Elementary Mathematics Planning Commentary Planning Commentary Directions: Respond to the prompts below (no more than 9 single-spaced pages, including prompts) by typing your responses within the brackets following each prompt. Do not delete or alter the prompts; both the prompts and your responses are included in the total page count allowed. Refer to the evidence chart in the handbook to ensure that this document complies with all format specifications. Pages exceeding the maximum will not be scored. 1. Central Focus a. Describe the central focus and purpose for the content you will teach in this learning segment. [I chose fractions because it is one of the main components of the third grade math curriculum. A large portion of the state standards and state standardized test cover fractions, and they are included in the Common Core State Standards as well. We began our year learning about fractions. It is time for us to review what we know and build on that knowledge to gain new information. The students not only have to recognize and name fractions, but they must also use their higher-order thinking skills, such as problem-solving to compare fractions. ] b. Given the central focus, describe how the standards and learning objectives within your learning segment address: Conceptual understanding Procedural fluency Mathematical reasoning OR problem solving skills [The students must first have a sound basic conceptual understanding of naming, identifying, and writing fractions before they can move on to the higher-order skills. The review is to be sure that has occurred. Next, the students will use their mathematical reasoning abilities to compare fractions using models or pictures that they can see. With that knowledge, the students will be ready to learn the procedures for comparing fractions using cross-multiplication. ] c. Explain how your plans build on each other to help students make connections between facts, concepts, computations/procedures, and reasoning/problem solving strategies to deepen their learning of mathematics. [ The students will begin by reviewing what they already know, which is naming, identifying, and writing fractions. This will be followed by comparing fractions using models(fraction tiles) and then comparing fractions by cross-multiplying. Each lesson increases in difficulty, and the students would not be able to master the objectives without having learned the previous lessons. ] 2. Knowledge of Students to Inform Teaching For each of the prompts below (2a–c), describe what you know about your students with respect to the central focus of the learning segment. Consider the variety of learners in your class who may require different strategies/support (e.g., students with IEPs, English language learners, struggling readers, underperforming students or those with gaps in academic knowledge, and/or gifted students). a. Prior academic learning and prerequisite skills related to the central focus—What do students know, what can they do, and what are they learning to do? [Most of the students have a good basic understanding about fractions. The majority of them can name, identify, and write the correct fractions. Some of them still have difficulties explaining what fractions are in words. They are learning their multiplication facts. The students are at Copyright © 2012 Board of Trustees of the Leland Stanford Junior University. 1 of 5 | 9 pages maximum All rights reserved. V1_0113 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. Elementary Mathematics Planning Commentary different places of mastery on these, based mostly on the amount of time that they have spent practicing. For some of my inclusion students, it is related to their learning disabilities, and they were already struggling mathematically. ] b. Personal/cultural/community assets related to the central focus—What do you know about your students’ everyday experiences, cultural backgrounds and practices, and interests? [One way to make fractions relatable to my students is to discuss how fractions are used in cooking and baking, as many of them do with family members. Another way is to talk about how fractions can be used in measuring and building things like they may also do with relatives. Since this is a rural community, we have little cultural diversity in our classroom. Some of the children’s interests include video games, books, art/drawing, and sports.] c. Mathematical dispositions related to the central focus—What do you know about the extent to which your students perceive mathematics as “sensible, useful, and worthwhile,”1 persist in applying mathematics to solve problems, and believe in their ability to learn mathematics? [The majority of my students seem to like math and enjoy it. I will occasionally see some of them attempt to solve problems out using fractions. It may not always be correct, but I can tell that their minds are walking down that path. My students have displayed confidence when dealing with fractions. ] 3. Supporting Students’ Mathematics Learning Respond to prompts below (3a–c). As needed, refer to the instructional materials and lesson plans you have included to support your explanations. Use principles from research and/or theory to support your explanations, where appropriate. a. Explain how your understanding of your students’ prior academic learning and personal/cultural/community assets (from prompts 2a–b above) guided your choice or adaptation of learning tasks and materials. [Based on what I know about children in general and my students specifically, I wanted to include activities that would interest them, such as blowing bubbles with chewing gum, while getting them actively engaged, like when they are doing the motions for “multiply the butterfly” or “bottoms up.” I know that they will learn better if they are involved in hands-on learning instead of listening to me talk the whole time. Educational theorist Ralph Tyler (2008) believed that children learned best through hands-on experiences (Misencik, p.4). I included opportunities for the students to engage in collaborative learning by way of learning centers and completing work as a group, which is encouraged by the Constructivists (www.thirteen.org, n.d.). This allows the students to learn from each other and discuss fractions. Since this is the age of technology and I have students who are very involved in video games, I also try to include technology into my lessons whenever possible, and this learning segment was no different. I used several methods of technology and visual aids. Some of Piaget’s suggestions included using visual aids and giving the students hands-on and varied experiences (Mclendon, n.d.] 1 From the Common Core State Standards for Mathematics Copyright © 2012 Board of Trustees of the Leland Stanford Junior University. 2 of 5 | 9 pages maximum All rights reserved. V1_0113 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. Elementary Mathematics Planning Commentary b. Describe and justify why your instructional strategies and planned supports are appropriate for the whole class and students with similar or specific learning needs. Consider students with IEPs, English language learners, struggling readers, underperforming students or those with gaps in academic knowledge, and/or gifted students. [While I think that learning centers and collaborative group work are very important to children being successful learners, I also feel that whole-group instruction is just as important. The lessons that I taught as whole-group were activities that I felt the students would learn more from by us doing them together as a class. In whole-group instruction, I try to incorporate technology and visual aids whenever possible to reach visual as well as audio learners. As I stated in the previous question, it can also be helpful in holding the attention of some students. I think that this is especially beneficial for my inclusion students or any students who may be having difficulty with that particular objective. As we work through our lessons together, I usually put the problems and answers as we work them out on the whiteboard or document camera. When I place a document under the document camera, it is projected onto the Smart Board, which enables greater visibility for all of the students. It also allows both the students and the teacher to have the ability to circle or write on the board so that it looks like it is on the paper. Those students who sometimes struggle have extra opportunities to see not only the correct answers but also how we arrived there. The students in the class may also see another way to arrive at the answer than mine by hearing what others have to say during class discussions, and they even get a variety of answers for open-ended questions.] c. Describe common mathematical preconceptions, errors, or misunderstandings within your content focus and how you will address them. [Children have a hard time at this age understanding that if the numerator is the same, the fraction with the smaller denominator is actually the greater piece of the whole. Once we have reached the lesson about cross-multiplication, I will try to get the students to “multiply the butterfly” every time just to check their answers. They also think at this grade level that they can draw pictures to compare fractions, but I try to discourage that due to the fact that their parts are almost never equal or drawn to scale. It is also difficult for the students to remember to multiply diagonally from the bottom first, but I hope “bottoms up” will help that as well.] 4. Supporting Mathematics Development Through Language a. Language Demand: Language Function. Choose one language function essential for student learning within your central focus. Listed below are some sample language functions. You may choose one of these or another language function more appropriate for your learning segment: Categorize Compare/contrast Describe Interpret Model [Compare fractions.] b. Identify a key learning task from your plans that provides students with opportunities to practice using the language function. In which lesson does the learning task occur? (Give lesson/day number.) [The students will complete the Multiply the Butterfly Handout with the teacher in whole-group instruction on Day 3, using cross-multiplication to compare fractions.] Copyright © 2012 Board of Trustees of the Leland Stanford Junior University. 3 of 5 | 9 pages maximum All rights reserved. V1_0113 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. Elementary Mathematics Planning Commentary c. Additional Language Demands. Given the language function and task identified above, describe the following associated language demands (written or oral) students need to understand and/or use. Vocabulary and/or symbols Plus at least one of the following: Syntax Discourse Consider the range of students’ understandings of the language function and other demands—what do students already know, what are they struggling with, and/or what is new to them? [numerator, denominator, less than (<), greater than (>), equal to (=), equivalent, multiply a/b <,>,= c/d Fraction A (a/b) is less than/greater than/equal to Fraction B (c/d). The student would choose the appropriate comparison.] d. Language Supports. Refer to your lesson plans and instructional materials as needed in your response to the prompt. Describe the instructional supports (during and/or prior to the learning task) that help students understand and successfully use the language function and additional language identified in prompts 4a–c. [Essential questions are asked during the lessons to identify the parts of the fraction or language to be used in comparisons. At the end of Lesson 3, the students will put small posters in their math journals that label fractions as part/whole and numerator/denominator and show the steps for cross-multiplying to compare fractions. If any of the fractions compared are equal, the teacher will ask the students for another word for that. If the students are unable to remember equivalent, the teacher will prompt them or offer hints.] 5. Monitoring Student Learning Refer to the assessments you will submit as part of the materials for Task 1. a. Describe how your planned formal and informal assessments will provide direct evidence of students’ conceptual understanding, computational/procedural fluency, and mathematical reasoning/problem solving skills throughout the learning segment. [ Informal assessments, conducted mostly through observations while the students are working and during lessons, will allow me the opportunity to see how the students are progressing through their mastery of the standards during the lesson. That will allow me to make adjustments to my lesson if necessary or pull students aside for extra attention as needed. Homework assignments, which will also be used for formative assessment, will let me see how well the students truly understood the lesson and how well they were able to complete the tasks independently. The quizzes and tests can be used as both formative assessment to help me make future decisions about my teaching and my students and as summative assessment to be used as grading purposes and determination of mastery of the standards.] b. Explain how the design or adaptation of your planned assessments allows students with specific needs to demonstrate their learning. Copyright © 2012 Board of Trustees of the Leland Stanford Junior University. 4 of 5 | 9 pages maximum All rights reserved. V1_0113 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. Elementary Mathematics Planning Commentary Consider all students, including students with IEPs, English language learners, struggling mathematics students, underperforming students or those with gaps in academic knowledge, and/or gifted students. [The students will participate in learning centers with their peers. This will require little reading, which is the main difficulty that most of my inclusion students have, and they are able to complete the activity with the assistance of their peers if they encounter any problems. In the Fish Bowl Math Craft, the students will complete the activity as a group, so all of the members may again aid one another if anyone faces difficulty. This is another assessment with little reading. The whole-group lesson activities allow the inclusion students to answer any questions without having to read aloud if they do not want to, and they can work it out with me by their sides to be sure they are on the right track. The quizzes and tests either do not have many words or do not have very difficult words. However, all of my inclusion students with an IEP have most graded work read to them. I also have tests with a reduced number of answer choices for the students who need them.] Copyright © 2012 Board of Trustees of the Leland Stanford Junior University. 5 of 5 | 9 pages maximum All rights reserved. V1_0113 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.