose of this study is to investigate middle school students' reasoning and strategies at different grades when their algebraic thin king begin s to develop. First, 6 open-ended linear growth pattern problems as numeric, pictorial, and tabular representations were asked to 154 middle g rade students. Next, two students from each grade (6 th , 7 th , and 8 th grade) were interviewed to investigate how they interpret the relationship in different represented patterns, and which strategies they use. The findings of this study showed that students tended to use algebraic symbolis m as their grade level was increased. However, the students' conceptions about 'variable' we re troublesome.
The characteristics of junior high school students in pattern generalization
Journal of Physics: Conference Series, 2019
Much research on generalization of Algebra, but related to the generalization of the pattern is still lacking. In this study we characterizing middle school students generalization of pattern. The participants were 40 students grade 8 took the test with instruments that have been developed and analyzed students working. The findings indicate that students showed the two characterizing in generalization of patterns that: (1) Factual, (2) Symbolic. Possible reason are discussed and suggestions for teaching with generalization of patterns are presented.
Repeating patterns: Strategies to assist young students to generalise the mathematical structure
Australasian Journal of Early Childhood
THIS PAPER FOCUSES ON VERY young students' ability to engage in repeating pattern tasks and identifying strategies that assist them to ascertain the structure of the pattern. It describes results of a study which is part of the Early Years Generalising Project (EYGP) and involves Australian students in Years 1 to 4 (ages 5 – 10). This paper reports on the results from the early years' cohort (Year 1 and 2 students). Clinical interviews were used to collect data concerning students' ability to determine elements in different positions when two units of a repeating pattern were shown. This meant that students were required to identify the multiplicative structure of the pattern. Results indicate there are particular strategies that assist students to predict these elements, and there appears to be a hierarchy of pattern activities that help students to understand the structure of repeating patterns.
The aim of this article is to investigate the ability of the kindergarten children (5-6 years of age) to extend and reproduce different types of patterns which are constructed with a variety of materials, before formal teaching. From the record of their answers, a correlation was found between their actions in the different pattern constructs which formed six performance types: 1. Modification of the pattern. 2. Deficient extension (reproduction) of the pattern. 3. Random extension (reproduction) of the pattern. 4. Reverse extension (reproduction) of the pattern. 5. Sectional extension (reproduction) of the pattern. 6. Ordinary extension (reproduction) of the pattern. The
Pattern tasks: thinking processes used by 6th grade students
Relime Revista Latinoamericana De Investigacion En Matematica Educativa, 2012
Este documento es una descripción de un estudio en curso enfocado en tareas modelo de exploración y generalización, analizando el desempeño de cincuenta y cuatro alumnos de 6° grado cuando resuelven este tipo de tareas. El principal objetivo es entender las estrategias que utilizan, las dificultades que emergen del trabajo de los alumnos y averiguar el papel que desempeñan mediante la visualización en su razonamiento. Hasta ahora, los resultados indican que, en general, los alumnos tienden a usar planteamientos numéricos en lugar de planteamientos visuales. También tienden a usar estrategias incorrectas cuando intentan generalizar, siendo la más común un uso incorrecto de la proporción directa.