Colligan_Tania_EDC243_Report_2021

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Tania Colligan 17818782 EDC243Report Report Place Value Importance Place value is important for student to be able to use the number system inside and outside of school. It tells us what place the number sits and then its value for example, in 352 the digit 5 indicates there are five (how many) tens (place value). Knowing or understanding place value helps reading and writing numbers big and small, use money and complete functions of addition, subtraction, multiplication and division. (Reys et al., 2020) Teaching Place Value When teaching place value to students using manipulative materials it helps the students learn the concept in a deeper meaningful understanding. There are two types of materials pre-grouped and ungrouped that can be used to develop the concept of place value. Some examples of ungrouped materials are buttons, counters, pop sticks and beans. These require counting and students form them into groups. The pre-grouped materials are different as they are already grouped, and example of this is the base ten blocks. (Reys et al., 2020) Depending the concept, the teacher is focusing on to which materials are best used. For example, if the focus is there are 10 ones in one ten then using ungrouped materials like pop sticks will be the best option. If looking at counting in tens, then the MAB tens rods will be the materials to be used. (Hartnett, 2018). In a report it showed 96% of teachers surveyed that the recommended materials from curriculum documents benefited the children’s learning (Price, 1998). Price also commented that there is a need of planning resources that are appropriate to the where the children’s understanding is at. For example, there is no point using the MAB blocks if the child does not know or understand the relationship to each block. If the child is counting each segment to see if it’s a ten rod then they have not grasped that rod is 1 ten (Hartnett, 2018). Hands on materials is beneficial to develop the conceptual understanding of place value in teaching mathematics. When using these materials, it is ensuring the children that they have gained the place value concept and main ideas before moving on to other functions like addition, subtraction, multiplication and division.

Tania Colligan 17818782 EDC243Report The main ideas of Place Value There are main ideas that children need to understand about place value. Reys states there two key ideas for promoting number sense one, explicit grouping or trading. Using the base ten system with the importance of trading ten ones for one ten, then ten tens for one hundred and the grouping and trading continues in tens. It is important to note that the trading can be done up and down (Reys et al., 2020). It requires the child to reorganise their thinking structure, which is called unitizing, where they can look at individual items and encompasses a whole. Which means they can look at ten ones as being the same as one ten (Fraivillig, 2017). The second key idea is the position of a digit determines the number being represented. Every digit in a number has a place value. It shows whether the digit represents tens, hundreds or thousands in the number. For example, the digit 2 quantity in number 5432 is different digit 2 in 2345. It represents 2 ones in 5432 and 2 thousand in 2345. If there is no digit represented in the number, then a zero is placed to show there is no quantity in that place. When recording a digit each place up to the ones need to be filled to represent the right values. Understanding the place value of digits helps expand the number and tells the students how to read numbers. Building conceptual knowledge like this will be more beneficial than relying on procedures. Conceptual understanding vs procedures There is an importance of developing conceptual understanding rather than relying on procedures. Conceptual understanding is built from logical relationships developed from internally from existing ideas in the mind. Procedures do not build understanding of concepts or knowledge it is used as a tool for a routine math task. There are no physical concepts examples to be used to develop relationships to math concepts it is constructed in the child’s mind. For example, the child can identify the MAB rod as ten and large square block as 100 this is not knowing the concept. The concept is the relationship of the rod and cubes, ten is the same as ten ones.

Tania Colligan 17818782 EDC243Report Children need to develop concepts in their own mind and learn the relationship there is no procedure to help build that understanding. Study Issue - Partitioning three-digit numbers Taylor struggled partitioning the three-digit number of 592, an example that was given to split up the number in tradition way was 500 and 90 and 2. Time was given to think about it and an example was repeated. The response was 5000 900 02, this the lack of knowledge of place value and not demonstrating the ability to be able to think about the numbers in a flexible way. It is also showed by saying 5000 that not knowing the digit 5 is in the hundreds place and how to split that number into parts. It is achievement level 3 from First Steps that Taylor has shown lack of knowledge of not being able to partition whole numbers in a non- standard way. To which it means that Taylor needs to be given activities to help strengthen her understanding of splitting numbers into parts. First Steps Key Understanding six is what to use to develop place value concepts through looking at patterns in the way it is written and say numbers into parts. Taylor is in year 5 and portioning numbers is something in year 4 she should have developed it. In ACARA mathematics, number and algebra, content descriptor number and place value it states, “Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMINA073).” (ACARA, n.d.) Stages of place value Stages of place value is, counting, the 10s, two-digit pattern, extend the pattern to three- digit numbers and larger, and numbers. These stages are all important in developing place value concept and skipping or not doing one will affect the child in future mathematical tasks. It will affect the learning of addition, subtraction, multiplication and division. To determine how many, counting is needed. Learning to count 1-9 is the basis to the base ten system. Another part of counting is subitizing which being able to look at a group of objects

Tania Colligan 17818782 EDC243Report or dots and say the number without counting them. For example, a child playing a game using a die and it rolls showing 6 dots, the child instantly says 6 and moves six places. Part-part- whole is a skill that a child develops to help with place value understanding. It involves the child to able to see the number quantity in relation to its parts. For example, to see seven objects then also see that its 3 and 4 as well. Seeing numbers in different ways is an important part of place value. Partitioning numbers is another way of looking at numbers and their values in different ways. To be able see a number and rename it for example 542 can be 500 + 40 +2 or 400 +142. A significant part of number system and place value is 10, each place has a value of 10 times when moved to the right. It continues through the number system 10 ones is 1 ten, then 10 tens are 1hundred, next 10 one hundred is 1000 and keeps going (Gunningham, 2011). Tutoring sessions The first session involved looking at YouTube of partition three-digit numbers in different ways. This resource appealed to Taylor as she is a year 5 student and likes to use technology. Taylor watched the video, and it was paused to discuss the different ways that were shown. When it came to a different example it was paused and talked about different ways to partition that number then watch to see what ways the video displayed. When using digital manipulatives, it gives the student to look at mathematics concepts using pictorial and symbolic representatives (Larkin et al., 2019) Image 1 and 2 show Taylor watching and the non-traditional partition. Image 2 example of non-traditional partition to number 434. Image 1 Taylor watching the video.

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