First year mathematics Essay
It is often a daunting task to teach mathematics at any level, and at the grade one level this anxiety is often complicated by the idea that the formative years of mathematics training often colour’s the student’s view of the subject during the following years. Mathematics education in the early years is becoming increasingly important, especially in this technological age, when many new careers in technology depend on mathematics knowledge. A child’s understanding of mathematics is, like the understanding of anything else, dependent on the ability of that child to visualise the processes involved in any mathematical problem. In teaching subtraction to children of six and seven years old, then, the educator must develop ways in which related concepts might become visual so that the students might fully apprehend it.For these six- and seven-year-olds, fundamental to the concept behind numbers is the knowledge that a number of things can be arranged in different sets. For example, six can be arranged as two groups of three (33), as one group of four and another of two (42), and as a group of five and a single object (51). This idea of integers as representing discrete entities and therefore separable is an important stage in the visualisation process of arithmetic.
When a child can understand that the numbers can be viewed singly as well as collectively, the foundation will be better laid so that the concept of subtraction might be fully grasped. These numbers seen as having the ability to be arranged differently are now ready to be separated according to their sets. This can become a foundation for relating subtraction to the concept of taking away (Qualifications and Curriculum Authority, 2003).
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On the picture of a bus or a train, students might be shown several persons sitting together in groups. If the idea subtraction of three from seven (7-3) needs to be illustrated, for example, the students would be shown a picture of seven persons on a train sitting together in two activity groups. One group contains three persons while the other contains four persons. Then, a similar picture in another panel would illustrate the group of three persons getting off the train.
The final panel would show the group of four persons still sitting on the train and performing the activity they were doing before.The same idea could again be illustrated with counters representing the people on the train. The children could help with this second activity.
After the teacher draws a train on the chalkboard (or puts up a chart with a pre-drawn train) one child could be invited to place (or draw) seven counters (or other object) on the train. While this is taking place, the other students in the class would be simultaneously required to hold up seven fingers. Then, the same child would be called on to remove three of the counters on the train.
Meanwhile, the class will be asked to bend down three of their fingers. The child at the board would then be asked to count how many counters are left on the train. At this time, the students would also be asked to count how many fingers are left up (Primary National Strategy, 2003). Not only will these activities illustrate the concept of subtraction, but performing the two visualisation methods simultaneously will allow the students to realise two things about the idea of subtraction. The first is that it is transferable across activities; that is, it works no matter which objects are being handled. Second, it occurs often in everyday life.The idea that number sentences are associated with such activities is also an important one for these students to learn.
It is often not clear to students that an expression such as “7 – 6” might have practical meaning. Therefore, while performing such activities as the ones described above, it is a good idea to display the corresponding mathematical sentence on the board. It may also help to write the expression down in increments as the activity progresses (Primary National Strategy, 2003). Therefore, while the child places the seven counters on the train and the children hold up their seven fingers, the teacher would write the numeral 7 on the board.
Then at the second stage when the counters and fingers are being “taken away”, the teacher could reinforce the idea by writing “– 3” next to the 7. Finally, when the remaining fingers and counters are being counted, the teacher could write “=4” on the board.In order to assess the students’ understanding of the concept, they would be probed after the activity to make connections with their own experiences.
They would be asked to suggest reasons why the persons were separated into groups the way they were on the train. They might suggest that the groups were of relatives or of friends. They would even be asked to suggest reasons why the three persons left the train leaving only four.
To extend the concept of integers as discrete, students would be asked if they thought it possible for only two persons from the group of three to have left the train. Then, how many persons would have been left on the train if only those two had left.Further extension of this concept through questioning can lead to another scenario in which more than seven people are on a train or bus. The number twenty might be used, and the inability to use the fingers for computation of such a large number could lead to the introduction of the number line into the scenario.
Students would be given each a number line that goes up to twenty. Then they would be asked to visualise or imagine twenty persons on a bus. (They could be told that such a bus would be relatively filled up.) The teacher would point to the number 20 on the number line. Then, the students would be asked to imagine two persons leaving that bus (perhaps a man and his wife or two best friends from school). At the same time, the teacher would jump back two spaces on his/her number line (counting aloud “one, two…”) and children would be asked to follow. Children would then be asked to come up and illustrate similar problems if families of four, three (or groups of other small numbers) leave the bus .
For assessment and reinforcement purposes homework would be given in which students would make up scenarios of their own containing stories in which subtraction occurs (Primary National Strategy, 2003). They would be asked also to make mathematical sentences using the information from their stories. In addition, the students would be asked to construct a counting device capable of handling numbers up to twenty.
They would be encouraged to use everyday things from around the house or yard, such as bottle caps or marbles.Learning to visualise the concept of subtraction in mathematics through the use of such devices as scenarios from everyday situations encourages students to think mathematically and to link the situations of their life with mathematical concepts whenever they come across them. That is the objective of this lesson in subtraction: to get students involved in their own learning by picking ideas from their experiences and having them participate so that the concept becomes a general one for them. When students are able to see that numbers can be arranged in different patterns, and that these same numbers can be expressed in the form of people getting on or leaving a train or bus, they will be more likely to think of subtraction in those terms. They will also be apt to remember and use the rules of subtraction on occasions in which they engage in such activities. In that case, they will be more likely to understand and retain the concept.
ReferencesPrimary National Strategy. (2003). “Y1 Spring – Unit 3 Understanding addition and subtraction.” The Standards Site. Accessed 20 May 2006. Available: http://www.standards.dfes.
gov.uk/primary/teachingresources/mathematics/nns_un it_plan s/year1/Y1T2Unit3Understanding/nns_unitplan050803y1t2unit3.pdfQualifications and Curriculum Authority. (2003). “Mathematics glossary for teachers in key stages 1 to 4.
” QCA. November.