Performance-Based Assessment Purpose:

This is a performance-based assessment that was administered to one individual student

at Lower Dauphin Middle School, Lower Dauphin School District. I choose one student for my

performance-based assessment. This 14 year old Caucasian student has a learning disability in

numerical operations. This student will achieve a better understanding of functions. He/she will

have the ability to compare proportional relationships and know the different ways in which they

can be expressed. This student will achieve this by making sense of problems and persevere in

solving them, model with mathematics, use appropriate tools strategically, and by attending to

precision.

Description of School and Community:

Lower Dauphin School District is a midsize, suburban public school district located near

Hershey, PA. The Lower Dauphin Middle School is comprised of students from grade 6th

through grade 8. Each grade level has their own wing in the building. The 8th grade wing that I

am teaching in is located on the second floor towards the back of the school facing a baseball

field. In my 8th grade Pre-Algebra class, I have a total of 29 girls and 30 boys. These students are

split into three Pre-Algebra classes / periods. Two of these classes are inclusion classes. Student

desks are in groups / rows of two with a total of three columns, making the room large enough to

seat a total of 30 students at a time. The class does not have technology available to them at a

moment’s notice. If the teacher wants to incorporate laptops they have to get this approved a

head of time.

Out of my Pre-Algebra classes I have a total of 21 students who have IEP’s, 9 of those

students have ADHD as their learning disability. While the rest range from reading

comprehension and decoding, math computation, numerical operations, written expression, and

autism.

Objectives:

The student will determine if a relation is a function.

The student will be able to graph a linear equation.

The student will be able to determine the rate of change between two variables.

The student will be able to graph a linear equation using slope-intercept form.

Pennsylvania State Standards:

PA Common Core Mathematics Standards:

M08.B-F.1.1.1: Determining if a relation is a function

CC.2.2.8.B.3: Graphing Linear Equations (using tables)

CC.2.2.8.B.2: Determine rate of change and slope; comparing functions represented in different

ways

CC.2.2.8.B.3: Graphing Linear Equations in slope-intercept form

Standards of Mathematical Practices:

Make sense of problems and persevere in solving them

Model with mathematics

Use appropriate tools strategically

Attend to precision

Students are assessed every day when they do their morning warm up. The warm up is called

a Do Now. Students are to come into the classroom get situated and start on the Do Now Packets.

These problems can be on things we have learned in the past as a refresher or as an assessment of

what we learned the day before. Students are assessed by the teacher when we walk around the

classroom to see that they have completed their work. Do Nows are also collected and a

classwork grade is given.

Student homework is check every day for completion and accuracy, student receive a

homework stamp indicating that they understood the information and were able to complete the

homework. The calendars that are stamped are then collected at the end of the month and are put

in as a homework calendar grade.

Students will be assessed summatively through a Quiz given half way through the unit. This

unit is very large that is why we are using this Quiz as a summative assessment. The formative

assessments include tickets out the door, and answering questions at the board.

Meets Criteria:

This performance-based assessment was meaningful to the student because they were

able to implement what they learned later in the year specifically in April when taking the

PSSA’s standardized test. It was engaging and creative because the student had the opportunity

to pretend the x and y’s could date each other and that if x has more than one girlfriend he is not

a function. Student also were able to visually see why we circle the slope and box the y-intercept

and how that relates to graphing our slope. We start with the box and place that point on the y-

intercept the slope that we circle shows up if we are dropping and rolling or rising and running

and it tells us by exactly how many.

Instructional Actions:

If students do worse than expected:

If students do worse than expected I would use a post assessment to see exactly where

they are struggling. With that information I would re-evaluate the way I taught it and then devise

a plan to reteach it again but in a different way. If the student is having trouble with determining

if a relation is a function than I am able to go back and reteach that explaining it a different way.

First, we can make an X Y table, making a table will helps us answer this question. We look

back at the order pairs and plug them into our table. Looking at the table we can ask ourselves do

we have any repeats in the x column. If there are no repeats in the X column that means that

every element in the domain is paired with exactly one element in the range. That means that our

relation is a function. If there are repeats in the X column then we know that it is not a function.

If they have trouble with determining if the slope is positive or negative I have slope dog they

can be introduced too.

If student does better than expected:

In the case that the student does better than expected I will know that he/she feels

comfortable and accomplished. I would then ask that they, one last time, go through a step by

step process so that I can see what the/she is thinking and how he/she is approaching the

problem. I would then ask that person to be my helper in class if I notice someone else

struggling. This gives the student confidence because now they can pretend to be the teacher as

well as the student in need of help, he/she will feel less pressure because a peer is there to help

guide them in the right direction.

Final Assessment Scores:

My student was able to complete his/her final assessment with 85% accuracy. Although

time was spent reviewing for the quiz, the results show that these concepts are hard for students

to understand. My student gave their best and only lost points for minor errors. My guess is that

because there where so many parts to this quiz, the student might have become overwhelmed and

possibly missed some of the smaller parts that needed to be completed on the quiz.

Reflection on learning:

I learned once again that students will not all learn the subject material the first time you

teach it, nor the second for that matter. You can drill a specific way into a student’s mind 15

times but that doesn’t mean they will understand it. I learned to always have multiples ways to

teach the same material so that I don’t waste vital time trying to quickly think of something that

could make sense. I’ve learned to be over prepared. I learned that it is a lot easier working with

one student than it is working with three. I could answer the questions this student needed right

away; nobody else was there to interrupt. It was great hearing the student tell me that they

understood, they had the “ahh ha” moment. All this student needed was someone to take a

moment out of their day and go over the information a few times. It was a pleasure working with

this student and being a part of the success.

Further actions I would take to improve student learning would be trying to make more

connections from the content I’m teaching to the student’s life. I wish I could connect everything

to the interest of my students and sometimes it is very natural but other times I feel overwhelmed

because I can’t come up with a connection on the spot that would help the student understand it

clearer.

Areas in which I have grown would include organization and record keeping. Whether it

was attendance or identifying which question was missed the most, I recorded it and then used

that information in planning the next step in instruction for the following day. Organization was

taken to the next level, every piece of information I used was placed in clear file protectors and

in order in which they were taught. All graded materials were marked and dated so they could be

located quickly.

Pre- Assessment

Pre- Assessment Checklist

Review Worksheet:

Questions Numbers Got it Didn’t get it Almost got it

1

2

3

4

5

6

7

8

9

10

During the Pre-Assessment I observed that the student seemed to have an idea of how to

determine if a relation is a function. They knew the domain and the range of the relation and was

able to write that out. The graph shows that 60% of the time the student was able to determine if

a relation was a function. They were also able to use the vertical line test on numbers 5 and 6

because a graph was shown and that helped them understand if the relation was a function. On

number 7, the student did solve the equation correctly however, when plugging in the ordered

pairs the student did not show any work, this cause there to be a loss of points. On the back side

the student had a lot more steps to take in order to solve the problem and then graph it. The

student showed their work in solving the equations for Y, 75% of the time. However, when the

student filled in the table they were unsure where to replace the x-value and instead divided

everything by x. That was the cause of the whole table being wrong, as well as the graphing

aspect of the problem. For both these sections the graph above illustrates a zero percent

completion.

After the student had completed the pre-assessment and I checked over it to see where

that student needed some supplemental teaching. I came to the conclusion that the student was

ready to learn more about functions and that they would be able to grasp the concept with time

and some effort on their part.

Progression

The graph above illustrates the progression that the student made. The students post

assessment was a Unit 4 Quiz. The graph shows that the student did an incredible job stating the

domain and range of the relation as well as determining if the relation was a function. The next

part I looked at was when the student solved the equation for Y. The student created walls to

align everything and this kept things neat. That really helped in solving because they got every

part correct. Lastly, graphing and being sure to label the line. Students were all told to label lines

because the next unit would be graphing multiple linear equations and I wanted the students to

already be in the habit of labeling the lines now before it was too late. My student was able to

graph the lines and label them flawlessly. The quiz also shows the student circling the slope and

boxing the y-intercept. This time however the student didn’t have to create a table because we

taught them a different way of graphing a line using slope-intercept form.

Discussion

February 11, 2015

Students are learning about linear equations and how to find the slope of a line. Students

were given a salmon colored graphic organizer that is split into three sections. The first section is

what we went over today in class. This section is on determining the slope from a graph using

rise over run or drop and then roll. Students were then given homework.

Section 1

February 12, 2015

Today, students looked at the middle section of their graphic organizer, this section

introduced finding the slope of the line when given two points. The formula to find the slope of

the line was introduced M= y2-y1/x2-x1. Then, there was three examples we went over in class

in the “I do, we do, and you do” format. Then students were given a homework worksheet called

“What Do You Call a Duck That Steals?” During 11th period I met with the student I had chosen

for my Performance-Based Assessment. . I explained what I was doing and that I need the

students help; with a project for school. It would involve learning the same information they had

learned the day before or that morning but in a few different ways. The student was delighted to

get out of study hall in the other classroom and work with me. The student even explained that

math was their favorite subject. I asked the student to take out their homework and that we could

work on it together. I noticed the student’s homework calendar (while searching for their

homework) and saw that the student didn’t have very many stamps indicating that they complete

their homework every night. I asked them about it and they said that homework was dumb and

that they never complete their homework. This is where I made a deal with the student. It they

met with me during study hall from now on, I would help them complete their homework and

that they could get more stamps on their calendar which would later help the student’s grade.

They agreed but I wasn’t completely convinced that they would be willing to give me all their

time.

Once the student got the homework out, I ask what they were having trouble with

understanding. The student said that they understood it and so I watch as they started completing

the homework. Quickly I noticed that the student was having difficulty in determining whether to

rise and run or drop and roll when finding the slope. I then asked if the line was increasing or

decreasing the student couldn’t tell me. I showed the student a way in remembering and

connected it to reading. When reading we read left to right, so if the line goes down from left to

right then it is a decreasing slope and we use drop and roll to find the slope. If the line is going

up when looking at it from left to right, then it is increasing and we use rise and run to find the

slope of the line. The student then completed the homework and got a stamp the very next day.

February 13, 2015

Today, during class we went over the last section of the graphic organizer. This section

was on finding the slope of a line from a table. Student had to choose two ordered pairs from the

table and then plug them into the slope formula that they learned the day before. Students were

then given a worksheet for homework that had them using all three ways of finding the slope.

During our meeting we worked on labeling our ordered pairs so that we knew where to put them

in our formula. Then we continued to work on the homework. For the first two questions I asked

the student to tell me whether the line was increasing or decreasing. I noticed that the student

was still having trouble so I brought out “slope-dog”. Slope dog is a visual that helps students see

if a line is increasing or decreasing and how that relates to the slope of the line. If the line is

vertical then it goes towards the nose of the dog and that indicates that there is no slope (nose =

no slope). The mouth is indicated by a horizontal line and has two zeros on each end showing

that a horizontal line has a slope of zero. Plus and minus are the eyes of the dog they indicate if

the slope is positive or negative. If the line looks like the left eyebrow then it has a positive

slope. If the line looks like the right eyebrow then it has a negative slope. The student was happy

when I showed them the slope dog and explained that that would help them remember. After we

finished the homework the student told me that they were happy because this gave them a free

weekend with zero math homework to complete.

Here is the homework student had to

do that required them to use all three

methods for finding the slope of each line.

February 16, 2015

Today, I taught a lesson, my activating strategy was challenging the students to graph a

linear equation before me. First we had to rewrite the equation in slope-intercept form. Then

using a table students would find their ordered pairs and then graph each order pair. The reason

this was a great activating strategy was because the students thought they could beat me and they

got to choose the wager. If they beat me they had no homework for the rest of the week.

Inevitably, I won because I skipped all the parts of making a table and solving for ordered pairs.

Students felt that I cheated but this led the way into me explaining their next graphic organizer

and how we can bypass all those extra steps and learn Miss. Bernardi’s secret way. Students

loved it!

When I met with my student during study hall they explained that my lesson was cool.

And that they wanted a rematch now that they could bypass all those steps. I then helped the

student work on their homework by making sure they implemented what we learned on the note

page. The student circled their slope and put a box around the y-intercept. These visuals really

helped all the students in our class.

February 17-18, 2015

Taught students about rate of change and unit rates and how they are the exact same thing

as slope but with a label added onto it. Gave students a foldable as their graphic organizer and

did station teaching. The learning support teacher went over slope as a review, the cooperating

teacher taught the section labeled rate of change, and then I taught the section on unit rates. This

gave students the ability to move around the room and ask questions in small groups. This was a

two day lesson so that all students could get to every station and fill out their graphic organizers.

After our two day lesson the learning support teacher spoke with me and the cooperating

teacher. She explained that even though she was going over slope and it was mostly a review,

many of the students were still having trouble solving for Y. If they couldn’t solve for Y

correctly then their slope and y-intercept where most likely wrong too. I met with my student

11th period and realized that they were one of the students the learning support teacher was

talking about. While talking to my student they explained that they still had trouble solving for y.

Which then gave them trouble finding the slope. If they couldn’t find the slope then they

wouldn’t be able to graph the line. This then changed our plans completely for the next lesson.

February 19, 2015

Today we decided to split the class so that whomever needed additional help when

solving for Y would get that help in a smaller one on one environment. I took students out into

the hallway and we used white boards to solve an equation and put them in slope-intercept form.

I made sure students were circling their slope and boxing their y-intercept. I noticed that quite a

few students were also circling the x when circling the slope. I explained that the slope of the

line does not include the x-variable and that on a test that would be marked wrong. Student

enjoyed using the white boards and were happy with the help I gave them. Many students were

making minor errors when diving by a negative. I told these students to use their calculator

because once they make that little mistake their entire graph will be wrong. Students were given

homework where they were asked to just solve for Y. This then was checked the next day.

When I met with my student 11th period they had already completed part of the

homework and said that when they went in the hallway and used white boards they really

understood what they were doing wrong. I looked at their work and was happy to see the walls

they put up to help the equation look neater and that they were still circling and boxing the y-

intercept after they solved the problem. I asked the student if they were ready for the quiz that

they would get tomorrow. The student shrugged their shoulders and said I guess. I asked them

what they felt confident about and they explained that the equations would be okay if they

remembered to divide by a negative correctly. I told them not to worry and use their calculator.

February 20th, 2015

Today students were given a Unit 4 Quiz, before the quiz we briefly went over what a

relation was and if a relation was a function. Students came up with the idea of remembering this

by stating that x can date one and only one y value. If x tried dating more than one Y value then

he was a player and not a function.

Student’s results as a whole by class and by grade received on the review sheet.

Student’s results as a whole by class and by grades received on the Unit 4 Quiz.

The numbers

represented by 0-10

are the Number of

students that

received that grade.

This information shows that while some students are doing well others are falling behind.

This information also shows the difference in the Pre-algebra Inclusion classes compared to the

Pre-Algebra Class. As you can see more students are getting A’s in period 5/6 on the Quiz but

that is not an inclusion class so none of these students have IEP’s or 504 Plans. It is important to

note that most of our students that are in our inclusion classes are able to survive and understand

at least 70% or more of the materials. I chose these groups because I wanted to see what the

difference was between a group that has IEPs and a group that does not. Students are being

taught the same materials and the same way it’s just a matter of personal traits in each class. One

observation I noticed in this graph is that out of all three classes the highest number of F’s is in

our Pre-Algebra class, once again this class has no IEP’s in it.

THE STUDENT’S POST ASSESSMENT

& ANSWER KEY

STUDENTS QUIZ

Here you can see the impact of us teaching the students to circle the slope and box the y-intercepts.

ANSWER KEY

Check marks indicate that the student did that part correctly. One point is given for every

check mark. There was a total of 34 check marks making the quiz out of a total of 34

possible points.