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,
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
While reading this book I found out that under certain circumstances I am a fixed mindset rather than a growth mindset. One, very identifiable, area I have a fixed mindset in, is the math content area. When ever I think about being forced to learn or teach math, I completely shut down. I feel I’ve become this way because for years I’ve heard that I need more work in that area, and that I have a hard time understanding it. So I feel I’ve lost any drive to concur it when I’ve already felt defeated by it. Which after reading this book I have realized this mentality could easily transfer to my students because that is one thing I have learned again and again from this book it is that one fixed mid set can have an immediate impact on the mind set of those people who are interacting with the person.
In learning, Vygotsky theorised that in order for learning to occur effectively, the learning experiences had to be meaningful and authentic in cultural context (Eggan & Kauchak, 2010. pp 48). He...
The following information was conducted in an interview with Diana Regalado De Santiago, who works at Montwood High School as a mathematics teacher. In the interview, Regalado De Santiago discusses how presenting material to her students in a manner where the student actual learns is a pivotal form of communication in the
Learning, “as an interpretive, recursive, building process by active learners”, interrelates with the physical and social world (Fosnot, 1996). “Assuming the role as ‘guide on the side’ requires teachers to step off the stage, relinquish some of their power, and release the textbooks to allow their students to be actively engaged and take some responsibility of their own learning” (WhiteClark, DiCarlo, & Gilchriest, 2008, p. 44). Furthermore, constructivism involves developing the student as a learner through cooperative learning, experimentation, and open-ended problems in which students learn on their own through active participation with concepts and principles (Kearsley,
... relationship in one problem that doesn’t appear in others. Among all of this, there is such vastness in how one person might approach a problem compared to another, and that’s great. The main understanding that seems essential here is how it all relates. Mathematics is all about relationships between number and methods and models and how they all work in different ways to ideally come to the same solution.
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).
All children learn differently and teachers, especially those who teach mathematics, have to accommodate for all children’s different capacities for learning information. When teaching mathematics, a teacher has to be able to use various methods of presenting the information in order to help the students understand the concepts they are being taught.
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
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.
Schunk, D. H. (2000) Learning theories. An educational perspective. (3rd ed.) Upper Saddle River, NJ: Prentice-Hall.
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...
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)
A somewhat underused strategy for teaching mathematics is that of guided discovery. With this strategy, the student arrives at an understanding of a new mathematical concept on his or her own. An activity is given in which "students sequentially uncover layers of mathematical information one step at a time and learn new mathematics" (Gerver & Sgroi, 2003). This way, instead of simply being told the procedure for solving a problem, the student can develop the steps mainly on his own with only a little guidance from the teacher.