Task 4 Mathematics Boot Camp Fall, 2016

Components of Task 4 Context for Learning Choose a class and complete a Context for Learning template for Mathematics. Ask about student IEPs, speak with the Special Education and Gifted teachers to find out specific accommodations and modifications you should include on students. Include the teaching assistant who works with a group, special education teacher who comes in and works with students. Describe required curricula, assignments, assessments that are aligned to standards used for math. Any required text or scripted program (Engage New York) Explain how the math time frame is used.(ex.- 10 minutes for review, 20 minutes for guided practice, 20 minutes for individual practice. Some student are using the computer on a bookmarked lesson and special education has a small group working using manipulatives. Identify any text and instructional program include title, publisher, and date of publication.

List other resources used( electronic whiteboards, manipulatives, graphic organizers, anchor charts, workbooks, etc. Students in class-identify grade level and number of students and divided into number of males and females. Next part is the chart that summarizes the needed supports, accommodations or modifications for your students. It is important that you identify students in any of the groups listed on the form. Ask for help filling it out. You will address each of these groups in your lesson plans and in the commentary prompts. If you list the students on this form you must address the students in the commentaries. You CANNOT say you do not have any students with learning needs. In every class there will be students who learn differently than others.

Components of Task 4 Identify a learning segment and a central focus in math. (You Cooperating teacher can teach the unit and you will cite his/her lessons on the form Learning Segment Overview). USE TEMPLATE, Learning Segment Overview- briefly describe the lesson on the template. Each lesson will need an assessment to evaluate. The assessment should allow the students the opportunity to show conceptual understanding, procedural fluency, and mathematical reasoning or problem solving. The assessments MUST show student work. TWO PAGES ONLY- USE TEMPLATE Identify a central focus along with the content standards and objectives taught in the segment and assessed in the task. The central focus should support students to develop conceptual understanding, procedural fluency and mathematical reasoning/problem solving. Develop or adapt a formative assessment to deliver to the whole class that allows students to demonstrate conceptual understanding, computational/procedural fluency and mathematical reasoning/problem-solving skills. You will upload a blank copy of this assessment Task 4 Part C Mathematics Assessment

Assessment and Criteria Evaluation Rubric After you have created or adapted the assessment you plan to use in this task, create the evaluation rubric to go with it. Assessment MUST SHOW STUDENT WORK. Define the criteria you used to evaluate the assessment for each area of math. (Conceptual understanding, procedural fluency and math reasoning/problem solving). Rubric needs to address specific skills and understandings. Create a table or graph to show the results of students performance as it relates to the three areas. Look for patterns of learning: difference in student skills and understanding related to the topic. What is your evidence both for what was learned, but errors, confusions, and partial understandings. Look for quantitative patterns (number of similar correct responses or errors) and qualitative patters (specific understanding and/or misunderstandings). When discussing patterns of learning across whole class, BE SURE to provide specific examples.

Conceptual understanding -comprehension of mathematical concepts, operations, and relations, allows a student to apply and possibly adapt some acquired mathematical ideas to new situations. Example: the use of zeros with place value problems is simple, but critical for understanding. "What is 20 + 70?" A student who can effectively explain the mathematics might say, "20 is 2 tens and 70 is 7 tens. So, 2 tens and 7 tens is 9 tens. 9 tens is the same as 90.“ Procedural fluency-refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently. Students must know when, as opposed to just how, to use a procedure. And they must not only be able to perform procedures accurately, but also flexibly and efficiently. Example: performing basic computations with whole numbers (6+7, 17–9, 8×4, and so on) without always having to refer to tables or other aids. Mathematical reasoning/problem solving- Mathematical reasoning provides opportunities for students to develop and express insights about the mathematical competencies that they are developing. Problem solving allows students to draw on the competencies that they are developing to engage in a task for which the solution is not known.

Collect and analyze the assessments for the whole class. Students MUST show their work. CANNOT BE MULITPLE CHOICE. (You will need to cite the scores based on the evaluation criteria for all the students in the class.) Select and submit the files of the three focus students (remove student names, school, teacher’s name) that demonstrate an area of struggle from your analysis and explain the focus students’ errors or misunderstandings related to the struggle. Identify a targeted learning goal based on the analysis of work samples. Design a re-engagement lesson. Teach the re-engagement lesson. Collect and analyze the re-engagement work samples. Write comments on the samples and save for documentation. Evaluate the effectiveness of the re-engagement lesson.

Mathematics Assessment Commentary 1. Analyzing Student Learning— Whole Class, provide a graphic (chart or table) or narrative summary of student learning. Discuss all parts of the evaluation criteria for the assessment as it relates to the whole class. Use examples from summary to discuss patterns of learning as it relates to conceptual understanding, procedural fluency, and mathematics reasoning/problem solving. Example: Many students showed that they could … as we can see in Student 1’s work on problem 3. Like most students, students 2 and 3 showed in problem 6 that thery could not … 2. Analyzing Student Learning—3 Focus Students. Describe students’ struggles and cite specific examples from work samples. What do the errors tell you about their understanding? Be specific in discussing their errors and the focus students who had problems. One of the three focus students MUST have a specific learning need. For example you would cite evidence: The error was in regrouping, focus students did not change the number of tens in the problems to get the correct answer. This skill and understanding is needed to show understanding of regrouping in subtraction. When regrouping, the number of tens lessens by one if ten is added to the ones place. Student 2 did not lessen the tens by one, but instead subtracted the top ones numeral from bottom numeral instead of regrouping and adding ten ones.

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. Your strategy and representation MUST be different from the original lesson. b. Describe the re-engagement lesson- Your description should include: targeted learning objective/goal that you identified in the analysis of the three student work samples, 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 and assessments for monitoring student learning. You could use the same assessment from the original, but it must show new learning specifically related to the area of struggle. It needs to provide opportunities for students to demonstrate conceptual understanding, procedural fluency, and math reasoning.

4. Analyzing Teaching- using the re-engagement lesson Explain how the work samples are being submitted. Describe effectiveness of the lesson the re-engagement. Cite examples from the re-engagement work samples. Again in this part, give the evidence as it relates to specific problems like in the earlier analysis of the work samples. As you complete task 4, use the templates provided, Type inside the [ ]. Use Arial 11. Follow the specifications in the evidence chart. Refer to rubrics to make sure your are providing the necessary information. Have a peer review your work and ask for suggestions for improvement. After you are satisfied with task 4 save it as a word doc. to Course Den. Check to be sure that your files do not have any RED LINE ERRORS. If you do, fix the problem NOW. Do not wait until Submission Day. Once you have fixed ALL ERRORS and ARE SATISIFIED WITH YOUR SUBMISSION, SAVE IN AT LEAST THREE DIFFERENT PLACES. MAKE ONE A PDF. Save it to a flash drive, make a Google Drive, email it to yourself, and Course Den in the Seminar Class.

Learning Segment Overview Files for Task 4 Learning Segment Overview (Part B) Context for Learning (Part A) Student work samples from re-engagement lesson (Part F) Assessment Commentary (Part G) Mathematical Assessment (Part C ) Student Work samples from Assessment for Learning Segment (Part E) Evaluation Criteria for Math Assessment (Part D)

Rubric 16 Covers prompt 1 and Summary of student learning for whole class, evaluation criteria rubric, blank copy of the formative assessment. Describe what students did correctly and what they did wrong as it relates to conceptual understanding, procedural fluency, and mathematical reasoning/problem solving. Check to see the narrative or graphic summary aligns with your analysis. Cite examples from the assessment that describes what the students understand and what they struggled with understanding. Discuss how the math understanding and struggles relate to each other.

Rubric 17 Covers prompts 2, 3, and the three work samples of the focus students. For each focus student, describe the student’s struggles and misconceptions and cite examples as evidence. Evidence is aligned with identified area of struggle you identified as the area to reteach. Connect area of struggle of the three focus students to the mathematical concept. Your analysis shows how the error is connected to the area of struggle for each focus student. Your analysis describes the relationship between the concept and the area of struggle.

Rubric 18 Covers prompt 3 and 4 and three focus students’ reengagement work samples. Uses evidences from the work samples to explain how the re- engagement lesson was or was not effective for each focus student. Cite specific examples to support your explanation. Each student should be discussed separately on the effectiveness of the re-engagement lesson as it relates to mathematical understanding. Compare and discuss the changes noted in each student’s formative assessment and the assessment after the re- engagement lesson.

QUESTIONS ???????? Refer to handbook Ask peers Email Mrs. Steed