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EDUC 530 Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 1 of 5 | 8 pages maximum All rights reserved. V5_0916 The edTPA trademarks are owned by The Board of Trustees of the Leland Stanford Junior University. Use of the edTPA trademarks is permitted only pursuant to the terms of a written license agreement. A SSESSMENT C OMMENTARY Respond below by typing your responses to each prompt. Do not delete or alter the prompts. The commentary should be between 5 – 8 pages long , including the prompts. Please be sure to examine the Assessment Commentary Guiding document, two student work samples and the rubric for this assignment in LiveText to help with understanding and to maximize your grade. 1. Analyzing Student Learning—Whole Class a. Identify the specific learning objectives measured by the formative assessment that was provided for analysis. [For each lesson in the learning segment, the formative assessment will be taken during class discussion and group activities and will help guide the teacher as to if further instruction is needed and how much is needed. The learning objective for lesson 1 is students will be able to determine the volume of a rectangular prism by counting the amount of unit cubes needed to create the rectangular prism with 100% accuracy.] b. Provide a graphic (chart or table) that displays the students’ responses as it pertains to the number of questions they answered correctly, had the wrong answer where work was shown or explained, or had the wrong answer and no work was shown or explained. Please see the example chart inserted below. Also, provide a narrative below the chart that summarizes student learning for the whole class by incorporating the information you have provided in the chart. The summary should also describe the learning evidenced in the Volume Post Assessment. Whole Class Summary (Example Chart) c. Using the chart provided in 1b, discuss the patterns of learning across the whole class relative to  conceptual understanding  procedural fluency  mathematical reasoning/problem-solving skills Be sure that you mention conceptual understanding, procedural fluency and mathematical reasoning/problem-solving skills when discussing the patterns of learning across the whole class. You may ask yourself what problems you see in student learning as it relates to each of these three areas. This response should be detailed at no less than 2-3 paragraphs.

EDUC 530 Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 2 of 5 | 8 pages maximum All rights reserved. V5_0916 The edTPA trademarks are owned by The Board of Trustees of the Leland Stanford Junior University. Use of the edTPA trademarks is permitted only pursuant to the terms of a written license agreement. [The majority of students in the class showed they had a conceptual understanding of volume and were able to show the volume in both box A and box B, however more successfully identified the number of cubes in box B. For the first two questions which ask how many cubes fit in the box, the students that did not answer the question correctly were split between whether they were able to explain how they got the answer they did. Question 3 saw more students getting the answer incorrect, however all students that answered incorrectly did show their work and explained how they got their answer. Question 4 saw more students incorrectly answer the question, with no work or explanation shown. This question also appeared to require a more in depth understanding of the concept, showing that although students could correctly find the number of cubes in the shape, not all could use the concept at a higher level of understanding. Overall, I would say the class had good procedural fluency and taking into consideration the students that require additional accommodations and assistance, those students were able to explain the process even if not able to do the calculations correctly. Question 4 does show that 7 students struggle with the problem solving or reasoning portion of the concept.] 2. Analyzing Student Learning—3 Focus Students From your analysis of whole class student learning, identify one area where students struggled mathematically. Using the Volume student work samples, select from those samples to show how students struggled in this area. These student samples will be your focus students for this task. At least one of the focus students must have specific learning needs , for example, a student with an IEP (Individualized Education Program) or 504 plan, an English language learner, a struggling reader, an underperforming student or a student with gaps in academic knowledge, and/or a gifted student needing greater support or challenge. After evaluating the student work samples, one of those students should fall in a category above evidenced by their math abilities. a. In what form did you submit the work samples for the 3 focus students?  Written work samples in text files b. Analyze the 3 students’ work samples and describe the students’ struggle(s) as they relate to the underlying mathematical understanding and/or concept. Demonstrate how the Case Study examples from the Error Analysis Assignment help you here. This response should be detailed at no less than 2-3 paragraphs. For example, if a student error occurs in a subtraction problem, then the underlying mathematical understanding may include regrouping, meaning of subtraction, and/or subtraction as the inverse of addition. The related mathematical understanding becomes the basis for the targeted learning objective/goal for the students. [All work was submitted as a pdf version of the students’ written work. Student 1 is able to use the equation to find the volume of each box correctly, however basic multiplication skills have caused the student to misidentify the correct volume. For box A the student correctly identified 4X4 as 16, however they then identified 16X4 as 74 instead of 64. The student did show understanding of the concept in questions 2-4, missing part of question 4 because of his incorrect multiplication on question 1.

EDUC 530 Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 3 of 5 | 8 pages maximum All rights reserved. V5_0916 The edTPA trademarks are owned by The Board of Trustees of the Leland Stanford Junior University. Use of the edTPA trademarks is permitted only pursuant to the terms of a written license agreement. Student 2 showed partial understanding of the concept of volume, as they knew it would require numbers to be multiplied together. The issue that student 2 showed was an understanding of where the multiplication process ended. The student correctly multiplied the length, width, and height; however, they then continued to add or multiply additional numbers. For example, after properly multiplying 4X4X4 in question 1, they proceed to add 800. For box B after they multiply the correct numbers, they multiply the answer by 2 and add 600. In question 3 the student was able to correctly identify which box was bigger, but due to the incorrect operations in questions 1 and 2, he did not correctly answer question 4. Student 3 appears to generally understand the concept of volume; however, does not know the best way to compute the answer. For box A the student started using the formula for volume but had issues with the multiplication. They then decided to simply count the number of boxes, incorrectly identifying the volume of both box A and B. Once the student incorrectly answered question 1 and 2, the rest of the answers were incorrect.] 3. Developing Students’ Mathematical Understanding a. Based on your analysis of the focus students’ work samples, describe a targeted learning objective/goal for the students related to the area of struggle. [Based off the work samples of the three students, I would give further instruction in a small group environment. Although they show a general understanding of the concept, they struggled with fully implementing the concept properly. I think working with the students on volume and the operations needed to calculate volume would be most beneficial. In a small group, I would start by working on multiplication, as each of the focus students struggled with that portion of the formula. In order to calculate volume, each student must be able to do basic multiplication and 2-digit by 1-digit multiplication.] b. Describe the re - engagement lesson plan Using the bulleted prompts below, write a re-engagement lesson plan to develop each focus student’s mathematical knowledge in relation to the targeted learning objective/goal. Be specific here (just as you were in crafting your lesson plans during weeks 4 and 6). Be sure to also integrate what you have learned from the Meta-Analysis. Your description FOR EACH STUDENT analyzed in the Volume Pre and Post assessments should include  targeted learning objective/goal from prompt 3a  state-adopted academic content standards that were the basis of the analysis  strategies and learning tasks to re-engage students (including what you and the students will be doing)  representations and other instructional resources/materials used to re-engage students in learning  assessments for monitoring student learning during the lesson (e.g., pair share, use of individual whiteboards, quick quiz) [Before working with the three students on volume, I would work on multiplying 2-digit numbers. Based off the work samples, all three struggled with the operation of multiplication. After working on multiplication, I would re-engage the students on the previous lesson of determining the volume of rectangular prisms, with the objective of being able to correctly identify the volume with 100% accuracy after the one-on-one instruction with the teacher.

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EDUC 530 Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 4 of 5 | 8 pages maximum All rights reserved. V5_0916 The edTPA trademarks are owned by The Board of Trustees of the Leland Stanford Junior University. Use of the edTPA trademarks is permitted only pursuant to the terms of a written license agreement. Virginia Standards of Learning: 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. 5.8 The student will a) solve practical problems that involve perimeter, area, and volume in standard units of measure; and b) differentiate among perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation. Student 1 re-engagement plan: Student 1 showed a general understanding of how to calculate volume, however they were unable to correctly complete the multiplication portion of the calculation. In calculating the volume for box A the student properly multiplied 4X4 = 16. The issue came in the second multiplication of 16x4, which the student said equaled 74. The first concept I would review is volume, going over the options for calculating volume. The student did not appear to have an issue with the concept, or the formula used to find volume, allowing the teacher to move on to multiplication quickly. The first thing I would do is review basic multiplication facts to make sure the student had a good foundation. Next, I would have the student go over the multiplication problem step-by-step, making sure that the student understands how to correct the error they made. It is obvious that the issue came in carrying numbers from the ones place to the tens place. After working through the problem together, I will have the student complete additional problems together. After the student is comfortable with multiplying double-digit numbers, they will be given 5 practice problems to complete on their own. After the additional instruction, the student will be able to determine the volume of a rectangular prism by counting the amount of unit cubes needed to create the rectangular prism with 100% accuracy. Student 2 re-engagement plan: Student 2 shows partial understanding of how to calculate volume, however they did not know where they needed to stop in the calculations. The student did all of the multiplication correctly, so I would not work on multiplication with this student. The student missed question 1 and 2 because after multiplying the sides together, they continued to by multiplying the product of the length and width with the total of all three measurements. My work with this student would concentrate on what the formula is for volume and then what we do with the numbers we are given. I would start with a review of the formula l X w X h and explain that the only 3 numbers that need to be multiplied to find the volume. I would go over where the error was made on the assessment and then have the student complete 5 practice volume questions. Once the student had completed the problems, I would have them explain how they got their answer to ensure that they have the process on finding volume. After the additional instruction, the student will be able to determine the volume of a rectangular prism by counting the amount of unit cubes needed to create the rectangular prism with 100% accuracy. Student 3 re-engagement plan: Student 3 appears to understand what volume is but does not have the tools necessary to easily calculate volume. The first thing I would do is to go over the concept of volume and review how to use the formula for volume. The student did not appear to have the multiplication skills to use the formula, so next I would work on basic multiplication. Using questions 1 and 2, I would work through the problems with the student, allowing them to conduct each step as we talk it out. Once we have gone over the 2 problems and I am confident that the student better

EDUC 530 Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 5 of 5 | 8 pages maximum All rights reserved. V5_0916 The edTPA trademarks are owned by The Board of Trustees of the Leland Stanford Junior University. Use of the edTPA trademarks is permitted only pursuant to the terms of a written license agreement. understands how to multiply to find volume, I will give the student practice problems. Since the student’s work sample shows that the multiplication issue is with 2-digit by 1- digit multiplication, I will have 5 practice problems for the student to work out. Once the student has worked out each problem, I will have them walk me through the process to make sure they have a good understanding of the multiplication. After the additional instruction, the student will be able to determine the volume of a rectangular prism by counting the amount of unit cubes needed to create the rectangular prism with 100% accuracy.] This response should include one detailed paragraph for each student according to their individual work samples. You can label each paragraph Student 1, 2 and 3.

annotated-Assessment_Commentary_Template.doc

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