I need help writing the Reflection and Self-Evaluation

Use the following lesson reflection questions, which are tied to the Conceptual Framework components, to guide your reflective narrative. a. As you reflect on the lesson, to what extent were the students productively engaged in the learning process? Think of academic engaged time/time on task. (Methodology/Technology, Thinking Skills) b. Were students interested and motivated to learn during these lessons? Why or why not? Did you make changes during the lessons to enhance interest or motivation? (Human Relations/Diversity, Professionalism) c. Did the lesson allow for students to achieve mastery of the objective(s) and engage in activities and learning situations that were aligned with district, state, or national standards? (Methodology/Technology, Assessment, Thinking Skills) d. Did you adjust your teaching strategies and activities as you taught the lesson? If so, why and how? (Leadership, Professionalism, Human Relations/Diversity) e. What kind of feedback did you receive from the students indicating they had achieved understanding and that the objective(s) for the lessons were met? (Communication, Leadership) f. If you had the opportunity to teach these lessons again to this same group of students, what would you do differently? Why? (Assessment, Leadership, Thinking Skills) g. Did you receive any suggestions from the students or cooperating teacher that you incorporated into the lessons or that you would incorporate if you taught the lessons again?

Instructional Plans with Objectives Before Pre-Assessment

For the pre-assessment, the learning objectives are:

1. Students will be able to define and identify linear equations.
2. Students will solve basic one-step and two-step linear equations.
3. Students will apply linear equations to solve word problems.

Adjustments to Instructional Plans Based on Pre-Assessment Data

Based on the data from both the pre- and post-assessments, the following adjustments to instructional plans were made:

1. Define Linear Equations (75% to 90%)

• Pre-Assessment Mastery: 75%
• Post-Assessment Mastery: 90%

Adjustment:Since most students had a strong foundational understanding of defining linear equations (75%) and saw further improvement (90%), the instructional plan should briefly review this topic but not spend too much time on it. Focus could shift towards applying linear equations in real-world contexts or more advanced concepts, such as graphing linear equations or interpreting slope and intercept.

2. Solve One-Step Equations (65% to 85%)

• Pre-Assessment Mastery: 65%
• Post-Assessment Mastery: 85%

Adjustment: While students showed a significant improvement, a good portion still struggled before. Review basic strategies for solving one-step equations and consider integrating more practice problems in varying contexts. This could be paired with solving two-step equations for stronger connections between these skills.

3. Solve Two-Step Equations (45% to 75%)

• Pre-Assessment Mastery: 45%
• Post-Assessment Mastery: 75%

Adjustment: This area shows major improvement, but with the low initial mastery (45%), it is essential to revisit this concept more deeply. Use differentiated instructionsome students may need more foundational reviews of combining like terms or working with fractions. Consider small group instruction to provide more targeted support.

4. Solve Word Problems (35% to 70%)

• Pre-Assessment Mastery: 35%
• Post-Assessment Mastery: 70%

Adjustment: Word problems remain the most challenging area for students. Focus on breaking down word problems into smaller, more manageable parts, teaching students to identify keywords that translate into mathematical operations. Emphasize modeling word problems with equations and using real-life examples to make this skill more relatable.

Reinforcement and Extension: While students have improved across all areas, continued reinforcement of two-step equations and word problems is crucial. Use formative assessments to monitor ongoing progress and reteach concepts where needed.

Delivering Instruction and Formative Assessments

During the three lessons, I used several formative assessments:

• Lesson 1: Exit ticket to check if students can solve basic equations.
• Lesson 2:Group work to observe how well students solve multi-step problems.
• Lesson 3: A worksheet with word problems to check for comprehension.

The formative assessments helped identify students who were still struggling with multi-step problems. I adjusted my teaching in real-time, providing additional examples and one-on-one support.

The post-assessment was similar in format to the pre-assessment, including multiple-choice, short-answer, and word problems to measure students' mastery of the learning objectives after instruction.

Instructional Decision-Making :

Re-teaching Two-Step Equations:

• Since only 45% of students showed mastery of solving two-step equations in the pre-assessment, I dedicated additional time to this topic by incorporating more guided practice and hands-on activities. This allowed students to break down complex problems step-by-step, boosting their confidence and understanding.

Focus on Word Problems:

• Given that only 35% of students could solve word problems, I decided to introduce real-world scenarios and group discussions to make word problems more relatable. By connecting math to everyday life, students found it easier to understand how to approach these problems, and their mastery improved to 70% in the post-assessment.

Peer Tutoring for One-Step Equations:

• Although 65% of students mastered one-step equations, I paired them with students who were struggling, allowing the stronger students to reinforce their knowledge by teaching their peers. This not only helped the struggling students but also solidified the understanding of those who were already confident.

Frequent Formative Quizzes:

• Throughout the unit, I introduced short quizzes to monitor student progress regularly. This allowed me to quickly identify areas where students were struggling and adjust my teaching methods accordingly. This approach ensured that students could achieve 85% mastery in one-step equations by the end of the unit.

Strategies:

• I frequently used visual aids like graphs, number lines, and equation models to represent mathematical concepts. These visuals helped students, especially those who struggle with abstract thinking, to grasp the concepts of linear and two-step equations. I believe this strategy was effective because students could "see" the math, which deepened their understanding.

Collaborative Problem-Solving:

• I organized group activities where students worked together to solve multi-step problems. This collaboration encouraged peer learning, and students were able to discuss different problem-solving techniques. The strategy worked well because it allowed students to learn from each other and develop a deeper understanding of how to approach complex problems.

Formative Assessments:

• I used a combination of formative assessments such as exit tickets, in-class quizzes, and group discussions. After each lesson, I gave students a short quiz or an exit ticket to assess their understanding of that day's material. These quick checks allowed me to pinpoint any misconceptions and address them immediately in the following lesson. This ongoing assessment ensured that I could keep track of student progress and adjust my teaching as needed.

Barriers:

• One of the biggest barriers was that many students struggled with interpreting word problems. They often found it challenging to translate a verbal scenario into a mathematical equation. To address this, I had to break down word problems step-by-step and provide more real-world examples to make the problems more accessible.

Differentiating Instruction for Varying Skill Levels:

• Another barrier was the diverse range of skill levels in the classroom. Some students needed more time to grasp basic concepts, while others were ready to move on to more advanced problems. To overcome this, I used flexible grouping and differentiated instruction, offering additional support to those who needed it while giving more challenging tasks to advanced students.

The instructional decision-making process focuses on improving student mastery of solving two-step equations, word problems, and one-step equations. Initially, only 45% of students showed mastery of two-step equations, so I dedicated more time to re-teaching this concept using guided practice and hands-on activities. This method allowed students to approach complex problems step-by-step, enhancing their understanding. Word problems presented another challenge, with only 35% of students being able to solve them in the pre-assessment. To address this, the I introduced real-world scenarios and group discussions, helping students relate math to everyday life, which improved their ability in approaching word problems and increased mastery to 70%. Peer tutoring for one-step equations also helped, as students who had mastered the concept reinforced their knowledge by tutoring others students, benefiting both groups.

In addition, the use of frequent formative quizzes allowed me to monitor student progress and make quick instructional adjustments, leading to a higher mastery rate of 85% in one-step equations. Visual aids like graphs and number lines were effective in helping students, particularly those who struggle with abstract thinking, to grasp these mathematical concepts. Collaborative problem-solving activities further deepened understanding, as students worked together to solve complex problems. The use of ongoing formative assessments, combined with flexible grouping and differentiated instruction, allowed me to address the diverse range of skill levels in our classroom, offering additional support to students who needed it while challenging advanced learners. Ultimately, the combination of these strategies led to significant improvements in student performance across all areas.