As a contemporary mathematics education researcher, Richard Lesh is know for describing what has been known as models and modeling perspectives in regard to mathematical problem solving, learning, and teaching (Lesh & Doerr, 2003). Models are defined as “purposeful mathematical descriptions of situations, embedded within particular systems of practice that feature an epistemology of model fit and revision” (Lesh & Lehrer, 2003). What modeling involves is a series of tests for fitness on models developed by the students as they think mathematically about a presented problem situation. This is all drawn from the work of other cognitive theorists (Dienes and Vygotsky included) who believe that we learn by interpreting our experiences. Lesh suggests …show more content…
Included in the forms of communication are the spoken and written language, symbols, diagrams, metaphors, and computer-based simulations (Cramer, 2003; Johnson & Lesh, 2003). This is also related to what Wertsch (1985) described as “mediated activity” as an extension of Vygotsky’s social formation of learning which has become an important component of learning as different forms of media will emphasize different aspects of a problem situation and the conceptual systems within the …show more content…
The notion is that ideas develop over time and the level of a student’s understanding can be influenced by many factors (Lesh & Lehrer, 2003). The challenge is to provide the opportunity for students to “extend, revise, reorganize, refine, modify, or adapt constructs (or conceptual systems) that they DO have” versus defining or creating new ideas (Lesh & Lehrer, 2003). Vygotsky (1978) mentions that language has an influence on the thinking of a student, but models and modeling perspectives extends beyond just language in that there are other influences from the culture of a student beyond language that have an influence on their thinking (Cobb & McClain, 2001). Along a variety of dimensions is how models and modeling perspectives develop the conceptual tools versus Vygotsky focus on internalizing the experience (Lesh, 2002). Thus, Lesh extends Vygotsky’s zone of proximal development to a multi-dimensional region in which there are various ways to develop an understanding of a concept as well as different paths to travel while exploring the different regions (Lesh & Lehrer,
In the Variables and Patterns of Change (Annenberg Media, 2004), we are introduced to two classrooms during their first week of instruction. The first class is Ms. Green’s algebra. Ms.Green uses real life situation of wanting to get a pool in her backyard to teach dimensions and equations. During the example, she helps to guide the students learning by asking leading questions to help them figure out the problem. Once they understand the problem, she puts them into groups to figure out dimensions of different pool sizes and how many tiles it would surround them. While in groups, Ms. Green goes to each group to check their progress and answer any question.
...of teaching and learning. Modeling is a good way to promote learning. The teachers can use modeling to promote desired behavior. Teachers can enhance self-efficacy among students by teaching basic knowledge and then skills to mastery. Teacher can assure students that they can be successful and point other successful students like them who have been successful by using the techniques provided by the teacher (Ormrod, 2011). Teachers can promote self-regulated learning by encouraging students to set goals and performing self-evaluation. To conclude social cognitive theory describes learning as an internal phenomenon that may or may not be reflected in behavior and people’s observation of those around them affect their behavior and cognitive processes (Ormrod, 2011).
This reading reminded me about how Vygotsky’s theory is mostly based on the interactions and influences help children to learn. I really do believe this theory is very accurate, because students can learn from each other. If a teacher is having trouble explaining a complex topic to a student, another student can explain it in more relatable way. Also, I was fascinated when I read about what cultural tools, were and how they related to Vygotsky’s beliefs. Learning about what cultural tools were, helped me to broaden my understanding of how crucial cultural tools are to student’s learning process. Also, the chapter did a great job of elaborating on how these tools can help to advance and grow in the understanding of student’s thinking process. Another aspect of this reading that interested me was the elaboration on private speech and the Zone of Proximal Development. Each of the definitions displayed help me to advance my own thinking on what it was and how it is used in regards to the education of students. The description of what private speech and how it is basically the inner narration of their thinking process helped me to understand how this aspect can help with students learning. Also, the Zone of Proximal Development helped me to make a connection to both what is and how it relates to private speech as well. The Zone of proximal development plays a crucial role in the
Brooks, J.G. &Brooks, M.G. (1995). Constructing Knowledge in the Classroom. Retrieved September 13, 2002 for Internet. http://www.sedl.org/scimath/compass/v01n03/1.html.
Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175-189.
Lev Vygotsky developed his theory of learning in the 1920’s but it was not until the late 1960’s that his ideas about learning became popular and were used to contribute to “Constructivism” as a method of teaching. (Krause [et al.] 2010 p. p81).
In a social constructivist view on learning the brain is a complex, flexible, ever changing organism that reshapes itself in response to challenge (Abbott & Ryan, 2001). Constructivism view is that knowledge is obtained and understood through a student’s mental framework (Abbott & Ryan, 2001). Learning is not a passive process but it is a deliberate and progressive process that deepens meaning (Abbott & Ryan, 2001). The student does not only reply on a teachers lectures but also on their interactions with the environment around them (Abbott & Ryan, 2001). In this view it is important that the teacher sees the student as the centre of teaching endeavours, by assisting them to obtain information they can integrate into their already known knowledge. There are many ways that a teacher can assist their students, one example is Scaffolding. Scaffolding is where a teacher provides students with just enough help in order to complete the tasks themselves, then over time decreasing the amount of help so that a student can master this themselves.
Using literacy strategies in the mathematics classroom leads to successful students. “The National Council of Teachers of Mathematics (NCTM, 1989) define mathematical literacy as an “individual's ability to explore, to conjecture, and to reason logically, as well as to use a variety of mathematical methods effectively to solve problems." Exploring, making conjectures, and being able to reason logically, all stem from the early roots of literacy. Authors Matthews and Rainer (2001) discusses how teachers have questioned the system of incorporating literacy with mathematics in the last couple of years. It started from the need to develop a specific framework, which combines both literacy and mathematics together. Research was conducted through
Moore, Beverly. Situated Cognition Versus Traditional Cognitive Theories of Learning. Education, V119, N1, pgs 161-171, Fall 1998.
The processes which explain how development transpires can be described as mechanisms of development. Although Piaget and Vygotsky both focused their theories on cognitive development, the mechanisms needed to develop cognition differ for each theorist. Piaget focused on the mechanisms of cognitive organization, adaptation, and equilibration. Vygotsky, on the other hand, focused on a dialectical process, cultural tools, Zone of Proximal Development (ZPD), scaffolding, internalization, and private/inner speech. For Piaget, cognitive organization entails the tendency for thought to have structures in which information and experiences are then labeled into schemas (Miller, 2011). Schemas allow humans to organize categories of information they
A contemporary educational application of Vygotsky's theories is "reciprocal teaching", used to improve students' ability to learn from text. In this method, teachers and students collaborate in learning and practicing four key skills: summarizing, questioning, clarifying, and predicting. The teacher's role in the process is reduced over
This mentions that learning is likely to occur in an internal process isolated from the social environment. Nevertheless, it is prevalently seen that in PBL learners frequently employ the power of collaborative learning skills in groups to culminate the projects or partake in social interactions with others for mutual learning discussions, so PBL also lend some characteristics of social-constructivism of Lev Vygotsky (1980). The salient point of social constructivism is the significance of social interactions that influence on the individual cognitive development and the Zone of Proximal Development (ZPD) as well as the role of scaffolding (Barge, 2010). He valued social interaction as an integral role in one’s cognitive development and argued that learning is not merely through assimilation and accommodation processes of new knowledge of learners, but it should be integrated or combined in a social community where learners can interact (Harmer, 2014). In other words, based on Vygotsky’s arguments, one’ s world knowledge is bound to his/her individual experiences while mediated by social interplay with
Research has shown that ‘structured’ math lessons in early childhood are premature and can be detrimental to proper brain development for the young child, actually interfering with concept development (Gromicko, 2011). Children’s experiences in mathematics should reflect learning in a fun and natural way. The main focus of this essay is to show the effectiveness of applying learning theories by Piaget, Vygotsky and Bruner and their relation to the active learning of basic concepts in maths. The theories represent Piaget’s Cognitivism, Vygotsky’s Social Cognitive and Bruner’s Constructivism. Based on my research and analysis, comparisons will be made to the theories presented and their overall impact on promoting mathematical capabilities in children. (ECFS 2009: Unit 5)
Mathematics teachers teach their students a wide range of content strands – geometry, algebra, statistics, and trigonometry – while also teaching their students mathematical skills – logical thinking, formal process, numerical reasoning, and problem solving. In teaching my students, I need to aspire to Skemp’s (1976) description of a “relational understanding” of mathematics (p. 4). Skemp describes two types of understanding: relational understanding and instrumental understanding. In an instrumental understanding, students know how to follow steps and sequential procedures without a true understanding of the mathematical reasons for the processe...
One very important factor in every life is the education received as we mature. Education in all subjects is necessary to become a well-rounded individual. Even so, I feel that my subject area has more significance in one’s future because every person uses mathematics every day. Students need to understand why mathematics is important and why they will need it in the future. The way to do that is integrated into the views of the role of the teacher. Teachers need to be encouraging role models that provide students with safety, nurturing, and support in the classroom, along with providing excellent instruction by allowing students to explore and expand their minds in the content of mathematics. Teachers should set high expectations for all students and persuade the students to live up to those expectations. Along the same lines, teaching and learning are complementary concepts. Students need for the teacher to provide them with the knowledge that will be used not only in that class but also in their future endeavors. ...