Observation of an educator is a powerful way to learn, reflect, and see theoretical concepts come to life. You can also notice how, when something is missing, that impacts student learning and the classroom learning environment.
On a given day, a veteran teacher may identify students’ prior knowledge through informal or formal pre-assessments, teach concepts, demonstrate skills, provide timely-actionable feedback, and provide one-on-one support for students needing targeted attention based on their pre-identified or real-time identified needs.
Instructions
- Read the Observing peers develops practice, changes culture article.
- Download and save the Fieldwork Observation Template to take notes on during your observation and complete this assignment. This is free form, and you make record noticing in any format you prefer.
- Observe an in-person lesson of a current teacher within your content area who has been teaching for at least three years. You need to observe a lesson that is 7th or 8th grade or HS.*If you are currently employed as a PE or Music teacher in an elementary setting you may with the instructors permission observe a setting similar to your work setting.
- As you observe, use the template to record what you observe related to specific topics you are learning in this course. Note that this is similar to the Learning Map Template in the Week Four Signature Assignment, so you can seek to identify specific elements from the learning map in action. There is also an open section for notes/observations.
- After your observation, complete the “Relate and Review” section of the template. Your write-up should be at least 400 words in length. For guidance on writing, please reach out to the Writing Center at National University.
- Review and summarize the observational experience, sharing your three key takeaways from the observation
- Relate topics or concepts you have learned about in this course (e.g., clearly articulating learning expectations to students, the use of assessments to inform curriculum planning and instruction, instructional strategies to support equity, diversity, and inclusion of learners or the learning outcomes, UDL strategies, etc.) to strategies you observed the teacher(s) employ.
- One of your strategies must be an instructional strategy, technology, or tool you saw used that would provide equitable access to curriculum and support diverse learners.
CA Content Standard(s)
What is the subject of the class you are observing? What standard(s) are they teaching (if you can identify)?
The subject is 6th-grade math.
The standards being taught are:
6.EE.1: Write and evaluate numerical expressions involving whole-number exponents.
6.EE.2: Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.2a: Write expressions that record operations with numbers and with letters standing for numbers. 6.EE.2c: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
Lesson Focus
What is the focus of this lesson?
Evaluating Expressions with Exponents:
- Understanding and applying the order of operations (PEMDAS/GEMS) to evaluate expressions that include exponents and other arithmetic operations such as addition, multiplication, and division.
- Emphasizing the correct sequence of operations, particularly the importance of solving exponents first before proceeding to other operations.
Solving Expressions with Variables:
- Introducing the concept of variables as placeholders for numbers in expressions.
- Demonstrating how to substitute values for variables and then evaluate the expressions using the order of operations.
- Reinforcing understanding of how to deal with expressions, including variables and exponents.
Concepts
What are the concepts of this lesson?
Order of Operations (PEMDAS/GEMS):
- Understanding the sequence in which different operations (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) should be performed in mathematical expressions.
- Recognizing that operations within parentheses are done first, followed by exponents, multiplication/ division from left to right, and addition/ subtraction from left to right.
Exponents:
- Understanding what exponents are and how to evaluate expressions with exponents.
- Learning that an exponent indicates how often the base number is multiplied by itself.
Variables in Expressions:
- Introducing variables as symbols that represent unknown or variable quantities in expressions.
- Understanding how to substitute specific values for variables in expressions and then evaluate the expressions using the order of operations.
Evaluating Expressions:
- Learning to calculate the value of expressions that include a combination of numbers, variables, and operations, following the order of operations.
Skills
What skill(s) are students learning?
Evaluating Expressions: Students learn how to calculate the value of mathematical expressions that include numbers, variables, and various operations by following the order of operations.
Applying the Order of Operations: Students develop the skill of applying the correct sequence of operations (PEMDAS) when solving mathematical expressions, ensuring that calculations are performed in the right order.
Working with Exponents: Students learn how to interpret and evaluate expressions that contain exponents, understanding how exponents represent repeated multiplication.
Substituting Values for Variables: Students practice substituting specific numbers for variables in expressions and then evaluating the expressions, a foundational algebra skill.
Problem Solving: Through practice problems and examples, students enhance their problem-solving skills by applying their understanding of the order of operations and exponents to solve mathematical expressions.
Task
How is the teacher modeling the skills for students to learn?
Clear Explanation: Mr. Carruth provides clear and detailed explanations of the concepts, such as the order of operations (PEMDAS) and how to evaluate expressions with exponents. He ensures that students understand each step of the process.
Step-by-Step Demonstration: He demonstrates how to solve problems step-by-step, showing each operation and explaining why it is performed in that order. This helps students see the application of the order of operations in practice.
Use of Visuals: Using a whiteboard allows Mr. Carruth to represent the problems and the steps to solve them visually. This visual representation helps students follow along and understand the process more clearly.
Interactive Engagement: Mr. Carruth involves students in learning by asking them to solve problems and share their answers. This interactive approach encourages active participation and helps students apply their knowledge.
Providing Examples and Practice Problems: He provides multiple examples and practice problems for students to solve, covering different scenarios and levels of difficulty. This variety helps reinforce the concepts and skills, allowing students to practice and solidify their understanding.
Encouragement and Support: Mr. Carruth encourages students to ask questions and provides support when needed. He creates a supportive learning environment where students feel comfortable seeking help and clarifying their doubts.
Learning Objective
Is there a learning Objective? If so, what is it?
The first learning objective is for students to understand and apply the order of operations, including exponents, to evaluate numerical expressions.
The second learning objective is for students to understand how to write and evaluate expressions with variables and to connect real-world problems to addition and subtraction in expressions. This includes being specific when naming variables and considering units of measure in their answers.
Social and Emotional Learning Strategies
What, if any, social-emotional learning strategies do you see in action?
Creating a Positive Learning Environment: The teacher creates a welcoming and inclusive atmosphere, which is essential for fostering students’ sense of belonging and safety. This environment supports social-emotional development by making students feel valued and respected.
Encouraging Student Participation: The teacher actively encourages student participation by asking questions and providing opportunities for students to share their thoughts. This practice helps build students’ confidence and communication skills.
Providing Support and Feedback: The teacher offers support and constructive feedback to students as they work through the problems. This approach helps students develop resilience and a growth mindset as they learn to view challenges as opportunities for learning.
Modeling Respectful Interactions: The teacher models respectful and polite interactions throughout the lessons, demonstrating how to communicate effectively and listen to others. This sets a positive example for students to follow in their interactions with peers and adults.
Fostering a Sense of Accomplishment: By guiding students through the problems and acknowledging their success, the teacher helps foster a sense of accomplishment and self-efficacy. This is important for students’ emotional well-being and motivation to learn.
Student Misconceptions
Does the teacher address any misconceptions preemptively, or in real time?
Preemptive Addressing of Misconceptions:
- The teacher preemptively addresses potential misconceptions about the order of operations by emphasizing the correct sequence (PEMDAS) and explaining that multiplication/division and addition/subtraction are performed from left to right.
- The teacher also preemptively addresses misconceptions about solving equations by explaining the importance of balancing the equation and demonstrating the correct steps to isolate the variable.
Real-Time Addressing of Misconceptions:
- The teacher provides real-time feedback and corrections as students work through practice problems, helping address misconceptions arising during the lesson.
- In addition, the teacher asks probing questions and provides guidance as students work on solving equations, addressing any misconceptions that emerge in real time.
Lesson management structure
What behavioral expectations do you see modeled, expected, or reinforced?
Active Participation: The teacher encourages students to actively participate in the lesson by asking questions, engaging in discussions, and working on practice problems. This expectation is reinforced through the teacher’s interactions with students and the emphasis on student involvement in the learning process.
Responsibility for Learning: The teacher expects students to take responsibility for their learning by paying attention, following along with the lesson, and completing assigned tasks. This is reinforced through the teacher’s guidance and the structure of the lessons, which require active student engagement.
Following Directions: The teacher provides clear activity instructions and expects students to follow directions. This expectation is reinforced through the teacher’s monitoring of student progress and feedback during activities.
Assessment / Checking for Understanding
Assessments in action
Does the teacher use any informal, self-, formative, or summative assessments during the lesson? How do they use them? How do they provide feedback to students?
Yes, the teacher uses various forms of assessment during the lessons:
Informal Assessment: The teacher frequently asks questions throughout the lessons to gauge students’ understanding and to keep them engaged. This allows the teacher to assess students’ comprehension in real time and address any misconceptions immediately.
Formative Assessment: The teacher provides practice problems for students to solve. This formative assessment allows the teacher to monitor students’ progress and understanding of the concepts being taught.
Feedback: The teacher provides immediate feedback to students based on their perceived responses to questions and performance on practice problems. This feedback is specific and constructive, helping students understand possible mistakes and learn from them. For example, in the first lesson, the teacher addresses the students’ possible misunderstanding of the order of operations and provides a clear explanation to clarify the concept.
Summative Assessment: The teacher does not explicitly use summative assessments in these lessons, as summative assessments are typically used to evaluate student learning at the end of a unit or course. However, the formative assessments and feedback provided throughout the lessons are crucial in helping students prepare for any future summative assessments.
UDL in action
Do you see examples of UDL principles in action? If so, describe.
Multiple Means of Representation: The teacher uses various methods to present information, including verbal explanations, written examples on the board, and visual models like tape diagrams. This caters to different learning preferences and helps ensure all students can access and understand the content.
Multiple Means of Engagement: The lessons are designed to involve students actively in their learning. The teacher encourages participation, asks questions to prompt thinking, and provides opportunities for students to practice and apply what they have learned. This variety of activities helps maintain student interest and motivation.
Multiple Means of Expression: Students are given different ways to demonstrate their understanding, such as solving problems on paper, verbalizing their thought processes, and working with a partner. This allows students to express their knowledge in ways that suit their strengths and preferences.
Structured Student Learning Activities
What activities are students involved in during the lesson to support their achievement of the learning goal(s)?
Direct Instruction: The teacher provides clear explanations and examples to introduce and explain new concepts. This helps students understand the foundational knowledge they need to achieve their learning goals.
Guided Practice: Students work on problems or tasks with the guidance and support of the teacher. This allows them to apply what they’ve learned and receive immediate feedback, which helps reinforce their understanding and skills.
Independent Practice: Students are allowed to work independently on problems or tasks. This helps them consolidate their learning and develop confidence in applying the concepts and skills.
Collaborative Learning: In the second lesson, students work in pairs to solve problems and discuss their reasoning. This collaborative approach encourages peer learning and helps students develop communication and teamwork skills.
Question and Answer Sessions: The teacher frequently asks questions and encourages students to ask questions as well. This promotes active engagement and helps clarify misunderstandings, ensuring students are on track to achieve the learning goals.
Instruction to Support Learning
Instructional Strategies
What instructional strategies are observed? How do these support the learning outcomes identified by the teacher?
Direct Instruction: The teacher provides clear and concise explanations of concepts, such as the order of operations and evaluating expressions with exponents. This strategy ensures students understand the foundational knowledge necessary to achieve learning outcomes.
Guided Practice with Immediate Feedback: The teacher guides students through practice problems, providing immediate feedback and corrections. This helps students understand and apply the concepts correctly, reinforcing their learning and supporting the achievement of the learning outcomes.
Use of Visuals and Examples: The teacher uses visual aids and concrete examples to illustrate concepts, making abstract ideas more accessible and easier to understand. This supports students’ comprehension and retention of the material, contributing to achieving the learning outcomes.
Collaborative Learning: In the second lesson, students work in pairs to solve problems, discuss their reasoning, and explain their answers to each other. This strategy promotes peer learning, enhances communication skills, and deepens understanding, all supporting learning outcomes.
Questioning and Active Engagement: The teacher asks open-ended and probing questions to engage students in critical thinking and problem-solving. This encourages active participation and deeper understanding, which are crucial for achieving learning outcomes.
Differentiation: The teacher provides varied examples and adjusts the difficulty level to cater to students’ diverse needs. This ensures all students can access the content and progress toward the learning outcomes.
Resources and supports
What resources, materials, and/or educational technology are used during the lesson?
Whiteboard: The teacher uses a whiteboard to write down examples, problems, and key concepts, making it easier for students to follow along and understand the material.
Markers: These are used for writing on the board, allowing the teacher to highlight important information or differentiate steps in solving problems.
Practice Problems: Students are given practice problems to work on individually or in pairs. These materials help reinforce the concepts taught and provide practice in applying the skills learned.
Calculator: Students can use calculators to check their answers or perform calculations, especially when dealing with more complex expressions or equations.
Adaptations and accommodations
What adaptations and accommodations, including, as appropriate, assistive technologies, do you observe used during the instruction?
Visual Aids: The teacher used a whiteboard or chalkboard to write down examples, problems, and key concepts, providing visual support for students.
Guided Practice: The teacher guided students through practice problems, providing step-by-step explanations and support.
Repetition and Review: Key concepts and steps in solving problems were repeated and reviewed to reinforce learning.
Clear and Concise Instructions: The teacher provided clear and concise instructions to help students understand what was expected.
Checking for Understanding: The teacher frequently checked for understanding by asking questions and listening to students’ responses.
Closed Caption Video: The lessons were delivered via closed caption video.
Other Notes/Observations
Relate and Review
- Review and summarize the observational experience, sharing your three key takeaways from the observation.
During the observational experience of the two math lessons, I gained valuable insights into effective teaching practices for evaluating expressions with exponents and order of operations. The following are my three key takeaways from observation:
- Clear and Structured Teaching: The teacher used a clear and structured approach to teaching complex mathematical concepts. By breaking down the steps and using examples to illustrate each part of the process, the teacher made the material accessible and understandable for students.
- Active Student Engagement: The teacher encouraged active participation by students in the learning process through guided practice and checking for understanding. This approach helped students stay focused and involved in their learning.
- Emphasis on Fundamental Concepts: The lessons emphasized understanding the fundamental concepts behind evaluating expressions with exponents and the order of operations. By ensuring that students grasped these foundational ideas, the teacher laid the groundwork for more advanced mathematical learning in the future.
Overall, the observational experience highlighted the importance of clarity, engagement, and a focus on fundamental concepts in teaching math effectively.
- Relate topics or concepts you have learned about in this course (e.g., clearly articulating learning expectations to students, the use of assessments to inform curriculum planning and instruction, instructional strategies to support equity, diversity, and inclusion of learners or the learning outcomes, UDL strategies, etc.)
- One of your strategies must be an instructional strategy, technology, or tool you saw used that would provide equitable access to curriculum and support diverse learners.
During the observed lessons, the teacher effectively demonstrated several topics and concepts from the course, such as clearly articulating learning expectations. At the beginning of each lesson, the teacher stated the learning objectives and the steps required to achieve them, which set clear goals for the students and provided a roadmap for their learning journey.
The teacher used formative assessments, like checking for understanding during guided practice, to gauge students’ comprehension and adjust instruction accordingly. By doing so, the lessons were tailored to meet the students’ needs and inform future curriculum planning.
The teacher employed instructional strategies that supported equity, diversity, and inclusion. This was achieved by providing multiple representations of concepts, offering varied opportunities for student participation, and fostering a supportive classroom environment. As a result, all students felt valued and included.
Universal Design for Learning (UDL) strategies were incorporated into the lessons, allowing information to be presented in different formats, such as visual and verbal. Varied means of expression and engagement were also offered, and scaffolds and supports were provided to address the diverse needs of learners.
Using guided practice with immediate feedback was an instructional strategy that provided equitable access to the curriculum and supported diverse learners. All students could engage with the material and build their understanding, regardless of their prior knowledge or learning style.
Overall, the strategies and approaches demonstrated in the lessons align with the concepts learned in the course and highlight the importance of thoughtful and inclusive instructional design in promoting student success.
