Josh's Operational Conjectures: Abductions of a Splitting Operation and the Construction of New Fractional Schemes

2008 ◽  
Vol 39 (4) ◽  
pp. 401-430
Author(s):  
Anderson Norton
Keyword(s):  
Sixth Grade ◽  
Teaching Experiment ◽  
Theoretical Integration ◽  
Fine Grained ◽  
Learning Paradox ◽  
Sixth Grade Students ◽  
Scheme Theory ◽  
Splitting Operation ◽  
Problematic Situations

This article reports on students' learning through conjecturing, by drawing on a semester-long teaching experiment with 6 sixth-grade students. It focuses on 1 of the students, Josh, who developed especially powerful ways of operating over the course of the teaching experiment. Through a fine-grained analysis of Josh's actions, this article integrates Piaget's scheme theory (1950/2001) and Peirce's logic of abduction (1998) into a new theory about conjecturing that explains Josh's learning. Results indicate the power of Josh's operational conjectures in resolving problematic situations and constructing new schemes. Because of the context in which the teaching experiment and Josh's conjecturing occurred, results hold implications for research on fractions and on a particular operation called splitting (Confrey, 1994; Empson, 1999; Sáenz-Ludlow, 1994; Steffe, 2003). The theoretical integration of scheme theory and abduction also holds implications for resolving the learning paradox (Fodor, 1980; Glasersfeld, 2001).

scholarly journals Exploring Students’ Understanding of Statistical Mean

2020 ◽  
Author(s):  
Md Amiruzzaman
Keyword(s):  
Conceptual Understanding ◽  
Sixth Grade ◽  
Teaching Experiment ◽  
Central Tendency ◽  
Procedural Understanding ◽  
Know How ◽  
Sixth Grade Students ◽  
Mathematical Problems ◽  
The Mean

This study explores students’ understanding of one measure of central tendency, the mean. A teaching experiment was conducted to understand how sixth-grade students made sense of this concept. Findings suggest that the students know how to solve mathematical problems related to mean using procedural understanding and lack of conceptual understanding.

scholarly journals Fortalecimiento de las competencias matemáticas a partir de la resolución de problemas en operaciones básicas de números naturales, para estudiantes del grado sexto en Colombia

2017 ◽  
Vol 8 (1) ◽  
pp. 62-70
Author(s):  
María Alejandra Sánchez Díaza
Keyword(s):  
Educational Institution ◽  
Sixth Grade ◽  
The Other ◽  
San Jose ◽  
Problem Statement ◽  
Construction Of Knowledge ◽  
Problem Situations ◽  
Sixth Grade Students ◽  
Mathematical Problems ◽  
Problematic Situations

Resumen: A continuación, se describe en el siguiente artículo, referente a una investigación realizada cuyo objetivo es implementar talleres guías para el fortalecimiento de la competencia matemática de resolución en los sistemas numéricos a través del Método Polya, para los estudiantes de sexto grado de la Institución Educativa Colegio San José “El Trigal” de Cúcuta. La metodología empleada fue de investigación acción, donde se utilizaron como instrumentos para recabar la información: la observación directa, diarios de campo, prueba diagnóstica y talleres guía. Con respecto a la propuesta, su autora presenta diversas estrategias de aplicación de talleres guía, con el fin de atender la dificultad que tienen los estudiantes del grado sexto para la resolución de problemas: que consiste en leer, analizar y solucionar situaciones problemáticas en los distintos conjuntos de numeración, reflejadas en los hallazgos obtenidos en las pruebas institucionales y en las llamadas “PRUEBAS SABER”. Los resultados de la investigación determinaron que los participantes logran solucionar situaciones problemas, desde la Comprensión del enunciado del problema, Aclaración de dudas, Identificación de todos los datos y de lo que quería encontrar, Formulación de un plan para encontrar una solución, Realización de las operaciones correctamente y Verificación del resultado. Finalmente se propone a la Institución asignar una hora de Formulación y Solución de Problemas matemáticos, además la planeación de clases a partir de Talleres Guías, ya que facilitan la construcción de conocimientos a partir de aprendizajes significativos y la interacción con el otroPalabras clave Competencias matemáticas, Resolución de problemas, Operaciones básicas de Números NaturalesAbstract: Next, it is described in the following article, referring to a research carried out whose objective is to implement guides workshops for the strengthening of the mathematical competence of resolution in the numerical systems through the Polya Method, for the sixth grade students of the Educational Institution Colegio San José “El Trigal” of Cúcuta. The methodology used was action research, where they were used as instruments to collect the information: direct observation, field diaries, diagnostic test and guide workshops. With respect to the proposal, the author presents several strategies for the application of guiding workshops, in order to address the difficulty of sixth grade students to solve problems: reading, analyzing and solving problematic situations in different sets of numbers, reflected in the findings obtained in the institutional tests and in the so-called “TESTS KNOW”. The results of the research determined that the participants managed to solve problem situations, from the understanding of the problem statement, clarification of doubts, identification of all the data and what he wanted to find, formulation of a plan to find a solution, operations correctly and Verification of the result. Finally it is proposed to the Institution to assign an hour of Formulation and Solution of Mathematical Problems, besides the planning of classes from Workshops Guides, since they facilitate the construction of knowledge from significant learning and interaction with the other. Keywords Mathematical competences, Problem solving, Basic Operations of Natural Numbers

A Comparison of Four Adolescent Language Tests

1987 ◽  
Vol 18 (3) ◽  
pp. 250-266 ◽  
Author(s):  
R. Jane Lieberman ◽  
Ann Marie C. Heffron ◽  
Stephanie J. West ◽  
Edward C. Hutchinson ◽  
Thomas W. Swem
Keyword(s):  
Test Performance ◽  
Sixth Grade ◽  
Significant Discrepancy ◽  
Language Impaired ◽  
Language Functions ◽  
Language Tests ◽  
Significant Difference ◽  
Sixth Grade Students ◽  
Overall Performance ◽  
Selection Of

Four recently developed adolescent language tests, the Fullerton Test for Adolescents (FLTA), the Test of Adolescent Language (TOAL), the Clinical Evaluation of Language Functions (CELF), and the Screening Test of Adolescent Language (STAL), were compared to determine: (a) whether they measured the same language skills (content) in the same way (procedures); and (b) whether students performed similarly on each of the tests. First, respective manuals were reviewed to compare selection of subtest content areas and subtest procedures. Then, each of the tests was administered according to standardized procedures to 30 unselected sixth-grade students. Despite apparent differences in test content and procedures, there was no significant difference in students' performance on three of the four tests, and correlations among test performance were moderate to high. A comparison of the pass/fail rates for overall performance on the tests, however, revealed a significant discrepancy between the proportions of students identified in need of further evaluation on the STAL (20%) and the proportion diagnosed as language impaired on the three diagnostic tests (60-73%). Clinical implications are discussed.

PENERAPAN STRATEGI MENJAWAB SECARA BERGANTIANBERPOLA LINGKARAN ROUND ROBIN UNTUKMENINGKATKAN HASIL BELAJAR PPKn SISWA KELAS VISDN 002 UKUI DUA KECAMATAN UKUI

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Diyan Pertiwi
Keyword(s):  
Student Learning ◽  
Learning Outcomes ◽  
Sixth Grade ◽  
Student Learning Outcomes ◽  
Round Robin ◽  
Class Action ◽  
Sixth Grade Students ◽  
Teachers And Students ◽  
Improve Student Learning ◽  
Low Activity

This study is a class action that aims to improve learning outcomes in subjects PPKn sixth grade students of SDN 002 Ukui Dua. This research is motivated by the low activity and low teacher and student learning outcomes in subjects PPKn. The problem of this study is whether the implementation of a strategy to answer alternately patterned circle round robin can improve student learning outcomes in subjects PPKn in the sixth grade SDN 002 Ukui Dua? This PPKn was conducted over two cycles. Data collection techniques in this research using collection observation techniques, achievement test, and documentation. Techniques of analysis in this study is an analysis of the activities of teachers and students and learning outcomes in subjects PPKn sixth grade students SDN 02 Ukui Dua Kecamatant Ukui. The result showed that the activity of teachers has increased. At the first meeting of the first cycle of 41% was obtained with Simply Perfect category and the second meeting reached 55% with the category Fairly Perfect. In the second cycle 3 meeting to reach 75% by the Perfect category and the 4th meeting of the second cycle reaches 85% with the Perfect category. While the activity of students has increased. At the first meeting of the first cycle reaches 51% with the category Fairly Perfect and the second meeting with the percentage of 66% to the category Perfect. After the second cycle of the third meeting with a percentage of 75% with the Perfect category while in attendance for-4 with the percentage of 94% to the category of Most Perfect. Learning outcomes of students also increased from the previous students who achieve KKM only 8 votes with a percentage (45%) after the first cycle an increase in students worth over KKM which reached 14 people with a percentage of 70%. Cycle II students who achieve KKM 17 (85%).

PENERAPAN PENDEKATAN KONTEKSTUAL UNTUK MENINGKATKAN HASIL BELAJAR IPA KELAS VI SD NEGERI 004 TEMBILAHAN KOTA KECATAMATAN TEMBILAHAN

2018 ◽  
Vol 2 (2) ◽  
pp. 293
Author(s):  
Sarminah Sarminah
Keyword(s):  
Action Research ◽  
Learning Outcomes ◽  
Science Learning ◽  
Sixth Grade ◽  
Contextual Approach ◽  
Science Students ◽  
Student Activity ◽  
Sixth Grade Students ◽  
Classroom Action Research

The background of this research is the low of science learning result of grade 6 students of SDN 004 TembilahanKota. The purpose of this study is to improve the learning outcomes of science students of grade VI SDN 004Tembilahan Kota with the application of contextual approach. This research was conducted in class VI SDN004 Tembilahan Kota. This research is a Classroom Action Research with two cycles. The subjects of thisresearch are the sixth grade students of SDN 004 Tembilahan Kota lesson year which consist of 30 people with16 men and 14 women. Based on the results of the research from the teacher activity sheets appear to increase ateach meeting. At the first meeting of cycle I 64.3%, the second meeting of cycle I was 67.86%. At the firstmeeting of cycle II 71,43%, and second meeting of cycle II 78,57%. While the student activity also increasesevery meeting. At the first meeting of cycle I 67,86%, second meeting of cycle I 71,43%. At the first meeting ofthe second cycle of 75%, and the second meeting II cycle 78.57%. The learning outcomes in the first cycleincreased by 12.8% from the base score of 67.83% to 76.5%. In the second cycle increased by 17.2% to 79.5%.

Young learners’ voices: Towards a learner-centered approach to understanding language assessment literacy

2021 ◽  
pp. 026553222199227
Author(s):  
Yuko Goto Butler ◽  
Xiaolin Peng ◽  
Jiyoon Lee
Keyword(s):  
Language Assessment ◽  
Sixth Grade ◽  
Assessment Literacy ◽  
Supporting Evidence ◽  
Structured Interviews ◽  
Assessment Practice ◽  
Young Learners ◽  
Assessment Tasks ◽  
Sixth Grade Students ◽  
Assessment Skills

Language assessment literacy (LAL) has recently gained substantial attention among language educators and other stakeholders. However, existing models focus almost exclusively on teachers, test developers, and administrators, and lack students’ perspectives in their conceptualizations. To address this gap, with this exploratory study we aimed to understand young learners’ LAL. The participants were fourth- and sixth-grade students (ages 9–10 and 11–12, respectively, with 10 participants in each age group) in China. After taking English mock tests, the children participated in individual, semi-structured interviews that covered their understanding of the following: (a) assessment purposes and theories (their knowledge about how assessment works); (b) assessment skills (their views of assessment designs, procedures, and content); and (c) assessment principles (their notion of fairness, cheating, and feedback). The data were analyzed qualitatively in line with current LAL models. The results suggest that the children already had substantial assessment literacy in knowledge, skills, and principles. Although their teachers’ assessment practice remains form-focused, children generally want more communicative-based and diagnostic assessment. They also want more cognitively challenging and enjoyable assessment tasks. Our findings provide solid supporting evidence for the importance of considering students’ perspectives, along with the views of other stakeholders, in order to have a more balanced understanding of LAL.

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