I. Brief Background & Reason for Project
As inclusive classrooms are becoming the norm, differentiation is key in order to meet all students’ needs. In short, “Differentiated instruction is a philosophy or approach to planning and teaching based on the premise that teachers must consider who they are teaching as well as what they are teaching” (Boyle and Provost, 2012, p. 116). Additionally, as told by Gambrell and Morrow (2015), “[differentiation] is an approach to teaching that includes active planning for student differences” (p. 9). Classrooms, especially in an alternative high school setting, have a wide range of student learning abilities. Special education students are fully integrated into most classrooms and teachers need to adjust instruction. Teachers must accommodate the needs of each and every student and create the least restrictive environment for learning.
When differentiating, “[teachers] are meeting the individual needs of their students without diminishing expectations or sacrificing curricular rigor” (Gambrell & Morrow, 2015, p. 9). Successfully implementing differentiated instruction can be difficult and time consuming. According to Tomlinson (1999) “To make differentiation work—in fact, to make teaching and learning work—teachers must develop an alternative approach to instructional planning” (p. 116). In other words, one assignment is not always going to work for each student. A teacher must manipulate that assignment or activity for the different learners in the classroom. The manipulation of a lesson can occur at different levels. For example the assessment could be adjusted, as well as adjusting how students gain access to a body of knowledge (Tomlinson, 1999).
Spending the past four years as an alternative high school math teacher, I have noticed students lack drive and perseverance in mathematics and specifically in story problems. My goal is to be able to assess my student by understanding her current learning level and to help her understand and deepen her knowledge on specific learning objectives. My ultimate goal as a teacher is to use differentiated instruction to meet their learning needs and help them see the value of mathematics in their daily lives. I believe by focusing on deepening my student’s knowledge of one objective, she could open her mind to the possibility of doing the same in all classrooms. I believe that by focusing on expanding her depth of the topic, I am furthering my goal to help impact students’ view of mathematics used in their everyday lives. I hope to continue to use these skills and strategies in the future as a math literacy teacher.
II. Home and Family
The student I chose for my Literacy Learners Analysis, Vanessa, is a 16 year old female that is currently in 10th grade. She moved to Hartland from the Jackson area in December, but she lived in Hartland prior to her time in Jackson with her biological father. She became a student at LEGACY Alternative High School and was declared homeless prior to her enrollment. She lives in a small apartment with a foster mom and her two sons, but she refers to them as her mom and brothers. Vanessa’s biological mom and sister are not in the picture, but she has talked to me about them in the past. While LEGACY’s population is 96% Caucasian, she identifies as Mexican, Italian, Native American and African-American. Although she does know how to speak a bit of Spanish and frequently listens to Spanish music, English has always been spoken at home. She is very outgoing, bubbly and open, but she does have some days where she appears sad or distraught. I remember one day in particular, she came to school crying. I asked Vanessa about the incident the next day and she told me it was because of Child Protective Services. Despite challenges she has faced in her life, she is motivated to do well in school and hopes to attend Michigan State University, her dream school.
When I asked Vanessa about her reading habits, she told me she usually reads around 1 book a year. When she took the SRI assessment in April, she scored a 970, which puts her just below the 9th grade reading level. She is motivated to read assignments and work because she is driven to earn better grades than she has in the past. Vanessa works hard to keep her grades at As and Bs. There are no structured routines at home for reading and writing, but she did tell me her family has made it a goal to read more. Our school does not assign homework, so she does not work on assignments at home. Vanessa’s biggest struggle with reading is trying to comprehend what the passage means, especially with science or math. In both of her math classes, I notice the student struggles to comprehend our daily learning objectives, so I spend a lot of time sitting next to her to help her complete class assignments. At home, she primarily reads messages on her phone through texting and social media, but if she was to read a book it would focus more on mythology or romance. She also gets discouraged from reading when story lines do not progress the way she wants. She recently read 13 Reasons Why after watching the TV series on Netflix and told me she was frustrated that the book did not have certain aspects from the TV series, causing her to get frustrated and stop reading the book.
III. Emotional Climate
The biggest component to my school is a caring environment. Every day, the entire staff of 4 teachers, 1 principal, 1 counselor, and 1 social worker greets students as they walk in with smiles and friendly faces. We have the opportunity of having one-on-one conversations with students on a daily basis because of our small class sizes and alternative atmosphere. All of our students have come to our school because at one time in their lives they struggled behaviorally, socially, or academically.
Every day, I give class notes with definitions, step by step instructions, and example problems. I go over the notes with students to help them learn the weekly objective. My notes are interactive between me and my students. I actively have them volunteer to write on the board, give answers, or explain a solution in their own words. Since this is an alternative setting with many at-risk students, participating in class is a huge step for many of them. Going up to the board or giving an answer out loud is not something that most of my students are comfortable with, but overtime, they grow to see our school is a very accepting and encouraging community. Often times, when I give students story problems, they shut down and stop trying. They struggle to comprehend what the question is asking and they lack perseverance when doing assignments that involve multiple story problems.
Vanessa excels in the alternative setting. Since arriving in December she has emerged from her shell. She typically does not hesitate to answer a question, especially if she feels confident about her response. As Vanessa has one of the highest reading levels in the school, she has more confidence to read aloud and participate in literacy activities than other students. Unfortunately, if the work is above her level and she cannot easily figure out the solution, Vanessa becomes extremely outspoken and disruptive. There have been times where she has been removed from classroom for disrespect and profane language. Other times, Vanessa has shut down in the classroom. Typically, this does not happen over frustration with schoolwork, but with personal issues at home or confrontations at school. For example, she had a huge slip in grades at the end of last quarter. She was coming to school and not talking, wearing a baseball cap low over her head, and seemed to be not well groomed. I later discovered that her change in mood and attitude was due to CPS intervening at home. Furthermore, as Vanessa is one of the only ethnically diverse students, she has been occasionally teased and bullied. These types of instances create frustration and disinterest in her school work as she tries to manage all of her emotions.
My goal as the math teacher is to help show students that math is used in everyday life. The budgeting project I did with my financial mathematics class grabbed their interest, because they knew being able to budget was an essential skill they needed to use in life. Reading is not specifically rewarded at our school, but I do have incentives to complete assignments, behave properly, and work hard. I give students “Nash-Cash” at the end of the class period when I notice them go above and beyond my expectations. At the end of the week, I draw a name and that student gets lunch on me. So although this is not directly correlated to literacy, in order to complete the assignments students must use their notes and follow the directions outlined for them.
Vanessa is a very competitive individual. She is one of the few female students to participate in the intermural sports teams at school. Nash-Cash does not always motivate every student to try daily, but Vanessa is determined to win herself Chinese take-out for Friday lunch. Vanessa has won the weekly prize three times since her arrival. For the most part, Vanessa thrives when positive feedback and positive encouragement is given. She likes the individual attention and really aims to please me and the other teachers. With constant encouragement and compassion from all the teachers, Vanessa has many more good days than bad.
IV. Literacy History
Vanessa spent the majority of her childhood moving from one city to the other. When I asked her about her literacy history, she told me her family does not focus on reading as much as she would like them to. With her past family struggles of alcoholism and moving in and out of homes between her foster parents and her biological parents, Vanessa has struggled academically. I have seen huge improvements in her schoolwork over the course of this year, and I know she plans to continue to strive for As and Bs. In the past, she did not push herself academically and struggled to pass her classes in the traditional classroom setting. Literacy was never a major focus in her home, there were no reading norms set, she rarely witnessed her family members read for pleasure, and her family never encouraged her to read.
Throughout Vanessa’s schooling, she remembers feeling discouraged academically. She used to find herself distracted by things going on at home instead of being able to focus on her schoolwork. This is something she still has problems with today. Vanessa told me that she lacked confidence in science and mathematics, but she felt stronger in her reading and writing skills. She couldn’t remember specific strategies used when she was in elementary and middle school, but she does remember a large emphasis on March’s Reading Month and “Stop, Drop and Read.” This was designated time in elementary school when teachers had students read for 20 to 30 minutes daily. She remembers finding herself distracted and unable to focus on her book for the entire time period. Vanessa is currently taking English 10 and Reading. In Reading, Vanessa logs her reading journal weekly and gets the opportunity to reflect on what she read. Students get to choose any book they would like. The English teacher even asks them what book she can purchase for them. I think that the emphasis on being able to choose your own book, helps students learn how to love to read. I know in English 10, she has had a lot of experience doing different activities including writing a reflection paper, reading shorter passages, discussing news articles and writing poetry. In her science and mathematics classes she has had the opportunity to read and analyze. Our main focus as a school is to improve our students score on the ACT Workkeys test, so much of the reading is focused on preparing students for careers and being able to read information and analyze how to apply it to a situation.
V. Assessments Given and Summary of Test Results
When I was choosing the pre and post-tests, I wanted the tasks to be complex and engaging for the student. I knew I wanted to focus on real-life math examples and reading context in order to solve a problem. I remember completing a task in a teaching course at MSU my senior year, that was complex and engaging while having real-life applications. Before then, I never used that type of thinking process in the classroom. Students were given the challenge of estimating how many bars, community parks and movie theaters were in a very specific area of Los Angeles. They were given structured tasks in order to have reasoning and logic when solving the problem. I wanted my students to have to think more deeply and critically as well, but if the assignment was not structured and scaffolded correctly, my students, including Vanessa, would lack the motivation and confidence to complete the task on their own. I found tasks produced by Mathematics Assessment Resource Service that structured in an engaging way that included real-life problems and situations. The students would have to read and understand a scenario and solve a problem using logic and reasoning skills. My objective was for my student to be able to read and apply the given information in order to solve a problem, in this case, involving volume.
The pre-test was titled “Estimating Volume: the Money Munchers.” In this task, Vanessa was given a specific situation. The mom in the story problem kept $24,400 in dollar bills under her mattress. She was planning on moving the money to the bank because she did not want bed bugs to eat her cash. The goal of the assignment is to determine how far the mattress will lower after the money is removed from under the bed. When Vanessa reasoned through this task, I noticed she had some really good questions, such as, “How big is a dollar? How big is her mattress?” However, she also asked questions that were irrelevant or that she was already given. I noticed Vanessa lacked attention to detail, she told me we need to know what kind of bills she has under her bed. I told her to re-read the problem, but even after re-reading she missed the detail that it was all $1 bills. Vanessa was also concerned about the box spring and other parts of the bed, but I had to help redirect her since we did not need to know that type of information for this problem. I found that she lacked confidence to do the calculations, although she could set up how the problem needed to be solved. To complete this assignment, Vanessa needed small group/one on one attention. After allowing Vanessa to brainstorm with another student, I had to intervene to help their thought process. At this point, Vanessa concluded that the dollars all needed to be in even stacks under the bed in order for the mattress to lay flat, but did not understand what math equation would need to be involved. I had to question Vanessa to lead her in the right direction. I had to ask questions such as “What math term would we use to describe the space that the dollar bills are taking up?” and “What type of dimensions do we have to work with?”. At first, Vanessa was stuck on the idea of the calculation being for area, but upon realizing that we had dimensions for length, width, and height, she was able to realize that volume was what we were looking for. Once Vanessa, had the estimated dimensions and the equation for volume, she was able to plug the numbers correctly and solve the problem. Her calculations were correct and she was able to successfully complete the assignment. The pre-test really helped me understand her lack of focus and attention to detail. The pre-test also made me realize I needed additional scaffolding in my lessons to support her and help build her confidence in solving problems that involved multiple steps.
When looking for a post-test, I wanted to keep the mathematics topic constant, while still involving my goal of reading and applying context given the situation. The post-test task was titled, “Fearless Frames.” In this task, students were expected to find out how to maximize a containers volume, with only 60 meters of suitable metal tubing to create a rectangular prism and triangular prism. Although I felt the story was less engaging than the pre-test, I found it was just as applicable to real life and Vanessa understood the relevance of the problem. She asked me questions that were more focused on the task, and more on track than in the pre-assessment. When solving for the rectangular prism, she remembered what was learned in the second lesson and knew in order to maximize tubing the three numbers needed to be as close to each other as possible. Vanessa successfully calculated and solved the first portion of this assignment on her own. She seemed very comfortable working with the dimensions of a rectangular prism. The next portion of the post-test required the students to solve using the same information but now creating a triangular prism. Vanessa became frustrated when she did not know the prism formula and needed my assistance. I had to once again provide Vanessa with questions that would lead her to determine the formula that she would need. Once Vanessa knew the prism formula, she tested different numbers to find the patterns that helped maximize her volume. Vanessa is great at solving math problems if all the information is given directly, but she really needs support if any of the formulas or information needs to be concluded from text or past lessons. I did noticed her confidence improved over the course of the two lessons and she was able to complete the post-test with less assistance.
When giving Vanessa the tests, I was most impressed to see that she had good thought processes and reasoning in both the assessments. I noticed this had a lot to do with her ability to read and engage in the problem, although at times she skipped over a few details. I think that by helping her over the course of the assessments and lessons, she became more confident in her questioning and reasoning, which made her less dependent on me in the post-test.
VI. Lesson Plan Matrix
Lesson #1
Lesson Foci/Date
Objectives (include including performance, conditions, and criterion. State the Common Core State Standard (or standards used in your discipline) at the end of each objective.)
Instructional materials (what will use to deliver the main objectives of the lesson)
On-going assessment (to measure attainment of objectives)
This lesson helped the student interpret results from the pre-test by focusing on samples of student work and comparing it to how she solved the pre-test.
June 7, 2017
The student will be able to read and interpret student work and use strategies from their reasoning to solve problems.
CCSS: Craft and Structure: 4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone
CCSS: Math Practice 3. Construct viable arguments and critique the work of others.
CCSS: 7.G. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
The teacher will give the student copies of sample work from multiple students (provided from the Money Munchers pre-test resource). The student will also look back at the pre-test results and assess themselves on their performance, now that they have gotten the chance to look at other student work. I will also discuss the answers the student writes and question them and guide them when they are finding themselves lost or confused on a given situation.
By watching the student assess themselves on the original assessment you can identify if the student has learned where she could have done more to accomplish the task and where she was strong.
Lesson #2
Lesson Foci/Date
Objectives (include including performance, conditions, and criterion. State the Common Core State Standard (or standards used in your discipline) at the end of each objective.)
Instructional materials (what will use to deliver the main objectives of the lesson)
On-going assessment (to measure attainment of objectives)
This lesson focuses on a real-life situation involving luggage and the dimensions to maximize a suitcase. Students will be expected to read and utilize information given to solve a problem, they will also work backwards in finding specific side lengths given the volume of the suitcase.
June 8, 2017
The students will be able to read and work through a real-life story problem. They will also be able to work backwards from volume to find the missing dimension of an object.
CCSS: Craft and Structure: 4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone
CCSS: Math Practice 3. Construct viable arguments and critique the work of others.
CCSS: 7.G. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
The student will be given the assignment to complete independently at first. After she has answered the first questions, I will ask her what she thinks about creating the biggest shape. I will help her visualize different rectangular prisms by drawing the shapes and stretching them, using online tools if necessary (fixing the volume and stretching the height to see how the shape changes). Discussion will help the student
After the main task is completed, the student will be given the situation in reverse. This will help me assess her understanding of how the problem was originally done and if that had any effect on solving it the opposite way.
VII. Reflections on Your Literacy Lesson Plans
When giving Vanessa the literacy tasks she came up with tons of great ideas, but struggled to complete the task without my assistance. On the pre-test she lacked drive, and she struggled focusing on the end goal even though it was clearly provided in each task. In the Article, Student Motivation – an overlooked piece of School Reform, the authors state, “Motivation can affect how students approach school in general, how they relate to teachers, how much time and effort they devote to their studies, how much support they seek when they’re struggling, how they perform on tests, and many other aspects of education” (“Student Motivation – an overlooked piece of School Reform”, 2012, p. 2). Teaching in the alternative high school setting, I found this statement to be extremely true. I have been extremely fortunate to teach at a school where we can help work to encourage and push students that lack motivation. With a smaller classroom setting, more one-on-one interactions and by grouping students based on learning styles, we have noticed improvements in motivation at our school (“Student Motivation – an overlooked piece of School Reform”, 2012, p. 6). Vanessa shared with me that mathematics was something she had always struggled with, so her lack of drive comes from a place of insecurity to complete tasks correctly. This has directly effected her motivation and could be one reason why she ended up at our alterative high school. I also noticed that in the pre-test, she would write and explain good ideas verbally, but lacked the confidence to do the task without my support for the majority of the time. She told me she liked that the tasks were a bit more challenging and made her thinking about the “why?” but she didn’t feel that it was relevant or interesting, although this was one of the few times I saw her fully engage in a math task. Student interest is also critical when thinking about ways to motivate the student (“Student Motivation – an overlooked piece of School Reform”, 2012, p. 2). I assisted Vanessa by discussing thoughts about the task with a classmate and myself during the entire pre-test. My choosing to give her peer-to-peer support and one-on-one teacher support I believe she became more confident in her abilities and found herself being able to take away key concepts from the Pre-test. In the first question, Vanessa had to figure out how to find the solution and in the second question she had to utilized strategies from the first problem and got a solution that accurately represented the situation. Since she was able to apply knowledge from the first question, this shows Vanessa learned how to utilize the information in the story problem. I also learned that although I thought the task was relevant and interesting, she did not see the relevance it had in her life and was not interested in it like I expected her to be. If I were to do this task again, I would come up with it in a different way in order to make it more fun and interesting to the students. However, I think that by noticing her disinterest in the task early on, I was able to review my lessons and post test in a new way and I tried to make them relevant to her.
During the first lesson, she enjoyed being able to reflect on the work she did during her pre-test. Before starting the worksheet, I told Vanessa it was important for her to think about the ways in which she solved the problem. We also went over her reasoning and starting thinking about how she accomplished the pre-test. I think this was beneficial to her in completing the lesson. She told me it made her feel more connected and confident to the previous task. Although I still provided peer support and helped differentiate the task by providing leading questions, I noticed Vanessa lacked precision to detail when reading other student responses, which was what the lesson focused on. She looked at examples of student work and compared and contrasted their work to what she did. She felt that she had a better understanding for the task and she seemed to start to understand what goes into solving a more complicated story problem that has multiple steps you have to think out. When answering questions about the student work, Vanessa was able to identify the good parts of other student’s work. Vanessa was also able to see if their estimates were reasonable by comparing her work to theirs. However, she struggled when she was asked if she could elaborate on ways to improve the other student’s solution. I believe that this was due to the fact that she struggled in comprehending the thoughts of the other “students”. If I taught this lesson again, I would make sure to work through the first example of student work with the class or individual students in order to help ignite some strategies of what to look for in the lesson.
During the second lesson, Vanessa struggled to apply what she learned in the first lesson and pre-test. This worksheet applied similar concepts, but did not have the same scenario or situation. She didn’t expect that going into the lesson. In the future, I would spend time summarizing the first lesson and explain to students that similar strategies could be used in other scenarios or story problems. I think this would have made Vanessa more prepared when attempting to solve the problem in the next lesson. Vanessa had to find the volume of a suitcase given the sum of the three dimensions was 45 inches. She had to find the maximum volume and work backwards to solve different equations involving volume. This was the same math topic that was covered in the first lesson and in the pre-test, but the story-problem questions were less complex. Vanessa understood how to complete the tasks and had more success with finding the solutions without my assistance. However, she struggled when she had to solve the problems backwards. I had to sit with her and help her recall formulas from previous knowledge and reminded her how to solve for a missing variable. I think this was truly the turning point in the lesson, because without my assistance she would have given up and not completed the task.
Finally in the post-test, I found Vanessa did not need my assistance when solving the problems for the task. She did not have trouble understanding what the task was asking, but she had trouble recalling the volume formula of a triangular prism from memory. This was a moment in the post-test that made her be completely independent in solving the problems given to her. Also, many of my students struggle with: recalling previous classroom learning objectives. In the future I would provide more strategies for students to be able to easily recall formulas, for example using songs to remember formulas, reviewing formulas on flashcards, using online games to engage students in to grow a deeper memory of the formula. Vanessa was able to complete the tasks in the given scenario correctly without much assistance from a partner or myself. Overall, she showed huge strides in her understanding of story problems and told me she felt the tasks were more relevant when she thought about the ways in which area and volume are used in her everyday life.
From when we started the assessments and lessons, to the time we finished, I noticed Vanessa look more at the key details in the story problems provided for her. I believe she had an easier time finding the information because of what she learned in our one-on-one discussion, as well as the discussion she had with her peer.
VIII. Recommendations to Teachers and Parents/Caregivers
Over the past week, I have been able to work with Vanessa on her math literacy skills, more specifically the way she understands and comprehends story problems in relation to volume, the most previous section we have covered in Geometry class. My goal of the lessons was for Vanessa to gain confidence in applying mathematical concepts into a specific scenario pertaining volume. When she worked with a peer, or when I helped her, I noticed Vanessa had confidence in her mathematical knowledge and had no problem reading or understanding the scenario. However when she worked alone, she tended to lack perseverance and motivation when completing her assignments and had trouble missing out on key details that would help her find the correct answer. I think that is due to the lack of connection she sees between every day activities and mathematics. I try to connect math into real-world examples daily in the classroom, but it would be beneficial for you to help her see the connections between mathematics and activities you do in the home, such as cooking, board games, or budgeting. In order for Vanessa to make deeper connections of math concepts, she will need to be able to see the value of math in every day life. This is shown in the NCTM article titled Making Mathematical Connections and I recommend you reading this in order to understand the importance of this topic.
Vanessa was never afraid to ask a question or advocate for herself when needing my assistance. Before completing the second lesson Vanessa had trouble remembering specific volume formulas. As soon as I reviewed them with her, solving the problems came easily to her. I think that if she had more practice solving volume problems, she would have been able to remember the formulas more easily. I also noticed she struggled when solving for a variable, I know that Vanessa has had tons of practice with this in Algebra but she struggled to remember how to accomplish this task. In order for her to recall formulas and strategies, she needs to practice math more. I know at times she struggled to complete assignments and I believe if she did complete all of her assignments, she would have remembered formulas and concepts.
At the beginning of next school year, I would love to review this task with Vanessa and see her growth in math literacy. I know that when she completes the assignments she was given and starts to relate math into her everyday life, we will see huge growth in Vanessa’s math confidence and literacy skills.
IX. Appendices of Work
Nash - Outline for Lesson Plan #1
Date: June 7, 2017
Objective(s) for today’s lesson: The student will be able to read and interpret student work and use strategies from their reasoning to solve problems.
CCSS addressed (use the ones in the LLA project folder):
CCSS: Craft and Structure: 4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone
CCSS: Math Practice 3. Construct viable arguments and critique the work of others.
CCSS: 7.G. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Rationale:
In life, students are expected to interpret situations around them and create an argument. I think that by giving them an engaging pre-assessment task that captures an example of how math is used in an argument, it helps show them the real-life application of math.
Materials & supplies needed:
-Pencil, Paper, Examples of Student work packet
Procedures and approximate time allocated for each event
• Introduction to the lesson
The purpose of this lesson is to help students reflect the pre-test by analyzing a set of example student responses. I will help students make connections by reviewing what they did in the pre-test and spending time analyzing how they solved the problem. I will also talk to them about real-life uses of volume and we will discuss ways they see volume in life. I will motivate them by helping them connect the task to real life situations. (10 minutes)
• OUTLINE of key events during the lesson
Students will be given student work packets and will work with the teacher and peers to help analyze student work. Students will first be given time to work on this independently, then with a peer and ending with the teacher. Teacher will help relate the student work to the results of the pre-test for the student. How was what you did similar to this? How was what you did different? Did you find any patterns that were the same? What did you notice to be a key theme of these problems? Students will understand they need to work together and that the expectation is to complete the packet and ask questions when necessary in order to solve the problems (based on classroom norms set). I will hand students material after the introduction is completed. (25 minutes)
• Closing summary for the lesson (How will I bring closure to the lesson and actively involve children in reflecting on their experiences? How will I help them make connections to prior lessons or prepare for future experiences? What kind of feedback do I want from them at this time?)
Students will be given a closing activity that asks them questions about the work they did on the pre-test and comparing it to student work. Students will be expected to complete the assignment by writing their thoughts about what they did. This will help them continue to make a connection between what they have done and what the example work helped them see. (15 minutes)
• Transition to next learning activity- Students will discuss how volume is used in every day life, what are other examples of story problems you have seen involving volume?
Academic, Social and Linguistic Support during each event
The student will be fully supported by the teacher, one-on-one support with guiding questions. The student will also work with another student on this task to help promote intellectual discussion and support.
Assessment
The student will look at her pre-assessment with her new critical eye from this lesson and describe in writing three things she struggled at originally with the task and at least one strategy she could use to solve the task more efficiently. I will look to see that she understands where she struggled and where she thrived. If I notice she is unable to properly assess herself, then I will help guide her and show her why she is strong in certain areas and help her see her weaknesses and learn from them.
Academic, Social, and Linguistic Support during assessment
Teacher will be available to student for any support when formulating thoughts she has gained from the lesson.
Nash – Outline for Lesson #2
Date: June 8, 2017
Objective(s) for today’s lesson:
The goal of this lesson is to understand how to solve problems using real life examples and applying math concepts. Students will be able to read a situation and use math to solve the problem, more specifically maximize volume and solve for the variable.
CCSS addressed (use the ones in the LLA project folder):
CCSS: Craft and Structure: 4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone
CCSS: Math Practice 3. Construct viable arguments and critique the work of others.
CCSS: 7.G. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Rationale (Explain why this content and/or skill is important and worthwhile, and how you will work to make it relevant to your students’ lives):
Students will see the value in this activity by relating it to a trip they might be planning for or may want to plan for in the future. By comparing volume to travel luggage, students will become invested because most students will eventually (if not already) experience airports and luggage restrictions.
Materials & supplies needed:
Pencil, Lesson #2 Worksheet, Calculator
Procedures and approximate time allocated for each event
• Introduction to the lesson
At the beginning of the lesson, students will look at all different types of luggage, different shapes and sizes. Students will understand the objective of maximizing volume by the visual representation given, and the learning objective will be written on the whiteboard in the front of the room. I will help students make connections by giving them examples in the warm up that will help them think about different sizes and what would maximize their dimensions, this directly relates to using math in the real world. I will motivate students by discussing their dream vacations or favorite vacation, I think this will help them want to solve the problem. (10 minutes)
• OUTLINE of key events during the lesson
After showing students different examples of suitcases, I will pass out the worksheet. I will then give then start to go over it with them. We will write down all the volume formulas before they start working on the assignment with peers. I will read through all questions with students to help them understand the questions being asked. I will give students time to work. After they complete #1-2, I will review their thoughts with them and their reasoning. Students will understand behavior expectations by the norms already set in my class. Students will have experience working with others and discussing math productively (25 minutes)
• Closing summary for the lesson
When students complete the worksheet, we will discuss issues and concerns they had. This will help me address their misconceptions, we will talk about why they got the answers they did and how they knew they were right. Students will understand how to check work to see if answers are correct, so this won’t be an issue. We will talk about why we believe a certain suitcase could fit more and why the dimensions are specific numbers. I will help them make connections by showing them how I utilized this when choosing a piece of luggage. I will review the concepts of volume at the end of the lesson and beginning of the lesson for students to understand the unit is focused on volume and this activity helps them think about it more deeply. I want to be able to give them feedback if their work has errors, or if they did it correctly. It is important for me as the teacher to look at the students work and check it when we are summarizing by discussing. (15 minutes)
• Transition to next learning activity- Summarizing the volume formulas and working backwards to continue the next lesson
Academic, Social and Linguistic Support during each event
The student will be fully supported by the teacher, one-on-one support with guiding questions as needed. The student will also work with another student on this task to help promote intellectual discussion and support.
Assessment
At the end of the lesson, I will give students a ticket out the door. I will give them a question directly relating to what was covered in class. This ticket will help me gauge their knowledge of working backwards (solving for the variable) in regard to volume. I will look for work shown, correct steps, and a good thinking process. I will use the results from this ticket to help guide my next lesson. If many students are confused by the concepts, I will re-teach the material to help them have a better understanding from a different point of view.
Academic, Social, and Linguistic Support during assessment
Teacher will be available to student for any support when formulating thoughts she has gained from the lesson.
X. References
Boyle J. R. & Provost M. C. (2012). Strategies for teaching students with disabilities in inclusive classrooms: A case method approach. Upper Saddle Creek, New Jersey: Pearson Education, Inc.
Gambrell, L. B. & Morrow, L. M. (2015). Best practices in literacy instruction (5th ed.). New York, NY: The Guilford Press.
Kohler, B. & Alibegovic, E. (2015). Assessing for learning. Mathematics Teaching in the Middle School, 20 (7), 424-433.
Tomlinson, C. A. (1999). Mapping a Route Toward Differentiated Instruction. Educational Leadership, 57(1), 12-16. http://blog.elanco.org/gsgsteacherresources/files/2015/01/Mapping-a-Route-Towards-Differentiated-Instruction-1synvr0.pdf
Mathematics Assessment Resource Service University of Nottingham & UC Berkeley. (2015). Estimating Volume: The Money Munchers. Mathematics Assessment Project Classroom Challenges A Formative Assessment Lesson. Retrieved May 26, 2017, from http://map.mathshell.org/download.php?fileid=1643
Mathematics Assessment Resource Service. (2011). Fearless Frames. Retrieved May 26, 2017, from http://map.mathshell.org/download.php?fileid=806
Valencia, S. (2011). Using assessment to improve teaching and learning. In S.J. Samuels & A.E. Farstrup (Eds.), What research has to say about reading instruction (4th ed.), (p. 379 - 405). Newark: DE: International Reading Association.
Student Motivation – an overlooked piece of School Reform (2012). 2140 Pennsylviania Avenue NW, Washington, DC: The George Washington University. Retrieved From: http://files.eric.ed.gov/fulltext/ED532666.pdf
Gojak, L. M. (2013). Making Mathematical Connections. NCTM Summing Up. Retrieved From: http://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Linda-M_-Gojak/Making-Mathematical-Connections/
As inclusive classrooms are becoming the norm, differentiation is key in order to meet all students’ needs. In short, “Differentiated instruction is a philosophy or approach to planning and teaching based on the premise that teachers must consider who they are teaching as well as what they are teaching” (Boyle and Provost, 2012, p. 116). Additionally, as told by Gambrell and Morrow (2015), “[differentiation] is an approach to teaching that includes active planning for student differences” (p. 9). Classrooms, especially in an alternative high school setting, have a wide range of student learning abilities. Special education students are fully integrated into most classrooms and teachers need to adjust instruction. Teachers must accommodate the needs of each and every student and create the least restrictive environment for learning.
When differentiating, “[teachers] are meeting the individual needs of their students without diminishing expectations or sacrificing curricular rigor” (Gambrell & Morrow, 2015, p. 9). Successfully implementing differentiated instruction can be difficult and time consuming. According to Tomlinson (1999) “To make differentiation work—in fact, to make teaching and learning work—teachers must develop an alternative approach to instructional planning” (p. 116). In other words, one assignment is not always going to work for each student. A teacher must manipulate that assignment or activity for the different learners in the classroom. The manipulation of a lesson can occur at different levels. For example the assessment could be adjusted, as well as adjusting how students gain access to a body of knowledge (Tomlinson, 1999).
Spending the past four years as an alternative high school math teacher, I have noticed students lack drive and perseverance in mathematics and specifically in story problems. My goal is to be able to assess my student by understanding her current learning level and to help her understand and deepen her knowledge on specific learning objectives. My ultimate goal as a teacher is to use differentiated instruction to meet their learning needs and help them see the value of mathematics in their daily lives. I believe by focusing on deepening my student’s knowledge of one objective, she could open her mind to the possibility of doing the same in all classrooms. I believe that by focusing on expanding her depth of the topic, I am furthering my goal to help impact students’ view of mathematics used in their everyday lives. I hope to continue to use these skills and strategies in the future as a math literacy teacher.
II. Home and Family
The student I chose for my Literacy Learners Analysis, Vanessa, is a 16 year old female that is currently in 10th grade. She moved to Hartland from the Jackson area in December, but she lived in Hartland prior to her time in Jackson with her biological father. She became a student at LEGACY Alternative High School and was declared homeless prior to her enrollment. She lives in a small apartment with a foster mom and her two sons, but she refers to them as her mom and brothers. Vanessa’s biological mom and sister are not in the picture, but she has talked to me about them in the past. While LEGACY’s population is 96% Caucasian, she identifies as Mexican, Italian, Native American and African-American. Although she does know how to speak a bit of Spanish and frequently listens to Spanish music, English has always been spoken at home. She is very outgoing, bubbly and open, but she does have some days where she appears sad or distraught. I remember one day in particular, she came to school crying. I asked Vanessa about the incident the next day and she told me it was because of Child Protective Services. Despite challenges she has faced in her life, she is motivated to do well in school and hopes to attend Michigan State University, her dream school.
When I asked Vanessa about her reading habits, she told me she usually reads around 1 book a year. When she took the SRI assessment in April, she scored a 970, which puts her just below the 9th grade reading level. She is motivated to read assignments and work because she is driven to earn better grades than she has in the past. Vanessa works hard to keep her grades at As and Bs. There are no structured routines at home for reading and writing, but she did tell me her family has made it a goal to read more. Our school does not assign homework, so she does not work on assignments at home. Vanessa’s biggest struggle with reading is trying to comprehend what the passage means, especially with science or math. In both of her math classes, I notice the student struggles to comprehend our daily learning objectives, so I spend a lot of time sitting next to her to help her complete class assignments. At home, she primarily reads messages on her phone through texting and social media, but if she was to read a book it would focus more on mythology or romance. She also gets discouraged from reading when story lines do not progress the way she wants. She recently read 13 Reasons Why after watching the TV series on Netflix and told me she was frustrated that the book did not have certain aspects from the TV series, causing her to get frustrated and stop reading the book.
III. Emotional Climate
The biggest component to my school is a caring environment. Every day, the entire staff of 4 teachers, 1 principal, 1 counselor, and 1 social worker greets students as they walk in with smiles and friendly faces. We have the opportunity of having one-on-one conversations with students on a daily basis because of our small class sizes and alternative atmosphere. All of our students have come to our school because at one time in their lives they struggled behaviorally, socially, or academically.
Every day, I give class notes with definitions, step by step instructions, and example problems. I go over the notes with students to help them learn the weekly objective. My notes are interactive between me and my students. I actively have them volunteer to write on the board, give answers, or explain a solution in their own words. Since this is an alternative setting with many at-risk students, participating in class is a huge step for many of them. Going up to the board or giving an answer out loud is not something that most of my students are comfortable with, but overtime, they grow to see our school is a very accepting and encouraging community. Often times, when I give students story problems, they shut down and stop trying. They struggle to comprehend what the question is asking and they lack perseverance when doing assignments that involve multiple story problems.
Vanessa excels in the alternative setting. Since arriving in December she has emerged from her shell. She typically does not hesitate to answer a question, especially if she feels confident about her response. As Vanessa has one of the highest reading levels in the school, she has more confidence to read aloud and participate in literacy activities than other students. Unfortunately, if the work is above her level and she cannot easily figure out the solution, Vanessa becomes extremely outspoken and disruptive. There have been times where she has been removed from classroom for disrespect and profane language. Other times, Vanessa has shut down in the classroom. Typically, this does not happen over frustration with schoolwork, but with personal issues at home or confrontations at school. For example, she had a huge slip in grades at the end of last quarter. She was coming to school and not talking, wearing a baseball cap low over her head, and seemed to be not well groomed. I later discovered that her change in mood and attitude was due to CPS intervening at home. Furthermore, as Vanessa is one of the only ethnically diverse students, she has been occasionally teased and bullied. These types of instances create frustration and disinterest in her school work as she tries to manage all of her emotions.
My goal as the math teacher is to help show students that math is used in everyday life. The budgeting project I did with my financial mathematics class grabbed their interest, because they knew being able to budget was an essential skill they needed to use in life. Reading is not specifically rewarded at our school, but I do have incentives to complete assignments, behave properly, and work hard. I give students “Nash-Cash” at the end of the class period when I notice them go above and beyond my expectations. At the end of the week, I draw a name and that student gets lunch on me. So although this is not directly correlated to literacy, in order to complete the assignments students must use their notes and follow the directions outlined for them.
Vanessa is a very competitive individual. She is one of the few female students to participate in the intermural sports teams at school. Nash-Cash does not always motivate every student to try daily, but Vanessa is determined to win herself Chinese take-out for Friday lunch. Vanessa has won the weekly prize three times since her arrival. For the most part, Vanessa thrives when positive feedback and positive encouragement is given. She likes the individual attention and really aims to please me and the other teachers. With constant encouragement and compassion from all the teachers, Vanessa has many more good days than bad.
IV. Literacy History
Vanessa spent the majority of her childhood moving from one city to the other. When I asked her about her literacy history, she told me her family does not focus on reading as much as she would like them to. With her past family struggles of alcoholism and moving in and out of homes between her foster parents and her biological parents, Vanessa has struggled academically. I have seen huge improvements in her schoolwork over the course of this year, and I know she plans to continue to strive for As and Bs. In the past, she did not push herself academically and struggled to pass her classes in the traditional classroom setting. Literacy was never a major focus in her home, there were no reading norms set, she rarely witnessed her family members read for pleasure, and her family never encouraged her to read.
Throughout Vanessa’s schooling, she remembers feeling discouraged academically. She used to find herself distracted by things going on at home instead of being able to focus on her schoolwork. This is something she still has problems with today. Vanessa told me that she lacked confidence in science and mathematics, but she felt stronger in her reading and writing skills. She couldn’t remember specific strategies used when she was in elementary and middle school, but she does remember a large emphasis on March’s Reading Month and “Stop, Drop and Read.” This was designated time in elementary school when teachers had students read for 20 to 30 minutes daily. She remembers finding herself distracted and unable to focus on her book for the entire time period. Vanessa is currently taking English 10 and Reading. In Reading, Vanessa logs her reading journal weekly and gets the opportunity to reflect on what she read. Students get to choose any book they would like. The English teacher even asks them what book she can purchase for them. I think that the emphasis on being able to choose your own book, helps students learn how to love to read. I know in English 10, she has had a lot of experience doing different activities including writing a reflection paper, reading shorter passages, discussing news articles and writing poetry. In her science and mathematics classes she has had the opportunity to read and analyze. Our main focus as a school is to improve our students score on the ACT Workkeys test, so much of the reading is focused on preparing students for careers and being able to read information and analyze how to apply it to a situation.
V. Assessments Given and Summary of Test Results
When I was choosing the pre and post-tests, I wanted the tasks to be complex and engaging for the student. I knew I wanted to focus on real-life math examples and reading context in order to solve a problem. I remember completing a task in a teaching course at MSU my senior year, that was complex and engaging while having real-life applications. Before then, I never used that type of thinking process in the classroom. Students were given the challenge of estimating how many bars, community parks and movie theaters were in a very specific area of Los Angeles. They were given structured tasks in order to have reasoning and logic when solving the problem. I wanted my students to have to think more deeply and critically as well, but if the assignment was not structured and scaffolded correctly, my students, including Vanessa, would lack the motivation and confidence to complete the task on their own. I found tasks produced by Mathematics Assessment Resource Service that structured in an engaging way that included real-life problems and situations. The students would have to read and understand a scenario and solve a problem using logic and reasoning skills. My objective was for my student to be able to read and apply the given information in order to solve a problem, in this case, involving volume.
The pre-test was titled “Estimating Volume: the Money Munchers.” In this task, Vanessa was given a specific situation. The mom in the story problem kept $24,400 in dollar bills under her mattress. She was planning on moving the money to the bank because she did not want bed bugs to eat her cash. The goal of the assignment is to determine how far the mattress will lower after the money is removed from under the bed. When Vanessa reasoned through this task, I noticed she had some really good questions, such as, “How big is a dollar? How big is her mattress?” However, she also asked questions that were irrelevant or that she was already given. I noticed Vanessa lacked attention to detail, she told me we need to know what kind of bills she has under her bed. I told her to re-read the problem, but even after re-reading she missed the detail that it was all $1 bills. Vanessa was also concerned about the box spring and other parts of the bed, but I had to help redirect her since we did not need to know that type of information for this problem. I found that she lacked confidence to do the calculations, although she could set up how the problem needed to be solved. To complete this assignment, Vanessa needed small group/one on one attention. After allowing Vanessa to brainstorm with another student, I had to intervene to help their thought process. At this point, Vanessa concluded that the dollars all needed to be in even stacks under the bed in order for the mattress to lay flat, but did not understand what math equation would need to be involved. I had to question Vanessa to lead her in the right direction. I had to ask questions such as “What math term would we use to describe the space that the dollar bills are taking up?” and “What type of dimensions do we have to work with?”. At first, Vanessa was stuck on the idea of the calculation being for area, but upon realizing that we had dimensions for length, width, and height, she was able to realize that volume was what we were looking for. Once Vanessa, had the estimated dimensions and the equation for volume, she was able to plug the numbers correctly and solve the problem. Her calculations were correct and she was able to successfully complete the assignment. The pre-test really helped me understand her lack of focus and attention to detail. The pre-test also made me realize I needed additional scaffolding in my lessons to support her and help build her confidence in solving problems that involved multiple steps.
When looking for a post-test, I wanted to keep the mathematics topic constant, while still involving my goal of reading and applying context given the situation. The post-test task was titled, “Fearless Frames.” In this task, students were expected to find out how to maximize a containers volume, with only 60 meters of suitable metal tubing to create a rectangular prism and triangular prism. Although I felt the story was less engaging than the pre-test, I found it was just as applicable to real life and Vanessa understood the relevance of the problem. She asked me questions that were more focused on the task, and more on track than in the pre-assessment. When solving for the rectangular prism, she remembered what was learned in the second lesson and knew in order to maximize tubing the three numbers needed to be as close to each other as possible. Vanessa successfully calculated and solved the first portion of this assignment on her own. She seemed very comfortable working with the dimensions of a rectangular prism. The next portion of the post-test required the students to solve using the same information but now creating a triangular prism. Vanessa became frustrated when she did not know the prism formula and needed my assistance. I had to once again provide Vanessa with questions that would lead her to determine the formula that she would need. Once Vanessa knew the prism formula, she tested different numbers to find the patterns that helped maximize her volume. Vanessa is great at solving math problems if all the information is given directly, but she really needs support if any of the formulas or information needs to be concluded from text or past lessons. I did noticed her confidence improved over the course of the two lessons and she was able to complete the post-test with less assistance.
When giving Vanessa the tests, I was most impressed to see that she had good thought processes and reasoning in both the assessments. I noticed this had a lot to do with her ability to read and engage in the problem, although at times she skipped over a few details. I think that by helping her over the course of the assessments and lessons, she became more confident in her questioning and reasoning, which made her less dependent on me in the post-test.
VI. Lesson Plan Matrix
Lesson #1
Lesson Foci/Date
Objectives (include including performance, conditions, and criterion. State the Common Core State Standard (or standards used in your discipline) at the end of each objective.)
Instructional materials (what will use to deliver the main objectives of the lesson)
On-going assessment (to measure attainment of objectives)
This lesson helped the student interpret results from the pre-test by focusing on samples of student work and comparing it to how she solved the pre-test.
June 7, 2017
The student will be able to read and interpret student work and use strategies from their reasoning to solve problems.
CCSS: Craft and Structure: 4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone
CCSS: Math Practice 3. Construct viable arguments and critique the work of others.
CCSS: 7.G. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
The teacher will give the student copies of sample work from multiple students (provided from the Money Munchers pre-test resource). The student will also look back at the pre-test results and assess themselves on their performance, now that they have gotten the chance to look at other student work. I will also discuss the answers the student writes and question them and guide them when they are finding themselves lost or confused on a given situation.
By watching the student assess themselves on the original assessment you can identify if the student has learned where she could have done more to accomplish the task and where she was strong.
Lesson #2
Lesson Foci/Date
Objectives (include including performance, conditions, and criterion. State the Common Core State Standard (or standards used in your discipline) at the end of each objective.)
Instructional materials (what will use to deliver the main objectives of the lesson)
On-going assessment (to measure attainment of objectives)
This lesson focuses on a real-life situation involving luggage and the dimensions to maximize a suitcase. Students will be expected to read and utilize information given to solve a problem, they will also work backwards in finding specific side lengths given the volume of the suitcase.
June 8, 2017
The students will be able to read and work through a real-life story problem. They will also be able to work backwards from volume to find the missing dimension of an object.
CCSS: Craft and Structure: 4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone
CCSS: Math Practice 3. Construct viable arguments and critique the work of others.
CCSS: 7.G. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
The student will be given the assignment to complete independently at first. After she has answered the first questions, I will ask her what she thinks about creating the biggest shape. I will help her visualize different rectangular prisms by drawing the shapes and stretching them, using online tools if necessary (fixing the volume and stretching the height to see how the shape changes). Discussion will help the student
After the main task is completed, the student will be given the situation in reverse. This will help me assess her understanding of how the problem was originally done and if that had any effect on solving it the opposite way.
VII. Reflections on Your Literacy Lesson Plans
When giving Vanessa the literacy tasks she came up with tons of great ideas, but struggled to complete the task without my assistance. On the pre-test she lacked drive, and she struggled focusing on the end goal even though it was clearly provided in each task. In the Article, Student Motivation – an overlooked piece of School Reform, the authors state, “Motivation can affect how students approach school in general, how they relate to teachers, how much time and effort they devote to their studies, how much support they seek when they’re struggling, how they perform on tests, and many other aspects of education” (“Student Motivation – an overlooked piece of School Reform”, 2012, p. 2). Teaching in the alternative high school setting, I found this statement to be extremely true. I have been extremely fortunate to teach at a school where we can help work to encourage and push students that lack motivation. With a smaller classroom setting, more one-on-one interactions and by grouping students based on learning styles, we have noticed improvements in motivation at our school (“Student Motivation – an overlooked piece of School Reform”, 2012, p. 6). Vanessa shared with me that mathematics was something she had always struggled with, so her lack of drive comes from a place of insecurity to complete tasks correctly. This has directly effected her motivation and could be one reason why she ended up at our alterative high school. I also noticed that in the pre-test, she would write and explain good ideas verbally, but lacked the confidence to do the task without my support for the majority of the time. She told me she liked that the tasks were a bit more challenging and made her thinking about the “why?” but she didn’t feel that it was relevant or interesting, although this was one of the few times I saw her fully engage in a math task. Student interest is also critical when thinking about ways to motivate the student (“Student Motivation – an overlooked piece of School Reform”, 2012, p. 2). I assisted Vanessa by discussing thoughts about the task with a classmate and myself during the entire pre-test. My choosing to give her peer-to-peer support and one-on-one teacher support I believe she became more confident in her abilities and found herself being able to take away key concepts from the Pre-test. In the first question, Vanessa had to figure out how to find the solution and in the second question she had to utilized strategies from the first problem and got a solution that accurately represented the situation. Since she was able to apply knowledge from the first question, this shows Vanessa learned how to utilize the information in the story problem. I also learned that although I thought the task was relevant and interesting, she did not see the relevance it had in her life and was not interested in it like I expected her to be. If I were to do this task again, I would come up with it in a different way in order to make it more fun and interesting to the students. However, I think that by noticing her disinterest in the task early on, I was able to review my lessons and post test in a new way and I tried to make them relevant to her.
During the first lesson, she enjoyed being able to reflect on the work she did during her pre-test. Before starting the worksheet, I told Vanessa it was important for her to think about the ways in which she solved the problem. We also went over her reasoning and starting thinking about how she accomplished the pre-test. I think this was beneficial to her in completing the lesson. She told me it made her feel more connected and confident to the previous task. Although I still provided peer support and helped differentiate the task by providing leading questions, I noticed Vanessa lacked precision to detail when reading other student responses, which was what the lesson focused on. She looked at examples of student work and compared and contrasted their work to what she did. She felt that she had a better understanding for the task and she seemed to start to understand what goes into solving a more complicated story problem that has multiple steps you have to think out. When answering questions about the student work, Vanessa was able to identify the good parts of other student’s work. Vanessa was also able to see if their estimates were reasonable by comparing her work to theirs. However, she struggled when she was asked if she could elaborate on ways to improve the other student’s solution. I believe that this was due to the fact that she struggled in comprehending the thoughts of the other “students”. If I taught this lesson again, I would make sure to work through the first example of student work with the class or individual students in order to help ignite some strategies of what to look for in the lesson.
During the second lesson, Vanessa struggled to apply what she learned in the first lesson and pre-test. This worksheet applied similar concepts, but did not have the same scenario or situation. She didn’t expect that going into the lesson. In the future, I would spend time summarizing the first lesson and explain to students that similar strategies could be used in other scenarios or story problems. I think this would have made Vanessa more prepared when attempting to solve the problem in the next lesson. Vanessa had to find the volume of a suitcase given the sum of the three dimensions was 45 inches. She had to find the maximum volume and work backwards to solve different equations involving volume. This was the same math topic that was covered in the first lesson and in the pre-test, but the story-problem questions were less complex. Vanessa understood how to complete the tasks and had more success with finding the solutions without my assistance. However, she struggled when she had to solve the problems backwards. I had to sit with her and help her recall formulas from previous knowledge and reminded her how to solve for a missing variable. I think this was truly the turning point in the lesson, because without my assistance she would have given up and not completed the task.
Finally in the post-test, I found Vanessa did not need my assistance when solving the problems for the task. She did not have trouble understanding what the task was asking, but she had trouble recalling the volume formula of a triangular prism from memory. This was a moment in the post-test that made her be completely independent in solving the problems given to her. Also, many of my students struggle with: recalling previous classroom learning objectives. In the future I would provide more strategies for students to be able to easily recall formulas, for example using songs to remember formulas, reviewing formulas on flashcards, using online games to engage students in to grow a deeper memory of the formula. Vanessa was able to complete the tasks in the given scenario correctly without much assistance from a partner or myself. Overall, she showed huge strides in her understanding of story problems and told me she felt the tasks were more relevant when she thought about the ways in which area and volume are used in her everyday life.
From when we started the assessments and lessons, to the time we finished, I noticed Vanessa look more at the key details in the story problems provided for her. I believe she had an easier time finding the information because of what she learned in our one-on-one discussion, as well as the discussion she had with her peer.
VIII. Recommendations to Teachers and Parents/Caregivers
Over the past week, I have been able to work with Vanessa on her math literacy skills, more specifically the way she understands and comprehends story problems in relation to volume, the most previous section we have covered in Geometry class. My goal of the lessons was for Vanessa to gain confidence in applying mathematical concepts into a specific scenario pertaining volume. When she worked with a peer, or when I helped her, I noticed Vanessa had confidence in her mathematical knowledge and had no problem reading or understanding the scenario. However when she worked alone, she tended to lack perseverance and motivation when completing her assignments and had trouble missing out on key details that would help her find the correct answer. I think that is due to the lack of connection she sees between every day activities and mathematics. I try to connect math into real-world examples daily in the classroom, but it would be beneficial for you to help her see the connections between mathematics and activities you do in the home, such as cooking, board games, or budgeting. In order for Vanessa to make deeper connections of math concepts, she will need to be able to see the value of math in every day life. This is shown in the NCTM article titled Making Mathematical Connections and I recommend you reading this in order to understand the importance of this topic.
Vanessa was never afraid to ask a question or advocate for herself when needing my assistance. Before completing the second lesson Vanessa had trouble remembering specific volume formulas. As soon as I reviewed them with her, solving the problems came easily to her. I think that if she had more practice solving volume problems, she would have been able to remember the formulas more easily. I also noticed she struggled when solving for a variable, I know that Vanessa has had tons of practice with this in Algebra but she struggled to remember how to accomplish this task. In order for her to recall formulas and strategies, she needs to practice math more. I know at times she struggled to complete assignments and I believe if she did complete all of her assignments, she would have remembered formulas and concepts.
At the beginning of next school year, I would love to review this task with Vanessa and see her growth in math literacy. I know that when she completes the assignments she was given and starts to relate math into her everyday life, we will see huge growth in Vanessa’s math confidence and literacy skills.
IX. Appendices of Work
Nash - Outline for Lesson Plan #1
Date: June 7, 2017
Objective(s) for today’s lesson: The student will be able to read and interpret student work and use strategies from their reasoning to solve problems.
CCSS addressed (use the ones in the LLA project folder):
CCSS: Craft and Structure: 4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone
CCSS: Math Practice 3. Construct viable arguments and critique the work of others.
CCSS: 7.G. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Rationale:
In life, students are expected to interpret situations around them and create an argument. I think that by giving them an engaging pre-assessment task that captures an example of how math is used in an argument, it helps show them the real-life application of math.
Materials & supplies needed:
-Pencil, Paper, Examples of Student work packet
Procedures and approximate time allocated for each event
• Introduction to the lesson
The purpose of this lesson is to help students reflect the pre-test by analyzing a set of example student responses. I will help students make connections by reviewing what they did in the pre-test and spending time analyzing how they solved the problem. I will also talk to them about real-life uses of volume and we will discuss ways they see volume in life. I will motivate them by helping them connect the task to real life situations. (10 minutes)
• OUTLINE of key events during the lesson
Students will be given student work packets and will work with the teacher and peers to help analyze student work. Students will first be given time to work on this independently, then with a peer and ending with the teacher. Teacher will help relate the student work to the results of the pre-test for the student. How was what you did similar to this? How was what you did different? Did you find any patterns that were the same? What did you notice to be a key theme of these problems? Students will understand they need to work together and that the expectation is to complete the packet and ask questions when necessary in order to solve the problems (based on classroom norms set). I will hand students material after the introduction is completed. (25 minutes)
• Closing summary for the lesson (How will I bring closure to the lesson and actively involve children in reflecting on their experiences? How will I help them make connections to prior lessons or prepare for future experiences? What kind of feedback do I want from them at this time?)
Students will be given a closing activity that asks them questions about the work they did on the pre-test and comparing it to student work. Students will be expected to complete the assignment by writing their thoughts about what they did. This will help them continue to make a connection between what they have done and what the example work helped them see. (15 minutes)
• Transition to next learning activity- Students will discuss how volume is used in every day life, what are other examples of story problems you have seen involving volume?
Academic, Social and Linguistic Support during each event
The student will be fully supported by the teacher, one-on-one support with guiding questions. The student will also work with another student on this task to help promote intellectual discussion and support.
Assessment
The student will look at her pre-assessment with her new critical eye from this lesson and describe in writing three things she struggled at originally with the task and at least one strategy she could use to solve the task more efficiently. I will look to see that she understands where she struggled and where she thrived. If I notice she is unable to properly assess herself, then I will help guide her and show her why she is strong in certain areas and help her see her weaknesses and learn from them.
Academic, Social, and Linguistic Support during assessment
Teacher will be available to student for any support when formulating thoughts she has gained from the lesson.
Nash – Outline for Lesson #2
Date: June 8, 2017
Objective(s) for today’s lesson:
The goal of this lesson is to understand how to solve problems using real life examples and applying math concepts. Students will be able to read a situation and use math to solve the problem, more specifically maximize volume and solve for the variable.
CCSS addressed (use the ones in the LLA project folder):
CCSS: Craft and Structure: 4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone
CCSS: Math Practice 3. Construct viable arguments and critique the work of others.
CCSS: 7.G. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Rationale (Explain why this content and/or skill is important and worthwhile, and how you will work to make it relevant to your students’ lives):
Students will see the value in this activity by relating it to a trip they might be planning for or may want to plan for in the future. By comparing volume to travel luggage, students will become invested because most students will eventually (if not already) experience airports and luggage restrictions.
Materials & supplies needed:
Pencil, Lesson #2 Worksheet, Calculator
Procedures and approximate time allocated for each event
• Introduction to the lesson
At the beginning of the lesson, students will look at all different types of luggage, different shapes and sizes. Students will understand the objective of maximizing volume by the visual representation given, and the learning objective will be written on the whiteboard in the front of the room. I will help students make connections by giving them examples in the warm up that will help them think about different sizes and what would maximize their dimensions, this directly relates to using math in the real world. I will motivate students by discussing their dream vacations or favorite vacation, I think this will help them want to solve the problem. (10 minutes)
• OUTLINE of key events during the lesson
After showing students different examples of suitcases, I will pass out the worksheet. I will then give then start to go over it with them. We will write down all the volume formulas before they start working on the assignment with peers. I will read through all questions with students to help them understand the questions being asked. I will give students time to work. After they complete #1-2, I will review their thoughts with them and their reasoning. Students will understand behavior expectations by the norms already set in my class. Students will have experience working with others and discussing math productively (25 minutes)
• Closing summary for the lesson
When students complete the worksheet, we will discuss issues and concerns they had. This will help me address their misconceptions, we will talk about why they got the answers they did and how they knew they were right. Students will understand how to check work to see if answers are correct, so this won’t be an issue. We will talk about why we believe a certain suitcase could fit more and why the dimensions are specific numbers. I will help them make connections by showing them how I utilized this when choosing a piece of luggage. I will review the concepts of volume at the end of the lesson and beginning of the lesson for students to understand the unit is focused on volume and this activity helps them think about it more deeply. I want to be able to give them feedback if their work has errors, or if they did it correctly. It is important for me as the teacher to look at the students work and check it when we are summarizing by discussing. (15 minutes)
• Transition to next learning activity- Summarizing the volume formulas and working backwards to continue the next lesson
Academic, Social and Linguistic Support during each event
The student will be fully supported by the teacher, one-on-one support with guiding questions as needed. The student will also work with another student on this task to help promote intellectual discussion and support.
Assessment
At the end of the lesson, I will give students a ticket out the door. I will give them a question directly relating to what was covered in class. This ticket will help me gauge their knowledge of working backwards (solving for the variable) in regard to volume. I will look for work shown, correct steps, and a good thinking process. I will use the results from this ticket to help guide my next lesson. If many students are confused by the concepts, I will re-teach the material to help them have a better understanding from a different point of view.
Academic, Social, and Linguistic Support during assessment
Teacher will be available to student for any support when formulating thoughts she has gained from the lesson.
X. References
Boyle J. R. & Provost M. C. (2012). Strategies for teaching students with disabilities in inclusive classrooms: A case method approach. Upper Saddle Creek, New Jersey: Pearson Education, Inc.
Gambrell, L. B. & Morrow, L. M. (2015). Best practices in literacy instruction (5th ed.). New York, NY: The Guilford Press.
Kohler, B. & Alibegovic, E. (2015). Assessing for learning. Mathematics Teaching in the Middle School, 20 (7), 424-433.
Tomlinson, C. A. (1999). Mapping a Route Toward Differentiated Instruction. Educational Leadership, 57(1), 12-16. http://blog.elanco.org/gsgsteacherresources/files/2015/01/Mapping-a-Route-Towards-Differentiated-Instruction-1synvr0.pdf
Mathematics Assessment Resource Service University of Nottingham & UC Berkeley. (2015). Estimating Volume: The Money Munchers. Mathematics Assessment Project Classroom Challenges A Formative Assessment Lesson. Retrieved May 26, 2017, from http://map.mathshell.org/download.php?fileid=1643
Mathematics Assessment Resource Service. (2011). Fearless Frames. Retrieved May 26, 2017, from http://map.mathshell.org/download.php?fileid=806
Valencia, S. (2011). Using assessment to improve teaching and learning. In S.J. Samuels & A.E. Farstrup (Eds.), What research has to say about reading instruction (4th ed.), (p. 379 - 405). Newark: DE: International Reading Association.
Student Motivation – an overlooked piece of School Reform (2012). 2140 Pennsylviania Avenue NW, Washington, DC: The George Washington University. Retrieved From: http://files.eric.ed.gov/fulltext/ED532666.pdf
Gojak, L. M. (2013). Making Mathematical Connections. NCTM Summing Up. Retrieved From: http://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Linda-M_-Gojak/Making-Mathematical-Connections/