Assessing fraction knowledge

One of the many difficult things in teaching is finding out what children know or understand about an aspect of mathematics so that an idea of where to start teaching new material can be established. This assignment requires and supports you to tackle that issue.
You will work with 2 children from Years 4 to 7 (inclusive) *YOU CAN MAKE THESE UP* to investigate how children complete mathematics tasks and diagnose what they know about place value. You will present them with two tasks related to place value that are available from the Assessment 2 page on Blackboard *SEE ATTACHED FILE*. The children can be of different ages/Year levels, but regardless of their ages/Year levels you will need to plan for being flexible when you implement the tasks with the children, so that you are able to find out about the children s thinking. As a result, you will have to consider and plan in advance for how you might present the tasks, and what you might say to or ask of the children, particularly if they initially do not know what to do. Do not attempt to teach them or offer them clues about the tasks, as this is a diagnostic interview.
Process
The following steps are required to complete the assignment:
1. Identify the two children
b. Ask the parent/caregiver about the mathematics understanding of the child to enable you to get an idea of their background;
c. Schedule time to conduct the diagnostic assessment (anticipate around 30 minutes per child).
2. Review the tasks that the students will complete:
a. Refer to the two resources under the Assessment 2 information;
b. Select two tasks from those available in the document specified on the Assessment 2 page that are most suited to the children you will be working with (note that you will need to discuss why you selected these tasks);
c. Summarise the tasks your students will complete to include in the appendix of your submission, with appropriate referencing and acknowledgements.
3. Complete the tasks yourself, consider how you completed them, then write this up for inclusion in your assignment.
4. Plan for your diagnostic assessment for each child:
a. Write up the background you have on each child;
b. Organise the resources you will take (for example, paper, pencils/pens, manipulatives for the child to use when explaining their thinking);
c. Create steps you will take if the child has difficulties with any of the tasks (remember, you are not to teach the child).
d. Write potential prompt questions that can be used to assist the child to explain how s/he completed each task (that is, you want to ;
e. Write up the planning you undertook.5. Conduct your diagnostic assessment with each child.
6. Write up your results as a report, outline the following for each child:
a. What s/he can do;
b. Issues of difficulty that were noted.
7. Consider your results in terms of the readings you have completed and write this up in your Discussion.
8. Relate the children s knowledge to the Australian Curriculum: Mathematics, and misconceptions where appropriate.
9. Create a lesson for a whole class that addresses the next piece of learning from one of the students diagnostic assessment reports.
This assignment must be completed individually, although you might want to team up with another person to assist you with recording observations of the children. In the latter case, you will need to organise 4 children, so that you each have data for 2 children. An advantage of this teamwork is that when one of you is working with the children and acting as the interviewer , the other person serves as an observer or record keeper. If the child cannot complete the task, you might ask him or her to offer you a similar one that is possible, or to try it using the resources you have provided, or abandon the task and move to the next or finish the interview.

Assignment structure

You are required to use (as a minimum) the following bolded headings in your report:

Introduction

Background
â—¦
Briefly define place value.

â—¦
Explain and discuss where place value sits within mathematics education.

â—¦
Discuss how you completed the tasks.

Diagnostic Assessment
â—¦
The students

â—¦
The selection of the tasks

â—¦
Planning

â—¦
Results

â—¦
Discussion

Teaching Place Value
â—¦
What needs to be considered when teaching place value.

â—¦
What are effective teaching strategies to help children understand place value?

â—¦
What your lesson plan will address (link the lesson plan to the results of the diagnotic tasks for one of the children).

â—¦
Lesson plan

Conclusion

References

Appendix

â—¦
Brief task descriptions

Planning for Diagnostic Tasks
Planning for the Tasks
Teachers need to know what their students know along with what they do not yet know or have incorrect or incomplete understandings or misunderstandings about. Diagnostic tasks are designed to assist teachers in gaining this knowledge about their students. The process requires teachers to plan what they will do and how they will do it to ensure they obtain a thorough understanding of their students knowledge. Specific points that need to be considered include:
Who your students are “ are they older or younger, able to read or not, ESL, experienced or novice with the task or environment, known to you or unknown.
Why you are using the task/s “ is it to determine pre-knowledge before planning or to assess what knowledge students have developed at the completion of a program of work.
How the tasks will be introduced and described to the students.
How many tasks are required “ depending on the targeted understanding, several tasks may be required to gain a full picture of what the student knows.
What type of task will be used “ written or verbal, short answer or interview, individual or group.
The instructions provided and explanations that may be needed to assist the student with completing the task.
What resources or concrete materials will be available for students to demonstrate their understanding or record or help with their explanation/s of their thinking.
What you want to find out from the task and how you will use what you learn “ this will impact on several points, such as how many tasks are required and the type of task.
What mathematical ideas are embedded in the task(s)?
Will you engage with the student or just observe (remember you are not teaching).
What potential misunderstandings or misconceptions are possible with the task(s)?
What questions will you ask (if any), why, and what answer/s will you want/need/expect/anticipate?
What prompts will you use to help students provide details of their thinking? (Remember, do not teach or lead the students.)
How you will record the student s work, for example, work samples or photographs of how students demonstrated their understanding with concrete materials.
What records will you keep (this is related to why you are using the task/s).

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