Is it desirable to avoid errors and misconceptions in Mathematics?
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
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“The most effective teachers .... Cultivate an ethos where pupils do not mind making mistakes because errors are seen as a part of learning. In these cases pupils are prepared to take risks with their answers” (OFSTED, 2003). As previously discussed, the focus seems to be that of the classroom environment that promotes absorbing the social and cultural dimensions of learning dialogue, and changing goals from completing tasks for teachers’ satisfaction to more personal long term gains and deep rooted understanding.
Mathematical dialogue within the classroom has been argued to be effective and a ‘necessary’ tool for children’s development in terms of errors and misconceptions. It has been mentioned how dialogue can broaden the children’s perception of the topic, provides useful opportunities to develop meaningful understandings and proves a good assessment tool. The NNS (1999) states that better numeracy standards occur when children are expected to use correct mathematical vocabulary and explain mathematical ideas. In addition to this, teachers are expected
...s the growing linguistic and cultural diversity within the classroom (Weinstein et al., 2003 p.270). Hack man (2013) argues that in order to provide an overall positive learning experience, teachers must be ever vigilant of the classes multicultural dynamics. Moreover, the environment of the classroom must be kept in mind when structuring these lessons, as a safe and supportive environment is not only requirement of the Quality teaching framework (2003), but it is a necessity in allowing students to take intellectual risks. This unit is centred on strategies, which incorporate socially justifiable principles, including student empowerment and social responsibility. The collaborative learning practices, which define this unit and ultimate assessment task, encourages students to listen and appreciate their peer’s perspectives that often appears different to their own.
Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.
In this essay, I will be exploring different ways on how ‘addition’ can be taught in Year 2 and how they link to the National Curriculum; looking at the best mental approaches that a child should take. I will then progress by exploring a particular calculation in extra detail, evaluating ways to teach how to solve the problem and use ‘manipulatives’ to support it.
Place value and the base ten number system are two extremely important areas in mathematics. Without an in-depth understanding of these areas students may struggle in later mathematics. Using an effective diagnostic assessment, such as the place value assessment interview, teachers are able to highlight students understanding and misconceptions. By highlighting these areas teachers can form a plan using the many effective tasks and resources available to build a more robust understanding. A one-on-one session with Joe, a Year 5 student, was conducted with the place value assessment interview. From the outlined areas of understanding and misconception a serious of six tutorial lessons were planned. The lessons were designed using
The second part of this memo contains a rhetorical analysis of a journal article written by Linda Darling-Hammond. Interview 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 actually learns is a pivotal form of communication in the field (Personal Communication, September 8, 2016).
Mathematics has become a very large part of society today. From the moment children learn the basic principles of math to the day those children become working members of society, everyone has used mathematics at one point in their life. The crucial time for learning mathematics is during the childhood years when the concepts and principles of mathematics can be processed more easily. However, this time in life is also when the point in a person’s life where information has to be broken down to the very basics, as children don’t have an advanced capacity to understand as adults do. Mathematics, an essential subject, must be taught in such a way that children can understand and remember.
I understand the importance of having a secure subject knowledge so that children are taught correctly, avoiding misconceptions in their learning. I feel confident in teaching a wider range of subjects after my experience in a key stage one class. According to Alexander (2010) to be a successful teacher, we must be ‘qualified, caring and knowledgeable’. Therefore, I am happy with the improvements I have made during my second-year placement but would find it beneficial to keep this target throughout my teaching practise. Action
To investigate the notion of numeracy, I approach seven people to give their view of numeracy and how it relates to mathematics. The following is a discussion of two responses I receive from this short survey. I shall briefly discuss their views of numeracy and how it relates to mathematics in the light of the Australian Curriculum as well as the 21st Century Numeracy Model (Goos 2007). Note: see appendix 1 for their responses.
Ward (2005) explores writing and reading as the major literary mediums for learning mathematics, in order for students to be well equipped for things they may see in the real world. The most recent trends in education have teachers and curriculum writers stressed about finding new ways to tie in current events and real-world situations to the subjects being taught in the classroom. Wohlhuter & Quintero (2003) discuss how simply “listening” to mathematics in the classroom has no effect on success in student academics. It’s important to implement mathematical literacy at a very young age. A case study in the article by authors Wohlhuter & Quintero explores a program where mathematics and literacy were implemented together for children all the way through eight years of age. Preservice teachers entered a one week program where lessons were taught to them as if they were teaching the age group it was directed towards. When asked for a definition of mathematics, preservice teachers gave answers such as: something related to numbers, calculations, and estimations. However, no one emphasized how math is in fact extremely dependable on problem-solving, explanations, and logic. All these things have literacy already incorporated into them. According to Wohlhuter and Quintero (2003), the major takeaways from this program, when tested, were that “sorting blocks, dividing a candy bar equally, drawing pictures, or reading cereal boxes, young children are experienced mathematicians, readers, and writers when they enter kindergarten.” These skills are in fact what they need to succeed in the real-world. These strategies have shown to lead to higher success rates for students even after they graduate
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
...ett, S. (2008) . Young children’s access to powerful mathematical ideas, in English, Lyn D (ed), Handbook of international research in mathematics education, 2nd edn, New York, NY: Routledge, pp. 75-108.
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...
...nd dynamic changes in the competitive nature of the job market, it is evident to myself that being eloquent in all aspects of numeracy tools and knowledge is imperative in the 21st Century. The calculator is one such tool for children which supports mental computation to check answers to develop independent learning, as discussed earlier. It also fits into the pre-operation developmental stage of a child to enhance their symbolic thinking, similar to that of an adults scheme of thinking, as opposed reliance on senses alone. The interviews further grounded my reasoning around my argument and allowed me to not only gain an insight to how those similar to me think and those not so similar. This investigation has strengthened my argument that the use of calculators in the primary school classroom, if used appropriately, are an invaluable tool for teaching and learning.
In today’s classroom, the teacher is no longer viewed as the sole custodian of knowledge. The role of a teacher has evolved into being amongst one of the sources of information allowing students to become active learners, whilst developing and widening their skills. Needless to say, learning has no borders – even for the teacher. One of the strongest beliefs which I cling to with regards to teaching is that, teaching never stops and a teacher must always possess the same eagerness as a student. Through several interactions with other teachers, I always strive for new ideas, techniques, teaching styles and strategies that I might add to my pedagogical knowledge. Furthermore, through personal reflection, feedback and evaluation...