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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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