Under any circumstances, teachers’ knowledge helps teaching occur and central to any teaching endeavour is children’s learning. Researchers have been into earnest works seeking the aspects of mathematics teachers’ knowledge which would contribute to effective teaching and learning. Take Bass (2010) as for one who claimed that having mathematical knowledge, teachers should be able to present mathematical concepts to students in understandable form. In this vein also Fennena (2010) stressed that what mathematics teachers know limits what is done in their classrooms and ultimately what their students learn. Moreover, Mewborn (2011) expanded that because of this limiting effect of teachers’ knowledge to child’s learning, teachers must not only …show more content…
He added that PCK includes an understanding of what makes the learning of specific topics easy or difficult, the conceptions and preconceptions that students of different ages and background bring with them to the learning of those most frequently taught topics and lessons. He later elaborated that it is that special blending of knowledge into an understanding of …show more content…
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). Furthermore, over the years since the time of Shulman, PCK have been viewed dynamically. It has been described as “elusive butterfly” because it is a construct of knowledge not amenable to static representation (Schneider, 2011). As for the purpose of this study, it was decided to narrow down to 4 manageable aspects of PCK, (1) Teachers’ knowledge of mathematical structure and connections, (2) Teachers’ knowledge of representations of concepts, (3) Teachers’ knowledge of the cognitive demands of mathematical tasks on learners, and (4) Teachers’ knowledge of students misconceptions and choice of
What is head knowledge when you cannot apply it? What use is academics when you cannot make rational decisions? Why would you go to school if you do not yearn for knowledge? As a teacher, I want to instill in my children these desires and the abilities to not only succeed academically but as a whole person as well. I believe that the role of an elementary teacher is not only to teach the “Three R’s” and the “Four W’s”, but also to foster within children a desire to learn and the ability to make wise choices. In our classrooms, we are raising the leaders of tomorrow, if all they know is what 2+2 equals or how to spell “beautiful” are they really going to be the future that we need and look forward to? Through the hard work of teachers promoting their students’ success and ability to do good work and make good choices, we can see the world change in radical ways! When we as teachers understand that not only do our students need to know the what but also the how, we can help them succeed in building critical thinkin...
Any school curriculum should aim at enabling children to be able to think in broader terms, motivate them to want to be more knowledgeable and above all, allow them to come up with new approaches to problem solving. However, more too often teachers tend to limit the students to only the known facts in text books, something which prompts them to remain in their comfort zones. Additionally, the purpose of any formal education is not only to gain formal knowledge but also to gain social knowledge. Different teachers will have different approaches to achieve this. Despite the approach used, in the end of the day, they are expected to have involved and impacted positively on the different characters of children in their classrooms that is, the shy,
Teacher knowledge has always been the basis to an effective learning experience. Without a knowledgeable teacher, students are not able to receive a quality educational experience. This pillar encompasses the influence teachers have on student learning and achievement, possession of research based knowledge, and effective teaching practices. I thrive to be educated and knowledgeable on the information presented to my students. By having a variety of teaching techniques that work and I use often in my classroom, I am able to mold my instruction around student needs and provide efficient and
Teachers help us expand and open our mind by giving us skills throughout students’ early life to help students when they are older. By learning information from teachers, students become better people, in a couple of ways. Besides inquiring knowledge from their teachers, students learn to work with one another, open their mind to other peoples’ thoughts and ideas, respect one another, and learn different techniques for life’s issues.
I believe that teaching and learning is both a science and an art, which requires the implementation of already determined rules. I see learning as the result of internal forces within the person student. I know that children differ in the way they learn and grow but I also know that all children can learn. Students’ increased understanding of their own experience is a legitimate form of knowledge. I will present my students with opportunities to develop the ability to meet personal knowledge.
This assignment will distinguish the relationships between teaching practice, children’s mathematical development and errors and misconceptions. Hansen explains how “children construct their own knowledge and understanding, and we should not see mathematics as something that is taught but rather something that is learnt” (A, Hansen, 2005). Therefore, how does learning relate to errors and misconceptions in the class room, can they be minimised and is it desirable to plan lessons that avoid/hide them? Research within this subject area has highlighted specific related topics of interest such as, the use of dialogue in the classroom, the unique child and various relevant theories which will be discussed in more depth. The purpose of this
Consider what you have observed, read and experienced about teaching and learning to date. What, in your view, constitutes best practice in the teaching of maths? Introduction Mathematics is an important subject in the National Curriculum, in England. Ofsted (2012) quotes “Mathematics is essential for everyday life and understanding our world”. It is a creative subject with its own questions and methods.
Sherley, B., Clark, M. & Higgins, J. (2008) School readiness: what do teachers expect of children in mathematics on school entry?, in Goos, M., Brown, R. & Makar, K. (eds.) Mathematics education research: navigating: proceedings of the 31st annual conference of the Mathematics Education Research Group of Australia, Brisbane, Qld: MERGA INC., pp.461-465.
Kirova, A., & Bhargava, A. (2002). Learning to guide preschool children's mathematical understanding: A teacher's professional growth. 4 (1), Retrieved from http://ecrp.uiuc.edu/v4n1/kirova.html
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...
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.
Devlin believes that mathematics has four faces 1) Mathematics is a way to improve thinking as problem solving. 2) Mathematics is a way of knowing. 3) Mathematics is a way to improve creative medium. 4) Mathematics is applications. (Mann, 2005). Because mathematics has very important role in our life, teaching math in basic education is as important as any other subjects. Students should study math to help them how to solve problems and meet the practical needs such as collect, count, and process the data. Mathematics, moreover, is required students to be capable of following and understanding the future. It also helps students to be able to think creativity, logically, and critically (Happy & Listyani, 2011,
Socrates, a famous philosopher, once said, “I cannot teach anybody anything; I can only make them think.” This quote is interesting in the fact that in modern times it is mandatory to go to school for a certain length of time to be taught in order to learn. We have teachers that share their knowledge with their students so that the generations to come can continue to grow and develop. When a student is asked what their teachers do at school they will most likely respond with something along the lines of, “they teach.” This response is both true and false to an extent. While the teachers can provide their students with knowledge, it is important for the students to do their part by using their minds to understand it for themselves. Socrates
" A student must earn the right to say ‘I know’ by his own thoughtful efforts to understand" (Ebel, 5). The intellectual proficiencies many educators hope to teach are, like information, essentially useless to Ebel without a knowledge base on which to draw from. Ebel feels that a good teacher can "motivate, direct, and assist the learning process to great advantage".
... generally accepted that a teacher’s main role is to facilitate learning rather than to be the source of all knowledge” (p.2).