Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary
TASK 4: MATHEMATICS ASSESSMENT COMMENTARY Respond to the prompts below (no more than 8 single-spaced pages, including prompts) by typing your responses within the brackets following each prompt. Do not delete or alter the prompts. Commentary pages exceeding the maximum will not be scored. Attach the assessment you used to evaluate student performance (no more than 5 additional pages) to the end of this file. If you submit a student work sample as a video or audio clip and you or your focus students cannot be clearly heard, attach a transcription of the inaudible comments (no more than 2 additional pages) to the end of this file. These pages do not count toward your page total. 1. Analyzing Student Learning—Whole Class a. Identify the specific learning objectives measured by the formative assessment you chose for analysis. [The learning objective that is measured by the chosen formative assessment is students being able to partitioning circles and rectangles into two, three, or four equal shares and describing the shares using the words halves, thirds, fourth, half of, a third of, and fourth of. ] b. Provide a graphic (chart or table) or narrative that summarizes student learning for the whole class. Be sure to summarize student learning for all evaluation criteria submitted in Mathematics Assessment Task 4, Part D. [
The bar graph above is based on one of the formative assessments of the learning segment. This graph illustrates the student learning of the whole class. Regarding the formative Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 1 of 6 | 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 of a written license agreement.
Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary
assessment, the horizontal axis shows what each of the four questions focused on. Each column shows the percentage of students who got the question correct. In question # 1, 79% of the whole class was able to correctly identify one-third of a square with 9 pieces. In question #2, 100% of the class was able to correctly color in one-half of a circle that had 12 pieces. In questions #2b and #2c, 50% of the class was able to correctly color in one-fourth and one-third of a circle that had 12 pieces] c. Using examples from the summary chart, discuss the patterns of learning across the whole class relative to ◼ conceptual understanding ◼ procedural fluency. ◼ mathematical reasoning/problem-solving skills [Conceptual understanding - After analyzing student data, it shows that students do not have a strong conceptual understand of the mathematical concepts being taught in this learning segment. Students are not able to apply their knowledge to new contexts. For example, most students can identifying one-third of a square (question #1) but the majority of the students cannot identify one-third of a circle (question #2b). Being unable to apply their knowledge in a different context may be because they do not yet have a strong understanding of the concepts being taught. Procedural fluency - Based in the chart, the majority of the class has not yet developed procedural fluency in regards to these math concepts. In question #1, 79% of the whole class was able to applying their knowledge to correctly identify one-third of a square, however, they were not able to apply the same knowledge to correctly identify one-third of a circle. Exactly half of the class answered question #2b incorrectly. They were not able to transfer and apply their knowledge to a different problem, which in this case was applying it to a different shape. Mathematical reasoning/problem-solving skills - Based on the student data, I noticed there is a lack of mathematical reasoning and problem solving skills across the majority of the class. I noticed this pattern within questions #2b and #2c. Every students in this class is able to correctly identify one-half but half of them lack the problem solving skills to reason that dividing the one-half in two will result in one-fourth of the shape. This is evident in that only 50% of the students correctly answered questions #2b.] 2. Analyzing Student Learning—3 Focus Students From your analysis of whole class student learning, identify one area where students struggled mathematically. Select 3 student work samples that represent the struggles in this area. These students 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 or challenge. a. In what form did you submit the work samples for the 3 focus students? (Delete choices that do not apply.) ◼ Written work samples in text files b. Analyze the 3 students’ work samples and describe the students’ struggle(s) as they relate Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 2 of 6 | 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 of a written license agreement.
Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary
to the underlying mathematical understanding and/or concept. Cite specific evidence from the work samples in relation to mathematical errors, confusions, and partial understandings. What do the students’ errors tell you about their mathematical understanding? 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. [n analyzing student work, I noticed that Student 1 and 2 struggling in identifying one-fourth and one-third of a circle. Question #2b asked students to identifying one-fourth of a 12 piece circle. Both students colored in 4 pieces which actually illustrates one-third. Question #2c asked students to identify one-third of a 12 piece circle. Student 1 and 2 both colored in 3 pieces which actually identifies one-fourth. Both students confused the one-fourth and one-third. These errors convey confusions in the underlying mathematical understanding that the term one-fourth ask for the total amount of pieces to be put into 4 equal groups and that one-third ask for the total amount of pieces to be put into 3 equal groups. Student 3 correctly identified one-fourth of the 12 piece circle correctly but struggled in identifying one-third of the circle. Student 3 shaded in 3 pieces to show one-fourth and colored in the same amount to show one-third. This errors conveys that the student does not understand what the term one-third is asking for. Student 3 has the same error in their underlying mathematical understanding as Student 1 and 2.] c. If a video or audio work sample occurs in a group context (e.g., discussion), provide the name of the clip and clearly describe how the scorer can identify the focus student(s) (e.g., position, physical description) whose work is portrayed. [ ] 3. Developing Students’ Mathematical Understanding a. Based on your analysis of the focus students’ work samples, write a targeted learning objective/goal for the students related to the area of struggle. [Based on my analysis of the focus student’s work samples and their area of struggle, the targeted learning objective is for students to successfully partition amounts into three and four equal shares using the academic vocabulary one-thirds and one-fourths. ] b. Describe the re-engagement lesson you designed to develop each focus student’s mathematical knowledge in relation to the targeted learning objective/goal. Your description 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) [Targeted learning objective/goal - Students will successfully partition given amounts and Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 3 of 6 | 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 of a written license agreement.
Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary
shapes into three and four equal shares using the academic vocabulary one-third and one-fourth. State-adopted academic content standards - CCSS.MATH.CONTENT.2.G.A.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Strategies and learning tasks to re-engage students - In the beginning of the re-engagement lesson, the whole class will be solving example problems together. I will show that I have 18 cube manipulatives. Then I will call on 3 volunteers to stand in front of the class. I will ask the class how could we equally share the 18 cubes among the three students, or put them into 3 equal groups. The class will solve the problem together, discuss, and then repeat the process with 12 cubes. The process will be repeated with 12 cubes being put into 4 equal groups, so 4 student volunteers will stand in front of the class. I will ask the class how could we evenly share 12 cubes among 4 students. Next, the class will repeat the process using 20 cubes and sharing among 4 students. I will lead a discussion about how we could use finding one-half first to help us find one-fourth (dividing each one-half into two parts to find one-fourth of the amount). Next, the students will be put into pairs. Each pair will be given two half sheets of paper and 25 cube manipulatives. One half sheet of paper will be folded in thirds to show three parts and the other will be folded in fourths to show four parts. These one-third and one-fourth mats will assist the students throughout the activity. With the students in pairs, I will ask them to put the 25 cubes into four equal groups using the one-fourth mat. The pairs will work together, discuss, and then will be called on to share with the class their answer and how they solved it. They will use the one-fourth mat to do the same process with 12 cubes and 8 cubes. I will ask the students to switch their mats to the one-third mat. I will ask the paris to count out 21 cubes and to use their one-third mat to put these cubes into three equal groups. This process will be repeated with 18 cubes and 9 cubes. At the end of the lesson, students will be given a summative assess. This is a worksheet that ask students to identify one-third and one-fourth of given amounts and of circles with different amounts of pieces. This assessment is done individually. Representations and other instructional resources/materials used to re-engage students in learning - Materials used to re-engage students in learning are block manipulatives, one-fourth mats, and one-third mats. Assessments for monitoring student learning during the lesson - Pair Shares will be used throughout the re-engagement lesson. Students will be working in pairs to solve the given problems. When solving the problems, they will collaborate, discuss, and then have the opportunity to share with the whole group. Their verbal answers when sharing will be formative assessment to monitor student learning throughout the lesson. Before responding to prompt 4, you will teach your re-engagement lesson. This lesson may be taught with the 3 focus students one-on-one, in a small group, or with the whole class. 4. Analyzing Teaching Cite evidence from the 3 focus students’ work samples from the re-engagement lesson to your response to prompt 4b. Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 4 of 6 | 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 of a written license agreement.
Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary
a. In what form did you submit the 3 students’ work samples from the re-engagement lesson? ◼ Written work samples in text files ◼ In audio files ◼ In video files [The 3 students’ work samples form the re-engagement lesson are submitted as written work samples in text files.] b. Analyze the effectiveness of the strategies you used during the re-engagement lesson to develop students’ mathematical understanding in the identified area of struggle. Consider the change in students’ mathematical understanding or misconception(s) in relation to the identified area of struggle when describing the effectiveness of the re-engagement lesson. [The strategies I used in the re-engagement lesson were partially effective in developing students’ mathematical understanding in the identified area of struggle. The area of struggle that I identified was errors in the students’ understanding that the term one-fourth ask for the total amount of pieces to be put into 4 equal groups and that one-third ask for the total amount of pieces to be put into 3 equal groups. The summative assessment of the re-engagement lesson included 4 questions that asked the students to identify one-fourth of given amounts and of circles with different amounts of pieces. Student 1 correctly answered only one of the 4 questions. Student 2 and 3 correctly answered 3 of these 4 questions. The assessment also included 4 questions that asked students to identify one-third of given amounts and of circles with different amounts of pieces. All of the focus student answered each of these 4 questions correctly. Based on the student data from the re-engagement lesson assessment, the strategies I used throughout the lesson were successful in regards to improving the students’ mathematical understanding of one-thirds. In the formative assessment (used to to create the student learning bar graph), all of the focus students incorrectly answered each question in which they needed to identify one-third of a circle. In the re-engagement assessment, they were all able to correctly identify one-thirds of various amounts in different contexts. The strategies I used were not as successful in improving the students’ mathematical understanding of identifying one-fourth. In the formative assessment, Student 1 and Student 2 incorrectly answered all of the questions regarding identifying one-fourth of a circle and they continued to incorrectly answer this type of question in the re-engagement assessment. Student 3 correctly answered this type of question in the formative assessment but in the re-engagement assessment correctly answer 3 out of the 4 questions. In a future lesson, I would need to review how to identify one-fourth of a given amount in different contexts.] c. If a video or audio work sample occurs in a group context (e.g., discussion), provide the name of the clip and clearly describe how the scorer can identify the focus student(s) (e.g., position, physical description) whose work is portrayed. [ ]
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Elementary Education - Mathematics Task 4: Mathematics Assessment Commentary
Below is a blank copy of the assessment from the re-engagement lesson.
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