Classrooms where productive discourse is utilized successfully do not just happen, but instead require educators to adequatly and thoroughly prepare. When creating lessons in which discourse is to be utilized Chapin, O’Connor and Anderson(2013) contend that educators must consider the goals of the lesson, anticipate confusion, brainstorm and develop questions to use as part of the facilitation of the discussion, and finally plan the implementaiton of the lesson delivery.
In order to develop a lesson in which students will gain understanding of the concept to be taught, educators must have a firm idea of the mathematics that will be the center of the discussion. Parrish (2010) suggests that educators should plan in advance the order of problems to be presented and which strategies that are the target of the lesson. This is supported by Chapin, O’Connor and Anderson (2013) who recommend that educators list ahead of time the key concepts, and along with this a list of possible strategies. They also believe that educators should find the solution for themselves using as many strategies as possible in an effort to flesh out possible methods and ideas that may be shared during conversations. In addition, they advocate the development of lists that include vocabulary related to the content and forms of representations and computational methods that are at the core of the concept. Through thoughtful planning these math talks can enable teachers to help students build connections among ideas, discover computational strategies and their connections to algorithms, and most importantly, these talks help students connect computational procedures to concepts. Educators must be mindful of the concept, goal and objective when determini...
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... J. W., & Hiebert, J. (1999). The Teaching Gap: Best Ideas from the World's Best Teachers for Improving Education in the Classroom. New York: The Free Press.
StudentAchievementDivision. (2014, March 21). Capacity Building Series. Retrieved from Asking Effective Questions: http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_AskingEffectiveQuestions.pdf
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Vygotsky, L. (1978). Mind in Society: The Development of Higher Psychological Processes. Cambirdge: Harvard University Press.
Vygotsky, L. S. (1929). The problem of the cultural development of the child II. Journal of Genetc Psychology, 415-432.
West, L., & Staub, F. C. (2003). Content Focusd Coaching: Transforming Mathematics Lessons. Portsmouth: Heinemann.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
VYGOTSKY, LS (1978), ‘Mind in Society: Development of Higher Psychological Processes’, Massachusetts: Harvard University Press.
In Vygotsky’s theory of socio cultural, he highlights the importance of a child’s exposure to specific social interaction with their peers as well as different cultures. “emphasizes that children live in rich social and cultural context”. Pg97 Children will learn to do more with the help of anyone who is more knowledgeable than them. For example a child would not know how to pronounce the alphabet by their own as they don’t know what the letters stand for, with the guidance of their teacher or caregiver they will know what sound each letter makes. “Through joint activities with more mature members of their society, children master activities and think in ways that have meaning in their society”pg97.
Lev Vygotsky was a Russian developmentalist who believed that adults in all societies “foster children’s cognitive development in an intentional and somewhat systematic manner” (Ormrod, 2011, pg.39). Vygotsky sociocultural theory focused on what a child could do with an adult’s assistance. Nature is the emphasis of this theory, highlighting children’s cultural and social environmental experiences that influence cognitive growth. Two main terms that are of uttermost importance in this principle are a child’s zone of proximal development (ZPD) and scaffolding (Ormrod, 2011, pg. 39).
Mead, G. H. 1934. Mind, self and society and society. Chicago: University of Chicago Press.
Vygotsky, L.S. (1978) Mind in Society: The development of higher mental processes, Cambridge, MA: Harvard University Press
Review of Mind in the Making presented by Victoria Molinar Vega, Undergraduate, University of Arizona, College of Education
Hill argued that PCK in mathematics includes knowledge and skills through mathematics education, knowledge of using alternatives to solve problems, knowledge of demonstrating representations, knowledge of articulating mathematical explanations, knowledge of anticipating what students are likely to think about the tasks chosen, and knowledge to analyse errors. As an aftermath, Hill reconceptualised PCK in mathematics as Mathematical Knowledge of Teaching (MKT).
Vygotsky was born in Russia in 1896 into a middle class family (Gallagher 1999). Vygotsky studied law at Moscow University and he did not have any formal educational training in psychology. In 1925, he began his first big research project in psychology, the Psychology of Art (Gallagher 1999). The government doubted his validity of his research, but it was kept alive by his students and followers. Vygotsky died in 1934 from tuberculosis, but his ideas and theories stayed alive. Vygotsky’s main theory is the sociocultural theory. According to Sternberg and Williams (2010), this theory concludes that cognitive development occurs from interaction with others and then the information is internalized and furthers their personal development (p. 51). Vygotsky focused on the influence of social and environmental factors in the process of cognitive development. Many of Vygotsky’s theories are seen in today’s classroom including his theories of zone of proximal development, inner voice, and internalization.
Activity based learning is based on the premise that children are much more effective active learners than passive recipients of information. When classroom material is given to them in a way that allows them to explore and come to conclusions on their own or with the help of teachers or facilitators students are much more able to be able to process and retain the information in a useful way. There are many great types of activity based teaching that can be used in the classroom to engage students. Group discussions are one great way to actively involve students in communicating about the learning material. By posing ...
Stein, J., Steeves, L., Smith, C. (April 13, 2001). Developing the Art of Teaching: Guidelines for
Hall, G., Quinn, L., & Gollnick, D. (2008). The Joy of Teaching. Old Tappan, NJ: Pearson Education, Inc.
Sociocultural theory grew from the work of Russian seminal psychologist Lev Vygotsky and his colleges Alexei Leontiev and Alexander Luria. Vygotsky believed that parents, caregivers, peers and the culture at large were responsible for the development of higher order functions (Zembylas, 2007, p. ). He believed that humans and animals shared elementary psychological processes such as attentional and perceptual process, but what differentiated the two was the social and cultural basis of human thought (Siegler & Alibali, 2005, p. 108). In sum he advanced the notion that development always results from internal mental processes, which are a result of the external mental processes (Siegler & Alibali, 2005, p.108). He suggests that for children's mind to develop, they have to be placed in sp...
Booker, G. & Bond, D. & Sparrow, L. & Swan, P. (2010) Teaching Primary Mathematics 4th Ed. Pearson, French Forest, NSW.
Mrs. Tijerina used a well balance of student-centered and teacher-centered in her classroom. The first two-days of the week she would explain the mathematical concept and the rest of the