Saturday, October 16, 2010

Research Proposal on Curriculum

Research Proposal on Curriculum

The Ministry of Education seem to be forever trying to improve upon what is being taught in the classroom, and the New Zealand Mathematics Curriculum and Numeracy Framework are two of many ways.

The Mathematics Curriculum and the Numeracy Framework, where they do not mirror each other, they more or less compliment one another. The Curriculum for sure is an extremely useful tool for teachers, as it tells teachers what students should know at what level, but it does not explain to the teacher how to teach the things which The Curriculum asks.

The Curriculum is a broadened version of what is to be taught in New Zealand classrooms, and is a simple guide to what students should be achieving. The Framework however, is a more in depth expansion of The Curriculum. The Numeracy Framework is designed to be easy to follow, and is broken down into two simple groups, Knowledge, and Strategies. The Framework is also based upon the key idea that teachers should begin to teach from where the child is at, not what level The Curriculum says that a child of whatever age should be. In The Framework, instruction is based upon how children think.


The Curriculum sets all of the Achievement outcomes from Primary levels, right up to High-school levels, and states the learning outcomes which students need to achieve. It is kind enough to include a few examples of ‘suggested learning experiences’, but it fails to focus in any detail how students can develop mental strategies to solve problems of each level. The Framework however, explores how students of different stages of learning can use different strategies to solve problems under the same requirement in The Curriculum levels.

In relation to the Achievement Aims and Objectives, The Framework makes clear distinctions between two main strands, strategy and knowledge.

The Framework categorises number exploring as knowledge, and all the different ways of working problems out on the basis that students use knowledge and strategy.

The Numeracy project began in 2001, based on an Australian project with similar ideas, called ‘Count me in too’. Because New Zealand was following behind, the team who designed the New Zealand version had the chance to sit back and see where Australia had missed parts, or not explained things fully enough, and made adjustments as they saw fit. From here, the Numeracy Framework was born. A key idea of The Framework, and something that goes against everything I myself was ever taught in Maths, is that the most important Maths is done in your head, not with pencil and paper. Children are to begin with tactile equipment, then move on to counting with their fingers, to imaging and so on. Writing Maths problems, comes last.

From my personal experience, I recall doing a whole lot of worksheets, where we were to answer 20 addition, or subtraction problems, we were given one minute, and we had to see how far we could get. Needless to say, I myself never got very far. With textbooks, the class would start at the beginning of the session on a chapter in the textbook, and you were to be finished by the end of the lesson. If not, I suppose it was a bit of tough luck, as you still had to move on to the next section in the next Maths class, even of you hardly understood the previous chapter. It was not at all an independent thing, you had to keep up with the class, which is not always possible, as everyone has different strengths, and weaknesses.

The Framework, however, has the idea that you cannot push students into moving up a level, until comes a time when they are completely comfortable with the level they are on, and understand the strategy behind it to move on. This is similar in The Curriculum where all the levels fade in and out over a certain number of years, for example a student may be in Year Three, but still at the tail end of Level One in The Curriculum. In The Framework however, it is slightly different. Students can sometimes be in-between stages, (The Framework has ‘stages’, while The Curriculum has ‘levels’)

The Number Framework believes that once students have knowledge, they build the foundation for Strategy. The strategy then creates new knowledge through use The Framework also stresses the importance of students making progress in both the Knowledge and Strategy strands. It is no good to be strong in one strand, or the other. Students need strong knowledge so that they can broaden their strategies, and knowledge is something that they need to design those strategies.

The Framework involves no writing in Maths until Stage 3-4, whereas The Curriculum has students reading and writing any two-digit numbers right from Level One. In The Framework it says that students need to be able to identify any two-digit number, but it does not say anywhere that they have to write it down.

To break each level/stage down into similarities and differences, I will begin at the start. I have roughly matched levels of The Curriculum, up with the stages of The Framework, beginning at Stage zero to two of The Framework, matched up with level one in The Curriculum.

Similarities between the two include that students can solve simple addition or subtraction problems in the range of 20. They must also be able to develop mental strategies for adding and subtracting numbers, and be able to find one half, and one quarter of a shape.

Differences include that in The Framework, for example, the mental strategy used in a particular activity, is the use of supporting materials, such as fingers which is clearly described in the strategies section. The Curriculum does not mention what the actual mental strategy used is, so teachers are to guess, or simply know all of the different mental strategies. Also, with the strategies section of The Framework, the students must solve multiplication and division problems by counting one to one, with the aid of materials. This is also not mentioned in The Curriculum at Level one.

In Stage three to four, I have matched it closest with Level Two of The Curriculum. Similarities between the two include mentally performing calculations involving addition and subtraction. Writing and solving story problems which involve whole numbers using addition, subtraction, multiplication and division. Also seeing the number ten as a complete count made up of ten ones, and solving addition and subtraction questions by using a combination of tens, and ones. They must also recognise sharing operations.

Differences are that the strategies section of The Framework means that strategies figure out that there is a transition from counting on materials, by imaging, and then advanced counting follow behind. The Curriculum suggests the developing of recall of multiplication facts through a programme that is done on a regular basis, for example at the start of every Maths lesson. This is not implemented in The Framework.

Roughly, I have matched Stage five to six of The Framework to Level three of The Curriculum. Similarities include that students maintain addition and subtraction facts. They can recall the basic multiplication facts, and solve practical problems, which require finding fractions of a whole number.

Differences are that students eventually establish part-whole strategies, these strategies involve finding the answer from basic known facts, such as ‘doubles’, or ‘fives make tens’ which is found in the strategies section of The Framework. The strategies section of The Framework also mentions that students can estimate answers and solve additions and subtraction tasks by choosing appropriately for a broad range of advanced mental strategies. It also says that students can find answers from known multiplication and division facts to estimate answers and solve fraction and proportion problems.

The Curriculum is different in that it says students will use calculators, concrete materials and mental methods to find fractions of a whole number. The Framework does not say this. In The Curriculum, it is difficult to tell how exactly, students think to solve the problems as strategies.

Stage seven to eight of The Framework, is roughly matched up to Level four of The Curriculum. Similarities include that students ca investigate possible ways of renaming numbers using decimals, to solve addition and subtraction tasks in relation to decimal numbers. They can also explain satisfactory algorithms for addition, subtraction, multiplication and division problems. They can find equivalent fractions and use unit fractions to solve problems with fractions, proportions and ratios. They can also convert decimals to fractions where appropriate.

Differences include that in the strategies section of The Framework, the students can use reversibility in decimal numbers. In the same section of The Framework, they can involve partitioning one, or more of the factors to solve multiplication and division problems, such as, for example 24x6 = (20x6) + (4x6). Still in the strategies section, students can find relationships between units of different quantities and convert between fractions, decimals and percentages to solve problems in relation to fractions, proportions and ratios. The Curriculum is different as can be seen, as it includes none of the above, which are all such important things for a student to know. The Curriculum is different to The Framework as it explains the outcomes of multiplication and division using decilmals, whereby The Framework does not.

In conclusion, it can be clearly seen that the major similarities are seen in the overall attention to the individual student in The Framework, whereas The Curriculum concentrates on the class group as a whole. Also the development of mental part/whole strategies is paid attention to far more in The Framework than in The Curriculum. The Framework also describes how students can achieve every aim through developing simple mental strategies in practical ways, while The Curriculum is more focused on the requirement for every level, and the mental strategies that students should have, but not necessarily how the students will achieve these strategies.

The Framework has it right, whereby it stresses the importance that the most important Maths is done in your head, The Curriculum stresses the importance of writing Maths, even though this is not the best way for children to learn. The Framework also bases teaching on the idea that by beginning to teach a child from where they are at, and not simply assuming every child has the same strengths and needs, and treating each child as an individual, the teacher can then assess their needs to become better Mathematically.

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