Mathematics
Microsoft Word - EDUC5502_New Assignment 1 description_2020 1 New Assignment 1: What do children know about numbers? (40%) In order to determine where to start teaching, it is important to find out what children already know and understand about an aspect of mathematics. The purpose of this assignment is to provide you with the opportunity to find out children’s prior knowledge of numbers through the use of think boards, and then develop appropriate activities to address an area of misunderstanding. This assignment also provides you with an opportunity to become familiar with how children communicate their understandings and ideas of mathematics. Please present this assignment in 12 point font, Times New Roman, using 1 ½ spacing. Please include your name, student number and unit title in the header. Include the page number in the footer. All sections are to be written in the third person, except the reflection. A detailed marking rubric can be found on LMS. In order to pass the assignments in this unit, all written work must be of a satisfactory standard in terms of written literacy and referencing. Written texts should be appropriately structured and clear in meaning. Correct and appropriate grammar, vocabulary and spelling should be used throughout. Referencing should conform to APA style. Written literacy and referencing expectations will normally be incorporated into assignment rubrics. For this assignment you will be using previous information that has been collected from Year 1 children. These children should be familiar with numbers up to 20, possibly up to 50, and may have started skip counting in 2s and 10s. The following nine sections describe the assignment. Parts A, B, E, F, G, H and I should be written up and submitted. Part A: Introduction Provide 1-2 paragraphs that state the purpose of the assignment, pseudonym of the child (which is given in the cases) and year level of the child. List the three numbers that were used for the think boards and why these numbers were chosen. Part B: Describing think boards (Approximately 1000 words) Provide a referenced description of think boards along with the advantages and limitations of using think boards in the classroom for mathematics education. Consider how think boards can be differentiated for high and low ability students. Part B of the assignment is to be submitted through Turnitin by Monday March 23 (9.00am) for marking and feedback on your understanding of think boards. Part C: Introducing the activity (working with the child) This is what you would have done. It is still important to read through this information to understand the context in which the information was collated. Introduce yourself to the child and inform them that you wish to find out how much they know about numbers by completing three simple activities. Assume the child has never seen a think board before. Model how to use the think board with the number 4, using a spare think board. Show the child each section of the board and how to complete it. Prepare your think boards on paper, not mini whiteboards. 2 Have a story book or game based on number ready to use in case your child completes all the think boards quickly. I will also have some of these available. Part D: Determining Prior Knowledge (working with the child) This is what you would have done. It is still important to read through this information to understand the context in which the information was collated. Select three numbers that will provide you with as complete a picture as possible of the children’s knowledge and understanding. These three numbers should aim to include one that is well known to the child, one that may be known, and one that should be challenging. For example, for a child in Year 1 this could be a number between 6 and 9 (should know), a number between 15 and 19 (may know) and a number between 31 and 35 (may find challenging). Be guided by how well (or otherwise) the child completes each think board. Provide the child with the range of numbers and allow them to select one they want to do. For example, for the first think board, ask the child to select a number between 7 and 9. However, be aware that the child may not understand the term ‘between’, so you may have to think of another way to say this. Avoid using large numbers, such as 50+, as children tend to lose interest. Do not glue anything on the think board as it takes up precious time. Use the think boards to find out what the child knows about numbers. You will need three think boards ready to use (plus spares, to be fully prepared). When introducing the think board, encourage the child to tell you everything they know about the number. It is suggested that you start in the ‘Concrete’ section, as this tends to be the easiest. Have some concrete materials for the child to use, and/or encourage them to also find something from outside (leaves, twigs) to illustrate the number. Please do not bring small objects as they become difficult for children to use. I will supply boxes of counters. You do not need to stick anything to the think boards. Then move to the ‘Picture’ section. In the ‘Picture’ section ask them to draw that number of objects. [There is a difference between “Draw a picture of 16” and “Draw 16 objects”.] For larger numbers (such as above 20) you may wish to ask the child how many are left to draw, when they are near the end of their drawing. If you ask them in the middle of their drawing they may lose concentration on what they are doing. In the ‘Symbol’ section ask them to write the number down or associated number sentences. Do not be concerned if the child inverts their numbers, especially numbers in the teens. This is quite normal for Year 1 children. Children tend to have most difficulty with the ‘Story’ section, so you may wish to do this last. Because they find this difficult, it is important to model it in your first think board with the number 3. Scribe the story they tell about the number. Listen carefully to the language the children use and try and capture it. How do the children count – is it one-by-one or do they skip count naturally? Take photographs of the completed think boards, but do not include any faces of children. As a courtesy, ask the child if you can take the photograph first, and then show them the photograph once taken. Be aware of children who take a long time to draw their picture and/or colour it in, and encourage them to move along. The children can keep their completed think boards if they want them. Please remember that this is an exercise in determining children’s prior knowledge. Do NOT teach the child anything. If you found they are counting large number by ones, then ask them if they can think of an easier way to do this. But do not try and teach them skip counting or place value, as we are there as observers only. Also, do not count for them – let them say the numbers first and you repeat. Do NOT correct them. Do NOT place any emphasis on literacy, as this is a mathematics exercise. Once the think boards are completed, thank your child with a few stickers and return them to their classroom. 3 Part E: Reporting (Approximately 500 words) This section has been changed compared to the original assignment. Select one of the 18 cases presented on LMS under Assignment 1. Each case is presented in the same way: the number, a photograph of the completed think board, and a short summary of what the child did or said while completing that think board. All names are pseudonyms. Please copy the case directly into your assignment as we need to see it while marking your assignment. Using the evidence from the think boards, summarise what the child knows about numbers and where there are areas of misunderstanding or gaps in knowledge. Remember to refer to the think boards to support your reasoning. This part does not require any references as you will only be using the information from the think boards. Please place this information after your selected case, as it is a summary of the case. Part F: Location of child within the curriculum documents (Approximately 1500 words) Using the information from the previous section, locate the child on the following documents: First Steps in Math’s Diagnostic Maps – Number WA Curriculum: Mathematics, Number and Place Value, Year 1 (Foundation if a weak child or Year 2 if a strong child) Counting principles – which of the five counting principles have been demonstrated? Be aware that children should be able to complete the requirements of their year level in the WA Curriculum by the end of the year. You may have a child ‘working towards’ the year level requirements. Make sure to justify your location of the child by referring to the content of their think boards. Part G: Recommendations and Activities (Approximately 1000 words) From the previous two sections, clearly identify the child’s major area of misunderstanding or gaps in knowledge. If there are no misunderstandings or gaps in knowledge, then identify what the next area of development should be for the child. Select only one mathematical content area (eg. skip counting). A lack of ability to write number stories cannot be used here, as all children have problems with this. Describe two activities that could be used with this child over the next two sequential lessons based on the major area of misunderstanding. There should be one activity for each lesson, based around the same topic (eg. skip counting by 10s). Look for activities other than those presented in the workshops. For each