9-4-13
Name of Teacher:
School:
HCPSS Student Learning Objective
Mathematical Practices 2 & 3: Reasoning and Explaining
Component
Student Learning
Objective (SLO)
Description
100% of students will demonstrate growth in Common Core State Content
Standards for Mathematics with connections to the Standards for Mathematical
Practice (Practices 2 and 3: Reasoning and Explaining), as evidenced by
performance on worthwhile mathematical tasks and/or high quality formative
assessment items1 and participation in effective classroom discourse.
The task selection checklist can be used to support identification of worthwhile mathematical tasks
and/or high quality formative assessment items.
1
Population
Learning Content
Instructional Interval
Evidence of Growth
Baseline
Rationale for Student
Learning Objective
(insert grade) grade mathematics students
Common Core State Standards:
2. Reason Abstractly and Quantitatively. (SMP2)
3. Construct Viable Arguments and Critique the Reasoning of Others. (SMP3)
School year 2013-14
Pre/post teaching data collected through the Student Performance Rubric.
 Analyze pre-teaching data collected through Student Performance
Rubric (attached)
 Attach class roster to share students’ scores of pre-teaching data.
The 8 Standards for Mathematical Practice (SMP) describe the behaviors of
mathematically proficient students. These are the behaviors that mathematics
teachers should seek to develop in their students. Together, practices 2 and 3
(below) can be described as reasoning and explaining.
2. Reason Abstractly and Quantitatively. (SMP2)
3. Construct Viable Arguments and Critique the Reasoning of Others. (SMP3)
The behaviors are described in the Student Performance Rubric (attached). The
rubric is a tool to measure student performance. With teacher guidance, student
proficiency will progress from the baseline to more advanced proficiency levels.
Target
The chart shows growth targets for all students. Values are based on the
Student Performance Rubric.
Students scoring this value2 on the
Will increase to this score on the
pre-assessment:
post-assessment.
0-2
3-5
3-5
6-7
6-7
8-9
8-9
8-9
2 Multiple tasks can be measured with the rubric and an averaged performance can be used as a
performance value.
*Please note: Students identified by IEP teams as having significant cognitive disabilities will have
individual targets.
This SLO is a sample. Targets need to be adjusted based on your students’ data. Student growth should be
achieved for all students.
9-4-13
Evidence of Growth
Pre/post teaching data collected through the Student Performance Rubric.
Criteria for
Effectiveness
Full Attainment of
Target
More than 90% of
students meet agreed
upon learning targets
identified in the chart
in the Target section
above.
Mathematics Content
Standards and
Mathematical Practices
Standards 2 & 3
Strategies
Partial Attainment of
Target
Between 75% and 90% of
students meet agreed
upon learning targets
identified in the chart in
the Target section above.
Insufficient Attainment
of Target
Less than 75% of students
meet agreed upon
learning targets identified
in the chart in the Target
section above.
 Be purposeful when planning lessons to include challenging mathematical
tasks that elicit the Mathematics Practices in their students. (SMP2 and 3)
 Monitor instructional progress. (SMP2 and 3)
 Ask students to explain their thinking regardless of accuracy (SM2)
 Highlight flexible use of numbers (SMP2)
 Facilitate discussion through guided questions and representations.
(SMP2)
 Accept varied solutions/representations (SMP2).
 Provide opportunities for students to listen to or read the conclusions or
arguments of others (SMP3)
 Establish and facilitate a safe environment for discussion. (SMP3)
 Ask clarifying and probing questions. (SMP3)
 Avoid giving too much assistance (e.g., providing answers or procedures).
(SMP3)
 Pose rich problems and/or ask open ended questions (SMP3)
 Provide wait-time for processing/finding solutions (SMP3)
 Embrace diverse solutions and/or justifications (SMP3)
 Recognize and model efficient strategies for computation (SMP2)
 Model to develop student oral and written communication in mathematics
(SMP3)
This SLO is a sample. Targets need to be adjusted based on your students’ data. Student growth should be
achieved for all students.
Student Performance Rubric
Reason and Explain • Standards for Mathematical Practices 2 and 3
Reasoning
about
Problems
Reasoning
about Numbers
Explaining
• Uses symbols/equations
to solve problems.
• Represents problems
with tools, drawings, or
equations.
• Understands
reasonableness of the
solution.
• Interprets solutions
including remainders.
• Represents problems
with tools, drawings,
equations.
• Uses symbols/equations
to solve problems.
• Represents problems.
Representations are flawed
or inaccurate.
• Uses symbols/equations
incorrectly or
inconsistently.
• Does not represent
problems.
• Does not use
symbols/equations.
3
2
1
0
• Estimates answer before
calculating to determine
reasonableness of answer.
• Uses numbers flexibly,
does not use standard
algorithms for all
computation situations
• Computes accurately.
• Relies on procedural
methods for computation
in inappropriate situations.
• Computes accurately.
• Relies on procedural
methods for computation
in inappropriate situations
• Computation is flawed.
• Cannot apply a procedure
for computation.
• Procedure is flawed.
• Computation is flawed.
3
2
1
0
• Explanation is clear and
complete.
• Uses examples in
explanation or describes
mathematical concept not
just procedure.
• Uses representations in
explanation.
• Uses correct math
vocabulary in explanation.
• Explanation is clear and
complete.
• Uses representation in
explanation.
• Uses correct mathematics
vocabulary.
• Partial explanation
• Some/partial use of math
vocabulary.
• Vocabulary is not
consistently correct.
• Missing explanation
• Explanation is irrelevant
or unrelated
• Explanation simply
restates prompt.
• Missing math vocabulary
or used incorrectly.
3
2
1
0
Task Selection Checklist
This checklist supports the identification of worthwhile mathematical tasks and/or high
quality formative assessment tasks. All 3 elements are present in such tasks.
 The task/item explicitly requires students to communicate their reasoning and
understanding.
 The task/item allows for multiple solutions/strategies but not necessarily
multiple correct answers.
 The task/item requires student engagement in the overarching habits of mind of a
productive mathematical thinker. For example, the task/item MAY require students to:

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Make sense of quantities and relationships in problem situations
Represent abstract situations/problems symbolically and understand the meaning
of quantities
Create a coherent representation of the problem
Consider the units involved
Flexibly use properties of operations
Use definitions and previously established causes/effects (results) in constructing
arguments
Make conjectures and use counter examples to build a logical progression of
statements to explore and support their ideas
Communicate and defend mathematical reasoning using objects, drawings,
diagrams, and/or actions
Listen to or read the arguments of others
Decide if the arguments of others make sense and ask probing questions to clarify
or improve the arguments.