Table of Contents
Table of Contents
Section Page
Contextual Factors 2-12
Learning Goals 12-19
Assessment Plan 19-28
Design for Instruction 28-36
Instructional Decision-Making 36-38
Analysis of Student Learning 39-43
Reflection and Self-Evaluation 43-47
References 47
Appendix 48-65
Learning Goal Graphs 49-51
Student Work 52-65
Contextual Factors
There are multiple factors that may affect the teaching and learning process in my classroom. Some factors may affect all the students in my classroom, while others affect possibly just one. These factors could come from the community, the district, the school, the classroom, or the student him/herself.
Community Factors
The community in which I student taught is a rural community with a population of just over 600 people. Recent statistics state the racial makeup of the city is 97.57% White, 0.16% African American, 0.81% Native American, 0.65% Asian, 0.16% from other races, 0.65 Hispanic or Latino. The majority of the population’s age is either less that 18 years or 24-44 years of age. The median income of households is $37,614, with 0.0% of the community’s families below the poverty line. Although it is a small community, there are larger cities that employ residents with an average 30 minute commute. This community brings in many new families because of its low property taxes, and has shown school support by passing tax laws which give money to help the district.
District Factors
The district in which I student taught consists of students from three neighboring cities. The district population has been decreasing in the recent years and is currently at 476 students. The gender ratio in the district stands very close to 50:50. There is a very small population of non-white students. Currently there are less than 1% of students with Hispanic origin and less than 1% of students with Native American origin. The district currently has 23% of students with free or reduced lunch.
Level III special needs students are sent to a neighboring school district, and there is currently no need for an ELL teacher. There are Special Education teachers placed in all school buildings who work with those students that need remediation or extra help with their classes. Talented and Gifted students are not recognized through extra curriculum until fifth grade, where they are chosen based on test scores and teacher recommendation.
The district has incorporated some initiatives throughout all of the schools. These include CRISS strategies, E2T2 mathematics, Second Chance Reading, and a Positive Behavior Support System. All new teachers go through CRISS training before the school year. Mathematics teachers receive E2T2 training and reading teachers experience Second Chance Reading instruction. The Positive Behavior Support System in the districts way of preventing bad behavior and is implemented through all school buildings.
School Factors
The school building in which I student taught contains 5th grade through 8th grade. This year’s population is 126 students. The male to female ratio is 31 males to 32 females. There is a 1.2% minority population in the school building. The free and reduced lunch in this building is 26%, which is just a small amount higher than the district percentage. Students with behavior problems are recommended for a local boys and girls private school. There are two special education classrooms, one for 5th and 6th grade, and another for 7th and 8th grade. Most students are pulled out only for remediation or one-subject support. The students chosen for T.A.G. are pulled from class for two hours every Friday.
The school building implements CRISS strategies, and there is a day-long professional development day that all teachers will attend this school year. The school building also implements a Positive Behavior Support System where all students are taught correct manners and behaviors at the beginning of the year. They are given ROYAL reminders throughout the year for both positive behaviors and negative behaviors. Negative behaviors result in either loss of recess or a lunch time learning session. Positive reminders are rewarded by the principal and then sent home to inform the parents of the student’s good behavior. All mathematics teachers use E2T2 strategies and attend seminars throughout the school year, while all reading teachers use Second Chance Reading strategies and also attend yearly seminars. The current principal has been at the school for 10 years creating positive moral for teacher and students alike. The teachers in the building range from first year teaching to more than 25 years. The positive attitudes and joyous personalities of each teacher have had a great impact on the school’s learning community.
Classroom Factors
I student taught in a sixth grade mathematics classroom. The room is around 27 feet by 21 feet and was filled with 18 desks, the teacher’s desk, a desk for myself, various small tables for books and student work, a television stand, an overhead projector and stand, a large storage cabinet, and two large filing cabinets. The desks and other furniture took up most of the area of the room, allowing minimal space for students to work in anything other than a whole class setting or a two to three person group. The desks were in rows facing the white board at the front of the room with two large windows to the left, the door and teacher’s desk to the right, and a window to their backs. The windows emit light, making a glare on the white board. The students can see the door from where they are sitting during a lesson, potentially causing them to become distracted if a visitor were to enter the classroom. The teacher’s desk sat towards the back of the classroom. This allowed the students to ask questions without their peers looking on incase they were uncomfortable. The classroom was on the third floor of a school building with no air conditioning. This caused the room to become stuffy and hot during the day. Because of the heat, two fans were constantly running, causing problems with blowing papers and noise.
The main technology in the classroom included an overhead projector, a television, a DVD/VCR player, the teacher’s computer, and twenty calculators. The television and DVD/VCR player sat near the teacher’s desk. This was due to the fact that the school would be receiving Geometer’s Sketchpad in the future and the only way the teacher could show anything through the television was from her computer. Because of the television’s placement, student would have to turn their desks in order to see the movie being played. The overhead projector was on a moving cart, and in order to use it, the students will have to move away from the center of the room so it can project the text large enough for all students to read. Every time I use the overhead, I will have to adjust the students and return the overhead to the corner of the room when I’m done. Although this is a pain, it is the only way for me to easily display information to the whole class without writing it all on the whiteboard. There are twenty new calculators hanging in the back of the classroom for students to use anytime they need to. These are all tattooed with the school’s name and are not to leave the room. This is helpful for students who forgot their calculator or do not own their own. Currently, the school hasn’t received their copies of Geometer’s Sketchpad so I am unable to use it during my teaching. There is a computer lab at the school. However, during sixth grade math, it is in use for eighth grade technology every day. This means I will have to sign up for the portable laptops. Currently, all of the laptops are being cleaned out and fixed up so I am unable to use them.
Parental involvement is a strong point at this school. When it comes to parent-teacher conferences, 95% to 100% of parents attend. Of those attending, close to 50% of their sons and/or daughters attend also. Parents are quick and willing to help if they are asked. The free or reduced lunch for students in the sixth grade stands at about 16%. Students are placed in a traveling group, either A or B, which they stay in as they attend science, social studies, mathematics, reading, English, and any other specials. Exceptions include the two fifth grade students who enter 6A for mathematics class, the six sixth grade students who enter 7A for mathematics, and the one sixth grade student who enters the Special Education classroom for mathematics.
Students follow the ROYAL guidelines where they respect each other, organize themselves and their time, take responsibility, always are on time and ready, and lead by example. Royal Reminders are issued for those students misbehaving or leading by example and can result with either a loss of recess or lunch time learning session. Positive Royal Reminders are given to the principal who recognizes those students and also informs the parents of their successful child. Crowns are given to students for positive behavior. These crowns can be used like money at the school store.
Student Factors
The students I will be focusing on for my Teacher Work Sample are in 6A mathematics. There are ten sixth graders and two advanced fifth graders, with an average age of 11 years old. There are eight males and four females. These students are all Caucasian. Of the 16% of students with free or reduced lunch in this grade, 13% are in this class. The students weren’t placed this way on purpose, the higher percentage was just an outcome of random placement into 6A.
One student in the class is in T.A.G. Half of the sixth graders in the class are in Second Chance Reading because their reading scores from last year were very low. One student received mathematics reinforcement in the Special Education classroom last year, but is now fully included in sixth grade mathematics and is only in Special Education for reading and English.
The achievement levels in this class are widely varied. There are some students who score very high in mathematics and can do this with little to no effort. There are also those students who struggle and try extremely hard, but often fail to succeed. In the middle, there are those students who understand mathematics, but have to put forth a lot of effort to succeed. The class ranges from a fifth grader who topped off all of his tests on the Iowa Tests of Basic Skills, to a sixth grader who was previously in the Special Education classroom for mathematics.
The developmental levels also range widely in this class. Some students are mature for their age and actively participate in class and do their homework. Other students are lazy and often are quick to give up when they don’t understand right away. One student lacks maturity and may throw a temper tantrum if he/she is wrong and thinks he/she is right. Another student understands what is being taught in class and answers freely and correctly any questions brought up in class, but can’t seem to transfer this knowledge onto paper when he/she is doing his/her homework. Yet another student will be active in class and participate, he/she will answer randomly when called upon, even though he/she knows he’s/she’s wrong. Although there are these specific students, there are other students in the class who have their own quirks, but haven’t shown them yet.
As for culture, this class has all grown up in the same community and gone to the same schools. They all speak English as a first language and none are fluent in any other language. Their interest, though somewhat varied, includes topics such as sports, movies, video games, hanging out with friends, and music. The students took a survey about their learning styles, and of the twelve students in 6A: five prefer hearing someone describe how to do a task, six prefer watching someone do a task, and one prefers doing the task him/herself. Mathematics is a very visual subject area. There is one student who may benefit from auditory teaching because he is extremely smart, but lack the skills to pay attention. Some students will benefit from a more hands-on approach, which will help keep them interested in the content.
Student Skills
The first unit in sixth grade mathematics is a review chapter. There were three students I focused on and studied their work during this unit. These students, Student A (SA), Student B (SB), and Student C (SC), are all in 6A. SA is a high achieving, top scoring student on all of the worksheets and previous testing. This student has problems paying attention and gets easily distracted. The student makes random movements and noises, has problems controlling his/her impulses, lack organization skills, and has been considered borderline autistic. The student participates in special programs during the summer and is in T.A.G.
SB is an average achieving student in the class. He/She works hard to achieve his/her grade. The student is ready and willing to ask questions if he/she doesn’t understand the problem. Most of the student’s errors are silly mistakes because of working through the problem too fast. He/She gets great support from home. An example is his/her step-father making him/her do extra mathematics homework at home. Even though there are times when he/she isn’t successful at them, he/she is quick to recognize the concept in class.
SC is a lower achieving student. There are times when this student works very hard and can succeed. There are other times when the student easily gives up and just writes down random answers. The student is always willing to participate in class, even though he/she knows he/she’s wrong. The student has difficulty paying attention when the teacher is in front of the room teaching and the students are taking notes. He/She is easily distracted and at times starts interrupting class by talking out of turn. He/She had mathematics remediation last year, and the student has very little parental support. There are many times he/she will give no effort, and is actually smarter than he/she gives him/herself credit for.
Instructional Implications
The following are instructional implications from the different factors that will influence how I plan and teach my unit to the 6A mathematics class.
Classroom Factors:
1. The size of the classroom and little amount of moving space will affect the way I plan and teach. If I plan activities where students are broken into groups, I will have to restrict students to groups of two or three. If I want to use groups larger than three, I will have to find an open room where we could transfer all of our materials and there would be more room for larger groups.
2. There are two fans running non-stop in the classroom because of the heat. Not only do they cause problems with blowing papers all over the classroom, but they are constantly making noise in the classroom. I will have to make sure I talk loudly and clearly at all times so that every student can hear me. It is important that I not only tell the students the directions, but that I also post the directions for students to read if they were unable to hear me clearly.
Student Factors:
1. There are ten sixth graders and two fifth graders in the class. This will affect my planning and teaching because there may be times when we cover content the two fifth graders haven’t seen before. If this is the case, I will either have to cover this content in front of the whole class, or I will have to pull the two students aside and cover the content while the rest of the class is working.
2. The skill level in this class varies widely. This is a huge factor in planning and implementing my unit. I will have to plan for those students who may not understand the first time, as well as plan ways to gain the interest of those students who may be bored with a simpler lesson plan. All the while, I will have to make sure I don’t let the average achieving students fall behind either.
Student Skills:
SA
1. Because this student is easily distracted and quick stop paying attention when someone is instructing them at the front of the classroom, I will have to keep checking on the student as I’m teaching and calling upon them to answer questions. This will help gain and keep their attention on what I’m teaching.
2. This student is a very high achieving student who tends to work on his/her own. When I make groups, I will have to be cautious of whom I place him/her with. If I place him/her with someone who is very low achieving, SA may do all the work and their partner ends up not helping or learning what the activity was supposed to teach them.
SB
1. This student tends to make mistakes when he/she works through the problems too fast. By keeping the problems and questions simple and less complex, I can be confident that the student can work through the problem and not accidentally skip parts and make silly errors. I also need to remember to give the student praise for their hard work to show that I realize he/she is working hard and that hard work is paying off.
2. Because this student has to work hard and the mathematics doesn’t come easy, I will have to be careful who I place him/her with during group work. It would be frustrating for him/her if I placed him/her with a student who could easily fly through the assignment with little to no effort. It could also be a problem if I place him/her with someone who needs a lot of peer support because he/she would focus on helping his/her classmate before being able to focus on him/herself. It’s best if I place him/her with someone similar in ability.
SC
1. This student has problems paying attention in class and keeping his/her attention focused on the teacher at the front of the room. I will place the student towards the front of the class where he/she can be close to me as I’m teaching and I can keep his/her attention focused.
2. This student may have problems understand material that I discuss during the lessons because he/she is more of a hands-on learner. After teaching the lesson, I will check with him/her first to make sure he/she understands the content and homework. By stopping by him/her first, I can make sure I check on his/her progress before the end of class. If it is needed, I can help him/her with any problems or misunderstanding that may occur.
Learning Goals
Students will be able to:
➢ Measure length using customary and metric units (LG1)
➢ Use scale drawings to find actual lengths (LG2)
➢ Create and interpret frequency tables and line plots (LG3)
➢ Display data using bar graphs (LG4)
➢ Plot points on coordinate grids and make line graphs (LG5)
➢ Describe data using mean, median, mode, and range (LG6)
These learning goals are directly from chapter two in the sixth grade math book. Being a math class, some learning goals may sound like activities. An example is LG1. Even though measuring is an activity, in my unit it is a skill that I want my students to be able to do. Another example is plotting points, which although it sounds like an activity, the skill of placing a point in the correct spot on a grid is a skill I want the students to master during this unit. If I were to change the learning goals to sound less like activities, I would be changing the skill I want the students to be able to master.
Alignment with Standards
LG1 aligned with:
School Benchmarks (received from the cooperating teacher)
❖ Standard 4: Students will be able to understand and apply basic and advanced properties of the concepts of measurement
▪ Select and use appropriate tools for given measurement situations
NCTM Standards (from )
Measurement (grades 6-8)
❖ Students will be able to understand measurable attributes of objects and the units systems, and processes of measurement
▪ Understand both metric and customary systems of measurement
❖ Students will be able to apply appropriate techniques, tools, and formulas to determine measurements
▪ Use common benchmarks to select appropriate methods for estimating measurements
▪ Select and apply techniques and tools for accurately find length, area, volume, and angle measures to appropriate levels of precision
LG2 aligned with:
School Benchmarks
❖ Standard 4: Students will be able to understand and apply basic and advanced properties of the concepts of measurement
▪ Select and use appropriate tools for given measurement situations
NCTM Standards
Measurement (grades 6-8)
❖ Students will be able to apply appropriate techniques, tools, and formulas to determine measurements
▪ Solve problems involving scale factors, using ration and proportion
LG3 aligned with:
School Benchmarks
❖ Standard 6: Students will be able to understand and apply basic and advanced concepts of data analysis
▪ Read and interpret tables, graphs, and charts
NCTM Standards
Data Analysis and Probability (grades 6-8)
❖ Students will be able to formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
▪ Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population
LG4 aligned with:
School Benchmarks
❖ Standard 6: Students will be able to understand and apply basic and advanced concepts of data analysis
▪ Read and interpret tables, graphs, and charts
NCTM Standards
Data Analysis and Probability (grades 6-8)
❖ Students will be able to develop and evaluate inferences and predictions that are based on data
▪ Use observations about differences between two or more samples to make conjectures about the population from which the samples were taken
LG5 aligned with:
School Benchmarks
❖ Standard 6: Students will be able to understand and apply basic and advanced concepts of data analysis
▪ Read and interpret tables, graphs, and charts
NCTM Standards
Data Analysis and Probability (grades 6-8)
❖ Students will be able to formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
▪ Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatter plots
LG6 aligned with:
School Benchmarks
❖ Standard 6: Students will be able to understand and apply basic and advanced concepts of data analysis
▪ Understand appropriate measures (mean, median, mode, range)
NCTM Standards
Data Analysis and Probability (grades 6-8)
❖ Students will be able to select and use appropriate statistical methods to analyze data
• Find, use, and interpret measures of center and spread, including mean and interquartile range
Types and Levels of the Learning Goals
Each of the learning goals can be associated with one or more of the different levels of Bloom’s Taxonomy.
LG 1- This learning goal can be aligned with evaluation. Students will have to decide which unit of measurement they will want to use when measuring different objects. One example of a question I could use to challenge my students at this level would be, “Which unit of measurement, (foot, mile, inch, centimeter, kilometer, etc) would be best to use when measuring how much floor space I would need to carpet our classroom floor?”
LG 2- This learning goal can be aligned with application. Students will have to apply their knowledge of scale drawings in order to find actual distance, or going from actual distance to creating their own scale drawing. One question I could ask to challenge my students at this level would be, “How would you use the scale of 1:3 on this drawing to find the actual distance from point A to point B?”
LG 3-This learning goal can be aligned with comprehension. Students will have to interpret frequency graphs and line graphs in their own words. One question I could ask to challenge my students at this level would be, “Read the line graph we made together and write down two things you know just from looking at it.”
LG 4- This learning goal can be aligned with synthesis. Students will have to use their given supplies and materials to collect their data and create a bar graph to display that information. One question I could ask to challenge my students at this level would be, “Given the information on the tables you created when collecting your data, devise a bar graph that could display this information.”
LG 5- This learning goal can be aligned with application. Students will have to apply their knowledge on how to graph ordered pairs to construct a line graph of their information. One question I could ask to challenge my students at this level would be, “Now that you have your data, construct a line graph showing the change you’ve seen from the experiment.”
LG 6- This learning goal can be aligned with knowledge. Students will need to have knowledge of central tendency which they will use to analyze data. One question I could ask to challenge my students at this level would be, “Describe the set of data you have using mean, median, mode, and range.”
Appropriateness of Learning Goals
LG 1
This goal is appropriate for the development of 6th grade students because students have been exposed to measurement and units of length in prior years. This is a skill has become, or will become in the near future, important in their everyday lives. Most students know how to use a ruler to measure to the nearest inch and centimeter. Through this goal, students will learn to measure to the nearest half inch or millimeter. They will also learn when it is necessary to use each different unit of length. There aren’t any students who have problems with fine motor skills prohibiting them from using a ruler.
LG 2
This goal is appropriate for the students because scale drawings are seen frequently by students, especially in social studies classes. Through learning how to draw their own scale factors, students will have a better understanding of how to read them. The students will have some knowledge of using a scale because they have had map skills in their social studies class.
LG 3
The third goal deals with a skill all students should know as well. Frequency tables are common in the real world, in close to every profession. Although students have been introduced to tallying, this skill will be somewhat of a new challenge for them. Although this is just the beginning of learning this skill, it is very important students learn how to create and interpret frequency tables and line plots correctly.
LG 4
Goal number four deals with graphing as well. There are many different skills associated with graphing. Each of these skills is important for students to know and be able to do, which will help them succeed in the future. Bar graphs are often seen in the real world. When students can correctly read and interpret these kinds of graphs, they will be able to better understand the information they are trying to process.
LG 5
The fifth goal of the unit is a skill the students need to learn to help them in their future mathematics classes. Graphing and plotting ordered pairs is a skill that every students needs to learn to be successful in upper level mathematics classes. The knowledge of how to graph these points will help the students learn how to interpret graphs they see in their everyday lives.
LG 6
Some of the most important skills and those used most frequently are met through goal six. Measures of central tendency are seen and used on close to a daily basis for many people. Students have used some of these skills, such as mode, but they aren’t familiar with median and range. Mean is also a concept they are not used to using. These skills touch on the students’ prior knowledge of adding, dividing, subtracting, and placing numbers in chronological order. Students will have to pull from their prior learning to help them get comfortable using these skills.
Assessment
|Learning Goal |Assessment |Format of the Assessment |Adaptations |
| | | | |
|LG1 |Pre-Assessment |Measure three objects from around the room in different|Demonstrate to the whole class. Repeat to and assist those |
|Measure length using| |units using a measuring tape. |students who struggle. Allow students to choose their own |
|metric and customary| | |objects and move freely around the room. |
| | | | |
|Units |Formative |Worksheet 2.1A: Students measure lines, draw lines to a|Work one-on-one with struggling students during work time. |
| | |given length, and depict between customary and metric |Re-teach if needed. |
| | |units of length. | |
| | | | |
| | |Chapter 2 Review (2.1-2.4): Measure given line segments| |
| |Formative |to the nearest centimeter and millimeter. Order units |Directions are written simply and clearly. Point out units on |
| | |from smallest to largest. |a ruler or meter stick to help students visualize. Use |
| | | |measurement benchmarks (inch: paperclip) to help students |
| | | |visualize. |
| | |Chapter 2 Quiz I: Students will decipher between | |
| | |customary and metric units of length. They will |Verbally go over directions before students start their quiz to|
| |Formative |measure a given line segment to the nearest millimeter.|point out specifics. |
| | | | |
| | |Chapter 2 Test: Students will give examples of | |
| | |customary and metric units of length. They will | |
| | |measure a given line segment to the nearest inch. |Allow students extra time if they do not finish in the class |
| | |- |period. Simplify directions. Give students a unit and ask to |
| |Post-Assessment |Iowa Map: Students will use an Iowa map and its scale |tell if it is customary or metric, instead of naming a |
| | |to answer given questions. |customary or metric unit. |
| | | |- |
| | |Scale This Room: Students will use a given scale and |Verbally work through the questions. Simplify scale and/or |
|- |- |measure and draw the classroom, including specific |distances. |
|LG2 |Pre-Assessment |features decided on by the teacher. | |
|Use scale drawings | | | |
|to find actual | |Chapter 2 Review (2.1-2.4): Students will use a given |Measure some features together. Re-teach if needed. Simplify |
|length |Formative |scale to find actual lengths of different model |if needed. Provide multiple explanations and model measuring. |
| | |measurements. | |
| | | |Directions are written simply and clearly. Draw out the |
| | |Chapter 2 Quiz I: Students will use a given scale to |“actual to model” visual we used during this lesson. Simplify |
| | |find the model length of an actual measurement. |or re-teach if needed. |
| |Formative | | |
| | |Chapter 2 Test: Students will find actual lengths by |Verbally go over directions before students start their quiz to|
| | |using the scales and model measurements given. |point out specifics. |
| | | | |
| | |- |Allow students extra time if they do not finish in the class |
| |Formative |Tally Phone Numbers: Students tally the last four |period. Simplify directions. Use “actual to model” visual if |
| | |digits of their phone numbers on the board and create a|needed. |
| | |frequency table of the data. |- |
| | | |Show an example on the board first. Students who don’t know |
| |Post-Assessment |Line Plot Family: Students will create a “number of |their number will be given a four digit number to use. |
| | |people in their family” line plot as a class. | |
| | | | |
| |- | |Show an example on the board to model how to make a line plot, |
|- |Pre-Assessment | |and then have students come to the board to add their “x”. |
|LG3 | |Worksheet 2.4 A: Students will match vocabulary words, |Students can use “people they live with” if they don’t live |
|Create and interpret| |make frequency tables and line plots of given data, and|with their family. |
|frequency tables and| |answer questions based on their tables or plots. | |
|line plots |Pre-Assessment | |Numbers and data will be simplified for those students who are |
| | |Chapter 2 Review (2.1-2.4): Students will make a |overwhelmed. Re-teach if needed. |
| | |frequency table of letters in given words, line plots | |
| | |of numbers in a given table, and answer questions about| |
| | |the results. | |
| |Formative |Chapter 2 Quiz I: Students will make a line plot and |Directions are written simply and clearly. Problems will be |
| | |frequency table of the given data. |simplified for those students who struggle. Re-teach if |
| | | |needed. |
| | |Chapter 2 Test: Students make a frequency table of | |
| | |given data, find which number occurs the most, and |Verbally go over directions before students start their quiz to|
| | |answer questions about a given line plot. |point out specifics. Simplify if needed. |
| |Formative |- | |
| | |Graphing Ice Cream: Students will choose their favorite|Allow students extra time if they do not finish in the class |
| | |flavor of ice cream from a given list. As a class, |period. Simplify directions or problems if needed. |
| | |students will make a bar graph by coloring in their | |
| | |square. | |
| |Formative | |- |
| | |Double Bar Graph: Students will make a double bar graph|Lines will be bolded in so squares are easily visible for |
| | |in their notebooks comparing their class ice cream |students to color in. Help students transfer graph into their |
| | |graph and the graph from the other class, and write two|notebooks if needed. |
| |Post-Assessment |sentences comparing the data. | |
| | | | |
| | |Worksheet 2.5: Students will be asked to make a single |Draw the first set of bars before asking students to finish the|
| | |bar graph and a double bar graph from the data given, |rest. Help students transfer graph into their notebook if |
| |- |and answer questions dealing with an already |needed. Give an example of a sentence if student struggles. |
| |Pre-Assessment |constructed graph. | |
|- | | | |
|LG4 | |Chapter 2 Review (2.5-2.8): Students will construct a |Simplify data. Have graph drawn and labeled except for the |
|Display data using | |bar graph from the table of data given and answer |bars for those students who struggle with labels. Verbally ask|
|bar graphs | |questions about the resulting graph. |questions for struggling readers. Re-teach if needed. |
| |Pre-Assessment | | |
| | |Chapter 2 Quiz 2: Students will be asked to construct a|Directions are written simply and clearly. Have pre-labeled |
| | |bar graph from the data displayed. |graph and verbally ask questions. |
| | | | |
| | |Chapter 2 Test: Students will be asked to construct and| |
| | |answer questions relating to given bar graphs. | |
| |Formative |- |Verbally go over directions before students start their quiz to|
| | |Plot A Point: Students will choose a partner and play a|point out specifics. Have pre-labeled graph. |
| | |“tic-tac-toe” type game where they roll dice and plot | |
| | |the point corresponding to the roll. |Allow students extra time if they do not finish in the class |
| | | |period. Simplify directions. Have pre-labeled graphs. |
| | |Bean Line Graph: Students will gather data from a bean | |
| |Formative |lab and then graph the resulting regression in the form|- |
| | |of a line graph. |Visually show how the game is played before students start. |
| | | |Place stronger students with weaker. Allow faster finishing |
| | |Chapter 2 Review (2.5-2.8): Students will be asked to |students to play multiple games. |
| | |match given ordered pairs to points plotted on a | |
| | |coordinate grid and plot their own points. Students |Visually go through an example before students start. Give |
| |Formative |will also create and answer questions dealing with the |pre-labeled graphs and pre-made tables to struggling students. |
| | |line graph. | |
| | | | |
| | |Chapter 2 Quiz 2: Students will create a line graph |Directions are written simply and clearly. Have pre-labeled |
| |Post-Assessment |from data given. |coordinate grids. Simplify questions if needed. Re-teach if |
| | | |needed. |
| | | | |
| |- |Chapter 2 Test: Students will be asked to plot points | |
| |Pre-Assessment |on a coordinate grid. They will also be asked to read | |
| | |and interpret given line graphs. | |
| | |- |Verbally go over directions before students start their quiz to|
|- | |Students will write the number of siblings they have on|point out specifics. Simplify data if needed. |
|LG5 |Formative |the board. Everyone will then use the given data to | |
|Plot points on | |find mean, median, mode, and range. |Allow students extra time if they do not finish in the class |
|coordinate grids and| | |period. Simplify directions. Have pre-made coordinate grids. |
|make line graphs | | |- |
| | |Worksheet 2.8: Students will be asked to match |Show an example on the board. Students are allowed to use |
| |Formative |vocabulary words. They will also find mean, median, |step-siblings if needed. If students don’t know how to find |
| | |mode, and range of given sets of data. |mean, median, mode or range, they can do as much as they can |
| | | |(since it is a pre-assessment). |
| | |Chapter 2 Review (2.5-2.8): Students will be asked to | |
| | |define mean, median, mode, and range, and find them of |Simplify data sets. Have students find one concept per set of |
| | |a given set of data. |data. Re-teach if needed. |
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| | |Chapter 2 Quiz 2: Students will find mean, median, | |
| |Formative |mode, and range of a given set of numbers. | |
| | |Chapter 2 Test: Students will find mean, median, mode, |Directions are written simply and clearly. Simplify data sets.|
| | |and range of a given sets of numbers. |Have students find one concept per set of data. Re-teach if |
| | | |needed. |
| |Post-Assessment | | |
| | | |Verbally go over directions before students start their quiz to|
| | | |point out specifics. Simplify data set. |
| |- | |Allow students extra time if they do not finish in the class |
| |Pre-Assessment | |period. Simplify directions. Simplify data sets. Questions |
| | | |can be made into multiple choice questions if needed. |
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|LG6 | | | |
|Describe data using | | | |
|mean, median, mode, | | | |
|and range |Formative | | |
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| |Formative | | |
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| |Formative | | |
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| |Post-Assessment | | |
The assessment plan that I chose is mostly a quantitative approach. This is a mathematics class and many of the concepts I will be teaching can be easily measured using a pre and post test. However, I decided as I was planning to use some qualitative approaches when pre-assessing my students. I chose to do this because the unit I was teaching could have been a very overwhelming pre-test. I will have my students brainstorm and write down what they know about measuring and graphing prior to starting the unit, which allows me to see what they know, whether or not there are any misconceptions, and what I will have to focus on. I will keep track of their knowledge by charting whether or not they fully understood the concepts.
Pre-Assessments
LG1-The pre-assessment I chose to use will allow the students to move freely around the room instead of being stuck in their desks. They have the freedom to decide what they want to measure; all I will tell them is that one object needs to be measured in inches, one in centimeters, and one in millimeters. I will have the freedom to travel around the room to help those students in need, see whether or not students are using the rulers correctly, and if they know how to use a ruler to measure in three different units. This will allow me to know exactly what I will need to focus on.
LG2-The students will be answering questions on a given worksheet using an Iowa map. This will allow the students to see that scales are used in their everyday lives. After checking over their worksheets, I will be able to know if I need to start at the very beginning (what a scale looks like) or if I can move on a little quicker and focus on how we can use a scale to make our own models.
LG3-Students will be tallying on the board for this pre-assessment. Students will add their own tally, as well as record what is happening on the board in their notebooks. Going up to the board allows me to see any misunderstanding when it comes to making tallies. I will also start a frequency table on the board and have the students finish it in their notebooks. I can walk around the look at all students, especially those that I know may need a little more help. When it comes to line plots, we will do the same type of data collecting and recording in their notebooks.
LG4-This pre-assessment is very similar to the assessment from LG3. Students are up and out of their seats, as well as recording everything that is written on the board in their notebooks. I can see any misconceptions right away and discuss them before too many students become confused.
LG5-Students will be playing a game as the pre-assessment for this goal. The game will draw away from the fact that it is “math” and allow me to walk around the room and find any misconceptions or problems that may arise. It also allows the students to help each other out and teach student-to-student.
LG6-This pre-assessment is similar to LG3 and LG4. Having students go to the whiteboard allows them to be active, as well as me see if there are any misconceptions. I want to see if students know how to find mean, median, mode, or range. This means I will let them struggle. I would rather they answer what they can, as well as they can, than for me to tell them how to find it during the pre-assessment.
Formative Assessments
LG1-I will start by having the students do a worksheet on measuring. This will allow me to see if there were certain concepts that the students didn’t get from the lesson. I can re-teach to those students who need it as well. I will also have a review before the mid-unit quiz. This way, since LG1 was met during the first lesson, students will have it refreshed in their minds. The review allows me to see if I need to re-teach again as well. The same goes with the quiz.
LG2-I have planned multiple formative assessments dealing with this learning goal. I will have students create a scale drawing of the classroom. This will allow them to be up and moving around and physically active in the process of making the drawing. I can see from this assignment if students understand the point of a scale drawing and how they are made. Other assignments dealing with this goal are more qualitative and will have students using a scale to find actual and model measurements. It seems like I have a lot of assessments, but this way I can find misconceptions, re-teach if needed, and give the students practice in multiple ways.
LG3-A worksheet will allow me to see if students understood the topic of frequency tables and line plots. I can re-teach the students if I need to if I find problems after checking their homework. The review is for the students to practice what will be on their quiz, and the quiz will let me see if they understand and have learned or met my learning goal.
LG4-Students are given a worksheet of data which I will ask them to turn into bar graphs and double bar graphs. They will also be asked to read a given bar graph and answer questions. This will allow me to see if any students struggle with creating a bar graph or reading a bar graph and I can re-teach as necessary. They will be asked to do the same types of tasks on the review and quiz. Both are assessments for me to see if the students remember what they’ve learned and if I need to re-teach.
LG5-Students will be collecting their own data for this activity. Through gathering their data, I hope that some of the students will be able to predict what their graph will look like before they make it. The data will have a deeper interest to the students as well because they have a hand in collecting it. I will be able to use this graph the same way I used the bar graphing assignment by seeing what students are struggling and re-teach if needed. Students will be asked to do the same types of tasks on the review and quiz, which are both assessments that I will use to monitor their learning.
LG6-I’ve learned from past experiences that students at this grade level struggle with mean, median, mode, and range. They tend to get the different measures mixed up, or other simple mistakes (forgetting to divide when finding mean or forget to put numbers in numerical order when finding median). The in the worksheet and review I broke up the data and asked students to find just one measure per set of data. This is one way in which I hope to simplify their work and have them focus on just one measure. I can look at the students’ work and find those which need re-taught.
Post-Assessments
All of my learning goals will have a summative assessment of a unit test. This test will have varied types of questions covering what I wanted the students to learn based on each learning goal. The criteria for successful learning of each goal for this age group are:
LG1
• Knowing basic customary units of length
• Knowing basic metric units of length
• Being able to state if a given unit is customary or metric
• Measuring to the nearest centimeter, millimeter, or inch
• Knowing appropriate times to use each measure
LG2
• Using a given scale to find actual and model lengths
LG3
• Create a frequency table from a given set of data
• Interpret a frequency table to find the most common piece of data
• Create a line plot from a given set of data
• Interpret a line plot to find the most common piece of data
LG4
• Display a given set of data in a bar graph or double bar graph
• Read a bar graph and answer questions relating to that specific set of data
LG5
• Correctly plot given ordered pairs on a grid
• Write an ordered pair for a given dot on a grid
• Plot points from a given set of data and create a line graph
• Read a line graph and answer questions relating to that specific set of data
LG6
• Know the difference between mean, median, mode, and range
• Know and be able to find mean, median, mode, and range of a given set of data
Adaptations
The students in this class have a wide range of abilities. Most of the adaptations I have made are for students who may be overwhelmed with the amount of data given. Many of the students need more of a physical adaptation, such as letting them move around the room, than a curriculum adaptation. From my observations, previous student work, and teacher insight, I have made many of the same adaptations for all of my learning goals. My main concern is that the students who have problems paying attention in class or those that get distracted easily will miss an important piece of information we discuss. This is why I have worksheets and reviews for them to do throughout the unit. This way, I can see if there are students who have a misconception or are unsure of how to do a specific task and I can re-teach if and when necessary.
I have made adaptations based on my contextual factors. Some of the students are in Second Chance Reading. This is a reason I will read and model directions before doing any activity, which also meets the majority of the learning styles the students chose. Some of the students do not have a lot of help at home, this is a reason I will give them time in class to work on their homework and ask me any questions that may arise. Many of my lessons and activities are hands-on and include moving around the room. This is a benefit to all students, especially those who may lose interest or need to be active.
Design for Instruction
Results of Pre-Assessment
I chose to take a different step when it came to pre-assessing the class. The students were asked to brainstorm everything they knew about measuring and graphing and write it down on a piece of paper. After a few minutes, they could share with a partner. Next we shared on the board for everyone. I did this to get the students minds turning about our upcoming unit. Next they answered “Getting Ready to Learn” questions from the text book. This was also to help get the students ready for the unit and for me to see what they knew.
I did not create a pre-test for the students to do. Because measuring and graphing has a vast amount of content, I chose to pre-assess the learning goals separately and on different days. I did know this would create a lot more work for myself because I would have to prepare the lesson as if the students knew nothing about the topic and would adjust by cutting out what I had pre-assessed they understood. I felt that this way the best way for me to see exactly what they knew before the lesson, rather than making a pre-test.
LG1: Students measure three objects from around the room
|Criteria Pre-assessing |Results (through observations) |
|Were students using the ruler |12 out of 12 students knew how to correctly use the ruler. |
|correctly? | |
|Were students lining up the object with|Eight students out of 12 were lining up the object with the beginning of the unit lines on the ruler. Three students were|
|the end of the ruler or the beginning |lining up the object with the end of the ruler, not noticing the space between the end of the ruler and beginning of the |
|of the units on the ruler? |units. After a short discussion with those three, they realized their mistake and made corrections. |
|Do the students know the difference |12 of 12students could point out the difference between inches and centimeters. Six of 12 students could point out the |
|between centimeter, millimeter, and |difference between millimeter and centimeter. *Will need to discuss millimeter and centimeter the difference when |
|inch? |measuring to that unit. |
|Were the measurements accurate and to |12 of 12 students could measure to the nearest inch. Nine of 12students could measure to the nearest centimeter. Four of|
|the nearest unit? |12 students could accurately measure to the nearest millimeter. *Will need to discuss measuring to the nearest millimeter.|
LG2: Students answer questions from an Iowa Map dealing with scales
|Criteria Pre-assessing |Results |
|Do they know what the scale looks like?|12 of 12 students could recognize the scale on the Iowa map and could describe it. |
|Do they know where the scale is |12 of 12 students could find the scale on the Iowa Map. |
|located? | |
|Can students use the scale to find the |10 of 12 students could find the distance between two points using the scale. However, when asked to discuss what they |
|distance between two points on the map?|did and how it worked, 0 students could. *Will have to discuss going from scale given (such as 1 in: 4 ft) and finding an|
| |actual or model distance. |
LG 3: Students tally phone numbers and make a frequency table, and make a line plot of family members
|Criteria Pre-assessing |Results |
|Can students make an accurate tally? |12 of 12 students knew how to make a tally. However, I did notice that some forgot to “cross four to make five.” This |
| |was just an error from the activity because it was hard to see all tallies make by other classmates. We had a short |
| |discussion on what to do when we got to four (all students actively participated and could show an example). |
|Can students transfer data into a |All students were unsure how to start. When I drew the outline of the table, all students were able to easily and quickly|
|frequency table? |fill in the data. *May need to discuss how to make the table itself (before entering data). |
|Can students make an accurate line |All students were unsure how to start. After a demonstration, students were able to quickly catch on. *Small |
|plot? |misconception of how to make the line and where to put numbers and “x” –good topic to cover. |
LG4: Students graph favorite ice cream flavors in the form of a bar graph
|Criteria Pre-assessing |Results |
|Do students know what a bar graph looks|12 of 12 students can correctly describe what a bar graph looks like. |
|like? | |
|Can students create a bar graph? |12 of 12 students could add to the bar graph we were creating as a class. *Can see some confusion, will need to focus on |
| |making their own from a set of data. |
|Can students read and interpret the bar|12 of 12 students could accurately write down which type of ice cream had the most students and which had the least. |
|graph? | |
|Can students create a double bar graph?|All students were unsure how to start. I drew the outline and the first set of bars. “Aha moment.” Students quickly |
| |finished. *Will have to discuss keys (one for each data set) and why bars are next to each other. |
|Can students read and interpret a |12 of 12 students could accurately write two sentences describing two differences they found between the two sets of data.|
|double bar graph? | |
LG5: Students play a Plot-a-point game to plot coordinates
|Criteria Pre-assessing |Results |
|Can students accurately plot a point? |Six of 12 students could accurately plot the point they rolled in the game. *Will have to discuss the steps in plotting a|
| |point. |
|Do they know ‘x’ comes first? |Six of 12 students knew ‘x’ came first when plotting a point. *Will need to emphasize that X always comes first! |
|Do they know the x and y axis? |Three of the 12 students could point out which was the x axis and which was the y. Other students did know which |
| |direction to move first when plotting the point, but didn’t know the names for the axis. |
|Can students look at a point and say |Six of 12 students could easily say the coordinate pair that corresponded to the point I gave them. Four students were |
|the coordinate pair that corresponds? |able to answer with a little prompting. One student was unsuccessful. *Will need to touch on going from the point to the|
| |coordinate pair instead of just the coordinate pair to the point. |
LG6: Students find mean, median, mode, and range of number of siblings
|Criteria Pre-assessing |Results |
|Can students gather data? |12 of 12 students were able to accurately collect the needed data. |
|Do students know and can accurately |Two of 12 students could correctly find mean. *Will need to discuss how to find mean, many students forgot to divide |
|find mean? |after adding. |
|Do students know and can accurately |Four of 12 students could correctly find mode. *Will need to discuss how to find mode. |
|find mode? | |
|Do students know and can accurately |Three of 12 students could correctly find mode. Three other students knew median meant middle, but didn’t put the numbers |
|find median? |in numerical order first. *Will need to discuss median and putting numbers in order first. |
|Do students know and can accurately |Five of the 12 students could correctly find the range of the data. Two other students could describe what it meant for |
|find range? |range, but couldn’t find it. *Will need to discuss finding range of a set of data. |
There are some patterns that I can see. Many of the students are quick to say “I don’t know how,” but when I start asking probing questions, they quickly catch on and realize what I’m asking is easier than they are making it. There are a few topics I can cover more quickly after pre-assessing the students. There aren’t any topics I can just skip, however, and feel I need to at least mention everything, even if all students accurately answered in the pre-assessment. Overall, I wasn’t surprised by much of the pre-assessments I made. However, the low number of students who could accurately find mean, median, mode, and range were a surprise. After a little more research, I found that this wasn’t a school benchmark until seventh grade, and this can account for the small number of students who understood mean, median, mode, and range.
Unit Overview
|Monday |Tuesday |Wednesday |Thursday |Friday |
|KEY: | |Think/Pair/Share |Ch 2.1 Measurement. |Ch 2.1 Measurement |
|NG (notetaking guide) | |Measurement/Graphing and “Get |Pre(measure three objects) |-Fill out NG |
|*Learning goal not one of | |Ready to Learn” |-LG1 |-Round robin share of three |
|six goals discussed in | | | |measured objects |
|this TWS | | | |-LG1 |
|*Ch2.2 Perimeter and Area |Ch2.3 Scale Drawings |Ch2.3 Scale Drawing |Ch2.4 Frequency tables/Line plots |Review Day |
|-Fill out NG |-Pre-(Iowa Map) |-Fill in NG |Pre(tally/table/plot on board) | |
|-Create your own Garden |-LG2 |-“Scale This Room” activity. |Finish NG |Do review activity for 2.1-2.4 |
|Activity. | |-LG2 |-Activity: making frequency tables, | |
| | | |line plots from given data |-LG1, LG2, LG3 |
| | | |-LG3 | |
|NO SCHOOL |Quiz 2.1-2.4 |Ch2.5 Bar Graphs. |Ch2.6 Coordinates |Ch 2.6 Line graphs |
| | |-Pre(Favorite ice cream activity) |-Pre(Plot-a-Point game) |-Fill in NG |
| |“Post-it” Review |-Activity: making bar graphs from |-LG 5 |-Activity: Bean lab, creating a |
| | |sets of data | |line graph |
| |-LG1, LG2, LG3 |-LG4 | |-LG5 |
|*Ch2.7 |Ch2.8 |Review Day |Quiz 2.5-2.8 |Test |
|Circle Graphs |Mean, Median, Mode, Range | | | |
|-Create a circle graph |-Pre(siblings activity) |Do review activity for 2.5-2.8 |“Post-it” Review |LG1, LG2, LG3, LG4, LG5, LG6 |
|from a line graph activity|-Activity: finding mean, | | | |
| |median, mode, and range from |LG4, LG5, LG6 |LG4, LG5, LG6 | |
| |a set of data | | | |
| |LG6 | | | |
Activities
“Scale This Room!”
This activity asks the students to create a scale drawing of their classroom. Students are given a scale (one tile on the floor equals one square on graph paper), object requirements (what objects must be shown on their scale drawing), and creative freedom as they do this activity. This activity focuses on LG2 and the point is to show how real life objects are “shrunk” into a scale drawing.
After pre-assessing the students, I could see that they understood how find a scale on a map, and many knew how to use it. I did notice that many didn’t realize how important scale drawings were and what exactly they showed. This activity is the reverse of the Iowa Map activity because students will be going from ‘actual to model’, instead of model to actual. The contextual factors of this classroom helped form activity also. This activity is a great way for students who struggle paying attention and have a lot of energy to move around the room. For those students who lose interest or who are easily distracted, this activity is something they’ve never done before and is active.
There are few materials students will need for this activity. They will need a piece of graph paper to draw their picture on. They will need to be in the classroom so that they can measure the object required. They will also need their worksheet describing the activity and listing the required objects. Students can also use the worksheet as a way of recording their data. There isn’t any technology required.
This is a formal assessment where I will be observing and checking their final products. I will observe how students are using the scale factor when collecting their data. I will be able to see if students are struggling and can model to those students who are in need. When checking their final drawing, I can see if they can follow directions and have included everything I’ve asked for, as well as if they could accurately use the scale given to depict the room’s objects.
Bar Graph Worksheet
This activity, which focuses on LG 4, asks the students to look at data given to them on a worksheet and create bar graphs and double bar graphs. Students are also asked to read bar graphs and answer questions. I chose to do a worksheet because it will allow the students to become familiar with the types of questions they will be asked on their quiz and test.
After pre-assessing students, I could see that they could make a bar graph when the labels, x-axis, and y-axis were already drawn and labeled. This worksheet will allow me to see if they can draw and label the graph themselves. It will also allow me to see if the students can take information given to them in the form of a table and transfer that into a bar graph. After review contextual factors, I know that there are a few students I will need to focus on when they begin working on this assignment. If the amount of data seems overwhelming for them, I can cut some out. For those students who have problems focusing when in their seats, I will allow them to find a spot in the classroom to work if they prefer. For students who prefer learning hands-on, this is a great activity where they are creating the graphs themselves.
The only materials students will need include their worksheet with the data tables and graphing paper to make it easier for them to create the bar graphs. There isn’t any technology required. Students will be observed as they start their graphing. I can re-teach or ask questions to get students on the correct track if it is needed. They will then be assessed on their final graphs. I will see if they have labels, if their bars are correctly drawn, and whether or not they can read the bar graphs by looking and their answer to questions.
Bean Lab Line Graph
For this activity, students will be collecting their own data. They will be using this data to create a line graph. The students will have already made bar graphs from given data, so this activity asks them to collect their own and will test their ability to create a line graph. This activity, which focuses on LG5, allows students to work in small groups and be out of their desks.
After pre-assessing the students, I saw there were some problems when it came to which direction to go first, right or up. I did emphasize in the lesson that “x always comes first.” I will have to walk around to make sure students start of correctly and remember to ‘go right and then go up’. This activity is another hands-on activity where students can be out of their seats and working together in small groups. This will help those students discussed in my contextual factors who had problems paying attention. In the small group setting, they will have an easier time paying attention.
There are a few materials I will need for this activity. I need bags of beans for each group. All of the beans are spray painted red on one side. Students will also need plates to pour the beans onto. They will need a sheet of paper to record their data, and graph paper to create their final graph on. There is no technology needed. Students will be assessed on their ability to plot their data points, correctly drawing and labeling their graphs, and connecting their points to make a line graph.
Technology
The classroom I’m teaching in doesn’t have a large amount of technology available. This wasn’t a problem when I was planning my unit. I will use the overhead projector almost every day, which will mean students will have to move their desks when it comes time to using it. Even though rulers, graph paper, and the white board are not thought of as technology, they are tools I will be using when teaching the students. Students will also be using the calculators when finding mean, median, mode, and range.
Contextual Factors
While I was planning my unit, I focused on the fact that a large number of my students were easily distracted or tended to lose focus. Many of the activities I planned are hands-on and have the students up and out of their seats taking part in the lesson. Much of the data we’ll use will be from the students themselves, giving the students a sense of ownership in the activity. The classroom we are in is a small space, much being taken up by the students’ desks. With the activities planned, we will have to work around the desks and move them if they are in the way. During this class, the library and computer lab are both in use, meaning we will have to stay in the classroom.
SA has problems paying attention in class. The hands-on activities will help draw his attention in to what he is doing. There are also small group activities, where attention can be kept easier than a large group setting. By breaking up the sitting time, SA’s impulses and random noises will be covered by the noise of the students working together and the bustle of the activities. Since it is important to be organized when dealing with collecting data, I will have many charts and graph outlines pre-made so students similar to SA will have a guide to work off of.
SB is always willing to do what is asked. The activities will allow this students to shine and allow him/her a chance to show peers how to do the activity. Since this student tends to make silly errors by working through problems too fast, it will be important for me to have activities broken into parts so they don’t seem overwhelming. By breaking them apart, students can focus on just one part of the problem. An example of this is during mean, median, mode and range where I only ask for one measure per group of data, not all four. This way, students such as SB will not accidentally forget to answer a part.
SC will be benefited by the activities just like SA is. SC has problems paying attention and staying on task. According to the survey’s the students answered, this student enjoys learning hands-on. Many of the activities we do will meet this need. I will be checking on SC to make sure he/she is not overwhelmed by the data. If he/she is, I can cut out some of it. Showing me that the student can graph five pieces of data, instead of ten, still shows me whether or not he/she can meet the learning goal of graphing the data.
Instructional Decision-Making
Example 1
A time when my formal assessment of the class changed my instruction was during the lesson I taught on bar graphs. In a previous lesson, students had learned about scale drawings. When I asked the students what a scale was on a graph, they quickly turned through their notebooks and found the definition we had made about scale drawing. Observing the students using their resources was wonderful, but, I told them, I didn’t want a scale drawing; I wanted a scale on a graph. Some students were confused, while others reached for their text books, another great resource, to look up a definition. However, the only definition they could find was that for scale drawings.
While observing the students’ reaction to this question, I realized I would have to immediately take time and discuss what a scale is on a graph and why it is important. This was not part of my original lesson plan for that day, but I made do. The students picked up on the concept of scales on a graph very quickly. They informed me that they see the numbers all the time, but never realized they were called the scale. Another modification I made, which occurred later on in the unit for the unit test, was to have the scales drawn on the graphs and all the students had to do was draw in the appropriate bars according to their data. I chose to do this because the goal for students at this age is to be able to create the bars and read a bar graph, not focus on the proper scale for their given data.
I found that the modifications I made worked very well for this class. After discussing the difference between scales on graphs and scale drawings that day in class, the students could easily tell me the difference whenever I asked them. The modifications on the test also worked well. During the review, I asked the students to make a bar graph but did not give them the pre-made labels. Every student really struggled deciding on the scale they should use and marking it on their graph. When I already had that part done for their test question, all the students had an easier time accurately drawing in the bars.
Example 2
Another time when my observations changed my plan of action was during the bean lab. This lab had the students collecting data, and then graphing that data. As students started out collecting their data, I found they were struggling doing just that. There was only one group in the whole class that could collect the data they were obtaining. Many of the groups were asking questions about how they should collect their data, what they need to do to write it down, what data they needed to write down, and many other questions.
Since they were going to be assessed on their graphs, I had to think quickly. My immediate modification was that I found two sets of data in a workbook and quickly made copies. This way, the students could have data to graph in the form of a line graph. My bean lab turned into data collecting practice and the students did not get a chance to graph this data. After discussing the results after class with my cooperating teacher, we discovered that they students did not have a lot of background knowledge collecting and recording data. Unfortunately, I didn’t know this before hand my activity did not work. However, students were able to graph the data I gave them, allowing me to see how well they could construct line graphs. I did make the same modifications later on when it came to having students graph data as I did with bar graphs where I had the graph labels pre-made.
Both modifications I made were successful. When the students came back the next day and I saw their graphs, I could easily see those who understood how to construct a line graph and those who struggled. Had I let them graph their bean lab data, it is possible their graphing mistakes could have stemmed from data collecting mistakes. I also found that my later modification, pre-made labels, helped the students tremendously. Just like with bar graphs, the students were evaluated on their ability to graph the data, not create the y and x axis and have a proper scale.
Analysis of Student Learning
Even though my unit was taught in a mathematics classroom, much of my assessing was observations and discussions with my students, instead of pencil-paper testing. Although my final is quantitative, I chose to assess my students in more of a qualitative way through the unit because of my observations during my first weeks at school. I knew from their work during the first unit, that a pencil/paper pre-test would not give me an accurate account of the pre-unit knowledge. Because of this, I chose to go a more challenging route and pre-assess my students on the topic at hand either the day of the lesson or the day before. I did know that this would make planning for my unit more difficult, but it was what I felt was best. The data I kept about my students through this unit is displayed in a table. I knew my learning goal and what specific concepts the students would need to learn before successfully meeting that goal. For each learning goal, I have from two to seven concepts the students would have to meet. For the students to successfully meet the goal, they would have to meet 75% of the criteria I had drawn out. This meant that for some of the goals, they would have to know all of the concepts. The concepts I want each student to learn and the number of concepts needed to be considered mastered are:
|LG1 (5 of 7) |LG4 (3 of 4) |
|1. Know basic customary units of length |1. Display a given set of data in a bar graph |
|2. Know basic metric units of length |2. Display a given set of data in a double bar graph |
|3. Be able to state if a given unit is customary or metric |3. Read a bar graph and answer questions relating to |
|4. Measure to the nearest centimeter |that specific set of data |
|5. Measure to the nearest millimeter |4. Read a double bar graph and answer questions |
|6. Measure to the nearest inch |relating to that specific set of data |
|7. Know when appropriate to use specific units | |
|LG2 (2 of 2) |LG5 (3 of 4) |
|1. Use a given scale to find actual lengths |1. Correctly plot given ordered pairs on a grid |
|2. Use a given scale to find model lengths |2. Write an ordered pair for a given dot on a grid |
| |3. Plot points from a given set of data and create a |
| |line graph |
| |4. Read a line graph and answer questions relating to |
| |that specific set of data |
|LG3 (3 of 4) |LG6 (3 of 4) |
|1. Create a frequency table from a given set of data |1. Know and be able to find mean |
|2. Interpret a frequency table to find the most common |2. Know and be able to find median |
|piece of data |3. Know and be able to find mode |
|3. Create a line plot from a given set of data |4. Know and be able to find range |
|4. Read a line plot to find the most common piece of data | |
Each student was assessed on the above concepts for each learning goal. I assessed them during the pre-assessment, formatively throughout the unit, and through a post-assessment which was their final test. I checked off the concept when, through observing and checking papers, I felt the student had mastered it. There are times when a student seemed to have mastered the concept during the pre-assessment, but didn’t later on in the unit. When I saw this, I pulled that student aside and we discussed what happened during that formative assessment and through the discussion I was able to see if they understood the concept.
|LG1 (graph representation of this data Appendix pg 49 ) |
| |Pre-Assessment |Formative Assessment |Post-Assessment |
|Concept |1 |
|#1 |
| |Pre-Assessment |Formative Assessment |Post-Assessment |
|Concept |1 |2 |1 |2 |1 |2 |
|Student | |
|#1 | | | |X |X |X |
|#2 | | | | |X |X |
|#3 | | | | | | |
|#4 | | |X |X |X |X |
|#5 | | | |X |X |X |
|#6 | | | | | |X |
|#7 | | | |X |X |X |
|#8 | | | | | | |
|#9 | | | | | | |
|#10 | | | | | |X |
|#11 | | | | |X |X |
|#12 | | | | | | |
|LG3(graph representation of this data Appendix pg 50) |
| |Pre-Assessment |Formative Assessment |Post-Assessment |
|Concept |1 |
|#1 |
| |Pre-Assessment |Formative Assessment |Post-Assessment |
|Concept |1 |
|#1 |
| |Pre-Assessment |Formative Assessment |Post-Assessment |
|Concept |1 |
|#1 |
| |Pre-Assessment |Formative Assessment |Post-Assessment |
|Concept |
#1 |X |X |X |X |X |X |X |X |X |X |X |X | |#2 | | |X |X |X |X |X |X |X |X |X |X | |#3 | | | | | | |X | | | |X |X | |#4 |X |X |X |X |X |X |X |X |X |X |X |X | |#5 | | | | | |X |X |X |X |X |X |X | |#6 | | | | | | |X |X |X |X |X |X | |#7 | |X |X |X | |X |X |X |X |X |X |X | |#8 | | | | | | |X |X | | |X |X | |#9 | | | | | | |X | |X | |X | | |#10 | | | | | | |X |X |X |X |X |X | |#11 | | | |X | | |X |X |X |X |X |X | |#12 | | | | | | |X | | |X |X |X | | Looking at the whole class, I can see that all students have improved on all learning goals. In the pre-assessment of LG1, one of twelve students met enough criteria to have successfully mastered the goal. After the post-assessment, eight of twelve had mastered the goal. Those that did not, were close. LG2 went from zero students to half of the students mastering the goal. LG3 started at two of twelve, and finished with 100%. LG 4 started at seven of twelve and finished with 100% as well. Half of the students knew enough for LG5 during the pre-assessment, and eleven of twelve had mastered the goal by the post-test. LG6 began with three of twelve mastering the goal, and finished with nine of twelve.
There were some students who had mastered a concept during the duration of the unit, but then when it came to the post-test, didn’t answer correctly. There are multiple reasons why this could have happened. One example is that the student is not a confident pencil-paper test taker. If they get nervous taking tests, they may make simple mistakes and get a question wrong, even though they know how to do the problem. This is one reason I evaluated the students throughout the unit with observations and discussions.
Copies of student work for SB and SC (both discussed in contextual factors) can be found in the Appendix pages 52-65. It was important for me to know what type of learners these two students were, as well as all the students, so that I could create activities and teach in a way that I could meet the most students.
SB is a student that will do anything asked. This student learns well during class when the teacher is instruction, as well as when the lesson is more student centered. However, this student may need a little extra help understanding the directions. Once he/she does, though, he/she is quick to start into the work. In the pre-assessment, SB received the following: LG1 2/7, LG2 0/2, LG3 2/4, LG4 ¾, LG5 ¾, LG6 0/4. In the post-assessment, SB received a perfect test meaning they mastered all the skills. SB worked hard throughout the unit and his/her test grade shows just that.
SC is a student who is easily distracted. It was necessary for me to know this because I needed to plan activities and lessons that would keep SC’s attention. It was also necessary to have activities where the student could get up out of his/her seat and be active. Knowing about this student meant I stopped by his/her desk often, as well as made sure I asked questions when he/she was working on homework to keep them focused. In the pre-assessment, SC received the following: LG1 2/7, LG2 0/2, LG3 2/4, LG4 2/4, LG5 1/4, LG 6 0/4. In the post-assessment, this student improved their scores and attained the following: LG1 4/7, LG2 ½, LG3 4/4, LG4 4/4, LG5 ¾, LG6 4/4. This student’s scores grew in every area. Unfortunately, according to the standards I set as to the scores needed to have mastered the learning goal, SC did not master LG1 or LG2. However, I see this as a success because SC went from 0 of 6 to 4 of 6 mastered.
Reflection and Self-Evaluation
The learning goal in which I feel the students were most successful was LG6. When I first started the lessons dealing with this goal, I found that many of the students were unable to distinguish between mean, median, mode, and range. One reason I think I was successful with this goal was the fact that I had the students give the data we used. I think it is important for the students to be actively involved in all areas of math, and providing data is one of those. I had the students list the number of siblings they had. Next, we found mean, median, mode, and range of the data.
Before we started, very few students could find the correct answers. As we worked through them together, students were able to make connections with the data which in turn seemed to leave a lasting impression. Looking at the pre-assessment where very few students knew the difference between the four words, much less how to find those measures, to the final assessment where nine of twelve students had almost perfect scores. The other three were able to answer many more than they could have in the beginning of the unit.
The student characteristics played a part in the success of this learning goal. The students in this class were having a good day when this lesson was being taught. As much as their attitudes are not under my control, it was a factor in the success of this lesson.
My instruction this day included having the students up and out of their seats and moving around, which may have been a reason this was a successful lesson. I found that days the students were actively moving, they were much more willing to pay attention and take more information from the lesson. Along with this, as a class we came up with ways to remember what each word meant. For mode we came up with most. Mode and most both start with ‘mo’, which was easy to remember. For median, we decided that it is a lot like middle. One student even realized that the median on a road is in the middle! Coming up with these ideas as a class helped the students take ownership as well.
The learning goal in which the students were least successful was LG 2. By looking just at the data, you can see that only half of the class met my requirements for mastering this learning goal. Considering the fact that every student was 0/2 during the pre-assessment, it is still a growth.
One possible reason for this is that there was a substitute in class for the first day of activities dealing with this learning goal. I was at a professional development day for mathematics teacher and had to plan for a substitute teacher. This meant I wasn’t able to give the students an overview of how to use a scale, such as 1 in: 4 ft, when there wasn’t a map in front of them. The students learned about scale factors that day only dealing with an Iowa map. When I was working with the students and re-teaching them, I noticed they struggled without the map there in front of them, even though the scale was the same. Not having that visual really hindered some of the students.
Another possible reason is that scale drawings are easily confused with scales on a map. Some of the students had trouble deciphering between the two. It is possible that they got confused when they were asked to use the scale and just couldn’t remember what to do. Doing both scale drawings and graphing in the same unit could have been a confusing concept for some students.
If I were to teach this again in the future, there are some things I would do differently. One would be that I would spend more that just two days working on this. It seemed like the students didn’t get enough time to digest the scale drawing information before moving on to the next concept. I would not do the Iowa Map activity either. Even though the students really liked it and it showed how math is used every day, it seemed to do more harm than good. Students had trouble going from using the scale with the map as a visual, to using a scale with no visual.
Many of the adaptations in my assessment plan were not needed during this unit. The students were very capable of doing everything I asked of them. There were times when I had to talk with students because they were giving up and not trying. It wasn’t because the work was too hard, but because the student didn’t want to try. All of my students, even the student who was in the Special Education classroom for math last year did very well with the unit. The main adaptation I had to make was re-teaching. However, instead of re-teaching just a single student or two, I re-taught the whole class. I took a couple minutes out of that day’s lesson to discuss a topic I noticed many of the students struggled with. Topics I re-taught were scale drawings, plotting ordered pairs, and finding mean, median, mode, and range. For the students who didn’t quite meet a learning goal, I would have liked more time to sit down and discuss with them one-on-one. From my experience at the school, I found that those students who did not meet the goals were capable of it, but just needed to sit down and take their time without rushing.
Professional Learning Goal
One professional learning goal I have is that I would like to know more about technology that can be used in the math classroom. Many of the students talked about computers and videogames. If I could find ways to use computers and/or videogames to teach a math concept, the students may be more interested. One step I will take is to use programs, like Excel, during graphing units. Programs, such as Excel, can be found on most computers in many schools. This is a program that doesn’t get a lot of use, and it should since it uses math. Another step I would take is to attend professional development meeting or informational meetings on new math technology. By being up to date on the technology, I can find new and interesting ways to teach math to a computer-aged world.
Another professional learning goal I have is to have students chart their growth themselves. I’ve seen teachers that have students keep track of their work. This allows them to see how they are doing and what they should work on. In my future classroom, I look forward to having students chart their growth through a unit or quarter. One step I plan on taking toward this goal is to talk to colleagues that do implement this into their classroom. During my eight weeks at this school, I saw three different teachers have their students chart their growth and work in three different ways. Just by talking to these colleagues, I can get insight on what works and what does not. Another step I will take is to research how charting their own grades can help students. I’ve heard that it is helpful, but I haven’t read an article on why it works. By reading and becoming more knowledgeable in the topic, I will be able to discuss with the students, their parents, or my colleagues, why I am having the students chart their growth and the benefits that will come from it.
References
McDougal Littell Middle School Math Notetaking Guide, sixth grade edition
McDougal Littell Middle School Math Text Book, sixth grade edition
NCTM Standards
Plot-a-Point, created by David C. Christensen
Appendix
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