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  1. 1. Data, Statistics, and Graphing A Work Sample Completed by: Jesse Gilbertson Dates of Teaching: November 2nd , 2009 – December 17th , 2009 For EL Authorization Level Fall 2009 George Fox University Master of Arts in Teaching Program - 1 -
  2. 2. Table of Contents Section 1: Contextual Information ……………………...Page 3 Section 2: Mapping, Standards, and Assessment …….....Page 11 Section 3: Lesson Plans and Reflections………………...Page 26 Section 4: Learning Gains Data……………………..…...Page 74 Section 5: Final Unit Reflection…………………..……...Page 91 Appendix………………………………………………....Page 98 - 2 -
  3. 3. Section One: Contextual Information Community Environment Dayton, Oregon is a small town located in the Willamette Valley approximately twenty five miles outside of Portland, Oregon. The city was founded in 1850 by Andrew Smith and Joel Palmer and was named after Smith’s hometown of Dayton, Ohio. This city itself is home to multiple historic landmarks such as the Joel Palmer House (now a restaurant) and Fort Yamhill, an 1800’s era military fortification in Oregon that was moved to Dayton in 1911, instead of its planned demolition. Today Dayton is in the center of the county’s rapidly growing wine & tourist industry and is home to several reputable vineyards. Dayton’s location makes it an easily accessible city. It is nestled in between Newberg and McMinnville, roughly fifty five miles from the coast, and twenty four miles from the state capital, making Dayton a centralized, yet quiet city. Dayton holds a population of nearly two thousand five hundred people in its .07 square mile area in Yamhill County, nearly 80% of them being Caucasian, 26 % Hispanic, and the rest being of Asian, African American, or mixed descent. Students, ages fifteen or younger, make up the cities largest demographic of 30.9% followed by adults ages twenty five to forty four at 30.2%. The medial household income in Dayton is just above $40,000 which is slightly lower than the national average of $41,000. The majority of the people here are married with a spouse, around 55%, graduated from high school, nearly 60%, and have their own transportation to and from their place of employment, 93%. School Environment The Dayton, OR school district is located in the Willamette Valley and is home to approximately one thousand students. Dayton Elementary School holds around four hundred fifty to five hundred students per year, given the year, and spans from kindergarten to fifth grade. Since the city itself isn’t large (.7 sq miles total area), economic factors play a big factor in the school environment. The percentage of students on a free or reduced lunch program is 58%, in comparison to the state average of 41.3% (NW Area Foundation). The amount of Hispanic children at the elementary level is around 28%, compared to the 13% state average. The English Language Development (ELD) program serves nearly 15% of the students, while, in reality, nearly 35% of the student body uses a primary language other than English at home. Dayton Elementary employs fifty certifies staff members within its twenty classrooms, including a principal, the classroom teachers, a music teacher, a physical education teacher, a special education teacher, a librarian, and a counselor. Dayton Elementary follows the motto: “We are a caring community that lights the way to life long learning in an atmosphere of mutual respect.” This creed is enacted by committee involvement, PTSO (Parent Teacher Student Organization), and a newly formed school council. The school council has recently created a school academic improvement plan to be implemented in the 2009-2010 school year. Its goals are to have 80% of students third through fifth grade meet state reading standards, 67% of students grades 3-5 meet state mathematic standards, and raise the percentage of students who meet the writing standard - 3 -
  4. 4. to 40% (Current percentages meeting state standards are as follows: reading 74%, mathematics roughly 60%, and writing 37%) . While these goals are substantial, the PTSO and the school’s committee of community members, comprised of parents, teachers, local college collaboration, and other local community members, are dedicated to making these goals become a reality. Classroom Environment The classroom of Mr. B is in the schools western wing near the end of the hallway. Inside the classroom you can find twenty eight fourth grade students studying social studies, history, mathematics, science, reading, and writing. Inside the classroom the students have six computers with educational software, at their disposal as well as a small library of books (fiction & non-fiction), compact disc players with read along cd’s, a television with a dvd player, two larger work tables with basic art supplies, and many small posters full of what I deemed “practical life advice” . The classroom’s high ceilings make it feel rather large but the class itself is around five hundred square feel total area. The students desks are arranged in three rows of two to four, separated down the middle by a walkway, all facing forward to the white board. Students are arranged by Mr. B in random order, minus the few exceptions whom he has sitting closer to his desk for closer supervision. The climate in the classroom is one of high respect and high responsibility. Mr. B has set into place a “community vibe” with every student being accountable for their wellbeing and actions first and their fellow classmates second. While the students seem to have their separate friend groups, the class as a whole seems to get along civilly during the majority of the day. The class itself has a few systems set up in it, mainly to help transitional times. There are students who gather and set out the trash cans in the room which alternate by day, students who lead lines down the hallway who also alternate by day, and there is a student who sits near Mr. B’s desk that has the official title of “class secretary” because she answers the class phone if Mr. B is away from his desk. At this point in the year, nearly two full months since school started, the students are getting better at transitioning quickly and quietly during their daily routines. What this contextual information means to my teaching… When I examine this information I get a clearer picture of the community that I am serving. I understand their social context of being a small rural town outside of two larger cities, their makeup of mostly Caucasian and Hispanic families, and their routines which help me organize how to effectively design curriculum and class time to better reach and teach the students. This information will also provide me with the basic knowledge of the families within the city. Being able to know where a family stands will help me conduct myself accordingly, given different situations. For example, if certain families cannot communicate as well because of a language barrier then I will be able to find resources or friends to help bridge that gap. Another thing that this contextual information brings to the table is the materials available. Knowing the materials I have in the classroom, such as the television, the projector, and the piano will help lesson plan design and preparation for activities as well as help me utilize different kinds of activities for multiple intelligences. - 4 -
  5. 5. MEMBERS OF THE COMMUNITY Developmentally - Who are my students? Socially The Students at Dayton Elementary fall within the normal stages of human development. Socially they are beginning to develop a heightened sense of perspective, racial awareness, peer relationships, and sexual orientation. Students in the fourth grade are nine or ten years of age and in the process of understanding multiple perspectives. Students can put themselves in others shoes but at times fail to understand reciprocity, specifically with negative actions. Race is another aspect of development that begins taking more precedence at this age. Students begin to understand that there is diversity amongst humans but at this stage, students don’t always understand the social ramifications of race (prejudice, racism, etc.). Peer relationships remain somewhat simple at this stage of development. Students generally have small, same sex, peer groups, based on shared values and interests. The final stage of social development that students begin to gain understanding in is gender orientation. At this age of development the subject of same gender relationships are sometimes considered taboo depending upon the greater social context (the community the students live in). This difference is difficult to distinguish at this age compared to others because of it being a person’s personal decision and because it doesn’t necessarily have any distinguishable physical or emotional traits. Students social lives rapidly transform during this period of life, making them budding social beings, eager to communicate, express, and influence one another. Utilizing a 4th grade classroom’s social development will be fairly simple. While the students have their individual peer groups, getting a classroom of nine and ten year olds to get up and interact with each other should require minimal effort. Providing the students with activities, especially mathematics activities, that get them up and talking to their peers will help students realize that learning doesn’t have to be restricted to their desk. Emotionally While students change in their social lives, they change similarly within their own thoughts and actions. At this age students begin to realize that multiple emotions can take place at the same time and the specific causes for those emotions. This relates directly to perspective taking, peer relationships, and a students own emotional self regulation. At this stage in development students are able to target the emotional causes of stress and implement strategies to help reduce and eliminate it. This stage of development is also characterized by the beginning of a students self identity. At these very early stages, self concept begins with students realizing truths and beliefs within themselves which are later followed by exploration and firming of these ideals. Another aspect of a student’s development at ages nine and ten is moral development. When using Kohlberg’s theory of moral development we find that students are typically within the category of conventional moral reasoning. Students will obey society’s rules in order to please someone and gain their approval, looking for adult - 5 -
  6. 6. guidance throughout the process. This process is the first step towards students recognizing that societal values and norms have a set place and purpose in everyday life. Knowing where my students lie emotionally helps me explain things to them in a way they understand. To be more specific, it helps me realize that students at the 4th grade level will not always understand the reasoning for my instruction, meaning that I will have to know how to explain myself in a language they understand. It will also assist me in reading my students emotions better when they are confused or when they are having a difficult day. Physically Students in fourth grade are undergoing major physical growth. A student’s brain is still considered to have high plasticity, meaning that their brain has the ability to change with more ease than an adult’s brain. Students’ senses are also changing but not as dramatically as other parts of their bodies. While senses continue to fine tune, students begin to find themselves more and more attracted to stimuli that excite and rouse the nervous system such as varied textures, colors, and scents. When it comes to a fourth grade student’s body, their gross motor skills should nearly all be present and growing. Running, jumping, and throwing a ball are all familiar to this age, given there is no physical disability. Student’s fine motor skills are similar to gross motor skills in that they should be present and progressing. Students are able to write, draw, play instruments, and multiple other things that adults do. Knowing where students lie upon the physical spectrum can help me plan physical activities that the entire class can participate in, so as to not alienate any students that are not at the same physical level as their peers. This information also helps me understand what physical activities my students enjoy participating in. Knowing that information can be a good tool for analogies and helping tie in information to a student who is struggling. Cognitively A student’s brain, as mentioned previously, is very able to change and adapt. At ages nine and ten the brain is beginning to better control attention and memory, focusing on the important information while learning new strategies to filter out useless material. Students also begin to increase their memorization, rehearsal skills, comprehension, and organizational skills. All of these skills become filters for attention and memory in that they help process information more quickly and in a more efficient order. As students move through this process, differentiated instruction and activities that engage multiple intelligences will be great tools to help foster the students growing minds. What have these students studied previously about the topic of my work sample unit? Many of the students, if not all of them, have been introduced to the topics of graphing, data, and statistics, including range, median, and mode. Since it is still early in the year, much of what I will be teaching will be review for students from last year’s curriculum. My job will be to reintroduce it in an exciting way so that students recall their existing knowledge while learning new ways to comprehend the information. - 6 -
  7. 7. Brief explanation of Cooperating Teacher’s teaching philosophy: Mr. B’s teaching philosophy is centered in the notion that teachers as well as students are responsible for the well being of their classroom and fellow classmates. He believes that the teacher should be prepared, reflecting constantly, creating a safe and loving environment, and constantly striving for new ways to teach and assess a classroom. Mr. B also believes that since all learners are individuals with unique learning styles that a teacher’s job is not only to be able to adjust to their needs, but to also use their individuality to promote diversity and respect within the classroom. Strengths and previous experiences of student teacher going into this experience: In the spring of 2007 (April-June) I co-taught a preschool classroom in Corvallis, OR with five other classmates, for a practicum at Oregon State University. Our classroom was run by a head teacher and her assistant who graded our assignments and helped us progress along throughout the months. Each of the co-teachers had a focused week where they assumed the role of head teacher in the classroom, directing the other co-teachers and activities for a five day period. This included prep work, a parent teacher conference, and an at home visit with parents. My unit was interesting because the activities I spent the most time preparing and organizing were the ones the students were least interested in. My final activity was a chemistry experiment that had two clear liquids that when mixed turned dark purple. The students absolutely loved this and it was a good experience to end my head teaching week on. Specific goals for student teacher’s growth during this unit: I have three goals that I would like to accomplish in this first practicum 1) To be able to change a lesson completely, on the fly, if the lesson plan turns out to be a bust. 2) Learn a realistic time setting within a normal classroom. 3) To learn how to transition between activities, periods, or portions of the day, seamlessly. What does this information mean to me as I plan and teach the work sample? This information about my students shows me more in depth where they are developmentally, how they’re growing, and where they could and should be moving throughout the school year. Knowing where students fall on the developmental spectrum makes it easier to understand why students do the things they do and hopefully shed some light on how I can prepare lessons that will expand their understanding and get them thinking about the subject more deeply. Utilizing their developing social and cognitive minds, I can design lesson plans that get them interacting with their peers while getting them to think about mathematics more abstractly, meaning thinking about math as more than just numbers. Knowing where students fall physically will help me know when the - 7 -
  8. 8. students need to get up and move around to prevent boredom and stagnation. Finally, knowing students emotionally helps me read the students and see their confusion or frustration levels. This will help me better focus on what I need to explain more clearly to the class. Knowing what the students have previously learned also ties into that. Teachers, to be effective, need to keep their classes progressing forward, and by knowing what your students already have in their skill sets, one can continue to build upon them, as opposed to reiterating the same information over and over. Knowing my co-teachers philosophy is similar to coming into a company and understanding how the boss runs the operation. Once you understand how things run in the classroom then you can place yourself in positions that make you valuable and very useful. Becoming a respected addition to the classroom is something I strive for. Finally, remembering my previous strengths also brings up weaknesses in my mind. Realizing your strong and weak points helps you create goals for the future. By having goals and knowing where I stand while realizing where students are developmentally I will be able to design lessons that are relevant and interesting for the students while making them challenging and fun as well. Student Information Name Information about this student OAKS test score from 3rd grade - Mathematics Student 1 High functioning autism, IEP – Speech, Enjoys reading, keeps to himself, even tempered. This student will not be participating in the unit OAKS Score: 208 Assisted Entry. Student 2 Misses a lot of school due to family issues. Positive attitude, enjoys cinema, likes to draw OAKS Score : 207 Student 3 Very positive attitude, interacts well with all students within the classroom OAKS Score : 204 Not Met Student 4 Has recovering broken foot, well liked by peers, very bright, positive attitude OAKS Score : 212 Student 5 Quiet, very good student helper, in charge of answering the class telephone and holding the door open during transitional times in the classroom, has many siblings OAKS Score : 203 Student 6 Positive attitude, hard worker, intelligent, enjoys sports, well liked by peers OAKS Score : 213 Student 7 Very positive attitude, occasionally has trouble with written grammar, strong reader. New student this year. No OAKS record. Student 8 ELL – Level 3, Good sense of humor, enjoys mathematics, friends with entire class OAKS Score : 208 Student 9 ELD – Level 2+, Enjoys social activities, good behavior, Hard worker OAKS Score : 201 Not Met - 8 -
  9. 9. Student 10 Shy at first, very well behaved, helps neighboring students when they don’t understand curriculum OAKS Score : 205 Student 11 Smallest student in the class, very bright, strong math and reading skills, good sense of humor, friends with entire class OAKS Score : 217 Student 12 Positive attitude, athletic, sits next to student 1 and helps when he looses his temper, enjoys math OAKS Score : 206 Student 13 IEP – Mathematics, This student will not be participating in math unit. Quiet, seems to do most things under the radar OAKS Score : No score, Not Met. Student 14 ELL – Level 2, IEP – Reading. This student has not been in class due to illness since my arrival OAKS Score : 178 Not Met Student 15 Well behaved, very positive attitude, athletic, enjoys all subjects, friend with the entire class OAKS Score : 211 Student 16 Lots of energy, easily excitable, very bright, occasionally disruptive but means well, enjoys reading OAKS Score : 218 Student 17 Well liked by peers, occasionally disruptive, good sense of humor, very social, athletic OAKS Score : 208 Student 18 ELL – Level 3, Positive attitude, quick with numbers, good sense of humor OAKS Score : 217 Student 19 Mental Retardation, ELL – Level 2, IEP – All subjects Extremely hard worker, rarely talks, leads pledge of allegiance, positive attitude. This student will not be participating in this unit OAKS Score : No score. Not Met Student 20 Interested in the classes business, occasionally disruptive, enjoys athletics, dislikes reading OAKS Score : 198 Not Met Student 21 Well liked by peers, energetic, strong at mathematics, athletic, asks intuitive questions OAKS Score : 215 Student 22 Intuitive, has many friends in class and in other classrooms, good sense of humor OAKS Score : 216 Student 23 Quick to give answers, generous, occasionally disruptive, cause of occasional mischief, enjoys science OAKS Score : 205 Student 24 Athletic, quiet, well liked by peers, fun to converse with OAKS Score : 204 Student 25 Extremely bright, athletic, good sense of humor, well liked by all peers and staff, very kind, very polite OAKS Score : 218 Student 26 Good natured, athletic, high parent involvement, good sense of humor OAKS Score : 217 Student 27 ELL – Level 3, very patient and calm, enjoys reading, takes care of her row OAKS Score : 209 Student 28 Likes to draw, often off task, good sense of humor, vivid imagination, creative OAKS Score : 207 - 9 -
  10. 10. English Language Learners (ELL): ELL students’ scores are based on a scale of 1-3. This scale is as is as follows: 1) Needs more time, 2) Growing knowledge/proficient growth, and 3) Strong steady Growth. Growth describes the students knowledge and comprehension of the English language. Each ELL student is assessed initially through the ELPA test and then two more times throughout the year by the ELL instructor, Mrs. S. OAKS Mathematics scores for 3rd grade - Students participate in the OAKS (Oregon Assessment of Knowledge and Skills) test annually in a variety of subjects including reading, writing, and mathematics. The scores that my unit will use as a bearing for what students can comprehend are their math scores. These test scores are from the previous school year (2008-09). All students in this classroom, unless stated otherwise, have passes this portion of the OAKS test. How did you gather this information? • Observation • Interview • Information from teachers • Observation from student work What is useful and dangerous about the information above? The information above is useful because it provides me with an in-depth look into my students personalities, abilities, and weaknesses. Being able to understand what path my students are taking to get to an answer helps me effectively ask them “custom” questions that can aide them getting there. By “custom” I mean a question that uses the individual student’s abilities and knowledge to help get them on the right track for the correct answer. It is also useful for managerial purposes. Understanding what pairs of students do not work well together, whether that be because they get off task or just don’t get along, helps me organize the class so everyone is getting an optimal experience. Finally it is useful just for the fact that you get to know your students and their daily behaviors better. Being able to tell when a student is having an ‘off’ day helps you know how to help them feel better and how to get them to still feel motivated. This information is dangerous for some of the same reasons that it is useful. Knowing a students strengths and weaknesses may make you cut a student slack in a subject that they don’t like or aren’t progressing in while helping them excel in the subjects that they are good at. It is easy to push a student along in the direction they are already moving, but it is more important to get a student turned around in a subject that they are not liking or struggling with. Also when it comes to knowing your students, it is very easy to want to show better treatment to the students who comply with all of the classroom rules and produce good work. That is a normal human reaction at all ages, with all people, an example being a police officer giving a very polite compliant person a warning instead of a traffic ticket. Getting to know the students needs to be as fair and balanced as possible and is a continual fine tuning process; however, it is not always easy. If favoritism is shown things can get dangerous with the other students behavior or even faculty. Finding the right balance is crucial and necessary to run a successful classroom. - 10 -
  11. 11. Section 2 Mapping, Standards, and Assessment: Data, Statistics, and Graphing - 11 -
  12. 12. - 12 - How to Analyze Information : Data, Statistics, and Graphing Subject: Mathematics Grade Level: 4th Grade Established Goal(s): From the State of Oregon • Students will be able to explain time and elapsed time using an analog clock and a calendar • Students will be able to interpret and display data using line plots and a variety of graphs. • Students will be able to determine Range, Median, and Mode from given data. • Students will be able to read and solve word problems using strategies such as Read/Plan/Solve and working backwards. State Standards • Mathematics: 4.1.4 Compare and order fractions and decimals. • Mathematics: 5.1.6 Use ordered pairs on coordinate graphs to specify locations and describe paths. • Mathematics: 5.1.7 Construct and analyze double bar, line, and circle graphs to solve problems involving fractions and decimals. Enduring Understanding(s): People can categorize and interpret elements of daily life with mathematics to gain a better understanding of things around them. By using mathematics to explain life occurrences, mankind has created many systems, such as the calendar and the clock, to help aide human advancement. Essential Question(s): • Is it possible to represent the same data in different kinds of graphs? • What does it mean when someone says that is the “average” result? • What daily event do we base our time system from? • Think about a global positioning system (GPS). What kind of graph does a GPS use to find where it is? Knowledge Knowledge of range, median, and mode. Knowledge of line plots as well as bar, line, picto, and coordinate graphs. Time, elapsed time, and dates from a calendar. Strategies to solve problems that in clued data, statistics, and graphing Skills Calculating range, median, and mode of given data. Draw and label line plots, bar, line, picto, and coordinate graphs Use a clock and a calendar to effectively display time. Dispositions A positive attitude Ability to work well with others Responsive to instruction Accepting of constructive criticism.
  13. 13. Daily Assessment of progress toward learning objective / Evidence of Learning Day Learning Objectives / State Standards Daily Activities & Assessment Pre Assessment • Mathematics: 4.1.4 • Mathematics: 5.1.6 • Mathematics: 5.1.7 Diagnostic Pre Assessment Day 1 Students will be able to tell time from an analog clock as well as take time and display it on an analog clock. Mathematics: 4.1.4 Intro to time : AM/PM activity – Activity on what AM and PM mean and when they take place. Telling Time mini lesson: Have a broken analog clock. Will have students come to the front of the class and demonstrate how to show time. Time worksheet: Activities on telling time from an analog clock and labeling time onto an analog clock. Time zone wrap-up: Discussion of time zones and their purpose. Assessment – Time worksheet & observation during class. Day 2 Students will be able to tell elapsed time by examining airplane schedules and filling in missing pieces Mathematics: 4.1.4 Trip planning exercise : Discussion of time planning on trips Day or Night? partner activity : Students, as a group, will use elapsed time to tell what portion of the day it is Minuets & Hours activity: Students will calculate elapsed time by using given time and time on an analog clock. Reflection slip: Students will write briefly what they have learned as well as why this skill would be useful. Assessment: Minuets & Hours activity & discussion responses. - 13 -
  14. 14. Day 3 Students will be able to effectively use a calendar by plotting out trip dates. Mathematics: 4.1.4 30 or 31? Warm up : Thumbs up/Thumbs down class warm up with months that have thirty or thirty one days What is a Day?: Discussion on what a day, month, and year represent. Road Trip! : Students will be given guidelines for a trip they have to take. Students may work with a partner and will design a trip. Using elapsed time, students will show how long their trip is, the day left and returned, and will plan it accordance with holidays. Assessment: Vacation! & thumbs up/thumbs down activity. Day 4 Students will be able to create line plots by examining data given. Mathematics: 5.1.7 Examining data warm up/mini lesson: lesson on how to interpret lists and tables of data. Walk the class through the process of examining a table or list of data, important factors about the table/list, and how to label them. Line plot group activity: Students will be assigned playing cards, and will move to designated areas with their numbers. A large line plot will be drawn by a teacher. Then a teacher will take a pre made line plot and have the students arrange themselves accordingly. Students will then write about their experience on a note card (exit slip). Plots to stats worksheet: line plots that students will analyze and put back into statistics form. Wrap up: precursor to graphing activity. Students will predict what line plots will evolve into. Assessment: Plot to stats worksheet/Line plot group activity. Day 5 Students will be able to calculate range, median, and mode of given data. Line plot review warm up: Review line plots with the same line plot group activity. - 14 -
  15. 15. Mathematics: 4.1.4 Mean, median, and range mini lesson: describing the terminology and how to conduct finding range, median, and mode. Grab bag activity: students will get in groups of 4, draw slips of paper with distances from school or work on them and record that data. From then they will calculate their range, median, and mode of their set of temperatures. Each group will then have a representative explain their data to the class. Line plot review wrap up: Each student, with their same group, will create a line plot for their data. Assessment : Line plot wrap up, questions during the activity Day 6 Students will be able to interpret and create pictographs from given data. Mathematics: 5.1.7 Picture math warm up: Class, as a whole, will use objects that represent numbers to determine values. Examining pictographs mini lesson: Lesson on how to arrange pictures (that represent a number) in a table, to represent data. Pictograph survey: Students will each be given a blank table with spaces for labeling in it. Every student will also be given stickers and will come up with an idea for a pictograph (favorite place to eat, favorite football team, least favorite animal, etc.) Students will then survey their classmates and create a pictograph when they are finished. Students will then share their results with a partner and then the class will share some of their results. Extra credit: if students can find a pictograph in a magazine or newspaper and bring it in with a brief summary of what the graph represent then students will be given extra credit. Assessment: Pictograph survey, listening during survey activity. Day 7 Students will be able to The joys of a bar graph mini lesson : Mini - 15 -
  16. 16. interpret and create bar graphs from given data. Mathematics: 5.1.7 lesson on how to convert a line plot into a bar graph and how bar graphs can take pictographs to the next level (multiple bars that represent different things) Bar graph survey: Same activity as in day 6, except for some modifications. Instead of students getting stickers they will just take a survey. This time they will break the data up by gender, creating two different colored bars per category in a bar graph. As before, the survey can be on what they like. Bar graph finally: Students will create bar graphs based on their data and will present them to their class. Assessment: Bar graphs, questions asked during the activity. Day 8 Students will be able to interpret and create coordinates on a coordinate graph. Mathematics: 5.1.6 Dayton, on the grid warm up: A map of Dayton, OR will be displayed on a grid map with some of the local landmarks labeled. Students will be asked if they know how to read the map. X & Y mini lesson: Mini lesson on how to use the x and y axis’ to find coordinates on a graph. Grid worksheet: A short worksheet where students will use coordinates to label a coordinate graph and take locations from a coordinate graph and name its coordinates. Create a city (portion of the grid worksheet): Students with a partner or in small groups will create a city, using templates, on butcher paper. They will label their major landmarks and mark their coordinates. Map trade wrap up: Groups will trade maps and complete a mini worksheet on where the other group’s buildings are. (Optional/if time permits) Assessment : Grid Worksheet, partner check - 16 -
  17. 17. in. Day 9 Students will be able to interpret and create line graphs from given data. Mathematics: 5.1.7 Mr. B’s classes: A graph representing Mr. B’s class sizes for the past 5 to 10 years. Tracking the progress mini lesson: Mini lesson on line graphs. Students will be asked how they are different from other graphs they’ve done so far. Tracking data over time will be main emphasis. Tribal worksheet activity: Students will be grouped as tribes (Native American theme/if the Native American social studies unit has started at this point) and will be given data for their tribe. They will individually create a line graph for their information then collaborate and create a unified line graph on butcher paper to show to the class. What else could you use a line graph for brainstorm: Whole class brainstorm on what other aspects of life could use a line graph for. Assessment: Tribal worksheet, Checking in with groups during their collaboration time. Day 10 Students will be able to examine and interpret data to determine correlations and solve word problems. Mathematics: 4.1.4 The tricky part of math-warm up: Students will be shown an extremely confusing word problem then asked to solve it on the spot. Explanation about how a lot of mathematics problems use word to explain them. Break to Build activity Breaking it down (partner or individual): Exercise in examining relevant data. Will have three problems, each with less guidance. This will show that students can gather information through clutter and can devise strategies to solve the information. Rebuilding: The same three problems will be used, but this time students will take the relevant information, strategies, and a plan, to work towards an answer to the problem. What did you do? Wrap up: After students - 17 -
  18. 18. have finished their activity they will be asked what they did. Assessment: Break to Build activity, What did you do? Wrap up Pre-requisite Skills: Students should be familiar how to use graph paper to create simple tables (for graphs), how to arrange numbers in sequential order, how to read an analog clock, understand how to read a calendar, how to add and subtract numbers, and how to read basic text. Students will also need to understand the expectations of the classroom including how to work in pairs and small groups, raising of hand for responses or questions, and completing class work in a timely manner. Plan for Literacy Inclusion: A number of the mathematics problems the students will be given will have written instruction on them in case a student has forgotten what their task is. There is also a day dedicated to story problems and how to decipher their meanings to get the correct answer. Students will filter out unneeded information while organizing pertinent data. To do this they will use strategies such as T-tables, a table where students can separate information into two categories, highlighting, ven diagrams, and simple notation to help organize and filter information. Environmental Set-Up and Changes During Unit: The only change that could occur is the spacing of the rows of desks. There are a few activities where students will need to walk around the room to survey each other. Extra room might be beneficial but not necessary. Besides those activities the rows of desks will remain in place. Plan for Differentiation Differentiation in my lessons will come in the form of the activities. They span the multiple intelligences of bodily-kinesthetic, visual-spatial, interpersonal, verbal-linguistic, and some intrapersonal communication as well. There are a few students, numbers 13 and 19, which are on IEP’s for math that leave the classroom or work with a special education teacher during the math portion of the day. They have their own curriculum that they work on outside of the class. Student number 1 isn’t on an IEP for mathematics but he generally works with student 13 and her separate teacher during the math portion of the day. The normal classroom assignments can be modeled to him prior to the lesson or simplified in a simpler work sheet format. Another plan for differentiation would be if a student would rather work alone during the group projects then they may. Plan for Family and Community Involvement: - 18 -
  19. 19. I have written a letter to the parents of my students to explain who I am, a brief background of myself, my purpose for being at the school, and the unit I am teaching. I have also left my contact information for any parents who wish to see my lesson plans or would like to meet me, even if it’s not in person. Since the school I am in is relatively small, five hundred students, there are many parent volunteers that give their time to the school. Meeting and collaborating with them will also be a high priority of mine. The parent letter can be found at the end of this section. Dear Parents, Hello! My name is Jesse Gilbertson. I am a student in George Fox University’s Masters in Teaching Program. As part of this program, I have been given the opportunity to be your child’s student teacher. I feel very fortunate to be working in the city of Dayton and have enjoyed the short time I have already spent with your children very much. They are full of energy and great ideas. I officially started my time with Mr. Blackburn on Nov. 2nd and will be working with your children until Dec. 18th (winter break). I was born and raised in Newberg, OR and progressed through the public school system there. After high school in 2003 I moved to Corvallis to get my undergraduate degree in Early Childhood Education at Oregon State University. From there I moved back to Newberg and after a year of working in construction, I had the means to complete the process of becoming a teacher. I feel extremely privileged to be under the guidance of Mr. Blackburn. His calm demeanor and high expectations for behavior and academics makes him very easy to collaborate with and learn from. My focus areas are on the subjects of mathematics and science, which I hope to teach next year. While I am in the classroom I will be teaching a unit on data, statistics, and graphing, all stemming from chapter 3 of your son or daughters McGraw/Hill mathematics text. I will be covering the topics of time, range/median/mode, interpreting word problems, and creating many different kinds of graphs. These topics are both fun and extremely practical. I will be starting these lessons on Nov. 30th so if any of you would like to have any further information on any of these topics please feel free to contact me. Also, you are more than welcome to join us for any of these activities in the classroom. I am really looking forward to spending the rest of this fall with your children and Mr. Blackburn and hope to get to meet as many of you as possible. Thank you for taking the time to read this and have a great day. Sincerely, Jesse Gilbertson Email : gilbertson.jesse@gmail.com Phone : (503) 317-5132 - 19 -
  20. 20. Diagnostic Pre Assessment Chapter 3 Pre Test Diagnostic test on chapter 3 of McGraw-Hill mathematics text. Will cover the topics of time, elapsed time, reading a calendar, line plots, range/median/mode, picto graphs, bar graphs, coordinate graphs, line graphs, and analyzing word problems. Post Assessment Chapter 3 Final Test Summative test on chapter 3 of McGraw-Hill mathematics test. Will be the exact same test as the pre test. Will cover the topics of time, elapsed time, reading a calendar, line plots, range/median/mode, picto graphs, bar graphs, coordinate graphs, line graphs, and analyzing word problems Chapter 3 Name ______________________ Date _______________________ This chapter deals with, Time, Graphing, Story Problems, and Averages. To help me figure out how to teach you guys the best, I need to know what everyone knows about these subjects. Please complete as much of this worksheet as you can. 1) Draw the following times on the blank clocks below A) 5:45 PM B) 8:10 AM C) 10:55 PM D) How many minuets are in a half hour? (1/2 of an hour)? 2) If you started riding your bike to Newberg and you left at 2:00 PM and you arrived in Newberg at 4:35 PM, how long did it take for you to get there? 3) If you took a ten day vacation, starting on December 7th , what day would you get back to Oregon? (Calendar located on back of page 2) - 20 -
  21. 21. 4) The numbers below show how many miles away students live from their school. Each number represents one person. In the blank table below fill in information where it is needed Miles from school: 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,5,5,5,6,6,7 Miles from School Tally for each student Number of students 5) Using the completed table above (from question 5), find the Median, Mode, and Range from the information in question 5. Median: Mode: Range: 6) Using the information in question 5, create a bar graph to show the number of students and how far they come to get to school - 21 -
  22. 22. 7) Answer the question using the table below Favorite Color Votes Red Blue Each = 4 people How many people voted for Red? Blue? 8) Answer the following questions using the coordinate graph above. What are the coordinates of The Goliath on the graph? What are the coordinates of Dejavu on the graph? What is located at coordinates (3, 4)? What is located at coordinates (9, 7)? - 22 -
  23. 23. 9) Examine the information below and then create a line graph for the data. Temperatures for the past two weeks: Days of the week Week #1 (temperature) Week #2 (temperature) Monday 75 78 Tuesday 77 80 Wednesday 76 83 Thursday 84 86 Friday 85 81 Saturday 72 77 Sunday 74 10) This problem has to do with airplane schedules. Use the table below to answer the final questions. (Use calendar on below if needed) Flight From To Departure Time Arrival Time 299 Portland Seattle 3:15 PM 4:30 PM 620 San Francisco Denver 11:45 AM 2:30 PM 888 Las Vegas Chicago 9:30 AM 12:25 PM 123 New York Miami 1:25 PM 5:30 PM A) How long is flight 888? B) On Wednesday, December 9th , Nate bought a ticket for Flight 620. His flight doesn’t leave until December 17th . On what day of the week will Nate fly from San Francisco to Denver? - 23 -
  24. 24. Attachments Calendar for questions 4 and 10 - 24 -
  25. 25. Pre and Post test Grading Rubric Category/State Standard Points Per Question Points Given TIME Time, elapsed time, and calendars • Mathematics: 4.1.4 Compare and order fractions and decimals. Q1 – 4 points (A,B,C,D -1 point each) Q2 – 1 point Q3 – 1 point DATA/STATISTICS Range/median/mode, tables, and word problems • Mathematics: 4.1.4 Compare and order fractions and decimals. Q4 – 2 points Q5 – 2 points Q10 – 2 points GRAPHING Bar, picto, line, and coordinate graphs. • Mathematics: 5.1.6 Use ordered pairs on coordinate graphs to specify locations and describe paths. • Mathematics: 5.1.7 Construct and analyze double bar, line, and circle graphs to solve problems involving fractions and decimals. Q6 – 2 points Q7 – 2 points Q8 – 2 points Q9 – 2 points - 25 -
  26. 26. Section 3: Lesson Plans & Reflections - 26 -
  27. 27. Lesson 1 Teacher Name(s): Jesse Gilbertson Lesson Title: AM to PM – Intro to Time Unit Title/Topic: Data, Statistics, Graphing Target Grade Level: 4th grade Estimated Time for Lesson: 30 to 40 minuets Standards: • Mathematics: 4.1.4 Compare and order fractions and decimals. Materials: Broken analog clock Time Worksheet Pencils Rulers (possibly) Lesson Objectives and Plan for Assessment: • Students will be able to tell time from an analog clock as well as take time and display it on an analog clock. • The assessment for this lesson will be the work of the Time worksheet as well as informal interviews with the students during their work. Anticipatory Set: A.M./P.M. Activity (10-15 min) • This activity will begin with the teacher asking the students what A.M. and P.M . stand for. • Once students give their definitions the teacher will explain their meanings and significance. o a.m. - ante meridiem – Latin for before noon o p.m. - post meridiem – Latin for after noon o They are part of our 24 hour time system, dividing our day into two periods. • Teacher will then ask the students if they know of any time systems. Specifically ones that do not divide the hours into two periods. Lesson Sequence: Telling Time Mini Lesson (10 min) • Teacher will have a broken analog clock in their hands that they use to explain time: o What the numbers on the clock mean – 5 min intervals - 27 -
  28. 28. o What quarter-hour increments mean – quicker way to tell time o What each hand one the clock symbolizes – hours, minuets, seconds *this should be a very basic review for most students. • While demonstrating these things, the teacher will have students come up to the front of the class and demonstrate it on the broken analog clock for the class. Time Worksheet (15 min) • Worksheet with analog clock to number conversions, number to analog clock conversions, and other assorted time questions. Closure: Time Zones Wrap Up (5 min) • Similar to the anticipatory set, a discussion about time zones and daylight savings time will be brought up. • Students, alone or with a partner will discuss the topic – What are time zones? Why are they in place? (separation of time based on when the sun rises, to keep things uniform). • Student pairs will share with the class what they think and once everyone is through, or a pair of students comes upon the answer, then the discussion will shift back into the teacher’s hands to finish out the lesson. Differentiation: Meeting needs of individual learners • Students who are having difficulty understanding or remembering concepts of basic time can be given a handout of all of the terms with examples of how to solve time problems. • For students who aren’t being challenged, a brief activity on elapsed time may be given to test their understanding. Reflection Daily Reflection: Lesson 1, 11-30-09 Lesson Title : AM/PM – An Intro to Time Synopsis of what happened: When I started my lesson today I told the students the subject of what we were studying, which led to muffled cries of “yes!”, “Nice!”, and “oh yeah oh yeah!”. However there were also cries of “uhhhhh…” and “awwww really?!”. Needless to say it was somewhat difficult to get a bearing on whether the class was going to enjoy the lesson. I began my lesson with a discussion of what am and pm stand for and luckily no students said a mini mart chain. I led the discussion like an open forum and every student, given that they raised their hand, could answer. Many students came up with good ideas such as “Actual - 28 -
  29. 29. Morning” and “Already Morning” for am, and ideas like “Post Morning” for pm. Once ten to twelve students gave their thoughts I decided it was best to move on. I gave them the real Latin meanings for the words and explained what they meant. I tried to reiterate that am begins at midnight and pm begins at noon. Some students seemed confused; others seemed to catch right on. Next I moved on to a short lecture on what each number on an analog clock represents, what quarter hour increments represent and what each hand on the clock represents. Most student immediately and unconsciously spoke “5 minuets” to my first question, but the class as a whole seemed to have a hard time grasping the concept of quarter hours, specifically the phrase “a quarter till”. All of the students in the class knew the hands of the clock and their purposes. After this mini lecture, I handed out a worksheet on telling time that I had created. The students worked on problems that required them to draw hands on a clock to a specific time, read clocks that had a specific time on them, and a few other assorted questions about the subject of time. The students seemed to do very well with this, even the students who seem to rarely try in class. I ended my lesson with a discussion on time zones. Half of the class was off task and ready to move on but the other half, which included a handful of students who struggle in math, participated and seemed to really understand the concept. One student in particular said “Ohhhh, I get it!” It was the saving grace for the rest of the class that was already transitioning into the next phase of the day. What I learned about teaching/ learning/ students/ self I learned that when you teach you need to at the very least present yourself as someone who knows what they are doing. If the students think that you might not know the answer, they probably won’t ask you. Presenting yourself as someone who understands the topic fully tends to give the students more respect and compliance, even if they aren’t consciously aware of it. I learned that learning is greatly varied amongst a group of nearly thirty ten-year-olds. Half of the students knew exactly what I was talking while I was giving my lesson while the other half seemed to be digging up distant information that they had learned somewhere. Learning, at least in my classroom, is something I need to be more conscious of, especially when planning things to do for early finishers. - 29 -
  30. 30. What I learned about my students is that they all do like to learn, but in different ways. They really don’t seem to enjoy another adult who talks at them, as opposed to an adult who talks to them. There were students who looked particularly bored during parts of my lesson because I was just telling them information, not writing it or giving examples. They conveyed to me that they need something more from me if I want them to stay engaged. I learned that I need to be a better actor while teaching. I went into the lesson with an attitude that it was going to be easy review for the students but soon realized it wasn’t review for many; it was re-learning a concept from the past. This threw me off and broke my confidence and the students showed me with their actions that they could tell. Being in better control and better prepared to speak to the class is going to be a must. What I may have missed: I covered all that I wanted to cover in my lesson. One thing that I would consider a miss is that I didn’t have a solid plan for students who finished their worksheets early. Suddenly students were done while I was still working with other students which then led to higher levels of noise and distraction. That will be a definite thing to fix tomorrow. What I anticipate about student response tomorrow: I think that students will be more on task tomorrow because it is a group activity and because it’s not the first day back from vacation. Progress toward objectives: When looking at my objective I think that a solid majority of the students met or exceeded it. When examining the worksheets, I saw that students were drawing clock hands correctly, some even taking into account the placement of the hour clock mid way through an hour, while most of the others placed the hands correctly in place. Students did even better at identifying what time it was by reading the hands of a clock. The only mistake I noted were students confusing the clocks hands. Adaptations for tomorrow: Tomorrow I will need to have a better plan for students who finish early as well as heightened supervision since tomorrow is a group activity. - 30 -
  31. 31. _______________________________________________________________________ _ Lesson 2 Teacher Name(s): Jesse Gilbertson Lesson Title: Time Keeps Tickin Away Unit Title/Topic: Data, Statistics, Graphing Target Grade Level: 4th Grade Estimated Time for Lesson: 30 to 40 Minuets Standards: • Mathematics: 4.1.4 Compare and order fractions and decimals. Materials: Index cards Black pen or crayon Pencils Lesson Objectives and Plan for Assessment: • Students will be able to tell elapsed time by examining airplane schedules and filling in missing pieces • Work off of the minuets & hours activity and reflection slip after the activities are finished. Anticipatory Set: Story of the Long Trip to Phoenix (5-10 min) • This story is about a trip that I took with two friends in September of 2009. Each day we planned our route, typed in our starting and ending location, and received the estimated time for the day’s drive from the GPS. system. The time the GPS gave us was our elapsed driving time. • Explanation of elapsed time o Time it takes something to happen. Can be short, can be long. o Briefly review quarter-hour increments and a.m./p.m. Lesson Sequence: Day or Night?: Activity (5-10 min) • Teacher will have broken analog clock in hand for word problems • Students will be given a note card and told to color one side of it completely black or a similar dark color. - 31 -
  32. 32. • Students will then be given word problems from the teacher who is using the broken analog as a visual tool. • Students will have to decide whether the elapsed time ended in the period of a.m. or p.m. and will hold up their cards, black or white, to express what they think. Black will represent p.m. and white will represent a.m. Minuets & Hours Activity (worksheet and teacher/student activity) (10-15 min) • This activity is a worksheet that has problems about elapsed time on them. • Students will solve problems on elapsed time using o Analog clocks o Given time o Teacher suggestion (based on students comprehension) • Teacher will look at a student’s worksheet to quickly assess where a student is at then will write in information onto the student’s worksheet, challenging the students appropriately. Closure: Reflection Slip (5 min) • Students will use their day & night activity card (should have one side still blank on it) to write a reflection on what they learned. Two question prompts will be asked. o Why is this useful? o What kind of event could you use this skill during? Differentiation: Meeting needs of individual learners • If a student is having difficulty with any of the activities, a partner who understands can be paired with them to help assist their learning. • For students who aren’t being challenged enough, a brief assignment on the use of a calendar will be given. Topics will include a calendars use, what each day represents, and how to plan a trip. Reflection Daily Reflection: Lesson 2, 12-1-2009 Lesson Title : Time Keeps Tickin Away Synopsis of what happened: Today my lesson was very different than yesterday. Because of a new portion of the school that is being built, there was a groundbreaking ceremony followed by an assembly during my scheduled lesson time, so like an adaptive teacher I taught my lesson early in the day instead of the afternoon. This had its drawbacks. First the students - 32 -
  33. 33. had P.E. right before my class and because of a behavioral issue that happened the Friday before Thanksgiving break, the class was held longer than usual. When they got to the class and were settled in, we had roughly thirty minuets, to complete all of the activities before recess. I started this lesson with more authority and the students responded quicker and more quietly today. I gave them index cards and told them to color the lined side black while I told my anticipatory set story about a recent road trip to Phoenix. Giving the students a task while a story was being told was great. The students were quiet and on task, but seemed confused for what the cards were for. When I finished my story and told them about elapsed time the students seemed to be following me. I explained that I was going to give examples of elapsed time, events starting in a time period and ending in another, and have them raise their cards according to what time period of the day that time fell in. Black representing PM and the white representing AM. Things seemed to be going alright until this point. The terms AM and PM confused some of the students. If I would have just said day or night the students would have all been perfect in their responses, but since AM and PM were reintroduced, some of the student’s responses varied. For the most part the students understood the concept and answered accordingly. After this activity was over I had the students find a partner of their choice and gave them an elapsed time worksheet that I created. The students were all suddenly quiet and on task, even the students who showed little interest in the previous activity. I monitored the partners and found that some were more conducive to getting their work done than others, but for the most part the students seemed to enjoy the activity. Some pairs began to merge into quads which I allowed if they asked politely and were on task. Students seemed to only have trouble with ‘partial hour increments’, meaning that fifteen minuets, half hours, and forty five minuet increments threw off some of the students. At the end of the lesson I tried to have the students fill out a comment card on why knowing elapsed time would be useful in real life, but time expired and the students, as a whole, didn’t understand how I phrased the question. Instead of trying to explain I told them to just give me their worksheets. The one card I actually got with a response was from a student who was having a lot of trouble with the worksheet. The card reads “when you late for”. How I interpret this is that its good to know elapsed time so that - 33 -
  34. 34. you know if you are going to be late. I’m not exactly sure if that’s what he meant but it was good to see he understood the reason even if he didn’t understand the process. What I learned about teaching/ learning/ students/ self Today I learned that teaching is something that requires an elastic mentality and schedule. It boggles my mind how many times a week my cooperating teacher has to modify his schedule for some school event or special test. Today was a prime example of this with a ceremony and assembly right in the middle of the day. Understanding that will help with more realistic expectations for my future classroom, at least as far as time is concerned. Today I learned that learning isn’t all about computation and getting things correct. Sometimes it’s about the bigger picture or the concept. The student I mentioned in my synopsis is a perfect example. He had a hard time figuring out the problems on the worksheet but he understood some of the conceptual ideas of the lesson. It’s interesting where learning takes place within a students head. Today I learned that my students like working in groups. The level of on task students was something I wasn’t expecting to that extent and it surprised me. I learned that I am becoming more and more fluid while going through the school days. Transitions are becoming easier to conduct and schedule changes are not as ‘day altering’ as they seemed to be at first. What I may have missed: I think that I would have had better results if I was given more time today. I wish I would have been able to teach at my normal time but that’s just something I had to deal with. What I anticipate about student response tomorrow: I think that tomorrow is going to go well. I am taking elements of the last two lessons and combining them into a fun partner activity. I have also made overhead copies for this lesson of the actual activity and have filled them out, trying to figure out possible snares that students would encounter. I addressed the problems I came across with my cooperating teacher and he and I worked out solutions to them that were simple and easy to implement. Progress toward objectives: My activity didn’t follow the lesson objective as well as I had hoped. In retrospect, having airplane schedules might have been a better way to have had the students work with elapsed time. That way would have also introduced the students to tables of data/information, which is coming up - 34 -
  35. 35. on Thursday. Adaptations for tomorrow: Tomorrow I am going to go through a sample activity with them. Modeling what I want the students to do should clarify expectations and get the class working productively while having a good time. _______________________________________________________________________ _ Lesson 3 Teacher Name(s): Jesse Gilbertson Lesson Title: Road Trip! Unit Title/Topic: Data, Statistics, Graphing Target Grade Level: 4th Grade Estimated Time for Lesson: 30 to 40 Minuets Standards: • Mathematics: 4.1.4 Compare and order fractions and decimals. Materials: Pencils Road Trip activity sheet Thumbs Blank paper for notes Colored pencils Atlas Lesson Objectives and Plan for Assessment: • Students will be able to effectively use a calendar by plotting out trip dates. • Assessment: Thumbs up/Thumbs down activity and Road Trip! activity sheet Anticipatory Set: 30 or 31? Warm-Up (5 min) o This warm up activity will be a thumbs up/thumbs down activity. - 35 -
  36. 36. o Teacher will ask the students as a class if they think a given month has 30 or 31 days in it. Students will respond with a thumbs up or a thumbs down. Lesson Sequence: What’s in a day? Discussion (5-10 min) • Discussion on what a day represents: review of am/pm, hours, and minuets • Discussion of what months and years represent. o During discussion students will be raising their hands for inquiries, and following along to notes that will be written on the overhead. ROAD TRIP! (20-25 min) • This activity is a partner activity. Students will choose their partner that sits within their own row. • Students will use an activity sheet to plan out a trip. • Front: Students trips will include starting and ending locations, daily plans, supplies, reasons for their trip, what they will do on the trip, and a picture of a map that they have drawn, mapping their route. • Back: Students will use the back as a daily itinerary. o The daily itinerary will include daily locations, a general route, time of departure, time of arrival, and elapsed daily trip time (the meat of the activity) • Students will plan their daily itinerary day by day, each day checking to see with the teacher if their times and dates match up. • Some students will have a long trip, while others might have a short trip or run out of time. Going day by day saves paper and gets the teacher more involved with the activity. Closure: Trip Sharing wrap up (10-15 min) • Students will be asked to share certain aspects of their trip with the class. Depending on time, groups that have remained on task will get to share more with the class. Differentiation: Meeting needs of individual learners • Students who have difficulty with this activity can choose to work alone or be partners with the teacher. • Students who aren’t being challenged can design a longer trip for their road trip activity. Reflection Daily Reflection : Lesson 3, 12-2-2009 Lesson Title : ROAD TRIP! Synopsis of what Today my lesson was about the topic of calendars and - 36 -
  37. 37. happened: planning a trip. I had the students start with a thumbs up/thumbs down activity that dealt with the amount of days in a month. I told the students that I was going to say a month then how many days that month had in it. If they agreed then they would give a thumbs up and if they disagreed they would give a thumbs down. This activity went alright from my perspective. Some of the students mistook some of the months but the majority had them right. When I asked about February all of the students got excited about the fact that they not only knew the amount of days but also knew it in the context of a leap year. My next step was to ask the students about what a day was, meaning anything that they thought a day represented. The answers I received were “when you are awake, when it is light out, 24 hours, and when you are at school,” to name a few. I then had a blank thought moment. I’m not sure why, possibly because I made eye contact with my teaching supervisor, but instead of explaining that days then translated into months then into years, I looked like a deer staring into headlights. I quickly snapped out of it and started the next portion of the lesson. My main activity was, in theory, a great activity but its hang up was, as I thought, the students concentrating more on the creative aspect of it instead of the mathematical portion. The activity was a road trip planning activity that had students paired in partners working on designing a road trip somewhere along the west coast during their winter break. I had a completed worksheet that I displayed on the overhead to give the students an idea of what they were suppose to do and then turned them loose. I realized right away that I didn’t do a good idea explaining what I wanted the students to do. Many groups were asking me questions I thought were simple concepts that they either understood or that I had already explained. I didn’t model what I really wanted the students to do very well. I showed them a finished product and assumed they knew enough information to ‘get it’. Now the students didn’t do anything incorrectly, but they didn’t have a clear goal in mind. I had them design a trip by planning a starting and ending location, a date of departure and arrival, a map they needed to draw, and a supply list. On the back of their worksheet the students used a daily itinerary to plan the days of their trip. The students, instead of getting to the daily itinerary where the actual math application took place, spent a majority of their time trying to figure out where they wanted to go, planning out their supply list, and drawing a map. I was urging them to get to the back of their worksheets so that they could get to the important part, but as I did so a fire drill took place. The students did this drill very quietly and quickly, perfect as far as a class of twenty six students can do it. - 37 -
  38. 38. When we got back in I had the students focus on the back side of the worksheet, primarily the right column, so that they could get some application with numbers. Some groups did so but others kept working on the front portion of their worksheet. When my time was over, I had them explain where they went on their trip and what they planned on doing there to the class then had them turn their worksheet(s) into me. The work was fairly good, but in retrospect, modeling more and starting the students with the time planning portion would have satisfied the objective first then let them expand afterwards. As my advisor Bill put it “convergent learning is hard, divergent learning is easy”, meaning that having the students start with a part of the project that doesn’t have to do with the main goal of the lesson can distract and take away from the whole point. In retrospect I think that I assumed too much about my students ability. Even with the pre test examined, I assumed that the students could easily tell time and elapsed time within another activity, but by having them start with a portion of the activity that didn’t have anything to do with the main goal hindered their learning. Also something like tying this into a social studies unit would really have been beneficial. What I learned about teaching/ learning/ students/ self Today I learned that teaching requires a lot more than a simple explanation. I’m not new to that idea but today I assumed that modeling wasn’t as important as I thought. In the future I will make sure to model more thoroughly and me more mindful of my students abilities. Today I learned that learning needs to be focused then expanded on. I wasn’t specific enough in the beginning of my lesson and I had to play catch up the rest of the time. I need to make sure that my students are getting the main point before breaking off and doing an activity. Today I learned that my students respond well to me. I am gaining a better position as a manager in the classroom and it’s showing in the students responses to my requests and instructions. The whole time I was being observed I felt as if I had my class under control and was happy to see my students respecting me in that manner. I learned that even if you think of some of the major snares in a lesson that there will always be more that will trip you up and that you need to be willing to accept and roll with the punches. Having Bill there today was nice because he gave me great feedback that made a lot of sense. I really think that it is going to help focus the rest of my lessons. What I may have What I missed was the order of how I presented my - 38 -
  39. 39. missed: information and my lack of good modeling for the students. Although most of the students got to a point to where they completed what I asked them to, they were still hung up on the other aspects of the assignment. What I anticipate about student response tomorrow: I think that as far as my control of the classroom goes that it will be as good as today if not better. I think that going in with a new mindset and focus on how to explain what I expect from the students will help their learning quite a bit. Progress toward objectives: Today my progress towards the objective was not stellar. Like I’ve mentioned multiple times above, the students were caught up in the other aspects of the activity. Adaptations for tomorrow: Tomorrow I am going to model much more as well as show examples in class. Having my expectations and goals demonstrated first and foremost is going to be a goal of mine for the rest of this practicum. Lesson 4 Teacher Name(s): Jesse Gilbertson Lesson Title: Check the Numbers Unit Title/Topic: Data, Statistics, Graphing Target Grade Level: 4th Grade Estimated Time for Lesson: 30 to 40 Minuets Standards: • Mathematics: 5.1.7 Construct and analyze double bar, line, and circle graphs to solve problems involving fractions and decimals. Materials: Paper Pencils Two decks of cards Butcher paper Half sheet worksheet Lesson Objectives and Plan for Assessment: • Students will be able to create line plots by examining data given. - 39 -
  40. 40. • Assessment: Line plot group activity, plot to stats worksheet wrap up. Anticipatory Set: Examining Data Mini Lesson: Mini Lesson About Data and Tables (10-15 min) • Teacher will lead the students through a list of data and its corresponding table. • Teacher will show students how to read lists of data and how they are interpreted onto a graph. • Two examples will be shown. o The first will be data that needs to be interpreted onto a table o The second will be a table of data that needs to be interpreted as raw data. Lesson Sequence: Line Plot Group Activity (15-20 min) • Students will be assigned a playing card with a denomination from two to nine. • There will be some individual cards as well as small groups of cards. These represent different size groups that could appear on a line plot. • Students will be asked to get into their respective groups and then clear some desks in the front of the room out of the way. • Students will then be instructed to line up in straight lines facing the board, in their respective groups, by numerical order. • The teacher will then use a pre made blank graph to plot out the student’s distribution. • The teacher will explain that each person is represented on the graph, but ordered according to their card. • Once students have completed this original line plot the students will be asked to return their cards to the teacher and asked to huddle around the teacher. The teacher will then explain that they are going to put up a pre made line plot and that the students will need to arrange themselves so that the line plot is correct. o The purpose of the huddle is so that students don’t get bent out of shape if they are not in the same line as all of their friends and so that they have a ‘team’ mentality going into the final stage of this activity. • Students will then get into their spots while the teacher monitors and directs the flow of traffic, if needed. Plot to Stats Mini Worksheet (5-10 min) • This worksheet will be a half a page and include a table that is labeled with the context data for the final line plot that the students arranged themselves in. • Students, with a partner or a foursome, will take the data from the line plot and interpret it back into a data format. • The teacher will then synthesize the information by walking the students through the process. This will be for students who are struggling and to further the connections that the students are making on the subject Closure: - 40 -
  41. 41. Line Plot Evolution Wrap Up (5 min) • Students will, on a blank piece of paper, write about their experience. The question of “what do you think that line plots could change into?” will be asked as a writing prompt for students to predict what kind of lesson could come next Differentiation: Meeting needs of individual learners • Students who do not wish to participate in this activity may choose to opt out of the experience. Students who are having difficulty understanding the concept may request a custom set of notes that explain the concepts and processes more clearly. • For the students who aren’t challenged enough, they may assist the teacher in directing the flow of traffic during the activity. Reflection Daily Reflection: Lesson 4, 12-3-2009 Lesson Title : Check the Numbers Synopsis of what happened: Today my lesson started with me explaining that the class was going to be learning about reading and analyzing data. I explained that data is information that is collected, sometimes for the sake of having information and other times to gather information for a purpose. I gave them the example of their pre test being data for me to design better lessons for them. I then told them I was going to gather information from them by using a survey. My survey was going to be on their favorite temperature, meaning weather outside, and had a blank overhead of an empty data table showing on the screen. I wrote “What the study or survey is about” above the far left column and in the top box of the table wrote “students favorite temp”. I continued filling in each row with a different temperature, in increments of ten degrees, starting with thirty and going up to one hundred. I then wrote “tally mark per student” in the top box of the second column. Next I started collecting data by asking students what their favorite temperature range was. For every student who raised their hand I marked a tally. After the tallies were all complete I wrote “# for tally marks” in the top of the third column. I asked the students what each number in that column should be and in unison they walked me through each row on the data table. So far so good. All of the students saw how to fill in a table with data. I then showed them how to represent this data as a simple list of data. For example, in the row that represented thirty degrees I had eight students. I wrote the number 30, eight times, explaining that each time I wrote - 41 -
  42. 42. the number it represented one person and the temperature they liked the most. Again, so far so good. I then had the students in the front row move their desks to make room for a line plot exercise. I passed out index cards with random numbers ranging from one to ten on them to all of the students. I then called up the students with the number one to the front (there was only one), followed by students with the number two. Three students came up for this number so I had them line themselves straight, facing forward towards the class. I did this for numbers three through ten and all of the students got to their designated places quickly and correctly. I then drew a line plot on a large piece of butcher paper that was hanging on the board. I explained to them that the left side of the plot represented the number of people with their number, and the bottom represented the number they were given; labeling each with numbers one through ten. I asked the student in row one how many people were in his row and he said “one”. I then marked an x above the number one on the bottom of the plot. I asked the students with the number two cards how many people were in their group. They responded “three!” to which I then marked three x’s over their card’s number. The class then seemed to get this and every group followed suit until the last group. I then brought out a pre made line plot and told them to arrange themselves into this formation. This took some more time than when they were assigned a number because they wanted to be with their friends and I didn’t stick with my original huddle idea in my lesson plan. However, all the students, within two minuets were correctly ordered. I then had them return to their seats to get ready for the final portion of the lesson. This is when things began to fall apart. I gave the students a half sheet of paper with a line plot on it, the same line plot that they had just arranged themselves into, followed by a blank line data table and told them that their job was to fill in the data table with the information from the line plot. The look of confusion shot up all over the classroom. That’s when I realized my connection between a line plot and a data table had never clearly been stated. I tried to scramble and explain it quickly but the student’s comments of “I don’t understand” started to get to me. I then decided to walk the students through the beginning of the worksheet and see if they could take the reigns from there. About three fourths figured it out after a little modeling but there were still confused students. The class finished the lesson by predicting what a line plot could turn into, but by that point they were confused on what a line plot - 42 -
  43. 43. represented and didn’t have any guesses that I was hoping for (graphs). I was upset by my lack of connection between the two ideas of representing data and I immediately wrote down how I should have done the lesson on the back of a worksheet. All in all the students understood the two separate parts of the lesson but because of my lack of connecting the two I wasn’t able to give them the full comprehension that I intended. At least I realized immediately after the lesson what went wrong and how to fix it. Before the lesson on range, median, and mode I am planning on re teaching this lesson, possibly extending my stay at Dayton Grade School another day. If the students get the connection quickly I might be able to stay on schedule. What I learned about teaching/ learning/ students/ self Today I learned that teaching is all about constant reflection. After I taught today I was left somewhat distraught but at the same time I was left with my mind racing. I couldn’t stop thinking about where things went off course and how I could fix it. Luckily I was given a twenty minuet period where the students left the classroom for another daily activity so I was given that time to reflect in silence. I paced back and forth through the room thinking about when in the lesson things started to get confusing and was able to pinpoint what I did wrong. Even though I feel like the lesson wasn’t completely successful, I feel that at least knowing where I went wrong and how to fix it is an important step in the teaching process. What I learned about learning is that, at least with the age group that I’m working in, modeling is really important. Doing an example of the work you want the students to duplicate is very key, especially if the students haven’t previously been exposed to the material. My analogy to this would be following someone, in a car, to their house. The person models the route they want you to take and you follow, hoping that you remembering landmarks (concepts) and turns (methods to solve the problem) to lead you to the correct end destination. The good thing about being a teacher is that you not only get to guide the students to the house, you get to point out the landmarks and make sure they know all of the turns to take. Today I learned something good about my students. With activities that involved more than just doing worksheets, students were really engaged. In the beginning of the lesson some of the students seemed wary of how the course of my instruction was going to play out, but as soon as we created the human line plot students were more than willing to participate and give feedback. Utilizing the student’s willingness to participate in activities could prove to be helpful later on in the - 43 -
  44. 44. work sample. Today I learned that I know how to reflect. I was glad that even though the lesson didn’t turn out the way I had hoped, I was able to realize what was wrong and how to fix it next time I teach. Making sure the connection between line plots and data tables is where I faltered, so in my review I will need to make sure that these connections are modeled correctly so that students will be able to ‘drive their car’ to the correct place. What I may have missed: In this lesson the thing I missed was explaining the connection between data tables and line plots. The students understood how data tables looked and represented and they also understood what line plots were and how they were represented, but a majority of them missed the connection between the two. During review, I feel as if I modify my activity to keep it interactive while modeling the entire time, students will have full comprehension. What I anticipate about student response tomorrow: My student’s response on Monday should be the same as it was today. They were engaged and participating very well and I expect the same out of them next time I am giving a lesson. Progress toward objectives: The progress towards the objective was not met in this lesson, but it was very close. Students know how to read data and label it in a table and they also know how to interpret and create a line plot, they just haven’t established that clear connection between the two, one being the picture representation, the other being the number representation, are interchangeable. Adaptations for tomorrow: My adaptations for tomorrow are going to be primarily in my review of data tables and line plots. Range, median, and mode might need to be moved back another day if this goal isn’t reached but if the connection is made quickly then lesson five should take place with no problem. - 44 -
  45. 45. Lesson 5 Teacher Name(s): Jesse Gilbertson Lesson Title: That’s About Average Unit Title/Topic: Data, Statistics, Graphing Target Grade Level: 4th Grade Estimated Time for Lesson: 30 to 40 Minuets Standards: • Mathematics: 4.1.4 Compare and order fractions and decimals. Materials: Pencils Paper Graph paper Lesson Objectives and Plan for Assessment: • Students will be able to calculate range, median, and mode of given data. • Assessment: Line plots from each student, as well as the group range, median, and mode activity sheet. Anticipatory Set: Line Plot Review (5-10 min) • Teacher will lead the students through a review of line plots. • Teacher will use the same line plots on butcher paper from the activities in lesson four. o Areas that will be covered will be what each X (or chosen symbol) on the line plot represents (how that corresponds to the y axis) and what the x axis represents (usually a measurement of distance or time). • Teacher will then transfer the data into a simple data table form. This is to synthesize the relationship between data and line plots. Lesson Sequence: Range, Median, and Mode Mini Lesson (5-10 min) • Teacher will lead a brief lecture style lesson on range, median, and mode. - 45 -
  46. 46. o Teacher will discuss the terminology, and provide examples of each on an overhead. • Teacher will lead the class in examining a data table and determining its range median and mode. Grab Bag Activity (10-15 min) • Students will get in groups of four (randomly or by choice… will be determined by teacher depending on the weeks prior group activities). • Students will then draw at random a data table of information about miles driven to work/school in Dayton. o The students will then find the data’s range, median, and mode. • Each student will be given graph paper to create a line plot for their data, but they may still work together as a group. • Each group will give a very brief explanation to the class of how far their group of people has to drive to work while explaining what their range, median, and mode were. Their line plots will also be shown to the class. Closure: Bar Graph Preview (5 min) • Teacher will use the same line plots, on butcher paper, from lesson four and will then change them into bar graphs. • Students will then have the knowledge that line plots and bar graphs are nearly the same thing, just drawn differently. Differentiation: Meeting needs of individual learners • For students who are having difficulty understanding the concept of range, median, and mode I will provide individual help or will place them in groups of students who have high understanding. • Students who are finishing early may help other students who are having difficulty, assisting them with concepts and computation. Reflection Daily Reflection: Lesson 5, 12-7-09 Lesson Title : That’s About Average – Range, Median, Mode Synopsis of what happened: Today my lesson was on the topic of range, median, and mode, and also a review of line plots and data tables. I started with the review of plots and data tables because last Thursday, when the students had the lesson on them, there was some confusion in the connection of the relationship of plots and data tables. I actually focused most of the lesson on this review because I need the students to understand this concept for the foundations of future lessons. I began the lesson telling the students that we were - 46 -
  47. 47. going to review what we had gone over on Thursday while I gave them a sheet of paper with a blank data table and a blank graph (x/y axis) axis for a line plot. I also told them that I had failed to explain the relationship of data tables and line plots. I had an overhead of the paper they had and I displayed it on the board. I then explained that the information on the data table is a way to show information with numbers, while a line plot, or graph, is a way to show information with a picture, or visual. The students seemed to understand this connection. I then handed out the same cards I used in lesson four, with a number from 1-10 on them. I then had the students get two colored markers/pencils/crayons out. I had them take one color and star the top left corner of the data table and the bottom potion of the blank graph. I explained to them how the information on these two sections was the exact same, even how it is labeled. Together we labeled the graph and the table with the information that was given (numbers 1-10 from the cards as well as the label ‘# on card’). Next we took the second color and starred the second column of the table and the left side of the graph. I asked the students what they thought these two stars represented. One student raised his hand and said “they mean the same thing?”… “exactly!” I responded. I told them that this column represented the number of students who have that given card. Together we labeled the graph and table ‘# of people with that card’. Once that was complete I surveyed the students. I asked who had what cards, students raised their hands, and other students counted and gave me information to fill into the table. When we had completed the table I inquired about the stars we had drawn and what they meant. One student, who usually doesn’t like or ‘get’ math blurted out “the same thing!” from the back of the classroom. I couldn’t help but smile, and responded “that is correct, now, can you tell me what I would do to the line plot then? What symbols we would use to show the information above, down here?” He responded “I think we use x’s or stars…” to which I responded “right again, how many x’s would we put here?” to which he replied “ummm…3”. A murmur of “oooohhhh” came from the class. I then asked students how the rest of the graph would look and students helped me complete the remainder of the lone plot. The connection was made but I wanted to synthesize further. I brought out another data table and line plot overhead, this one being half completed on the table and half completed on the line plot. There was initial confusion because the students were still looking at their completed sheet on their desks but when I explained that this was a completely new table and plot, they figured it out quickly. The class helped me fill in the missing data on the plot and in the table and together we - 47 -
  48. 48. completed both, including the correct labels. I felt good about this. Even though I wasn’t able to make the connection the first time through, I was able to get the class on the same page the second time. Where my lesson started loosing its focus was when I shifted the lesson from line plots and data tables, which took nearly twenty five minuets, to the topic of range, median, and mode. I could tell immediately that the students had already stretched their brains and wanted to move on past math, but I decided to see if they could stand it for a little while longer. I then gave a short lesson on range, median, and mode that I felt went well. The students seemed to understand the examples I gave them and how they worked. Next, I moved to an example of how to get range, median, and mode from a data table. I needed to spend more time doing this, making it more of an interactive activity where the class and I walk through the process, but my main focus for this lesson was on the review on line plots and data tables. In this lesson I showed them how to find the range you would just need to find the data category (in this case a number that represented the number of miles from a students house) that had the largest sample and the one with the smallest, then simply subtract the smallest from the largest. They seemed to get how to do it but the reason why or what it was used for was unclear. I didn’t fully explain to them that the range represents how far across the data spreads between the smallest and largest number. Median, that is a whole different story. In my example that explained what range, median, and mode were I had a sample of nineteen numbers to find the median in. In my example using data tables I had a sample of around thirty to thirty five numbers… meaning the students would have to write all of them out to find the median. The students were very hesitant to do this because at this point we were nearing forty five minuets of non stop math, new math, and it was too big of a bite to chew. They understood the concept but were drained by this point. Mode was simple for them, but some of them got it confused. Instead of saying “the mode is 6 because it has 12 votes” the students would simply say “the mode is 12”. There is clearly some confusion in the fact that the number of students is a factor of the data, not a category itself. I think that is something that becomes more and more concrete as you age but I should have made that more clear. A good portion of the students understood the lesson and turned in good work, but my instructions must not have been clear enough because lots of groups found the range for one problem, the median for another and the mode for the third. They didn’t do it incorrectly but only one group turned in what I - 48 -
  49. 49. was hoping for. I decided to cut it short when the lesson hit forty five minuets because of their lack of focus and my lack of being able to explain it off the top of my head. I plan on readdressing this after graphing is over with more detail and modeling. What I learned about teaching/ learning/ students/ self Today I learned that teaching goes well when you know exactly what you did wrong the first time. The feeling I got when all of the students were ‘getting it’ was amazing, but it was only possible because I had already taught on that subject and seen what I did wrong. I suppose that this is just a normal process of a teacher, constantly getting better ant understanding where the pitfalls are going to be before they come. I’m glad I planned reviews of the previous lessons in a lot of my lessons because it is giving me a second shot to explain a lot of things that I’m missing. I learned that learning, real solid connections in the brain, happens when you use more than one intelligence together. I tried just explaining the subject of line plots and data tables but it didn’t work. Using an overhead, drawing colored stars, and walking students through the process worked wonders. Students, especially at a fourth grade level need to see, hear, and interact all in one activity to really get what’s going on and remember it. What I learned about my students is that when they do get it, they all really do like to try. It’s interesting because some of the students who I’ve never seen excited about learning were raising their hands and sometimes just blurting out answers. I’m going to have to figure out how to explain every lesson in a similar format. Today I learned about myself that my reflections and second ideas after lessons are paying off and working well. Immediately after I taught last Thursday on line plots and data tables I sat down and wrote what I did wrong and what I needed to do to be successful the next time around. It worked and it felt good. Getting feedback from my CT is also a great thing and when he gives suggestions its good to internalize those and mix them into your own thoughts. I’m learning to do that well as this practicum moves along as well. What I may have missed: What I missed today was the time I decided to take for math. I basically had two different lessons, one that I was re- teaching and the other being a new subject. If I would have had time earlier in the day to do one that would have been amazing but the schedule didn’t permit it. I think that the range, median, and mode lesson wasn’t missing anything, but on the contrary, was packed with too much stuff. The students had a hard time sifting through the numbers and being at the end of the day after - 49 -
  50. 50. already doing half an hour of math made things more difficult as well. What I anticipate about student response tomorrow: Tomorrow I plan on doing my planned lesson instead of trying to review range, median, and mode and I think the students are going to enjoy it. The activity is about pictographs and is in a survey based format. Since my students enjoy working in groups they should be very engaged and on task. Progress toward objectives: The objective was not met on this lesson, but I did achieve the objective from the last lesson. I plan on readdressing the subject of range, median, and mode before my last lesson or possibly re-teaching it afterwards. Adaptations for tomorrow: Tomorrow will be anew subject, however, knowing that students in my class work best with a walkthrough will help me with how I present information. Lesson 6 Teacher Name(s): Jesse Gilbertson Lesson Title: Get the Picture Unit Title/Topic: Data, Statistics, Graphing Target Grade Level: 4th Grade Estimated Time for Lesson: 30 to 40 Minuets Standards: • Mathematics: 5.1.7 Construct and analyze double bar, line, and circle graphs to solve problems involving fractions and decimals. Materials: Data table sheets Pencils Misc. paper Stickers Lesson Objectives and Plan for Assessment: • Students will be able to interpret and create pictographs from given data. - 50 -
  51. 51. • Assessment: Pictograph survey sheets, written response on the back of the pictograph activity sheet. Anticipatory Set: Picture/Object Math Warm Up (5-10 min) • Class as a whole will be given the task of using objects or pictures as symbols for numbers. • Teacher will hold up an object then assign a number value to the object. Students will then gather the as many of the object as they can, calculate their total and return to their desk. • Teacher will then ask each row to calculate their totals and then share it with the class. For each row a rough pictograph will be created. Lesson Sequence: Examining Pictographs Mini Lesson (5 min) • Students will be shown two to three pictographs and be asked to explain what each mean. • Students will be shown that each picture on the graph represents a value, which will be given for each graph. Students will simply have to look at a picture and write down a number value. Pictograph Survey (15 min) • Students will be given a blank data table and will be instructed to think of a topic of a survey. • Examples will be provided, showing different survey ideas such as favorite football team, favorite color, favorite subject, etc. • Students will then write their categories (choices) in the left hand column. • Students will then begin their classroom wide survey. o Students will walk around asking their friends their subject question and giving them their options, tallying their results as they go. • After the students have surveyed their class they will return to their desk where there will be another blank table for them as well as stickers for them to create a pictograph. • Students will have to determine the value of each sticker on their graph and then create it. Closure: Picto to Line Plot to Bar Graph Conversion (10 min) • Students who have been on task and working well with their classmates will be chosen to share their pictograph with the class. • The teacher will then convert their pictograph to a line plot, then to a bar graph. • Students will then be asked to use the back of their pictograph to write on the writing prompt: - 51 -