Part E - Planning Commentary

Elementary Mathematics Task 1: Planning Commentary

TASK 1: PLANNING COMMENTARY Respond to the prompts below (no more than 9 single-spaced pages, including prompts) by typing your responses within the brackets. Do not delete or alter the prompts. Pages exceeding the maximum will not be scored.

1. Central Focus a. Describe the central focus and purpose of the content you will teach in the learning segment. [The central focus of the learning segment is comparing two-digit numbers using knowledge of place value. The content addressed within this central focus includes determining which of two numbers or base-ten pictures represents a greater value, writing inequalities using the greater than, less than, and equal to symbols, and interpreting and justifying these number sentences in reference to numbers of tens and ones. The purpose of the content is to support students in the development of strong number sense and the ability to reason about the nature of numbers. The content also serves to teach students the standard conventions of number sentences, so that they are able to convey their ideas about number comparisons in domain-specific ways. The ability to compare numbers and the ability to reason based on place value both serve as a basis for the mathematics education that students will encounter throughout the rest of their lives. Crucial future skills such as estimation, number operations, measurement, problem solving and reasoning – as well as others – all rely on a solid understanding of place value and the ability to compare. An immediate example is in the students’ next unit which focuses on adding and subtracting numbers within 100. Furthermore, not only are the skills in this segment necessary for success in students’ future academic lives, they are essential for every-day life in adulthood as well, as students have jobs, make purchases, cook meals, and so forth. The central focus of the learning segment is of utmost value, both academically and functionally.] b. Given the central focus, describe how the standards and learning objectives within your learning segment address

 conceptual understanding,  procedural fluency, AND  mathematical reasoning or problem-solving skills. [The standard for the learning segment requires students to “compare two-digit numbers based on the meaning of tens and ones.” This standard addresses conceptual understanding, as it requires students to work with the concepts of “bigger,” “smaller,” “more,” and “less” in order to make comparisons about numbers. For example, in the first lesson objectives, students are exposed to concrete, visual representations of progressively larger two-digit numbers so that students can visually internalize the value-related concepts of “bigger,” “smaller,” “more,” and “less.” The second lesson objectives also build conceptual understanding, as students connect current understandings of the concept of value with prior conceptual understanding regarding the meaning of the equal sign and the nature of equations to build new conceptual understandings about number sentences. By introducing inequalities, students expand their conceptual understanding of what a number sentence is. Finally, the third lesson objectives build conceptual understanding of place value and the concepts of tens and ones, as students must apply this to situations where they must compare. The standard and learning objectives also address procedural fluency. The first lesson focuses on gaining fluency in the ability to compare two-digit numbers. The objectives encourage students to develop more efficient strategies for comparing numbers in ways based on placeCopyright © 2016 Board of Trustees of the Leland Stanford Junior University. 1 of 10 | 9 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.

Elementary Mathematics Task 1: Planning Commentary

value rather than the number sequence. The standard requires that students record the results of their comparison with the greater than, less than, and equal to symbols. In the second and third lessons’ objectives, students engage in repeated practice as they complete number sentences with the symbols on cards, with their arms, on the computer, and on paper. They compare and record inequalities in different modalities in order to gain fluency. By the end of the segment, the expectation is that students can fluently implement the process of (1) deciding which number is greater and then (2) choosing the correct symbol. Finally, the standard and learning objectives address mathematical reasoning as students are expected to compare “based on the meanings of the tens and ones digits.” Even if students are able to correctly record number comparisons based on rote knowledge of the number sequence, this would not meet the standard. The standard itself explicitly requires that students make these comparisons by reasoning about traits of numbers based on place value. The first lesson objective begins to solicit this mathematical reasoning by asking students to notice patterns in how the numbers of tens and ones change as numbers get bigger, as well as by asking students to compare base-ten pictorial representations rather than written numerals. These help encourage the habit of reasoning with place-value right from the start of the segment. The third lesson objectives require even greater mathematical reasoning skills, as students must justify their inequalities based on knowledge of tens and ones.] c. Explain how your plans build on each other to help students make connections between

 concepts,  computations/procedures, AND  mathematical reasoning or problem-solving strategies to build understanding of mathematics. [The first lesson focuses on comparing numbers with visual base-ten representations. First, students build a hundreds chart that shows the base-ten representations for the numbers 1-100. Then, they make observations about changes, patterns, and trends they see in the chart, which builds on students’ concepts of “bigger,” “smaller,” “more,” and “less.” Students then practice identifying which of two base-ten pictures represents a greater value. This lesson helps students develop the first step in the procedure of writing number sentences – as they reason in efficient ways in order to identify the greater value. In the second lesson, students continue to work with concepts of value as they apply this to number sentence writing. In the prior lesson, students practiced the first step of the procedure as they identified which of two values was the greater value. In this lesson, students learn the second step in the procedure – choosing the correct symbol in order to record these comparisons. Students gain repeated practice in a whole group setting identifying the greater of two values and modeling the correct symbol in kinesthetic, spatial ways. Students then gain additional, individual practice identifying the greater of two values and writing the correct symbol. Students also begin to informally practice reading and justifying their number sentences with reasoning based on place value. In the third lesson, students begin by using what they have learned from the last two lessons to complete a problem-solving challenge. They must decide which of two numbers is greater; however, some of the digits are covered. Students need to think back to the place value concepts and procedures they have learned the previous days to reason about whether they have enough information to compare the two numbers. For the second part of the final lesson, students use knowledge of the concepts of “more” and “less” (focus of Lesson 1) to determine Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 2 of 10 | 9 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.

Elementary Mathematics Task 1: Planning Commentary

which of two two-digit numbers is greater; they complete the number-sentence writing procedure (focus of Lesson 2) by choosing and recording the correct greater than, less than, or equal to symbol; and they use reasoning based on place-value (focus of Lesson 3) to justify their assertion.] 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 or 504 plans, 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—Cite evidence of what students know, what they can do, and what they are still learning to do. [In terms of prior academic learning, in kindergarten, students compared one-digit numbers using matching and counting strategies. In first grade, all students recently mastered the understanding that ten ones are considered a “ten” and that numbers are made up of tens and leftover ones. Most students have also recently mastered the understanding that the two digits in a two-digit number represent the number of tens and the number of ones, respectively, although a few students do not yet consistently apply this knowledge across problems. Students have also recently worked with equations that do not follow the “addend + addend = sum” or “minuend – subtrahend = difference.” Thus their conception of what a number sentence looks like has already been expanding to include more types. However, throughout this recent unit, the students practiced interpreting the equal sign as meaning “is the same as,” so many students recently transitioned to reading it with this phrase rather than “equals” or “is equal to.” In terms of related prerequisite skills, most students have already mastered recognizing and producing the number names, written numerals, and sequence of the numbers 1-120. Only two students (one receiving tier 3 intervention and one with IEP) are not consistent in their attempts to recognize and produce written numerals; sometimes they mix up the order of digits in a number (i.e. mistaking the written numeral 14 for “forty-one”). Additionally, all of my students can count to 100 by both ones and tens. Most have mastered the counting concepts of one-toone correspondence and cardinality, although one (with IEP) does not do this consistently. All of my students understand that each number further along in the counting sequence is worth one more. Additionally, based on the most recent STAR test results, twelve of my students scored at a second-grade level in mathematics, so they likely already have some awareness of the content taught in this learning segment, though they have not yet had much explicit exposure to the skills and specific problem types.] b. Personal, cultural, and community assets related to the central focus—What do you know about your students’ everyday experiences, cultural and language backgrounds and practices, and interests? [The students love games. They enjoy repetitive games most because they understand the expectations. They are very social and love to do collaborative things with friends, despite the fact that they are still learning how to do this without getting frustrated. They also love technology. They enjoy viewing and listening to videos. Creating and interacting with their own multimedia pieces is newer to them, but it is exciting as well. The information I know about individual students’ personal assets can help me as well. For example, one of my two students Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 3 of 10 | 9 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.

Elementary Mathematics Task 1: Planning Commentary

who is most resistant to participate in activities is obsessed with superheroes and being on TV. My other student who is resistant to participate is very particular and likes his work to be just right. When he wants to share something with the class, it is essential to him that he shares it. One student speaks primarily Tamil at home, although his parents are fairly fluent in English as well. The rest of my students all come from English-speaking homes and learned English as their first language. Most of the students come from middle-class or upper-class backgrounds, but a few of the students are from lower-middle-class or low-income homes. All of the students live with at least one biological parent, and most live with two. All of the parents make frequent and positive contact and communication with the school, and are interested in what their students are doing at school. For the most part, students have good relationships with their parents and families. All of the students live near the area, within school district boundaries. Many of the students often see each other outside of school, either through purposeful get-togethers or simply because they live in the same neighborhoods. They often know each other’s families. They talk with excitement about community involvement such as carnivals, sports, and extra-curricular activities. The community is very involved with and supportive of the school. The students love their school and typically feel it is an exciting place to be. Most of the students have been together in school since the beginning of kindergarten.] 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  believe in their own ability to learn mathematics [Overall, the students perceive mathematics as sensible, useful, and worthwhile in a school context, but not necessarily in life outside of school. They recognize and accept that mathematics is something they do at school. They generally don’t yet notice the ways they will use it outside of school too, but this doesn’t seem to make mathematics less worth-learning in their eyes. There is a lot of variability in the extent to which my students persist in applying mathematics to solve problems. The majority of my students can work at an engaging problem or set of problems for a long time, and even enjoy it. Some of my students will rush through problems to get them “solved” quickly, though they don’t necessarily mind if they make mistakes. Two of my students have a difficult time having enough stamina to work on problems until they are done. After just a few minutes, they want help or they want to quit, even if they are capable of doing it on their own. All of the students believe in their own ability to learn mathematics. They recognize that their abilities are improving greatly and will continue to improve. Sometimes, a couple of the students lose sight of this in frustrating situations, however.] 3. Supporting Students’ Mathematics Learning Respond to prompts below (3a–c). To support your justifications, refer to the instructional materials and lesson plans you have included as part of Planning Task 1. In addition, use principles from research and/or theory to support your justifications.

1 From the Common Core State Standards for Mathematics

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Elementary Mathematics Task 1: Planning Commentary

a. Justify how your understanding of your students’ prior academic learning; personal, cultural, and community assets; and mathematical dispositions (from prompts 2a–c above) guided your choice or adaptation of learning tasks and materials. Be explicit about the connections between the learning tasks and students’ prior academic learning, their assets, their mathematical dispositions, and research/theory. [One way my choice of learning tasks reflects my students’ prior academic learning is that I focus on written numerals more than base-ten blocks. All of my students already understand the concepts of tens and ones, and know that the digits in a number represent these tens and ones. Therefore, they are all able to reason about tens and ones based on the written numeral alone. Most of my students have discovered that this is a more efficient way of determining how many tens and ones are in a number, and even prefer this strategy to working with manipulatives. However, because several of my students occasionally mix up the order of digits in a number, I also included opportunities in the Lesson 1 and 2 materials for students to compare values represented with base-ten blocks, to provide a chance for these students to show knowledge and abilities that might not be as apparent in problems with written numerals only. Finally, when introducing the inequality symbols in Lesson 2, I contrast it with their prior knowledge of balanced equations and the equal sign.. I also include the words “is equal to,” as well as “is the same as” on the equal sign poster in Lesson 2 to tie the target vocabulary with the phrase they currently use. I considered students’ personal assets through my use of the mystery numbers game in Lesson 3. My students love games and according to Parten’s Stages of Play (Parten, 1932), formal games with rules is developmentally appropriate. I also included collaborative activities such as building the hundreds chart together in Lesson 1, or working on their Seesaw assignment with a partner in Lesson 3, since my students are social and love collaborating with friends. This, too, is supported by theory, as children learn best through opportunities to engage with others (Vygotsky). The Seesaw assignment also provides a technological component of the segment which the students love. I also created the superhero, baseball, and gymnast activities for Lesson 1 by choosing personal and community activities that I know my students enjoy – particularly my student who is very resistant to participate in lessons. My choice in learning tasks was also informed by my students’ cultural backgrounds. The activity sheets for Lesson 1 depict characters that reflected all of the gender-race combinations in my classroom so students felt represented. I also used the Seesaw activity as a way to tie parents into the learning segment, allowing them to view, like, and comment on their child’s work. School-home ties are an important part of my students’ and their families’ cultures. Furthermore, Bronfenbrenner’s ecological systems theory also supports the idea that learning is most effective when all partners and settings in a child’s life are connected with each other (Bronfenbrenner, 1979). Finally, because there is a lot of variability in the extent to which my students persist in applying mathematics to solve problems, I integrated my students’ likes – games, superheroes, technology, etc. – into my lessons a lot to make them as engaging as possible. Since all of my students believe in their own ability to learn mathematics, with the exception being while a couple of my students are in the midst of frustrating situations, my plans reflect this through my adaptations. I will be receptive to my students with difficulty managing their emotions, by allowing them breaks as needed so they can return to the activity with a productive mindset. Research shows that students are unable to focus on learning until they have basic emotional needs met (Maslow, 1943).] b. Describe and justify why your instructional strategies and planned supports are appropriate for the whole class, individuals, and/or groups of students with specific learning needs. Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 5 of 10 | 9 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.

Elementary Mathematics Task 1: Planning Commentary

Consider the variety of learners in your class who may require different strategies/support (e.g., students with IEPs or 504 plans, English language learners, struggling readers, underperforming students or those with gaps in academic knowledge, and/or gifted students). [My instructional strategies are appropriate for the whole class, because they are founded in my knowledge of the class, as well as educational principles and research. For example, the segment is based on careful sequencing. Sequencing ensures that students are able to build off of related ideas to develop a deeper understanding and more complex thinking (Culatta, 2018). In the first lesson, students learn to identify the greater number. In the second lesson, they use this ability to write inequalities. In the third lesson, they add a justification. This “understand,” “apply,” “evaluate” pattern of objectives is also consistent with the theory of Bloom’s taxonomy (Bloom, 1956). The instructional strategies are also rooted in social constructivist theory, as learning tasks require or allow students to work together, promoting mathematical communication and leading to increased understanding and learning outcomes (Jaramillo, 1996). My instructional strategies and supports are also appropriate for my student with moderate-tosevere cerebral palsy. I provided subtle adaptations in order to eliminate any physical boundaries – for example, providing cards in Lesson 1 that were physically easy to access. I also included base-ten representations as well as written numerals throughout the Lesson 1 and 2 learning tasks. Some of my students receiving RTI services and my students with cerebral palsy are able to recognize the value of base-ten representations more consistently than written numerals, while others are the opposite. The variety of problem types gives all of my students with additional needs a chance to be successful. Additionally, constant access to base-ten blocks, number lines, and other manipulatives will also make the learning tasks more appropriate for my students who receive RTI services in math. My instructional strategies and planned supports are also appropriate for my students with social-emotional needs. The learning tasks are based on these students’ personal interests. The adaptations provide proactive solutions (such as calling on these students often) as well as reactive solutions (such as allowing students breaks to regulate their emotions as needed0. Finally, the adaptation to clarify the meaning of multiple-meaning words and phrases also makes the segment accessible to my English language learner. Because over half of my students are advanced in math, I accounted for this group of students in the original designs of the lessons rather than in the form of adaptations. For example, the mystery numbers game in Lesson 3 is challenging for students this age, because of their developing understanding of conservation and concrete operational thinking (Piaget, 1965). Additionally, while building the hundreds chart in Lesson 1, I plan to differentiate by giving my advanced students the cards with higher numbers of tens and ones.] c. Describe common mathematical preconceptions, errors, or misunderstandings within your central focus and how you will address them. [One common misconception is known as the “arithmetic” or “operational” view of the equal sign, rather than the “relational” view. Many young students see the equal sign as signaling the result of a process (i.e. adding or subtracting), as opposed to signaling an equal comparative relationship between two values (Byrd, McNeil, & Chesney, 2015). By introducing the inequality symbols by explicitly relating them to the equal symbol, this method is shown to reduce misconceptions about the equal sign and to build conceptual understanding of number sentences.

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Elementary Mathematics Task 1: Planning Commentary

The other common mathematical error I address in the learning segment is the belief that the greater than and less than symbols act as arrows that point to the greater number. I explicitly highlight this common error to students. I also chose not to use the common “alligator” metaphor for teaching the symbols and opted for more conceptual explanations. I will show students that the wide part of the sign is by the larger number and the small part of the sign is by the smaller number. I also include a kinesthetic (modeling with arms) and auditory/musical component (reading sentences with a crescendo or decrescendo) in order to further solidify the correct meaning of each symbol and diminish the possibility of the misconception.] 4. Supporting Mathematics Development Through Language As you respond to prompts 4a–d, consider the range of students’ language assets and needs—what do students already know, what are they struggling with, and/or what is new to them? a. Language Function. Using information about your students’ language assets and needs, identify one language function essential for students to develop conceptual understanding, procedural fluency, mathematical reasoning, or problem-solving skills 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

Justify

Please see additional examples and non-examples of language functions in the glossary. [The essential language function for this segment is to compare.] b. Identify a key learning task from your plans that provides students with opportunities to practice using the language function identified above. Identify the lesson in which the learning task occurs. (Give lesson day/number.) [One key learning task that provides students with the opportunity to practice comparing is the “Talk About COMPARING!” Seesaw activity from Lesson 3. Students must compare two-digit numbers with both a written and oral number sentence and justify their comparison.] c. Additional Language Demands. Given the language function and learning 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 [There are seven content-specific vocabulary words and three symbols that students must understand and use in order to be successful throughout the learning segment. In order to follow directions for learning tasks, students must understand the meaning of the word compare in the context of numbers (i.e. tell which number has a larger or smaller value). For example the materials from all three lessons contain directions that ask students to compare numbers. Students also must understand the meaning of the term number sentence, as they are asked in the pre-assessment and post-assessment to “read this number sentence out loud.” It is also essential that they understand the meaning in order to develop a stronger conceptual Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 7 of 10 | 9 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.

Elementary Mathematics Task 1: Planning Commentary

understanding of the relationship between the equal sign and inequality symbols. Students also must understand and use the meanings of the words tens (groups of ten ones) and ones (individual leftovers in a number after grouping by tens). They also have to be able to use the vocabulary words in order to justify their number sentences in the “Talk About COMPARING!” Seesaw activity in Lesson 3. Finally, students must be able to understand and use the words greater, less, and equal, as well as the symbols that represent these words (>, <, and =, respectively). Students must understand the words in Lesson 1 learning tasks, use the symbols in Lesson 2 learning tasks, and use the words and symbols in Lesson 3 learning tasks. Additionally, students will need knowledge of the conventional syntax used for writing and reading number sentences. During whole-group instruction in Lessons 2 and 3, students must build sentences on the board in a “number, inequality symbol, number” order. Additionally, in the Lesson 3 learning task, students must read number sentences from left to right, with the conventional pattern of “[number] is less/greater than [number]” or “[number] is equal to [number].”] d. Language Supports. Refer to your lesson plans and instructional materials as needed in your response to the prompt.

 Identify and describe the planned instructional supports (during and/or prior to the learning task) to help students understand, develop, and use the identified language demands (vocabulary and/or symbols, function, discourse, syntax). [One planned instructional support for helping students acquire the language function, vocabulary, and syntax is the use of posters showing the symbols and phrases that they stand for. Each symbol is paired with a sentence frame written directly on the poster to help students read the number sentences with the correct vocabulary and syntax, thereby providing them with the language needed to compare the numbers. The posters will be displayed on the wall and referred to as needed throughout the entire learning segment. Furthermore, the posters are used as manipulatives, allowing students to build number sentences out of the hundreds chart pieces and the symbol posters during whole-group time prior to the Lesson 2 and 3 learning tasks. Also during this time in the lessons prior to the learning tasks, I planned scaffolded practice using, reading, and justifying the number sentences with the conventional vocabulary and syntax. This whole-group practice is structured as repeated teacher modeling – with kinesthetic and musical components as added support to help students internalize the meaning of the symbols and target vocabulary – followed by a gradual release of responsibility. Finally, students are supported in their developing understanding of the terms compare and number sentence through explicit instruction at the very beginning of the segment, and review at the beginning of each lesson.] 5. Monitoring Student Learning In response to the prompts below, refer to the assessments you will submit as part of the materials for Planning 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 or problem-solving skills throughout the learning segment. [I have included several formal and informal measures of conceptual understanding throughout the segment. In the first lesson, I will informally assess students’ conceptual understanding of the value of numbers and the nature of tens and ones in Assessment 1.1 as they make observations about the patterns and trends they notice in the hundreds chart. At the end of the segment, Assessment 3.2 will provide direct evidence of students’ conceptual understanding as Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 8 of 10 | 9 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.

Elementary Mathematics Task 1: Planning Commentary

well. Students must apply their conceptual understanding of tens and ones to decide how many tens and ones make up given numbers, and what that says about the relative values of those numbers, in order to justify their number sentences. Assessment 1.2 will provide formal evidence of students’ ability to draw on multiple strategies (concrete pictures and counting strategies, as well as place value in written numerals) in order to fluently identify which of two numbers is greater. This is the first part of the procedure of comparing numbers. Assessment 2.1 and 3.1 provide more complete evidence of students’ procedural fluency, as students must continue to apply the first step of the procedure, but also now add on the next step of choosing the correct symbol to compare the numbers. Finally, I will informally assess students’ mathematical reasoning skills as I listen to their observations about trends in the hundreds chart in Assessment 1.1. By the end of the segment, I will formally assess students’ ability to reason mathematically by analyzing their justifications of their number sentences in Assessment 3.2. In order to justify their answers, they must reason based on place-value, the number sequence, or the composition of the numbers.] b. Explain how the design or adaptation of your planned assessments allows students with specific needs to demonstrate their learning. Consider the variety of learners in your class who may require different strategies/support (e.g., students with IEPs or 504 plans, English language learners, struggling readers, underperforming students or those with gaps in academic knowledge, and/or gifted students). [The design of my planned assessments will already be appropriate for my student who is an English language learner, my students receiving RTI services in reading, and my students who are advanced in math. My student who is an English language learner is at the bridging/nearproficient level, and only needs additional support with multiple-meaning words and phrases. The only such word present in the segment assessments is the word “greater” which has already been taught explicitly throughout the segment so it should not be an issue. Additionally, all assessment directions are read aloud to all students and clarified with gestures and additional explanations, so this will not be an obstacle for my students receiving RTI services in reading. Finally, Assessment 3.2 gives students with advanced math skills the chance to demonstrate advanced knowledge as they have the freedom to justify their number sentences – already a higher-level cognitive process – in more in-depth, conceptual ways. For example, they might discuss the relevance of the digit in the ones place in addition to the tens. I have also adapted the assessments so that they are appropriate for my students with cerebral palsy, my students with social-emotional needs, and my students receiving RTI services in math. For my student with moderate-to-severe cerebral palsy, the pictures of tens and ones blocks on the assessments will be highlighted in different colors to help him further delineate between them. I will also be available to clarify procedures or provide additional scaffolding as needed to ensure an accurate measure of the abilities of both of my students with cerebral palsy and my students receiving RTI services. The assessments also provide variety in the representation of numbers (picture and written numeral), the difficulty level of the questions (identify, apply, and justify), and the mode of answer required (written or spoken), so that all students have some chance to show their knowledge without additional confounding factors that act as barriers due to their particular challenges. Finally, the assessments are appropriate for my students with need for additional social-emotional support, as they draw on the students’ likes and personal assets to intrinsically motivate these students to participate and to be able to do so with a conducive attitude.] Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. 9 of 10 | 9 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.

Elementary Mathematics Task 1: Planning Commentary

References Bloom, B. S., Engelhart, M. D., Furst, E. J., & Hill, W. H.; Krathwohl, D. R. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook I: Cognitive domain. New York: David McKay Company. Bronfenbrenner, U. (1979). The ecology of human development. Cambridge, MA: Harvard University Press. Byrd, C. E., McNeil, N. M., Chesney, D. L., (2015). A specific misconception of the equal sign acts as a barrier to children's learning of early algebra. Learning and Individual Differences, 38. 61-17. Jaramillo, J. A. (1996). Vygotsky's sociocultural theory and contributions to the development of constructivist curricula. Education, 117(1). Retrieved from http://go.galegroup.com/ps/i.do?v=2.1&it=r&sw=w&id=GALE%7CA18960235&prodId=A ONE&userGroupName=uiuc_br1 Maslow, A.H. (1943). A theory of human motivation. Psychological Review, 50(4): 370– 96. doi:10.1037/h0054346 Parten, M. B. (1932). Social participation among preschool children. Journal of Abnormal and Social Psychology, 27(3): 243–269. doi:10.1037/h0074524. Piaget, J. (1965). The stages of the intellectual development of the child. Educational psychology in context: Readings for future teachers, 98-106.

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