Multiplicative thinking is a capacity to work flexibly and efficiently with an extended range of numbers, an ability to recognise and solve a range of problems and the means to communicate effectively in a variety of ways. Mathematical skills start from an early age, children start school equipped with an understanding of how the basic number system works. Teachers play the role of providing a wider and more complex range of information to advance their skills in understanding the number system. Effective teachers engage students, regardless of their prior understanding and implement lessons to build on prior knowledge, or create understanding, to advance the learner to become mathematical multiplicative thinkers. Children go through stages …show more content…
Multiplicative thinking allows students to solve a whole range of problems using various types of mathematics to work between quantities and strategies over a wide range of context. To achieve all mathematical outcomes students must be able to correctly identify how to solve various problems using different mathematical techniques, and understand the sequence in which to work the problem out (Department of Education, Western Australia, [DEWA, 2013). One way to determine if a student is working multiplicatively is for teachers to ask students how they came to their answer. For example, if they answer with I counted how many rows down and then, I multiplied by how many row across they show they are developing their multiplication skills. Multiplicative thinkers see and use the connections between addition and multiplication; they are able to use multiplicative arrays to see the flexibility with numbers and multiplicative problems. Additionally, they are able to use the notion and language of addition and multiplication and learn to extend to multiplication and division to solve problems. Hurst (2015) suggests three key elements for multiplicative thinking and development. Therefore, it is important for teachers to be aware of the …show more content…
Curriculum content is still presented in the same linear fashion as it was in previous curriculum documents and, as a consequence, many teachers continue to teach it in the same unconnected way and inevitably, many children learn it in the same unconnected way (Hurst, 2015). A purpose of the new Mathematics Australian curriculum was to make the curriculum “deep” rather than “wide” (National Curriculum Board, 2009). A way teachers can address this situation effectively is by thinking at more of a ‘macro level’ in terms of ‘big number ideas’. For example by teaching proportion, percentage and ratio, or decimals and fractions with associated language and is carried out with 'actions on objects ' engages students in activities with numerical quantities that are interesting, meaningful and develops links to multiplicative thinking. Language is an abstraction as much as the mathematical ideas are; therefore students must carry out the activity at the same time as the 'talking about ' what is going on for it to be
The following assignment shows the progress I have made throughout unit EDC141: The Numerate Educator. Included are results from the first and second round of the Mathematics Competency Test (MCT). Examples from assessment two, which, involved me to complete sample questions from the year nine NAPLAN. I was also required to complete a variety of ‘thinking time problems’ (TTP’s) and ‘what I know about’ (WIKA’s). These activities allowed me to build on my knowledge and assisted me to develop my mathematical skills. The Australian Curriculum has six areas of mathematics, which I used in many different learning activities throughout this study period (Commonwealth of Australia, 2009). These six areas will be covered and include number, algebra,
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.
, the value of teaching subitizing skills in the classroom is clear. This ability provides a visual tool to young students as they develop a basic understanding of numbers and one to one correspondence, and it establishes a firm foundation for the future skills of addition and subtraction facts. Possessing the knowledge of how and when students develop the cognitive understanding of this concept can drive a teachers instruction so that the students find greater success in the lesson. Knowing that comprehension of number conservation does not occur until age 5 or 6 will definitely have an effect upon early teaching of number sense.
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
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.
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.
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
...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.
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 .
The early acquisition of mathematical concepts in children is essential for their overall cognitive development. It is imperative that educators focus on theoretical views to guide and plan the development of mathematical concepts in the early years. Early math concepts involve learning skills such as matching, ordering, sorting, classifying, sequencing and patterning. The early environment offers the foundation for children to develop an interest in numbers and their concepts. Children develop and construct their own meaning of numbers through active learning rather than teacher directed instruction.
As a secondary subject, society often views mathematics a critical subject for students to learn in order to be successful. Often times, mathematics serves as a gatekeeper for higher learning and certain specific careers. Since the times of Plato, “mathematics was virtually the first thing everyone has to learn…common to all arts, science, and forms of thought” (Stinson, 2004). Plato argued that all students should learn arithmetic; the advanced mathematics was reserved for those that would serve as the “philosopher guardians” of the city (Stinson, 2004). By the 1900s in the United States, mathematics found itself as a cornerstone of curriculum for students. National reports throughout the 20th Century solidified the importance of mathematics in the success of our nation and its students (Stinson, 2004). As a mathematics teacher, my role to educate all students in mathematics is an important one. My personal philosophy of mathematics education – including the optimal learning environment and best practices teaching strategies – motivates my teaching strategies in my personal classroom.
The prominence of numeracy is extremely evident in daily life and as teachers it is important to provide quality assistance to students with regards to the development of a child's numeracy skills. High-level numeracy ability does not exclusively signify an extensive view of complex mathematics, its meaning refers to using constructive mathematical ideas to “...make sense of the world.” (NSW Government, 2011). A high-level of numeracy is evident in our abilities to effectively draw upon mathematical ideas and critically evaluate it's use in real-life situations, such as finances, time management, building construction and food preparation, just to name a few (NSW Government, 2011). Effective teachings of numeracy in the 21st century has become a major topic of debate in recent years. The debate usually streams from parents desires for their child to succeed in school and not fall behind. Regardless of socio-economic background, parents want success for their children to prepare them for life in society and work (Groundwater-Smith, 2009). A student who only presents an extremely basic understanding of numeracy, such as small number counting and limited spatial and time awareness, is at risk of falling behind in the increasingly competitive and technologically focused job market of the 21st Century (Huetinck & Munshin, 2008). In the last decade, the Australian curriculum has witness an influx of new digital tools to assist mathematical teaching and learning. The common calculator, which is becoming increasing cheap and readily available, and its usage within the primary school curriculum is often put at the forefront of this debate (Groves, 1994). The argument against the usage of the calculator suggests that it makes students lazy ...
Different measurement, time understanding, money and the ability to perform multi-step mathematics are considered as a fundamental for numeracy skills elite. In some extent it includes the ability to figure out what numeracy skills to be applied in a given situation (Montori & Rothman, 2005; Golbeck et al., 2005). These simple numeracy skills acquired helps the pupil to excel with the complex mathematics skills including calculations, fractions, algebra, function and geometry in mathematics learning. Unlike, its absence makes someone always struggle in pupils` learning due to fact that basic arithmetic operations, the ability to perform estimates, geometry and simple statistics have been affected hence cause difficult for a pupil in mathematics learning in next
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,