Tuesday, May 7, 2013

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:

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.

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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 10th, 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. 


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