Math Response 12

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Feb 20, 2024

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TEACHING MATHEMATICS AND LANGUAGE TO ENGLISH LEARNERS  WIDA CAN DO Descriptors o Assess language development along a six-level continuum of language proficiency.  level 1 are the least proficient in English, and those at level 6 are those who have achieved a level of proficiency that approximates that of non-ELs of the same age.  Prior knowledge assessment o identify where your ELs may need catching up as well as areas of knowledge that you can build on o Mathematics assessment that is pretranslated into multiple different languages  Understanding of home country mathematical nuances o Helps communicate to ELs and their families that you have an “asset-based” (rather than a “deficitbased”) view of the knowledge.  Linguistic demands of the mathematics problems o a text that is not comprehensible will only measure the vocabulary that a student does not know” - if students are unable to understand the language of the problem, they will be unable to demonstrate their understanding of the mathematics  Use of cognates can help emphasize the value of cultural relevance and conceptual familiarity in helping students acquire content understanding  Having your students explain their steps in complete written sentences using sequencing words (such as first, next, then, finally) can help reinforce vocabulary and content understanding while also providing EL students with a chance to do some thinking about a particular problem  By asking students to discuss their predictions, complete their calculations, and then explain their choices to others, you will add an important language practice step to the sequence of your lesson.  Word walls, anchor charts, and other visual aids o Creating word walls for different mathematical operations and adding to them as new words are encountered can help EL students build important vocabulary knowledge o Helps students recall important concepts and language when completing classroom activities  Teachers can use this understanding to provide opportunities for students to use mathematics to examine personal, communal, and social contexts.  Mathematics teaching should leverage students’ culture, contexts, and identities to support and enhance mathematics learning Think of yourself as a learner first  Provide students with confidence-building exercises that enable all students to succeed  Celebrate creative approaches to problems – regardless of the solution  Normalize mistakes and errors as learning opportunities

 Utilize real world connections to make the math relevant and meaningful  Emphasize the importance of perseverance  Use scaffolding questions to keep students out of their alarm zone  Provide opportunities for meaningful collaboration with peers  Incorporate hands on activities and manipulatives to build conceptual understanding  Vary assessment methods and include authentic assessments • Understanding the strengths and motivations that serve to develop students’ identities should be embedded in the daily work of teachers. • Mathematics teaching involves not only helping students develop mathematical skills but also empowering students to seeing themselves as being doers of mathematics. • Mathematics teaching should leverage students’ culture, contexts, and identities to support and enhance mathematics learning (NCTM, 2014). • We affirm mathematics identities by providing opportunities for students to make sense of and persevere in challenging mathematics. • Facilitate meaningful mathematical discourse • Support productive struggle in learning mathematics • Elicit and use evidence of student thinking • This kind of teaching cultivates and affirms mathematical participation and behaviors • We must provide opportunities that play to the strengths and challenges of students. • Effective teaching practices have the potential to open up greater opportunities for higher-order thinking and for raising the mathematics achievement of all students • Classroom environments that foster a sense of community that allows students to express their mathematical ideas. • Allocate resources to ensure that all students are provided with an appropriate amount of instructional time to maximize their learning potential. • Eliminate the tracking of low-achieving students and instead structure interventions that provide high-quality instruction and other classroom support, such as math coaches and specialists. • Provide support structures, co-curricular activities, and resources to increase the numbers of students from all racial, ethnic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement. • Consider teacher assignment practices to ensure that struggling students have access to effective mathematics teaching… • Maintain a school-wide culture with high expectations and a growth mindset.

• Develop and implement high-quality interventions. • Ensure that curricular and extracurricular resources are available to support and challenge all students. • Teachers • Develop socially, emotionally, and academically safe environments for mathematics teaching and learning… • Understand and use the social contexts, cultural backgrounds, and identities of students as resources to foster access, motivate students to learn more mathematics, and engage student interest. • Model high expectations for each student’s success in problem solving, reasoning, and understanding. • Promote the development of a growth mindset among students. How can you create opportunities in your courses to support and affirm identity development of English Learners and students exhibiting math anxiety? In order to create opportunities for affirm identity development of English Learners and students with math anxiety, teachers must first self-reflect on our own math identity, evaluating our preconceived notions about math difficulty as well assumptions regarding language barriers in mathematics. Teachers must understand their own relationship with math and how imposing their views on other students with varying math identities can greatly affect their development, having unintended consequences of students’ limited career options, financial implications, inability to accurately decipher statistics and suboptimal everyday decisions (Karnani, 2017). To truly affirm students’ math identity development, teachers must promote a growth mindset among students by examining and responding to the cultural backgrounds, social contexts, and identities that affect their approach toward math (NCTM, 2014). Determining a student’s current identity of themselves and how others view their math proficiency can be determined through prior knowledge self-assessments. For example, when referring to EL students, WIDA descriptors and dual language math problems are useful tools in revealing gaps (Leith, Rose, and King, 2016). Assessments are modified for students with math anxiety by lacking a time limit for answering questions and through the use scaffolded questions to keep students out of their alarm zone. Results from these assessments should shape lesson plans to open up greater opportunities for higher-order thinking. Understanding cultural backgrounds and social contexts, such nuances of home country mathematics, can help teachers maintain an “asset-based” view of mathematics knowledge. By making lesson more accessible to both EL students and those with math anxiety, providing more visual scaffolding and lessening the potential linguistic interference, teachers can provide a familiarity to students that allows them to demonstrate their understanding more clearly. In addition, leveraging the classroom setting, by incorporating hands on activities and manipulatives in group settings, rather than independent work, creates an environment where both EL and students with math anxiety can feel more comfortable and celebrated for creative approaches regardless of the solution. Ultimately opportunities for EL and students with math anxiety to affirm their math identity development require teachers to display understanding of the factors affects student’s identity, self-

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critique and modify lesson plan based on student’s abilities, and provide understanding through multiple instructional means and environments. High-quality mathematics curriculum, effective teaching and learning, high expectations, and the support and resources are needed to maximize their learning potential and develop a high sense of agency and math identity (NCTM, 2014).  How can technology integration support the needs of diverse learners, while advancing the skills and concepts fostered by the math standards? Technology integration encourages interaction form all types of learners. Technology features allow learners to feature software, do demonstrations, model processes, share learning experiences, guide discussion, or display independent work. This interactive approach aids in making the content more realistic and comprehensible to students. Yet, technology requires a school’s willingness to take risks in integration and professional training. The ensure the advancement of the skills and concepts fostered by math students, user must proactively address challenges of technology in pursuit of excellence in mathematics. The Digital Learning Visioning Committee determined that the continued pursuit of excellence in mathematics education can best be secured by proactively raising challenging  issues about technology integration and teaming with instructional technology leaders to address those issues.  The versatility of the whiteboard encourages its use with all types of learners  Whiteboards can be used to feature software, do demonstrations, model processes, share learning experiences, guide discussion, or display independent work  This interactive approach to learning will make the content seem more realistic to students.  What are the benefits and drawbacks of integrating technology into instruction? The benefits of technology include enabling students to become more active in the learning, feeling more motivated to participate and engage in communication and discussion with both peers and teachers. The versatility offered by technology helps students visualize and comprehend mathematics, while their teachers gain deep insights into student cognition and share their share their professional growth with a web-connected community (NCSM, 2015). The drawbacks of technology stems from monetary investment from school or political parties as well as professional training of teachers. When investments underfunded or the inappropriate systems are selected, students may not get the full benefit and their math identity will be stifled. Even when both the hardware devices and software are well-chosen, teachers must receive the correct technological training to ensure they are maximizing student

engagement rather than t becoming a computer proctors who are disengaged from their role in helping students to learn and grow  Integrating technology enables students to become more active in the learning process. When a student feels that he or she is more vested in actual learning, retention of the material tends to rise significantly  Research has shown that whiteboards have a positive impact on student motivation and engagement  Encourage students to compare and contrast similarities and differences. Then suggest that they reach their own conclusions and make any correlations that they find between the varying displays of data. The Internet can also be a ready source of graphs that contain different data sets.  Active participation by all students is encouraged and helps students think about the complexities of each different type of triangle.  Ball (2003) states that the whiteboard is bringing about changes in traditional teacher- pupil discourse. Communication and discussion among the fellow students also occurs naturally as many students begin to feel more comfortable with one another in this kind of learning environment.  There are, of course, other issues: The school must pay the start-up cost of the technology, and teachers must learn how to prepare materials and be willing to take some risks (Miller 2003)  On one hand, technology can help students visualize and comprehend mathematics, while their teachers gain deep insights into student cognition and share their professional growth with a web-connected community. On the other hand, technology can water down mathematics into competitive, drill and practice games for students, while relegating teachers to the role of computer proctors who are disengaged from their role in helping students to learn and grow. even when both the hardware devices and software are well-chosen, there is inadequate allocation of instructional technology staffing for successful implementation.  Some teachers find it difficult to successfully operate software and/or hardware when using technology to teach mathematics  Many interactive whiteboards and computer labs are underutilized in mathematics education because the professional staff, teachers and administrators are unprepared to take full advantage of these valuable resources.  Describe the teacher and student roles when technology is implemented.

Once technology is implemented, teachers must understand that their primary role is to be the key aspect of student interactivity. Teachers must ensure they develop the skills necessary to utilize their technology, feel comfortable with this technology, and fully understand the interactive features and capabilities that these new technologies can bring to the classroom. Through this, teachers can be agents of change in positively affecting students’ math identity. Students, on the other hand, role includes being open and willing to connect with technology to maximize their agency. Through a discovery approach, students must continue to ask questions and provide answers, shifting the primary learning away from the teacher, thereby allowing the teacher to facilitate the lesson and drive the content through more pedagogical practice and blended learning.  a teacher can manipulate shapes and words to represent objects in real time. Lessons using the whiteboard can reach students who exhibit all learning styles, but lessons seem particularly effective for those who learn best using visualization and spatial reasoning.  students are now able to both ask questions and provide answers, thereby shifting some of the learning away from the teacher. This discovery approach allows each student to feel more connected and in tune with the learning.  The skill of the teacher continues to be a key aspect of classroom interactivity ( Jones 2004). It will take time for the teacher to develop the skills, feel comfortable, and fully realize all the interactive features and capabilities that these new technologies can bring to the classroom. Teachers are the agents for this change in implementing much of these technologies into their subject matter and determining the quality of use (Armstrong et al. 2005). increase student agency, with a greater emphasis on student-centric learning environments and peer-to-peer collaborations as students matriculate from pre-kindergarten through grade In what ways do UDL strategies enhance our ability to support and affirm student development as achievers? Universal Design for Learning strategies enhance the ability to support and affirm student development as achieves through providing opportunities for how to engage students in their learning, how content is presented, and how students respond and demonstrate their understanding, The UDL framework is based in brain research and builds its principles on three learning networks: the affective network (means of engagement), the recognition network (means of representation), and the strategic network (mean of action and expression). Through providing multiple means of engagement, and action and expression, UDL strategy implementation allows students to develop into achievers who can assess their own learning needs, monitor their own progress, and regulate and sustain their own interest in the content. Furthermore, this allows students the opportunity to maximize their mathematic agency and identity. Curriculums that apply UDL strategies execute this through defining appropriate goals, assessing student’s varied needs, and assessing learning barriers. In defining goals, teachers must ensure goals allow student multiple means to demonstrate their understanding rather than a singular expected outcome.

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appropriate goals, assessing student’s varied needs, and considering learning barriers. In defining goals, teachers must ensure goals allow student multiple means to demonstrate their understanding rather than a singular expected outcome. In the Universal Design for Learning in Mathematics presentation, this is illustrated in the math problem on fractions presented by Ms. Flahive and Ms. Ramirez. Ms. Flahive stopped the class and directed all student to draw boxes to divide the fraction, whereas Ms. Ramirez asks the student to write what they know and initiate discussion on what strategy they are familiar with to approach the problem. In assessing student’s varied needs, teachers must identify the strengths, needs, and interests of individual students across the three learning network. This includes evaluating a student’s cultural background, learning and communication styles, and identity. In considering learning barriers, teachers must evaluate the curriculum to ensure students from diverse learning backgrounds, such as those EL students and those with math anxiety, are understanding the delivered content and adjustments are made to content knowledge to ensure students remain engaged. UDL strategies ultimately provide flexible learning options to customize the learning approach to each student, allowing for greater engagement, higher student achievement, and continuous motivation. 1. What do you see as the benefits of this approach to teaching mathematics? The benefits of teaching math across the curriculum include not only increased understanding in basic concepts and ability to reason and solve problems, but also provide better insight into connecting math in student’s everyday life. Rather than focus on mathematics as an isolated content which has a singular solution, math that allows for multifaceted student driven solution approach stimulates a growth mindset. In turn, students achieve higher success in both education and their careers. Furthermore, this growth mindset perpetuates students’ inquisitiveness in the world around and shapes their comprehension of how they fit into society’s structure as well as the social policies and issues that shape society. First, the not-so-subtle message is that math is basically irrelevant except for achieving success in future math classes, becoming a scientist or mathematician, or making commercial transactions. Second, students learn that math is not connected to social reality in any substantive way. Thus students approach math in the abstract and never are encouraged to seriously consider the social and ethical consequences of how math is sometimes used in society. Third, if students are not taught how math can be applied in their lives, they are robbed of an important tool to help them fully participate in society. my students’ interest and skill in math have increased, both in terms of their understanding of basic concepts and their ability to solve problems. Furthermore, they can better clarify social issues, understand the structures of society, and offer options for better social policies. Kids need every tool they can (Peterson)

Students should not just be memorizing past methods; they need to engage, do, act, perform, and problem solve, for if they don’t use mathematics as they learn it, they will find it very difficult to do so in other situations, including examinations (Penguin, 29) 2. How does your current practice of teaching math or integrating math into your content area compare with ideas outlined in the articles? I teach social studies to K-2 with topics ranging from the first Thanksgiving to George Washington and the American Revolution to dissecting maps and landforms. While many of Scholastics magazines I use to guide my lesson plan topic reference both Social Studies and Language standards, I try to incorporate mathematics whenever possible. As we study historical events, students pay particular attention to dates and data. When prompting the students after a video or reading, students are asked to compare their lives to today, thinking about the value of good of wages of workers as to fully immerse themselves in that time period. Learning about maps and landforms, students examine scales and determine heights or locations through mathematics. I have seen a markedly different engagement and more questions in lessons in which these activities are practices, so much so that I have had student’s parents commend me for their child’s continued interest at home. comprehension of how they fit into society’s structure as well as the social policies and issues that shape society. As we study history, we pay particular attention to dates and data. I try to highlight numbers that relate to social movements for equity and justice development of math literacy advances students' abilities to analyze, explain and reason—skills that support learning in all subjects. When teachers make cross- curricular connections between math and other content areas, they help demonstrate for students the relevance of math to their everyday lives (Jenkins and Ms. Neyda Fernadez-Evans, 2008) , Provide a 2-3 sentence description for EACH of the 8 standards that captures their role in creating a collaborative, engaging learning environment or support student mathematical thinking.

 Select TWO standards and complete the following tasks: o Find your grade-level on the list. o Read the description of the standard for your grade-level and view the associated clip o Discuss some of the instructional practices employed by the featured math teacher that would reinforce the skills and habits of mind required of the practice standards. 1. Make sense of problems & persevere in solving them – Students must understand a problem, use their knowledge in applying several ways to solve it, and ensure the finished work makes sense. Students focus on the process of solving the problem rather than getting the correct answer. 2. Reason abstractly & quantitatively – Students must display abstract thinking through their ability to decontextualize and contextualize. Using symbols and other representations, students apply multiple ways to solve problems rather than apply one algorithm. 3. Construct viable arguments & critique the reasoning of others – Student must be able to think through the steps to solving problems and be able to defend their position. By using reason to support or object to other’s work, student can develop communication skills to explain their math thinking. 4. Model with mathematics – Students must use what they know to solve problems in everyday life. Students use various mathematical methods to simply complex problems and identify important quantities for relationships. Upon drawing conclusions from relationships, student must reflect on results to ensure they make sense. 5. Use appropriate tools strategically – Students must know how to choose and use the right tools to solve a math problems. By recognizing the strengths and weakness of each tool, students can pose and solve problems as well as detect possible errors, thus deepening their understanding of mathematics. 6. Attend to precision – Students must communicate precisely to others, using mathematical definitions to explain their reasoning. Calculating accurately and efficiently, Student must understand the meaning of symbols and label quantities appropriately. 7. Look for & make use of structure – Students must identify patterns and structure in mathematics to identify new problems. Through repeated reasoning, students can solve more complicated problems using tools to break problems into separate parts. 8. Look for & express regularity in repeated reasoning – Students must use reasoning from the solution to one problem and relay that problem-solving technique to other problems. Through identifying repeated calculations and looking for generalizations and shortcuts, students must understand the broader application of patterns and see the structure in similar situations. In choosing to study assessments “look for and make use of structure” and “construct viable arguments & critique the reasoning of others,” I watched the video on Liz O’Neill’s First

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Grade math class on composing and decomposing numbers using base ten. While I teacher social studies to K-2 presently, I have experience incorporating some of the same related lessons last year as a second grade homeroom teacher. In looking for and making use of structure, Ms. O’Neill presents the challenge of calculating a target number of 34 through multiple methods. Ms. O’Neill expects students to explain the overall structure of the problem and the math methodology used to solve the problem. O’Neill calls on individual students at random not only to check for understanding, but also to see their induvial method of solving the problem and ensure they are able to explain their solution. Ms. O’Neill draw out each student’s method of solution on the board to show visual representation of the student’s proposed solution. Through this, Ms. O’Neill encourages students to look at something they recognize and have students apply the information in deconstructing the problem into smaller parts. Ms. O’Neill also provided another challenge I which students must rename he target number of 23 as many ways as possible. Before beginning the exercise, Ms. O’Neill ensure the class is already familiar with ten blocks as they are now going to build on this prior knowledge. After quickly showing a problem with 3 ten frames, students collaborate with a partner to support or reject each other’s findings. Like prior, Ms. O’Neill calls on each student to find out the method used to solve the problem. She displays each method in a sentence structure to incorporate language in the curriculum as well as visually show the structure of each methods used. For example, she shows the methods that include achieving 23 through counting by 2 blocks, 5 blocks, and 10 blocks. In constructing viable arguments & critique the reasoning of others, Ms. O’Neill uses a numbers game activity called “How Many are Hiding?” where students have 10 cubes and a paper plate, in which some of the cubes are “hidden” under the plate. Students work in pairs and one partner takes some of the cubes and "hides" them under the plate. The remaining are placed on the top. The second partner uses sentence frames to answer the questions "What number do you see?", "How many are hiding?", "How do you know __ are hiding"? By using sentence framing posted on the board, students can visually see the justification of their solving strategies and produce mathematic language to convince their partners. This encourages students to use proven mathematical understanding and ask questions which require student to justify their solution and their solution pathway. By pairing off into groups, Ms. O’Neill can ask students to compare and contrast various solution methods with other students but also readily identify students’ understanding. When reviewing both these standards practiced in Ms. O’Neil’s lesson, I noticed her reinforcement of skills by first establishing a baseline fore recall and building on previous knowledge. She continuously checked for understanding, both as a group and individually. When doing so, she not only asked the students if they understood, but if they could explain their understanding and how they arrived at their solution. To reinforce a broader understanding of multiple solution pathways, Ms. O’Neill incorporated partnering and sharing of solutions. This practice helped children develop communication but also reflect on their own work. Ms. O’Neill regularly spelled out each solution in both sentence framing and visual al diagrams and other manipulatives to differentiate the learning.

 Describe the math content standards that the task addresses (not the SMPs).  Describe 2-3 ways the task could support your content area.  What might students find challenging and how could you help them? K-2 Social Studies Will our U.S. flag change yet again? https://www.yummymath.com/2021/will-our-u-s-flag-change-again/

The lesson selected for this assignment, “Will our U.S. flag change yet again?” was categorized for social studies by YummyMath for grade 3 and 4 standards, specifically NJ Common Core Standards 3.OA and 4.OA. The applicable specific standards in 3.OA. include “representing and solving problems involving multiplication and division” as well “understanding properties of multiplication and the relationship between multiplication and division.” This means students must be able to understand that whole numbers can be interpreted as a certain number of objects partitioned into equal shares. In this case regarding the stars of the flag, students would have to identify that 50 starts are 5 X 10 = 50 or 50 = 5 X 10. The applicable standard in 4.OA. include “using the four operations with whole numbers to solve problems” and “gaining familiarity with factors and multiples.” This means students must be able to interpret multiplication equations as a comparison, solve word problems involving multiplication comparisons, and solving word problems using the four operations. Separately, students must determine whether a given whole is a multiple of a given one-digit number. Being that I teach K-2 Social Studies, the multiplication and division demands of 3.OA. and operations and familiarity with factors and multiples required of 4.OA. would be difficult for even my 2nd graders to achieve. For the purpose of this assignment, I will adjust this lesson to apply to NCCS 2.OA and 1.NBT. The CCSS 2.OA. refers “representing and solving problems involving addition and subtraction”, “adding and subtracting within 20”, and ”working with equal groups of objects to gain foundations for multiplication.” These operations and algebraic thinking standards are very similar to those practiced in the video of Liz O’Neill’s First Grade math class on composing and decomposing numbers using base ten. Similarly, to how Ms. O’Neill established a baseline before building on known knowledge, this task provides the “Betsy Ross” US flag used from 1777-1790 as it presents a simple number to grasp before as about the modern day flag with 50 stars. To apply the task to 3.OA., student would be required to compare and contrast the number of stars on different flags and explain how they arrived at that number. The CCSS 1.NBT. refers to “extending the counting sequence”, “understanding place value”, and “using place value understanding and properties of operations to add and subtract.” To apply this standard, students would show that they can readily count the stars in any of the US flags version, represented 50 stars by tens, fives, and ones, and draw out an operation using place value blocks. These math content standards could support my content by providing the concept that individual states make up the whole of the country. Paired with a map to show how the country grew and its coordinating state flag at that time would also introduce the concept of marts of a whole and set students up for multiplication and division requirements introduced in 3 rd and 4 th grade.

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Students may find it challenging to translate the number of stars into an equation. I would help them by referring back to the place value blocks and visually showing them by writing out the blocks, or stars in this case, and how they can write the operations into an equation. Similar to Ms. O’Neill’s video, I think it would be extremely beneficial to break the class up into pairs or groups and provide different flag versions to contrast to today’s flag so they can discuss their solutions with each other. Requiring students to explain out their solution as I visually display it on the whiteboard could help students visualize the problem. In using the attached worksheet for this U.S flag task, 1. Draft a description of a classroom (not a lesson) where connections to mathematics are integrated and the teacher’s lessons are scaffolded to meet the specific needs of English Language Learners and Students with Disabilities with research-based instructional strategies. Imagine you are an administrator walking into classrooms in your building, what would you be looking for in a classroom that integrates mathematics. Be sure to include concepts learned from each module. (Your description should not exceed 1 page and must be submitted as TEXT or as a MS Word document.)

Math Response 12

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