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## Problem-solving strategies

Identify student strengths and needs for future planning (as connected to students learning goals and standards). Engagement in this project will support teacher candidates in thinking about the ways in which students in early childhood mathematics settings exhibit both conceptual understanding and procedural fluency.
Beyond that, this project will provide opportunities teacher candidates to analyze both quantitative (numerical or categorical) and qualitative (descriptive or narrative) data and documenting student thinking and evaluating student thinking on a rubric.
Skills: The purpose of this assignment is to help you practice and implement the following skills, which are essential to your success in this course, as well as in teaching mathematics:
• Evaluating a performance assessment on a rubric
• Analyzing student’s problem-solving strategies
• Report on qualitative and quantitative data gained during assessment
Knowledge: This assignment will help you become familiar with the following important content and pedagogical knowledge in mathematics education:
• Identification of the ways in which young math learners demonstrate conceptual understanding and procedural fluency
• Strategies used to solve various problems involving the four operations
• Using questions to facilitate mathematical thinking and discourse during learning
• Using assessment to identify students’ strengths and future learning
• Plan for students’ future learning from strengths
• Make connections between students’ learning and standards
For this project, you will be given a set of second student data to us for your analysis. The participants for this data set are second grade mathematicians. You will be working on this project in class with your group, and then finishing it up on your own.
With your group analyze the students’ work (provided as a separate file) and provide a score on the provided rubric. Your group SHOULD NOT divide up the work samples but rather should come to a consensus about where to place each student on the rubric.
Once you have scored each student work sample, with your group discuss the following (I highly suggest having a group member take notes of your discussion):
• What quantitative (numerical or categorical) trends do you see in the whole class data? Summarize student learning via a chart or graph.
• What qualitative (narrative) trends do you see in the whole class data?
• What strengths did the students demonstrate?
• What struggles, partial understandings, and confusions students demonstrate in their work?
• What are the underlying mathematical ideas and misunderstandings these strengths and struggles are connected with (i.e prior learning experiences)?
• What would be an appropriate next step/targeted objective for the class? Use the data to justify your response.
On your own you will write up a summary the student data and your experience. The summary should be a representation of what you learned about the students’ knowledge and draw upon evidence from the student works as well as make connections to course readings. Be sure to attend to the following in your reflection:
a. How did this experience impact your abilities as a future teacher?
b. Specifically, how did this experience impact your ability to collect and analyze student data?
c. What quantitative (numerical or categorical) trends do you see in the whole class data? Summarize student learning via a chart or graph
d. What qualitative (narrative) trends do you see in the whole class data?
e. What strengths did the students demonstrate?
f. What struggles, partial understandings, and confusions students demonstrate in the interview?
g. What are the underlying mathematical misunderstandings these strengths and struggles are connected with (i.e prior learning experiences)?
h. What would be an appropriate next step/targeted objective for the class? Use the data to justify your response.
Criteria for Success:
In order to be successful on this assignment, you will need to submit the following items to both D2L and Chalk and Wire under the Assessment Assignment for 4408
• Your individual reflection
• Student Rubrics (1 rubric for each task completed the by the student- total of 3 rubrics per student)

Your work will be scored on the following rubric (highlighted portions will be scored in Chalk and Wire):
Exceeds Expectations Meets Expectations Approaching Expectations
Paper Format and Structure All components of paper are submitted including:
• Cover Page
• Completed Student Rubrics
• Reflective paper
• References in APA format
No grammatical, spelling or punctuation errors. Easy to read. Clear structure/organization. All components of paper are submitted including:
• Cover Page
• Completed Student Rubrics
• Reflective paper
• References in APA format
Some errors in grammar or spelling, but these do not impede the readability of the reflection 1 or more components of the paper is missing:
• Cover Page
• Completed Student Rubrics
• Reflective paper
• References in APA format
Numerous errors in grammar or spelling which impede the readability of the reflection

Reflective Paper (Experience) The ability to analyze data is addressed in the paper.
AND
The ability to use that analysis to improve their quality of instruction is clear in the paper.
The ability to analyze data are addressed in the paper.
OR
The ability to use that analysis to improve their quality of instruction is clear in the paper. Neither the ability to analyze data, or the ability to use that analysis to improve the quality of instruction is clearly addressed in the paper.

Reflective Paper (Quantitative Trends)
Trends are identified across the group in detail, making connections to standards and instructional needs.
Quantitative data connected to assessment is presented in a chart or graph with clear and thorough analysis. Trends are identified across the group, making connections to standards, strengths, and instructional needs Connections are vague, but emerging.
Quantitative data connected to assessment is presented in a chart or graph with some analysis.
Trends are identified across part of the group, but are minimally connected to standards, strengths and instructional needs.
Quantitative data connected to assessment is not presented in a chart or graph, or analysis of chart or graph is missing

Reflective Paper (Qualitative Trends)
Trends are identified across the group in detail, making connections to standards, strengths and instructional needs
Each student is discussed in detail with regard to their struggles, partial understandings, confusions and conceptions.
Trends are identified across the group, making connections to standards, strengths, and instructional needs Connections are vague, but emerging.
Most students are discussed with regard to their struggles, partial understandings, confusions and conceptions.
Trends are identified across part of the group, but are minimally connected to standards, strengths and instructional needs.
Some students are discussed in with regard to their struggles, partial understandings, confusions and conceptions, but this discussion is vague.

Reflective Paper (Next Steps)
The next steps designed are instructionally appropriate and based on the data collected. The data collected is clearly used to justify their decisions.
The next steps designed are instructionally appropriate and based on the data collected. Some of the data collected is used to justify this next step.
The next steps designed are not clearly connected with the data they collected. And/or the data collected is not used to justify their decisions.

Assessment Rubrics There are 3 completed assessment rubrics (one rubric per task) provided for ALL students. Assessment rubrics include thorough notes that accurately describe students’ work and utterances.
There are 3 completed assessment rubrics (one rubric per task) provided for some (more than half the class) of the students in the class.
OR
There are 3 completed rubrics for all of the students but they lack detail.
There are 3 completed assessment rubrics (one rubric per task) provided for some (less than half the class) of the students in the class.
OR
There are less than 3 completed rubrics for students in the class.
OR
There are 3 completed rubrics for all of the students and no notes with details are provided.