scholarly journals Selecting and Sequencing Students’ Solutions in Orchestrating Mathematical Discussions: Subtraction of Fractions

2020 ◽  
Vol 8 (4) ◽  
pp. 1-27
Author(s):  
Reyhan Tekin Sitrava
Keyword(s):  
Mathematical Discussions

Wearable Technology

2020 ◽  
pp. 332-349
Author(s):  
Esther Ntuli ◽  
Angie Godfrey
Keyword(s):  
Regression Analysis ◽  
Teaching And Learning ◽  
Student Thinking ◽  
Self Assessment ◽  
Mathematics Classrooms ◽  
Questioning Strategies ◽  
Education Experience ◽  
Questioning Techniques ◽  
Mathematical Discussions ◽  
Gathering Data

Teacher questioning is integral to teaching and learning in mathematics classrooms. Research indicates that purposeful questioning in mathematics classrooms engages, motivates, and deepens student understanding and critical thinking during mathematical discussions. This chapter used both qualitative and quantitative approaches to examine the levels of questions and questioning strategies used by elementary teachers while facilitating mathematical tasks. Findings indicate that teachers use more funneling questions than focusing questions while facilitating math tasks. Most teachers hardly arrive at that reflection and justification level of questioning. Teachers found the Pivothead glasses to be effective not only for teacher self-assessment of their questioning techniques but also for gathering data on student thinking. Regression analysis indicates that education, experience, and location are the most important variables influencing the level of questions asked and questioning strategies used by the teachers.

An Integral Part of Facilitating Mathematical Discussions: Follow-up Questioning

2019 ◽  
Vol 18 (2) ◽  
pp. 377-398 ◽  
Author(s):  
Woong Lim ◽  
Ji-Eun Lee ◽  
Kersti Tyson ◽  
Hee-Jeong Kim ◽  
Jihye Kim
Keyword(s):  
Mathematical Discussions

scholarly journals “Let us discuss math”; Effects of shift‐problem lessons on mathematical discussions and level raising in early algebra

2019 ◽  
Vol 32 (4) ◽  
pp. 743-763
Author(s):  
Sharon M. Calor ◽  
Rijkje Dekker ◽  
Jannet P. van Drie ◽  
Bonne J. H. Zijlstra ◽  
Monique L. L. Volman
Keyword(s):  
Control Group ◽  
Early Algebra ◽  
Seventh Grade ◽  
Group Setting ◽  
Student Groups ◽  
Shift Problem ◽  
Mathematical Discussions ◽  
Post Test ◽  
Quasi Experimental ◽  
Problem Condition

Abstract We investigated whether early algebra lessons that explicitly aimed to elicit mathematical discussions (shift-problem lessons) invoke more and qualitatively better mathematical discussions and raise students’ mathematical levels more than conventional lessons in a small group setting. A quasi-experimental study (pre- and post-test, control group) was conducted in 6 seventh-grade classes (N = 160). An analysis of the interaction processes of five student groups showed that more mathematical discussions occurred in the shift-problem condition. The quality of the mathematical discussions in the shift-problem condition was better compared to that in the conventional textbook condition, but there is still more room for improvement. A qualitative illustration of two typical mathematical discussions in the shift-problem condition are provided. Although students’ mathematical levels were raised a fair amount in both conditions, no differences between conditions were found. We concluded that shift-problem lessons are powerful for eliciting mathematical discussions in seventh-grade shift-problem early algebra lessons.

Engaging All Students in Mathematical Discussions

2017 ◽  
Vol 23 (6) ◽  
pp. 350-359 ◽  
Author(s):  
Damon L. Bahr ◽  
Kim Bahr
Keyword(s):  
Full Participation ◽  
Mathematical Discussions

Use these four strategies to promote full participation from your young mathematicians.

By Way of Introduction

1978 ◽  
Vol 25 (4) ◽  
pp. 3
Keyword(s):  
Mathematical Discussions

This month's cover has interesting possibilities for developing some mathematical insights and generating some mathematical discussions. Display the design someplace where all the children can see it and, after giving children a chance to look at the design, ask them to tell the class what they see in it. Some will see it as a configuration of plane figures—hexagons, triangles, squares, and so on. Others will see a stack of cubes. And some may see things that no one else sees.

Diverge Then Converge: A Strategy for Deepening Understanding Through Analyzing and Reconciling Contrasting Patterns of Reasoning

2020 ◽  
Vol 8 (2) ◽  
pp. 8-24
Author(s):  
Theresa J. Grant ◽  
Mariana Levin
Keyword(s):  
Elementary Teachers ◽  
Conceptual Understanding ◽  
Future Research ◽  
Conceptual Issue ◽  
Prospective Elementary Teachers ◽  
Written Responses ◽  
Teaching Content ◽  
Mathematical Discussions ◽  
Relevant Factors ◽  
Implementation Of The Strategy

One of the challenges of teaching content courses for prospective elementary teachers (PTs) is engaging PTs in deepening their conceptual understanding of mathematics they feel they already know (Thanheiser, Philipp, Fasteen, Strand, & Mills, 2013). We introduce the Diverge then Converge strategy for orchestrating mathematical discussions that we claim (1) engenders sustained engagement with a central conceptual issue and (2) supports a deeper understanding of the issue by engaging PTs in considering both correct and incorrect reasoning. We describe a recent implementation of the strategy and present an analysis of students’ written responses that are coordinated with the phases of the discussion. We close by considering conditions under which the strategy appears particularly relevant, factors that appear to influence its effectiveness, and questions for future research.

Cenário do Surgimento e o Impacto do Teorema da Incompletude de Gödel na Matemática

2018 ◽  
Vol 10 (3) ◽  
pp. 198
Author(s):  
Rosemeire De Fatima Batistela ◽  
Maria Aparecida Viggiani Bicudo ◽  
Henrique Lazari
Keyword(s):  
Mathematical Community ◽  
Incompleteness Theorem ◽  
Axiomatic Method ◽  
Mathematical Discussions ◽  
The Impact

Este artigo trata do panorama das discussões matemáticas mantidas entre os matemáticos à época em que Gödel apresentou à comunidade matemática seu teorema da incompletude. Argumenta-se que o Teorema da Incompletude de Gödel (TIG) é um teorema mais para a alma do que para as mãos dos matemáticos. Afirma-se ser ele importante porque mostra que a Matemática não pode comunicar (provar) todas as suas verdades. Porém, as provas de que a aritmética básica dos naturais é incompleta e incompletável e da impossibilidade de demonstrar a sua não contradição não impossibilita que a Matemática continue sendo produzida. A linha de argumentação exposta segue apresentando: o cenário matemático vigente no momento da publicação do TIG; o ponto de incidência deste resultado na Matemática, o impacto deste teorema nesta ciência, bem como, como ele foi compreendido e acolhido pelos matemáticos.Palavras-chave: Teorema da Incompletude de Gödel (TIG). Problema da Compatibilidade da Aritmética. Programa de Hilbert. Método Axiomático.AbstractThis article deals with the panorama of the mathematical discussions held among mathematicians at the time when Gödel introduced his incompleteness theorem to the mathematical community. It is argued that Gödel’s Incompleteness Theorem (TIG) is a more theorem for the soul than for the hands of mathematicians. It is said to be important because it shows that Mathematics can’t communicate (prove) all its truths. However, evidence that the basic arithmetic of the natural is incomplete and incomplete and that it is impossible to demonstrate its non-contradiction does not preclude mathematics from being produced. The line of argument exposed continues presenting: the mathematical scenario in force at the time of the publication of the TIG; The point of incidence of this result in Mathematics, the impact of this theorem on this science, as well as how it was understood and welcomed by mathematicians.Keywords: Gödel’s Incompleteness Theorem. Hilbert’s Second Problem. Hibert’s Program. Axiomatic Method.

Power in Numbers: Student Participation in Mathematical Discussions in Heterogeneous Spaces

2013 ◽  
Vol 44 (1) ◽  
pp. 288-315 ◽  
Author(s):  
Indigo Esmonde ◽  
Jennifer M. Langer-Osuna
Keyword(s):  
African American ◽  
High School Students ◽  
Mathematics Learning ◽  
Figured Worlds ◽  
African American Student ◽  
American Student ◽  
School Students ◽  
Mathematical Practices ◽  
Mathematics Classrooms ◽  
Mathematical Discussions

In this article, mathematics classrooms are conceptualized as heterogeneous spaces in which multiple figured worlds come into contact. The study explores how a group of high school students drew upon several figured worlds as they navigated mathematical discussions. Results highlight 3 major points. First, the students drew on 2 primary figured worlds: a mathematics learning figured world and a figured world of friendship and romance. Both of these figured worlds were racialized and gendered, and were actively constructed and contested by the students. Second, these figured worlds offered resources for 1 African American student, Dawn, to position herself powerfully within classroom hierarchies. Third, these acts of positioning allowed Dawn to engage in mathematical practices such as conjecturing, clarifying ideas, and providing evidence.

scholarly journals Enacting Number Talks in a Simulated Classroom Environment: What Do Preservice Teachers Notice About Students?

2021 ◽  
Vol 4 (4) ◽  
pp. 772-795
Author(s):  
Dawn M. Woods
Keyword(s):  
Preservice Teachers ◽  
Classroom Environment ◽  
Mathematical Reasoning ◽  
Mathematical Thinking ◽  
Learning Cycle ◽  
Missed Opportunities ◽  
Human In The Loop ◽  
Mathematical Discussions ◽  
Support Students ◽  
Number Talks

Number talks are short mathematical discussions offering sensemaking opportunities for students. Aside from bolstering students’ mathematical learning, this instructional routine may also support preservice teachers (PSTs) in investigating how to facilitate discussion-focused instruction. In this study, PSTs engage in a learning cycle to explore, plan and rehearse two separate number talks during human-in-the-loop simulations, and then reflect on these experiences. During the first simulation, PSTs focus on understanding the routine’s components while positioning avatar-students as sensemakers as they elicit their participation. In the second simulation, PSTs build their instructional skills as they record representations of students’ mathematical thinking, probe students’ thinking in order to make mathematics visible, as well as notice missed opportunities to support students’ mathematical reasoning during reflections of their experiences. Implications of this study suggest that simulations, when embedded within a cycle of enactment and reflection, support PSTs in developing professional noticing skills.

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