Final Reflection

edTPA is an assessment process designed by educators to answer the essential question: “Is a new teacher ready for the job?” As a teacher candidate in her last semester at Hofstra, it is extremely important that I not only plan lessons with the edTPA rubric components in mind, but that I am a reflective about my instruction after each lesson. Although I believe that all of the lessons that I implemented with Leydi Sanchez were strong, there was one in particular that was the most successful.

On Wednesday, March 20^th, 2013, I completed the third ELA lesson with my fifth grade student. The focus of the lesson was on writing rubrics, and the behavioral objectice was, “Utilizing the writing rubric and the RUBRIC strategy, the student will be able to accurately critique and assess at least two out of three “how-to” writing pieces.” The use of rubrics are connected to research and theory. Nitko (2001) stated that when grading rubrics are shared with students, the learning aims are clarified. Although teachers provide grades and feedback to students regarding the quality of their work, self-assessments and peer-assessments are necessary components that help students reflect on their performance. During the lesson, I could tell how excited Leydi was to grade other author’s essays and see her own essay graded in front of her. In doing so, it gave her writing a real purpose, and she learned the significance of a writing rubric. In fact, she told me that she wished that her teacher used writing rubrics to make her aware of what she needs to do to get a perfect score on an assignment, and so that she can see why she got a particular score.

This lesson made clear connections to the learner’s strengths and needs; I used my knowledge of Leydi’s strengths and needs to inform planning. During the second ELA lesson, I noticed that the student neglected to use the rubric to guide her writing. She had looked at it once or twice, but did not utilize it to help her compose the essay. When I asked her why she had put it off to the side, she explained that she still did not understand how it worked. With this in mind, I decided to focus this lesson on teaching Leydi how to use the writing rubric in order to accurately critique “how-to” essays. Due to the fact that Leydi is a strong reader, this plan engaged her to use her strengths to build upon her learning needs.

I adapted this lesson by permitting the focus learner to utilize the Spell Better application as an assistive technology. Leydi is a very bright young girl, but requires some assistance with spelling. This application helped her to assess the spelling and grammar in the essays that she evaluated. Leydi was able to target each spelling error in the essays, and correct them.

In order for Leydi to understand the requirements of this lesson, she had to fully understand what a rubric was. If students are to use this tool effectively, they must be properly introduced to them. Therefore, at the beginning of the lesson, I identified the vocabulary and the communication demands related to the learning target and language function by making connections to what she already knew and the unknown; I used the “How to Succeed in the Fifth Grade” writing rubric to help me discuss what a writing rubric is and describe its components (the columns on the left list the criteria for what must be included, and the columns on the right describe the different levels of quality). In doing so, not only did Leydi learn about writing rubrics, but she was given a support that helped her to assess other author’s essays. In addition, in order to help Leydi with the language function needed to carry out each task, I modeled the components beforehand, and gave her a RUBRIC strategy cue card, which she later used as a scaffold to self-direct herself in carrying out the behavioral objective.

This lesson had many supports that provided access to the behavioral objective and learning task. The writing rubric was one support that acted as a framework for the focus learner to understand the expectation of the assignment before it began. Leydi’s knowledge of the grading criteria and its importance in the product was strengthened because she was involved in using it. The RUBRIC strategy cue card was another support. It acted as a springboard, which activated Leydi’s memory on how to perform the task. The student was able to adhere to the learning task because the steps were right there in front of her.

As the teacher and the student collaborated with each other during the “Bring a buddy to help you rate again,” and the subsequent stages, the child developed greater language proficiency. Leydi was able to feed off of the teacher; she asked questions, learned new insights, and had her ideas validated. When the teacher and the student verbalized their thoughts, it improved the student’s understanding of the processes; she was able to have a conversation with the teacher and agree upon a score.

The teacher modeling stage, which is when I demonstrated the strategy to be learned, offered an invaluable support that provided access to the demonstration of the language demands and the behavioral objective. This stage is so important because it has been proven that when teachers act as models, it makes the concept or skill clear and learnable, and it enables students to make meaningful cognitive connections. The modeling was such an amazing support because I made sure that I included high levels of teacher-student interaction, and immediately followed it with opportunities for practice.

The support from the writing rubric and the RUBRIC strategy cue card, in conjunction with the support that the teacher provided during modeling and guided practice, moved Leydi towards generalization of the targeted vocabulary and communication. As I modeled the behavioral objective and the use of the strategies, I used thinking aloud to improve Leydi’s understanding of these processes. By the time Leydi had to complete the task independently, she had already witnessed a model of the performance, had an opportunity to practice the task with the teacher’s guidance, and had the teacher’s example and writing rubric to use as a reference.

The formal assessment—the use of a rubric to assess the student’s ability to follow the rubric in assessing other author’s essays—was aligned with baseline data. As I had learned in previous lessons, when Leydi is told what is required of her at the beginning of the lesson, she uses it to ensure that she carries out the behavioral objective. Also, a need that she had was to learn how to utilize rubrics. Therefore, this lesson used a rubric to assess the student’s ability to follow the rubric in assessing other author’s essays.

However, the student was not just assessed at the end of the lesson. The teacher informally monitored the student’s progress through learner questions and responses during instruction, and teacher observations of the learner. The teacher used the information from informally monitoring the student in order to modify support and feedback as necessary, so that strengths and needs were addressed. Due to the fact that Leydi seemed to have a pretty good grasp on rubrics, she was challenged to take what she had learned and apply it by independently assessing at least two out of three essays.

The informal assessment provided information about where the learner needed additional support to make progress and work toward generalized use of the skills. The “Bring a buddy to help you rate again” stage, and subsequent stages provided the instructor with the luxury of interacting one on one with the student and listening to them verbally announce their thought processes. Fortunately, Leydi did not need any additional support. The teacher was able to witness the student successfully carry out the behavioral objective. However, if the lesson were done with a different student in the future and they had difficulty, the teacher would be able to note exactly where and why the child struggled during the lesson, and then provide support as needed.

This lesson went extremely well and if it were implemented again, I would not do anything differently. The assistive technology, the supports, the alignment to the student’s strengths and needs, as well as the universal design of the lesson, allowed the focus learner to generalize what they had learned and self-direct themselves to successfully carry out the behavioral objective. 

Lesson 2 - Math

Universal Design for Learning Lesson Plan

Teacher: Esmeralda Tully   Date: 4/17/13  Subject: Mathematics

Common Core Standard:

NY.CC.5.OA: Operations and Algebraic Thinking

Write and Interpret Numerical Expressions

5.OA.1:Use parenthesis, brackets, or braces in numerical expressions, and evaluate expressions with these symbols

Behavioral Objective:

Given the application ‘Ooops,’ and the PEMDAS strategy, the student will be able to add parenthesis to make 4 out of 6 equations true.

Materials Needed:

• Computer with internet access
• iPad
• MyScript Calculator—App on iPad
• Math Order of Operations—App on iPad
• Ooops: The Order of Operations Game —App on iPad
• Loose leaf paper
• Pencils

Procedures:

•  Activating Prior Knowledge
• The teacher will assess/review prior knowledge by utilizing the Math Order of Operations application on the iPad. On the home screen of this app, there are two aliens who have solved “3 x (5 + 2)= “ two different ways (left to right and order of operations). The student must answer the question, “Which answer is correct?” and explain her rationale. This scenario is similar to the previous lesson’s activating prior knowledge stage, except this time, the student should know which answer is correct and why.
• Afterward, the student will watch the accompanying short clip in order to activate her background knowledge on the order of operations.
• Next, the teacher will resort back to the original problem “3 x (5 + 2) =” and will pose this question, “How would the answer be different if there were no parenthesis? What would you solve first? What would the new answer be?”

• Teacher Modeling
• Teacher will model how to use the interactive manipulative on Ooops: The Order of Operations Game to drag and add parenthesis into place to make the equation true.
• The example problem will be “4 + 2 x 3 = 10.” The teacher will remind the student that any operations inside the parenthesis happen before those outside. Teacher will utilize thinking aloud to verbalize her thinking and reasoning.
  • “Where can I add parenthesis to this expression to make the equation equal to 10? If I put parenthesis around 4 + 2, then I must solve that first because parenthesis are the first step in PEMDAS. I would then get 6 x 3, which equals 18. No, that’s not right, the answer must equal ten. Let me try putting parenthesis around 2 x 3, which would be simplified to 4 + 6. Yes that’s right! 4 + 6 = 10.”
• After the teacher is done with the problem (adding the parenthesis), the student will be permitted to click the “check answer” tab to see if the teacher’s answer is correct.

        

• Guided Practice
• Teacher will give the student the iPad to practice using Ooops: The Order of Operations Game application to drag and add parenthesis into place to make the equations true. Teacher will direct the student’s attention to the directions, which scaffold the child by reminding them that any operations inside the parenthesis happen before those outside.
• Student will be provided with loose leaf and a pencil to use as scrap paper to figure out where the parenthesis should go. Teacher will remind the student that it is okay if they do not get the problem correctly the first time; trial and error is a good method for solving problems.
• The teacher will be working next to the student on the problems as well. The teacher and the student will solve each problem, one at a time. After each problem, the teacher and the student will compare their answers and will have conversations about how they arrived at the answer.
• When the student is finished and has added the parenthesis to the problem, they will click the “check” tab to check their answer.

• Independent Practice
• The student will independently solve six numerical expressions on Ooops: The Order of Operations Game application, by adding parenthesis to make the equations true.

Assessment:

The teacher will review student work to determine whether they were able to add parenthesis to make 4 out of 6 equations true. The teacher will also informally assess the student during guided practice.

UDL ELEMENTS:

Multiple Means of Representation:

2.3   Support decoding text, mathematical notation, and symbols:   The Math Order of Operations clipused digital text with an accompanying human voice recording to meaningfully expose the student to the mathematical content.

3.2   Highlight patterns, critical features, big ideas, and relationships:   The teacher used examples and non-examples to highlight critical features (the alien scenario during the activating prior knowledge stage). The teacher also highlighted previously learned skills that could be used to solve unfamiliar problems.

3.4   Maximize transfer and generalization:   The teacher prompted the use of mnemonic strategies and devices—PEMDAS .

Multiple Means of Engagement:

7.1   Optimize individual choice and autonomy:   The Ooops application provided choices in such things as the level of perceived challenge. For each problem, there is a tab at the bottom that allows the child to increase the difficulty of the problem (Level 1- Level 5). The student also has the option of clicking “new puzzle,” which allows them to choose the problems that they want to solve.

9.3   Develop self-assessment and reflection:   The ‘check’ tab acts as a means for the learner to get feedback, have access to alternative scaffolds, and support understanding progress in a manner that is understandable and timely.

Multiple Means of Action and Expression:

5.2   Use multiple tools for construction and composition:   Student will use the Ooops application, which provides virtual manipulatives to solve numerical expressions.

6.2   Support planning and strategy development:   The teacher uses thinking aloud to model think-alouds of the process.

*****************************************************************************

edTPA rubric components:

#4Justification of Instruction & Support:

           

            Clear connections to research and/or theory

• Results related to teaching students with learning difficulties how to use a variety of mathematics cognitive strategies have been very positive and meet rigorous criteria used to identify evidence-based practices (Montague, 2009).
• Cognitive strategies are designed to help students remember the step-by-step process involved in solving computation or word problems. Memory tools, including mnemonic devices, key letters, key words, or key sentences help students remember procedural steps for solving problems (Miller, Stringfellow, Kaffar, Ferreira, & Mancl, 2011).

            Clear connections to the learner’s strengths & needs

• During the previous mathematics lesson, Leydi’s work indicated that she was able to independently solve numerical expressions using the correct order of operations. Therefore, I decided to progress to this lesson, by challenging her to add parenthesis to an equation to make it true.

            Plans for specific adaptations (if needed)

• Thus far, Leydi’s mathematics skills seem to be pretty strong, so no adaptations have been made as of yet. I will monitor student progress during this lesson, and will adapt the lesson if necessary. For example, if the problems are far too easy for her, I will increase the level of difficulty by having her solve problems in level 2 or higher.

#5 Supporting Language/Communication Development

            Identification of:

1)    vocabulary and/or symbols

• The teacher highlighted previously learned skills (the mneumonic device PEMDAS) that could be used to solve these unfamiliar problems.

2)    language/communication demands related to behavioral objective

• In order to help Leydi with the language needed in order to carry out the behavioral objective, she will be provided with a scaffold that reminds her that any operations inside the parenthesis happen before those outside. This scaffold is at the top of the page, and will be removed once a certain amount of problems have been correctly solved.

Justification: why supports will provide access to the learning task/behavioral objective

• The PEMDAS strategy will help the student remember the step-by-step process involved in solving the order of operations computation problems. PEMDAS acts as a scaffold for the student’s future reference or a springboard to activate memory on how to perform the task.
• The ‘check’ tab acts as a support because at any point, the student can check their answer by pressing the check button to see how their parenthesis have changed the result. This will show them the steps of the problem as the operations are performed in order.

Justification: why supports will provide access to the demonstration of

1)    language function

• As the student collaborates with the teacher, she will develop greater language proficiency. The teacher and the student can have conversations about their thought processes when they solved the problems.
• The mnemonic device PEMDAS provides access to the demonstration of language function, because the key words represent the first letter in the steps used to solve the problem.

2)    learning task/behavioral objective

• Teacher modeling demonstrates how students can achieve the behavioral objective by breaking down the lesson, and modeling each step very carefully.
• The mnemonic device not only helps students remember the steps involved in solving the problems, but it prompts the student to perform an overt action.

Justification: why supports move the learner toward maintenance and generalization or self-directed use of the targeted vocab/symbols or language/communication

• The support that the PEMDAS mnemonic device provides, in conjunction with the support that the teacher will provide during modeling and guided practice, shall move Leydi towards generalization of the targeted vocabulary and communication. As I model the behavioral objective and the use of strategies, I will use thinking aloud so that it improves Leydi’s understanding of these processes. When it comes time for Leydi to complete the task independently, she will have witnessed a model of the performance, had an opportunity to practice the task with the teacher’s guidance, and had the teacher’s example and their own mnemonic device to use as a reference.

#6 Planning Assessments to Monitor & Support Learning

Assessment: aligned with baseline data

• The child’s baseline data was gathered during pre-assessment, by both a systematic observation and a teacher made test. I used this information to guide instruction and align it with the assessment for lesson one and two. Leydi met the behavioral objective for lesson one, and the results from the assessment helped to guide and improve my instruction for this lesson.

Assessment provides evidence for monitoring learner’s progress at different points

in the learning segment

• The student will not just be assessed at the end of the lesson. The teacher will informally monitor student progress through learner questions and responses during instruction, and teacher observation of the learner.

Assessment reflects appropriate levels of challenge and support (in light of

learner’s needs, strengths & behavioral objective)

• The teacher will use the information from informally monitoring the student in order to modify support and feedback as necessary.
• This lesson will appropriately challenge and support the child. The child’s strengths will be supported because she has proficient knowledge related to the four computational operations (i.e., addition, subtraction, multiplication, division). However, she will be challenged to take what she knows (computation skills), and the order operations, to correctly add parenthesis to make numerical expressions true. PEMDAS, teacher modeling, and the collaboration during guided practice will support her to achieve this task.

Assessment: designed to provide diagnostic information about where learner

may need additional support to make further progress and work toward

generalized and maintained OR self-directed use and knowledge and/or skills.

• By informally assessing the child through observations, the teacher will be able to make note of exactly where and why the child struggled during the lesson.
• By assessing the student’s work, the teacher will be able to pinpoint where the student had difficulty, and which order the student solved the operations. This way, the teacher can provide additional, individualized support to the student so that they can make further progress.

REFLECTION

             On Wednesday, April 17^th, I implemented my second math lesson with my tutee Leydi Sanchez. This lesson was so beneficial for the student; it combined culturally responsive teaching, universal design for learning, and explicit instruction, which is vital for teaching diverse learners.

            The assessment data from the previous lesson indicated that Leydi was able to use the cognitive strategy (the mnemonic device PEMDAS) to remember the step-by-step process involved in solving order of operations problems. I used this data to guide instruction for this lesson. Due to the strength that I observed in Leydi’s newly developed mathematical procedural skills, I thought that it was appropriate to challenge her.

The behavioral objective for this lesson was: given the application ‘Ooops,’ and the PEMDAS strategy, the student will be able to add parenthesis to make 4 out of 6 equations true. The PEMDAS strategy was one support that provided access to the behavioral objective. It acted as a springboard to help Leydi remember the step-by-step processes involved in solving the order of operation computation problems. The ‘check’ tab on the game also acted as a support because at any point, the student could check their answer by pressing the check button to see how their parenthesis had changed the result. This showed her the steps of the problem as the operations are performed in order.

In order to assess/review prior knowledge, I utilized the Math Order of Operations application on the iPad. This application supported decoding text, mathematical notation, and symbols (multiple means of representation); the clip used digital text with an accompanying human voice recording to meaningfully expose the student to the mathematical content. I also incorporated culturally responsive teaching. I utilized a guided and informal discussion with the student in order to highlight patterns, critical features, big ideas, and relationships. This informal discussion provided Leydi with the opportunity to construct meaning, and allowed the teacher and the student to learn from each other by sharing their interpretations and questions.

For culturally responsive teaching, it is important for teachers to use a range of culturally sensitive instructional methods and materials. One such method, thinking-aloud, was used during teacher modeling. I utilized the think-aloud method, a procedure that takes advantage of the benefits of modeling, in order to demonstrate what to do, why, how, and when with Ooops, the order of operations game. This worked very well and it improved Leydi’s understanding of the step-by-step process. As I watched her during the subsequent stages of the lesson, I noticed that she talked through her thought processes when solving the problems.

During guided and independent practice, the student was provided with a range of instructional materials. She had the opportunity to use multiple tools for construction and composition: Leydi could use the iPad or my iPhone to play the Ooops game, and she was also provided with pencil and paper to use as scrap paper. When Leydi was finished with each problem, she was permitted to click the “check answer” tab. This developed self-assessment and reflection; it acted as a means for the learner to get feedback and have access to alternative scaffolds. Leydi was so excited to finish a problem and check to see if they were correct.

In guided practice, I worked alongside Leydi and solved the problems on a separate sheet of paper, just as I had done in the previous lesson. After each problem, we would compare answers before she checked them on the iPad. I felt that this was important because collaboration is involved in virtually every learning situation. People from different cultures and backgrounds need to learn how to work together to deal with common concerns. Due to the fact that Leydi did not have another student to work with, I felt that it was my job to develop a sense of reciprocity: “we win/I win.” This collaboration also provided access to the demonstration of language function; the student developed greater language proficiency.

During independent practice, Leydi had to independently demonstrate her ability to meet the behavioral objective. She was able to generalize and maintain what she had learned from my modeling and support, and she self-directed herself in using the PEMDAS strategy to exceed the behavioral objective: Leydi was able to add parenthesis to make 7 out of 8 equations true. As stated earlier, the goal was to solve six problems. However, Leydi was so engaged that she wanted to keep working.

The application was so dense, filled with so many useful resources; it provided positive reinforcements for correctly solving problems (stickers); choices in the level of perceived challenge (child has option to increase the difficulty of the problems); a “check answer” tab that developed self-assessment and reflection. There was also a button “new puzzle,” that I allowed Leydi to click. She was told how many problems she must solve, not what problems she had to solve. She was permitted to choose the equations that she wanted to work on.

This lesson was a huge success. By incorporating Leydi’s interests and giving her the power of options, she was able to stay completely engaged in the task. It was almost as if she had forgotten that we were doing schoolwork. It was so wonderful to not only see her learning, but witness her having a blast while doing so. Education should be something that all students enjoy and feel a personal connection with. I feel so proud that I was able to both teach and reach my child. If this lesson were to be implemented class wide, it would not only reduce barriers for culturally diverse learners, but it would increase the learning opportunities for all learners. 

Lesson 1 - Math

Universal Design for Learning Lesson Plan

Teacher: Esmeralda Tully   Date: 4/10/13 Subject: Mathematics

Common Core Standard:

NY.CC.5.OA: Operations and Algebraic Thinking

Write and Interpret Numerical Expressions

5.OA.1:Use parenthesis, brackets, or braces in numerical expressions, and evaluate expressions with these symbols

Behavioral Objective:

The student will be able to use PEMDAS in order to solve 6 out of 8 numerical expressions with three operations correctly.

Materials Needed:

• Computer with internet access
• Khan Academy—Introduction to Order of Operations—Video
• Khan Academy—Practice this Concept—Interactive (http://www.khanacademy.org/math/arithmetic/multiplication-division/order_of_operations/v/introduction-to-order-of-operations)
• iPad
• MyScript Calculator—App on iPad
• Pens/pencils
• Loose-leaf paper
• Guided Practice worksheet (5 order of operations problems)
• Independent Practice worksheet (8 order of operations problems)

Procedures:

•  Activating Prior Knowledge
• The teacher will introduce the topic by presenting this situation: “Two students evaluated the expression 15 + 12 / 3 + 5 and got two different answers. Neither made a computational mistake. How could this happen?” Have students discuss their reasoning.
  • The teacher will instruct the student to solve the problem left to right, while the teacher solves the problem using the order of operations.
  • Explain why the two answers are different. Explain how using the order of operations strategy PEMDAS gets the right answer [24].
• Teacher will then play the Khan Academy video: Introduction to Order of Operations, in order to further explain the concept and the rationale of using the PEMDAS strategy.  
• Teacher will help student remember the acronym PEMDAS by introducing them to the phrase “Please Excuse My Dear Aunt Sally” to help students remember the procedural steps.
• Student will be given the opportunity to create their own key words for memorizing the PEMDAS mnemonic device, so that it is more meaningful to them.

• Teacher Modeling
• Teacher will model how to use the PEMDAS strategy by clicking on the Khan Academy: “Practice this Concept”, tab on the top right corner of the webpage.
• Teacher will write PEMDAS at the top of the paper, and use it as a guide in solving the problems. In order to provide authentic explanations for the student, the teacher will utilize thinking aloud to verbalize her thinking and reasoning. (e.g., “First I have to check if there are any parenthesis in this expression. There are no parenthesis in this problem, so I can cross out the P in PEMDAS, and move on to exponents…” etc.)
• After the teacher is done with each problem, the student will be permitted to type in the teacher’s answer in the “Answer” box in order to check if it is correct.

        

• Guided Practice
• Teacher will give the student the guided practice worksheet, or the iPad (with the guided practice problems on a workmat) to practice solving numerical expressions with three operations. The teacher will remind the student to use PEMDAS to solve these equations and will provide feedback and/or support as needed.
• The teacher will be working next to the student on the problems as well. The teacher and the student will solve each problem, one at a time. After each problem, the teacher and the student will compare their answers and will have conversations about how they arrived at the answer.
• When the student is finished, they will utilize the MyScript Calculator application to check their answers.

• Independent Practice
• The student will independently solve eight numerical expressions (with three operations) either on the independent practice worksheet or on the iPad, using the PEMDAS strategy to perform the correct order of operations.
• When the student is finished, they will utilize the MyScript Calculator application to check their answers.

Assessment:

The teacher will review student work to determine whether they were able to use PEMDAS in order to solve 6 out of 8 numerical expressions with three operations correctly. The teacher will also informally assess the student during guided practice.

UDL ELEMENTS:

Multiple Means of Representation:

2.1   Clarify vocabulary and symbols:   The teacher pre-taught vocabulary, especially in ways that promoted connection to the learners’ experience and prior knowledge by allowing the student to create their own key words for memorizing the PEMDAS mnemonic device.

2.3   Support decoding text, mathematical notation, and symbols:   The Khan Academy video: Introduction to Order of Operations, used digital text with an accompanying human voice recording to meaningfully expose the student to the mathematical content.

3.4   Maximize transfer and generalization:   The teacher prompted the use of mnemonic strategies and devices—PEMDAS .

Multiple Means of Engagement:

7.2   Optimize relevance, value, and authenticity:   To recruit interest, the teacher provided the student with the option of making the mnemonic device more meaningful, by creating their own mnemonic device. This activity fostered the use of imagination to solve novel and relevant problems, or make sense of complex ideas in creative ways.

8.1   Heighten salience of goals and objectives:   The teacher uses the PEMDAS mnemonic device on the top of the page during guided practice as a prompt/scaffold for visualizing desired outcome.

9.3   Develop self-assessment and reflection:   The MyScript Calculator acts as a means for the learner to get feedback and have access to alternative scaffolds.

Multiple Means of Action and Expression:

5.2   Use multiple tools for construction and composition:   Student may use the iPad as an alternative to worksheets in order to solve numerical expressions during guided and independent practice.

6.2   Support planning and strategy development:   The teacher uses thinking aloud to model think-alouds of the process.

************************************************************************************

edTPA rubric components:

#4Justification of Instruction & Support:

           

            Clear connections to research and/or theory

• Results related to teaching students with learning difficulties how to use a variety of mathematics cognitive strategies have been very positive and meet rigorous criteria used to identify evidence-based practices (Montague, 2009).
• Cognitive strategies are designed to help students remember the step-by-step process involved in solving computation or word problems. Memory tools, including mnemonic devices, key letters, key words, or key sentences help students remember procedural steps for solving problems (Miller, Stringfellow, Kaffar, Ferreira, & Mancl, 2011).

            Clear connections to the learner’s strengths & needs

• During the mathematics pre-assessment, Leydi’s work indicated that she was not familiar with the PEMDAS strategy. Even though she got the order of operations problems correct, she did not use PEMDAS to arrive at her answer; she was lucky both times. I believe that teaching her this mnemonic device during this lesson will target her needs and help her to independently solve these problems successfully in the future.

            Plans for specific adaptations (if needed)

• Thus far, Leydi’s mathematics skills seem to be pretty strong, so no adaptations have been made as of yet. I will monitor student progress during this lesson, and will adapt the lesson, and subsequent lessons if necessary.

#5 Supporting Language/Communication Development

            Identification of:

1)    vocabulary and/or symbols

• Teacher will help student remember the acronym PEMDAS by introducing them to the phrase “Please Excuse My Dear Aunt Sally” to help students remember the procedural steps. Student will be given the opportunity to create their own key words for memorizing the PEMDAS mnemonic device, so that it is more meaningful to them.

2)    language/communication demands related to behavioral objective

• In order to help Leydi with the language needed in order to carry out the behavioral objective, she will be given multiple opportunities to memorize the memory tool. This way, she will learn the memory tool with automaticity so that she can apply it successfully to the mathematics problems that she will have to solve.

Justification: why supports will provide access to the learning task/behavioral objective

• The PEMDAS strategy will help the student remember the step-by-step process involved in solving the order of operations computation problems. PEMDAS acts as a scaffold for the student’s future reference or a springboard to activate memory on how to perform the task.
• Placing the mnemonic device on the top of the page during guided practice acts as a prompt for visualizing desired outcome.

Justification: why supports will provide access to the demonstration of

1)    language function

• As the student collaborates with the teacher, she will develop greater language proficiency. The teacher and the student can have conversations about their thought processes when they solved the problems.
• The mnemonic device PEMDAS provides access to the demonstration of language function, because the key words represent the first letter in the steps used to solve the problem.

2)    learning task/behavioral objective

• Teacher modeling demonstrates how students can achieve the behavioral objective by breaking down the lesson, and modeling each step very carefully.
• The mnemonic device not only helps students remember the steps involved in solving the problems, but it prompts the student to perform an overt action.

Justification: why supports move the learner toward maintenance and generalization or self-directed use of the targeted vocab/symbols or language/communication

• The support that the PEMDAS mnemonic device provides, in conjunction with the support that the teacher will provide during modeling and guided practice, shall move Leydi towards generalization of the targeted vocabulary and communication. As I model the behavioral objective and the use of strategies, I will use thinking aloud so that it improves Leydi’s understanding of these processes. When it comes time for Leydi to complete the task independently, she will have witnessed a model of the performance, had an opportunity to practice the task with the teacher’s guidance, and had the teacher’s example and their own mnemonic device to use as a reference.

#6 Planning Assessments to Monitor & Support Learning

Assessment: aligned with baseline data

• The child’s baseline data was gathered during pre-assessment, by both a systematic observation and a teacher made test. I used this information to guide instruction and align it with the assessment for lesson one. During the pre-assessment, the student did not use PEMDAS to perform the correct order of operations. Therefore, the teacher will review student work to determine whether they were able to use PEMDAS in order to use the order of operations to correctly solve numerical expressions.

Assessment provides evidence for monitoring learner’s progress at different points

in the learning segment

• The student will not just be assessed at the end of the lesson. The teacher will informally monitor student progress through learner questions and responses during instruction, and teacher observation of the learner.

Assessment reflects appropriate levels of challenge and support (in light of

learner’s needs, strengths & behavioral objective)

• The teacher will use the information from informally monitoring the student in order to modify support and feedback as necessary.
• This lesson will appropriately challenge and support the child. The child’s strengths will be supported because she has proficient knowledge related to the four computational operations (i.e., addition, subtraction, multiplication, division). However, she will be challenged to take what she knows (computation skills) and what she will learn during this lesson (order of operations) to correctly solve numerical expressions with three operations. PEMDAS, teacher modeling, and the collaboration during guided practice will support her to achieve this task.

Assessment: designed to provide diagnostic information about where learner

may need additional support to make further progress and work toward

generalized and maintained OR self-directed use and knowledge and/or skills.

• By informally assessing the child through observations, the teacher will be able to make note of exactly where and why the child struggled during the lesson.
• By assessing the student’s work, the teacher will be able to pinpoint where the student had difficulty, and which order the student solved the operations. This way, the teacher can provide additional, individualized support to the student so that they can make further progress. 

REFLECTION

            On Wednesday, April 10^th, 2013, I implemented the first math lesson with my fifth grade tutee, Leydi Sanchez. This lesson focused on teaching the PEMDAS strategy in order to solve numerical expressions using the order of operations.

            The student’s baseline data from the pre-assessment indicated that she was not familiar with this strategy. I believed that teaching her this mnemonic device would help her to independently solve these problems correctly in the future. Cognitive strategies are designed to help students remember the step-by-step process involved in solving computation or word problems. Research has demonstrated that memory tools, including mnemonic devices, key letters, key words, or key sentences help students remember procedural steps for solving problems. (Miller, Stringfellow, Kaffar, Ferreira, & Mancl, 2011). 

            The behavioral objective for this lesson was: the student will be able to use PEMDAS in order to solve 6 out of 8 numerical expressions with three operations correctly. The PEMDAS strategy is a support that provided access to the behavioral objective. It acted as a springboard to help Leydi remember the step-by-step processes involved in solving the order of operation computation problems.

            In order to activate her prior knowledge, I incorporated culturally responsive teaching. By encouraging Leydi to create her own key words for memorizing PEMDAS (“Please Excuse My Dear Annoying Sister”), I gave her the opportunity to find relevant connections within herself, with the subject matter, and the task I asked her to perform. This device was no longer a foreign concept; it became a strategy that optimized relevance, value, and authenticity. She was able to use her own key words to successfully remember PEMDAS—she wrote PEMDAS above every problem and as she did so, I heard her whisper, “Please Excuse My Dear Annoying Sister.”

            During the teacher-modeling portion of the lesson, I used multiple means of representation. The Khan Academy Video: Introduction to Order of Operations, used digital text with an accompanying human voice recording, which meaningfully exposed Leydi to the mathematical content. Leydi was completely engaged, and she often took the mouse to rewind the video so that she could see/hear something repeated.

            For culturally responsive teaching, it is important for teachers to use a range of culturally sensitive instructional methods and materials. One such method, thinking-aloud, was used during this lesson. I utilized the think-aloud method, a procedure that takes advantage of the benefits of modeling, in order to demonstrate what to do, why, how, and when. This worked very well and it improved Leydi’s understanding of the step-by-step process. As I watched her during the subsequent stages of the lesson, I noticed that she talked through her thought processes when solving the problems.

            During guided and independent practice, the student was provided with a range of instructional materials. She had the opportunity to use multiple tools for construction and composition: Leydi could use the iPad as an alternative to worksheets in order to solve numerical expressions. To my surprise, she preferred the pencil/paper format. However, she was excited to use the iPad application: MyScript Calculator, to check her answers. This developed self-assessment and reflection; it acted as a means for the learner to get feedback and have access to alternative scaffolds. Leydi was so excited to finish a problem and check to see if they were correct.

            In guided practice, I worked alongside Leydi and solved the problems on a separate sheet of paper. After each problem, we would compare answers before she checked them on the iPad. I felt that this was important because collaboration is involved in virtually every learning situation. People from different cultures and backgrounds need to learn how to work together to deal with common concerns. Due to the fact that Leydi did not have another student to work with, I felt that it was my job to develop a sense of reciprocity: “we win/I win.” As a matter of fact, members of learning communities are both teachers and learners, as well as producers and consumers of knowledge. For one of the problems, I actually solved it wrong, and Leydi solved it correctly. She explained and showed me her rationale, and she was so proud of herself. To see her succeed made me feel like I had also succeeded.

            During independent practice, Leydi had to independently demonstrate her ability to meet the behavioral objective. She was able to generalize and maintain what she had learned from my modeling and support, and she self-directed herself in using the PEMDAS strategy to carry out the behavioral objective: she used PEMDAS and correctly solved 6 out of 8 numerical expressions with three operations. As I reviewed her work, the two problems that she solved incorrectly were minor computational errors, not procedural errors. For example, for #4, she used the correct order of operations, but she solved “20 x 2 = 22” instead of “20 x 2 = 44.” When she checked her work on the iPad, she immediately said, “Oh no! I accidently added instead of multiplying. How did I do that?”

            This lesson was extremely successful. Together, culturally responsive teaching, universal design for learning, and explicit instruction is vital for teaching diverse learners. By making the materials, methods, goals and assessment accessible to Leydi, and connecting the importance of the student’s individual experiences into the various components of EI, the learner was able to successful learn and use new knowledge and skills.

           If I were to reteach this lesson, I would maintain all of the lesson elements. Do to its universal nature, it is accessible to all students. Therefore, I believe the lesson is perfect the way that it is, and I would not change anything if I were to implement it again.