Factors Affecting Students' Performance in Generalizing Algebraic Patterns (original) (raw)
Related papers
– 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.
Eurasia Journal of Mathematics, Science and Technology Education
This paper explores how a group of pre-service elementary school teachers training to become mathematics teachers for elementary schools arrived at generalizations based on patterns. Two representative problems were investigated with these preservice teachers. The focus of this study was how these preservice teachers analyze and symbolize algebraically their generalizations during a problem-solving process. The results indicate that the preservice teachers had difficulty making use of input-output (having two variables in the table) relationships in a generalization process associated with developing symbolic functions. This study identifies the crucial need for introducing students to pattern activities early on in their lives.
2020
Students' algebraic thinking skills must continue to be developed because they can support success in mathematics. Algebraic thinking relates to generalizing patterns learned at the junior secondary level. During the process of generalizing students use the perception of similarity or proximity. Therefore, the purpose of this study is to describe the algebraic thinking process of junior high school students in generalizing patterns. The approach used is qualitative with 3 research subjects who have different algebraic thought processes. The results showed that junior high school students carried out algebraic thought processes by perceiving images, representing, looking for functional relationships, making generalizations, and applying general formulas. The difference in perception is used early in the activity and in the search for functional relationships. The results of this study can be used in developing mathematics learning strategies so that students' algebraic thinki...
Generalization strategies of beginning high school algebra students
2005
This is a qualitative study of 22 9 th graders performing generalizations on a task involving linear patterns. Our research questions were: What enables/hinders students' abilities to generalize a linear pattern? What strategies do successful students use to develop an explicit generalization? How do students make use of visual and numerical cues in developing a generalization? Do students use different representations equally? Can students connect different representations of a pattern with fluency? Twenty-three different strategies were identified falling into three types, numerical, figural, and pragmatic, based on students' exhibited strategies, understanding of variables, and representational fluency.
Learning through patterns: a powerful approach to algebraic thinking
We are engaged in a project named Mathematics and patterns in elementary schools: perspectives and classroom experiences of students and teachers. Our aim is to analyze the impact of an intervention centered on the study of patterns in the learning of mathematics concepts and on the development of communication and development of higher order thinking skills. In this paper we present part of an ongoing research with pre-service teachers concerning the development of teachers’ algebraic thinking, in particular how they move through pattern tasks involving generalization. We will present some of the tasks used in the didactical experience and some preliminary conclusions of its implementation in the mathematics didactics classes of a mathematics elementary teachers’ course of a School of Education.
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.
Mathematical Thinking and Learning, 2005
The expectation that students be introduced to algebraic ideas at earlier grade levels places an increased burden on the classroom teacher to help students construct and justify generalizations. This study provides insight into the reasoning of 25 sixth-grade students as they approached patterning tasks in which they were required to develop and justify generalizations while using computer spreadsheets as an instructional tool. The students demonstrated both the potential and pitfalls of such activities. During whole-class discussions, students were generally able to provide appropriate generalizations and justify using generic examples. Students who used geometric schemes were more successful in providing general arguments and valid justifications. However, during small-group discussions, the students rarely justified their generalizations, with some students focusing more on particular values than on general relations. It is recommended that the various student strategies and justifications be brought to the forefront of classroom discussions so that students can examine the mathematical power and validity of the various strategies and justifications typically introduced by students. The introduction of algebraic concepts at earlier grade levels creates new challenges and possibilities for developing student understanding. To aid the transition to formal algebra, documents from the Australian Education Council (1994), the National Council of Teachers of Mathematics (2000) in the United States, and the Department for Education and Skills (2001) of Great Britain recommended the use of tasks in which elementary and middle school students generalize patterns. Additionally, these documents support an increased availability of technological tools (e.g., graphing calculators, computer spreadsheet software) that allow students to
GENERALIZATION OF PATTERNS: THE TENSION BETWEEN ALGEBRAIC THINKING AND ALGEBRAIC NOTATION
This study explores the attempts of a group of preservice elementary school teachers to generalize a repeating visual number pattern. We discuss students' emergent algebraic thinking and the variety of ways in which they generalize and symbolize their generalizations. Our results indicate that students' ability to express generality verbally was not accompanied by, and did not depend on, algebraic notation. However, participants often perceived their complete and accurate solutions that did not involve algebraic symbolism as inadequate.
MATHEdunesa, 2019
This research aims to describe the algebraic thinking of junior high school students, with systematic and intuitive cognitive style, in solving number pattern problem. There are four components of algebraic thinking, that are generalization from arithmetic, meaningful use of symbols, identify and extend a pattern, and mathematical modeling. The type of research is descriptive-qualitative research. Two eighth graders became the subject of this research who are determined based on systematic and intuitive cognitive styles. The data collection methode are assignments and interviews. The results show that both students understand the letter symbols as the subtitute of any number of objects in the problem when understanding the problem. When devising the plan, both students identifies the pattern by determining the difference between pattern and finding the number relationships, besides, student with systematic style look for the relationship between the term and the order by decontructing the known terms in the pattern. In carrying out the plan, student with systematic cognitive-style use ℎ term of arithmetic sequence equation to determine the term of a number pattern and use general form that had been found to determine the order of the term, but student with intuitive cognitive styles only use ℎ term of arithmetic sequence equation to determine the term and the order of the term of a number pattern. Both students don't do algebraic thinking in looking back.
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.