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.

Transforming K-12 Mathematics Classroom Teacher Pedagogy Through Virtual Number Talks

2021 ◽  
pp. 402-422
Author(s):  
Candace Joswick ◽  
Nicole Fletcher ◽  
Audrey Meador
Keyword(s):  
Teacher Learning ◽  
Mathematics Classroom ◽  
Mathematical Thinking ◽  
Classroom Teacher ◽  
Mathematics Learning ◽  
The United States ◽  
Learning Cycle ◽  
Teacher Pedagogy ◽  
K 12 ◽  
Number Talks

Number Talks is a popular K-12 mathematics routine utilized in classrooms across the United States. Number Talks allows teachers to elicit and respond to students' mathematical thinking through the development of an encouraging classroom community and provide opportunities for students to engage in critical thinking, collaboration, communication, and creativity. In this chapter, the authors report their “virtualization” of the Number Talks routine and the development of a teacher learning cycle that supports implementation of this practice. The virtualization of Number Talks is illustrated through the pedagogical transformation of one teacher, who begins the teacher learning cycle skeptical of the value of Number Talks and ends with an innovative Virtual Number Talks practice that benefited both students and teachers in her school. This teacher's implementation of Virtual Number Talks and engagement in the “4C” of 21st century learning demonstrate a transformation of pedagogy that uses technology to create rich online mathematics learning experiences.

Supporting PSTs in Using Appropriate Tools Strategically: A Learning Sequence for Developing Technology Tasks That Support Students' Mathematical Thinking

2017 ◽  
Vol 5 (2) ◽  
pp. 122-157 ◽  
Author(s):  
Milan F. Sherman ◽  
Charity Cayton ◽  
Kayla Chandler
Keyword(s):  
Preservice Teachers ◽  
Mathematics Teachers ◽  
Teacher Educators ◽  
Mathematical Thinking ◽  
Mathematical Tasks ◽  
Learning Sequence ◽  
Mathematics Teacher Educators ◽  
Preservice Mathematics Teachers ◽  
High Level ◽  
Support Students

This article describes an intervention with preservice mathematics teachers intended to address the use of Interactive Geometry Software (IGS) for mathematics instruction. A unit of instruction was developed to support teachers in developing mathematical tasks that use IGS to support students' high-level thinking (Smith & Stein, 1998). Preservice teachers used the IGS Framework (Sherman & Cayton, 2015) to evaluate 3 tasks, to revise a task, and ultimately to design a task using the framework. Results indicate that a majority of preservice teachers in this study were successful in creating a high-level task where IGS was instrumental to the thinking demands, and that the IGS Framework supported them in doing so. The article concludes with suggestions for use by fellow mathematics teacher educators.

scholarly journals The power of dialogue and discovery

2018 ◽  
Vol 42 (3) ◽  
pp. 113-122
Author(s):  
Kalina Jastrzębowska
Keyword(s):  
Teaching Methods ◽  
Classroom Environment ◽  
Group Work ◽  
Mathematics Learning ◽  
Learning Opportunities ◽  
Innovative Teaching ◽  
Dialogic Teaching ◽  
The Relationship ◽  
Academic Year ◽  
Number Talks

Greater emphasis must be placed on activities that promote innovative teaching methods in early childhood mathematics education in Poland. Our classrooms offer algorithmic and rote teaching methods, depriving students of important elements of successful mathematics learning. The aim of this action research was to investigate the relationship between a classroom environment that allows for dialogue and discovery and young children’s input into problem solving. Teaching six classes of elementary school within one academic year gave the author the opportunity to examine how dialogic teaching combined with a growth mindset approach can transform the attainment of knowledge, understanding and skills of learners, and how modern practices like number talks, solving open-ended tasks and group work can unleash students’ potential and activate them as thinkers and reasoners. The results confirmed that students who are challenged and offered concept-based learning opportunities not only genuinely engage in their tasks, but also help each other with deeper understanding of the concepts. They can cooperate with teachers in the creation of a new classroom in which students’ voices are heard and discoveries take place.

scholarly journals Resolución de problemas matemáticos en GeoGebra

2020 ◽  
Vol 9 (1) ◽  
pp. 26-42
Author(s):  
William Enrique Poveda Fernández
Keyword(s):  
Costa Rica ◽  
Problem Solving ◽  
Secondary School ◽  
Secondary School Teachers ◽  
Mathematical Reasoning ◽  
Mathematical Thinking ◽  
School Teachers ◽  
Mathematical Objects ◽  
Problem Solving Strategies ◽  
Problem Solving Process

RESUMENEn este artículo se analizan y discuten las ventajas y oportunidades que ofrece GeoGebra durante el proceso de resolución de problemas. En particular, se analizan y documentan las formas de razonamiento matemático exhibidas por ocho profesores de enseñanza secundaria de Costa Rica, relacionadas con la adquisición y el desarrollo de estrategias de resolución de problemas asociadas con el uso de GeoGebra. Para ello, se elaboró una propuesta de trabajo que comprende la construcción y la exploración de una representación del problema, y la formulación y la validación de conjeturas. Los resultados muestran que los profesores hicieron varias representaciones del problema, examinaron las propiedades y los atributos de los objetos matemáticos involucrados, realizaron conjeturas sobre las relaciones entre tales objetos, buscaron diferentes formas de comprobarlas basados en argumentos visuales y empíricos que proporciona GeoGebra. En general, los profesores usaron estrategias de medición de atributos de los objetos matemáticos y de examinación del rastro que deja un punto mientras se arrastra.Palabras claves: GeoGebra; Resolución de problemas; pensamiento matemático. RESUMOEste artigo analisa e discute as vantagens e oportunidades oferecidas pelo GeoGebra durante o processo de resolução de problemas. Em particular, as formas de raciocínio matemático exibidas por oito professores do ensino médio da Costa Rica, relacionadas à aquisição e desenvolvimento de estratégias de resolução de problemas associadas ao uso do GeoGebra, são analisadas e documentadas. Para isso, foi elaborada uma proposta de trabalho que inclui a construção e exploração de uma representação do problema, e a formulação e validação de conjecturas. Os resultados mostram que os professores fizeram várias representações do problema, examinaram as propriedades e atributos dos objetos matemáticos envolvidos, fizeram conjecturas sobre as relações entre esses objetos e procuraram diferentes formas de os verificar com base em argumentos visuais e empíricos fornecidos pelo GeoGebra. Em geral, os professores utilizaram estratégias para medir os atributos dos objetos matemáticos e para examinar o rasto que um ponto deixa enquanto é arrastado.Palavras-chave: GeoGebra; Resolução de problemas; pensamento matemático. ABSTRACTThis article analyzes and discusses the advantages and opportunities offered by GeoGebra during the problem-solving process. In particular, the mathematical reasoning forms exhibited by eight secondary school teachers in Costa Rica, related to the acquisition and development of problem solving strategies associated with the use of GeoGebra, are analyzed and documented. The proposal was developed that includes the elements: construction and exploration of a representation of the problem and formulation and validation of conjectures. The results show that teachers made several representations of the problem, examined the properties and attributes of the mathematical objects involved, made conjectures about the relationships between such objects, and sought different ways to check them based on visual and empirical arguments provided by GeoGebra. In general, the teachers used strategies to measure the attributes of the mathematical objects and to examine the trail that a point leaves while it is being dragged.Keywords: GeoGebra; Problem Solving; Mathematical Thinking.

Supporting Pattern Exploration and Algebraic Reasoning through the Use of Spreadsheets

2013 ◽  
pp. 228-233
Author(s):  
Ayhan Kursat Erbas ◽  
Sarah Ledford ◽  
Chandra Hawley Orrill ◽  
Drew Polly
Keyword(s):  
Middle School ◽  
Common Core State Standards ◽  
Middle Grades ◽  
Mathematical Thinking ◽  
State Standards ◽  
Educational Technologies ◽  
Core State ◽  
Geometric Patterns ◽  
The Common ◽  
Support Students

As teachers prepare to teach the Common Core State Standards for Mathematics (CCSSM), students’ exploration of patterns and relationships between numbers has gained more importance. Specifically, students’ conceptual understanding of numerical patterns is critical in middle school, as it lays a groundwork for fostering mathematical thinking at all levels. Educational technologies can enhance student’s explorations of patterns by providing opportunities to represent patterns, test conjectures, and make generalizations. In this chapter, the authors illustrate how spreadsheets can support students’ explorations of both arithmetic and geometric patterns in the middle grades.

scholarly journals Exploring the Effectiveness of Implementing Seminars as a Teaching and an Assessment Method in a Children’s Literature Course

2017 ◽  
Vol 10 (11) ◽  
pp. 1
Author(s):  
Sharifa Said Ali Al’Adawi
Keyword(s):  
Applied Sciences ◽  
Children's Literature ◽  
Conceptual Framework ◽  
Classroom Environment ◽  
Children’S Literature ◽  
Assessment Method ◽  
Positive Effects ◽  
Teachers And Students ◽  
Support Students ◽  
Practical Implications

The classroom environment should support students’ autonomy through teaching and assessment methods. This article highlights students’ perceptions about the value of implementing seminars as a teaching and an assessment method in a children’s literature course in a college of applied sciences (XCAS). Additionally, preparation considerations and limitations of such implementation are discussed. Findings indicted the positive effects of seminars in enriching classroom learning and students’ responsibility for their own learning which can be achieved through training for teachers and students. Practical implications of seminar implementations for future use are outlined and conceptual framework is suggested based on the findings.

scholarly journals Expansive Learning of Preservice Teachers Teaching Sustainable Development during Their Practicum

2020 ◽  
Vol 10 (2) ◽  
pp. 181
Author(s):  
Anthoula Maidou ◽  
Katerina Plakitsi ◽  
Hariton M. Polatoglou
Keyword(s):  
Sustainable Development ◽  
Preservice Teachers ◽  
Environmental Influence ◽  
Education For Sustainable Development ◽  
Learning Cycle ◽  
Teaching Intervention ◽  
Social Construct ◽  
Expansive Learning ◽  
Economic Entity ◽  
Positive Attitudes

Education for Sustainable Development (ESD) is a complex and multifaceted subject, including many aspects, environmental, societal, and financial. It is not a set of knowledge, which can be learned, because it is an evolving subject and in addition solutions that are successfully applied at specific locations might fail elsewhere. ESD should make students aware of the problems humankind is facing and encourage them to become active citizens. Thus, people must also have positive attitudes towards sustainability issues. In this study, we will present the results of a teaching intervention (TI) leading to a system of two expansive learning cycles. For the TI we used the topic of houses, which are a social construct, an economic entity, and have environmental influence. The researcher, an architect had to transform her knowledge to prepare the TI, thus starting an expansive learning cycle which was influenced by the outcome of the TI. The preservice teachers, who decided to use the topic of houses during their internship started their expansive cycle, which again influenced the researchers’ learning cycle. In this study, we will present the results of the TI and the implementation of the preservice teachers’ teachings of SD during their practicum. The preservice teachers reflected on their teachings in their written reports, which were used to analyze how preservice teachers chose to apply the topic ‘houses’ during their internship.

scholarly journals Scoping the meaning of ‘critical’ in mathematical thinking for Initial Teacher Education

2017 ◽  
Vol 15 (6) ◽  
pp. 713-728 ◽  
Author(s):  
Jane Furness ◽  
Bronwen Cowie ◽  
Beverley Cooper
Keyword(s):  
Teacher Education ◽  
Preservice Teachers ◽  
New Zealand ◽  
Adult Learners ◽  
Mathematical Thinking ◽  
Initial Teacher Education ◽  
Adult Participation ◽  
Achievement Data ◽  
Key Policy ◽  
Administrative Tasks

Current strong emphasis on literacy and numeracy in New Zealand educational policy, as elsewhere, reverberates in different ways in institutions charged with children’s and adults’ learning. A common response is to locate literacy and numeracy centrally in programmes aimed at preparing children for and enhancing adult participation in 21st century life and work. These agendas overlap in preservice teacher education. Preservice teachers enter Initial Teacher Education (ITE) programmes as adult learners engaged in building literacy and numeracy capability for teaching across the curriculum, working with student achievement data and administrative tasks, aspects of which may also be useful in their wider lives. These activities involve making judgements that require critical thinking, another key policy focus in New Zealand and internationally for children’s and adults’ learning. This article explores meanings of ‘critical’ in the context of mathematical thinking in ITE programmes. Given that mathematically based arguments can have both helpful and harmful consequences for humanity, we propose that development in preservice teachers’ capacity for critical mathematical thinking is crucial. In these times of significant global change we advocate for development of the kind of critical mathematical thinking that facilitates teachers working actively in pursuit of a socially just and sustainable world.

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