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
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
In this one experience, the employee showed a lack of ability to multiply, add, or logically reason that with bigger sections, the number of pieces needed to make forty feet would decrease. This is disturbing. Just as one would expect an adult to know how to read, to know who the President is, and to be able to find his home state on a map, one would expect an adult to be able to multiply six times seven. The Fidler employee was obviously not taught sound mathematical reasoning in school. Unfortunately, as much as the current educational system tries to neglect the value of math, its importance is inescapable, especially in today’s modern society. The time has come to reintroduce the public to mathematics, and the way to do it is to establish more and better math classes in American schools.
Mathematics education has undergone many changes over the last several years. Some of these changes include the key concepts all students must master and how they are taught. According to Jacob Vigdor, the concerns about students’ math achievements have always been apparent. A few reasons that are negatively impacting the productivity of students’ math achievements are historical events that influenced mathematics, how math is being taught, and differentiation of curriculum.
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.
Yanik, H. B., Helding, B., & Back, J. M. (2006). Students' Difficulties in Understanding Fractions as Measures. 28th Annual meeting of the North American Chapter of the Internation Group for the Psychology of Mathematics Education (pp. 323-325). Merida, Mexico: Universidad Pedagogica Nacional.
• I will begin the lesson by showing the class the multiplication chart I prepared. I will ask pivotal questions to start a discussion, “What do you think this chart shows”?, “What do the side numbers mean”?
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.
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
Macmillan, A. (2009). Numeracy in early childhood: Shared contexts for teaching and learning. Melbourne, Victoria: Oxford.
...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.
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
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 ...
Towers, J., Martin, L., & Pirie, S. (2000). Growing mathematical understanding: Layered observations. In M.L. Fernandez (Ed.), Proceedings of the Annual Meetings of North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ, 225-230.
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.
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,