Middle school students’ patterning performance on semi-free generalization tasks

Rivera, F. D.; Becker, Joanne Rossi

doi:10.1016/j.jmathb.2016.05.002

Cited by 18 publications

(9 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For older pupils and students, this topic has been examined from different perspectives. For example, Rivera and Becker (2016) investigated pattern generalization of seventh-and eighth-grade students in so called semi-free tasks. Here, students were asked to find two different continuations of figural patterns, given the first figure or the first two figures.…”

Section: Creating Figural Patternsmentioning

confidence: 99%

Mathematical creativity and mathematical giftedness in the primary school age range: an interview study on creating figural patterns

Aßmus

Fritzlar

2022

ZDM Mathematics Education

View full text Add to dashboard Cite

Relationships between mathematical giftedness and mathematical creativity have been widely studied, but few studies are available for primary school age. For an investigation in this age group, it seems appropriate to use a content area that not only has high relevance for mathematics and special potentials for creativity, but also requires only a little knowledge and is easily accessible. We therefore investigated whether mathematically gifted primary school students differ from non-gifted ones in high creativity in dealing with mathematical patterns and structures. This question was explored in an interview study in which 24 third graders were asked to invent as many different figural patterns as possible, which enabled creative mathematical activity also by combining arithmetic and geometric aspects. A detailed qualitative analysis of the data revealed among other results several types of flexibility concerning the invention of patterns. The selection of students ensured that all participants performed well to very well in regular mathematics classes and that 14 of them could additionally be assumed to be mathematically gifted based on a specific test. This allowed a comparison of both subgroups. Results indicate a high correspondence between mathematical giftedness and mathematical creativity concerning the invention of figural patterns.

show abstract

Section: Creating Figural Patternsmentioning

confidence: 99%

Mathematical creativity and mathematical giftedness in the primary school age range: an interview study on creating figural patterns

Aßmus

Fritzlar

2022

ZDM Mathematics Education

View full text Add to dashboard Cite

show abstract

“…These criteria are explained by the fact that mathematics teachers have difficulties in generalizing quadratic patterns, as is reported in the literature. Besides, inductive reasoning is one of the mathematical reasoning types necessary to solve quadratic pattern generalizing tasks (Cañadas, Castro, & Castro, 2009;Rivera & Becker, 2016). The quadratic equation concept was chosen because, in the mathematics curriculum in Mexico, it is associated with the activity of generalizing quadratic patterns (Ministry of Public Education, 2017).…”

Section: Context and Participantsmentioning

confidence: 99%

“…Inductive reasoning contributes to the formation of concepts because it 'lead [s] to detecting regularities, be it classes of objects represented by generic concepts, be it common structures among different objects, or be it schemata enabling the learners to identify the same basic idea within various contexts' (Klauer, 1996, p. 53). Secondly, it is one of the forms of reasoning that supports the process of generalizing numerical and figural patterns or mathematical objects (Cañadas, Castro, & Castro, 2008;2009;Rivera & Becker, 2016).…”

mentioning

confidence: 99%

Secondary School Mathematics Teachers’ Perceptions About Inductive Reasoning and Their Interpretation in Teaching

Moguel

Landa

2021

J. Math. Educ.

View full text Add to dashboard Cite

Inductive reasoning is an essential tool for teaching mathematics to generate knowledge, solve problems, and make generalizations. However, little research has been done on inductive reasoning as it applies to teaching mathematical concepts in secondary school. Therefore, the study explores secondary school teachers’ perceptions of inductive reasoning and interprets this mathematical reasoning type in teaching the quadratic equation. The data were collected from a questionnaire administered to 22 teachers and an interview conducted to expand their answers. Through the thematic analysis method, it was found that more than half the teachers perceived inductive reasoning as a process for moving from the particular to the general and as a way to acquire mathematical knowledge through questioning. Because teachers have little clarity about inductive phases and processes, they expressed confusion about teaching the quadratic equation inductively. Results indicate that secondary school teachers need professional learning experiences geared towards using inductive reasoning processes and tasks to form concepts and generalizations in mathematics.

show abstract

“…Therefore, learning mathematics in schools is expected can give all students the opportunity to understand mathematics and assist the students in developing mathematical knowledge that directs them to solve problems and explore new ideas, inside and outside the classroom. Mathematical problem solving plays an important role in schools, where this ability is an ability that requires students to solve mathematical problems quickly and carefully (Firdaus et al, 2019;Mason, 2008;Rivera & Becker, 2016;Walkowiak, 2014).…”

Section: Introductionmentioning

confidence: 99%

Investigating Middle School Students Generalization of Number Pattern Based on Learning Style

Firdaus¹,

Juniati²,

Wijayanti³

2021

TURCOMAT

View full text Add to dashboard Cite

Pattern generalization is an important aspect of mathematics contained in every topic in teaching. This study aims to investigate middle school students’ generalization of number patterns based on learning style. Descriptive qualitative, portraying or describing the events that are the center of attention (problem-solving abilities, student learning styles) qualitatively.This study explored 4 participants (12 to 13 years old) with their constructed number pattern they had generalized during individual task-based interviews. Questions that include indicators of the problem solving process in terms of student learning styles, and interviews. The data analysis used was namely data reduction, data presentation, drawing conclusions. We found that students who are converger, diverger, accommodator, and assimilator understands the problem by knowing what is known and asked and explains the problem with their own sentences. The converger and assimilator students look back without checking the counts involved, the diverger students do not see other alternative solutions and do not check the counts involved, accommodator students consider that the solutions obtained are logical, ask themselves whether the question has been answered, check the counts that are done, reread the question, and use other alternative solutions. The implication of this study indicated that students of the type of converger, diverger, accommodator, and assimilator are able to solve problems through the stages of implementing plans by interpreting problems in mathematical form, implementing strategies during the process and counting takes place. Based on several studies on pattern generalization, there have not been researchers who have revealed the number pattern generalization of high school students based on learning styles.

show abstract

Middle school students’ patterning performance on semi-free generalization tasks

Cited by 18 publications

References 18 publications

Mathematical creativity and mathematical giftedness in the primary school age range: an interview study on creating figural patterns

Mathematical creativity and mathematical giftedness in the primary school age range: an interview study on creating figural patterns

Secondary School Mathematics Teachers’ Perceptions About Inductive Reasoning and Their Interpretation in Teaching

Investigating Middle School Students Generalization of Number Pattern Based on Learning Style

Contact Info

Product

Resources

About