Content Area Assessment Plan - Functions Unit – 8th Grade

Running head: CAAP – FUNCTIONS – 8TH GRADE 1

Content Area Assessment Plan - Functions Unit – 8th Grade

Timothy M. Paccione

Marist College

2016

CAAP – FUNCTIONS – 8TH GRADE 2

Contents

Content Area Assessment Plan - Functions Unit – 8th Grade ............................................ 5

Learning Standards ............................................................................................................. 5

Learning Standards ......................................................................................................... 5

Discussion ....................................................................................................................... 6

Learning Objectives ............................................................................................................ 8

Learning Objectives ........................................................................................................ 8

Discussion ..................................................................................................................... 10

Rubric: Authentic Assessment .......................................................................................... 12

Rubric ............................................................................................................................ 12

Discussion ..................................................................................................................... 13

Authentic Assessment: Kids Sports Research, Inc. ........................................................... 15

Part 1: Description ........................................................................................................ 15

Part 2: Script and Materials........................................................................................... 16

Part 3: Learning Objectives Incorporated ..................................................................... 19

Discussion ..................................................................................................................... 21

Formative Assessments ..................................................................................................... 24

Formative Assessment 1: Plickers ................................................................................ 24

Example .................................................................................................................... 25

Formative Assessment 2: Exit Slips .............................................................................. 26


Example .................................................................................................................... 27

Formative Assessment 3: Oral Questioning .................................................................. 28

Discussion ..................................................................................................................... 29

Data Collection and Use ................................................................................................... 32

Formative Assessment 1: Plickers ................................................................................ 32

Data Sample & Analysis ........................................................................................... 34

Formative Assessment 2: Exit Slips .............................................................................. 35


Formative Assessment 3: Oral Questioning .................................................................. 37


Summative Assessment – Kids Sports Research, Inc. .................................................. 39


Discussion ..................................................................................................................... 42

Self-Regulation Strategies ................................................................................................ 44

Performance Strategy: Memory Devices for Algebra ................................................... 44

Examples ................................................................................................................... 45

Performance Strategy: Flashcards ................................................................................. 46

Example .................................................................................................................... 47

Reflection Strategy: SWOT Analysis ........................................................................... 48

Example .................................................................................................................... 49


Discussion ..................................................................................................................... 50

Student Portfolio ............................................................................................................... 52

Description .................................................................................................................... 52

Table of Contents .......................................................................................................... 55

Student Reflection Sheet ............................................................................................... 56

Discussion ..................................................................................................................... 57

References ......................................................................................................................... 59


Content Area Assessment Plan - Functions Unit – 8th Grade

Learning Standards

Common Core Standards

Standards: Common Core State Standards – Mathematics

Grade: 8th

Unit: Functions

Content Area: Define, evaluate, and compare functions.

CCSS.MATH.CONTENT.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The

graph of a function is the set of ordered pairs consisting of an input and the corresponding

output.


Compare properties of two functions each represented in a different way (algebraically,

graphically, numerically in tables, or by verbal descriptions). For example, given a linear

function represented by a table of values and a linear function represented by an algebraic

expression, determine which function has the greater rate of change.


Interpret the equation y = mx + b as defining a linear function, whose graph is a straight

line; give examples of functions that are not linear. For example, the function A = s2

giving the area of a square as a function of its side length is not linear because its graph

contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

(http://www.corestandards.org/Math/Content/8/F/)


Discussion

Before beginning my Content Area Assessment Plan (CAAP), I needed to first choose

which mathematics topic I would like to assess. This choice would be dictated by both the

desired structure of my lesson and which set of professional standards I would use to ensure my

students sufficiently learned the subject matter. Between the two choices for structure, a “Unit

Plan” and a “Year-Long Skill,” I decided on an individual unit. Considering this would be the

first assessment plan I had ever completed, limiting the scope of the content would allow me to

keep my efforts focused on the teaching itself.

After choosing the structure, the next step was to choose the standards that I would be

holding my assessments to. As I plan to be a math teacher, I chose a topic within mathematics,

“Operations and Algebraic thinking: Write and Interpret numerical expressions,” from the

Common Core set of standards for Fifth Grade Math (National Governors Association, 2010).

As with my structure choice, I felt that keeping my subject matter, and consequently its related

standards, as simple as possible would allow me to keep my focus on both lesson planning and

assessment development, rather than on the content itself. However, after receiving feedback

from both classmates and our instructor, I realized that choosing a fifth grade set of standards,

while perhaps simple, would do me a disservice by limiting my learning opportunities within the

assignment. My certification will be in secondary education, so I was better served choosing a

grade level and set of standards that would be applicable in my future classroom and could

provide the most value when I develop future lessons and assessments. In addition, the feedback

helped me realize that if the chosen standards were too simple, I could be at the disadvantage of

having too little information with which to form my learning objectives and subsequent

assessments. After considering all of these facts, I chose a new set of standards, “Functions:


Define, evaluate, and compare functions,” from the Common Core set of standards for Eighth

Grade Math (National Governors Association, 2010). This second set of standards fell into the

appropriate age group relative to my certification, while also providing complex enough

requirements to allow me to successfully complete the rest of my assessment plan.

The first step of my CAAP, while seemingly simple and straightforward, provided me

with some important lessons to apply during the rest of the process. I made some initial

assumptions as to what would best serve me within the assignment, but quickly learned that there

were more factors to consider than I had originally believed. I was able to use the feedback I

received in class to adjust my work and, before moving on to the next stage of my assessment

planning, resolved to make as few assumptions as possible moving forward.


Learning Objectives

Learning Objectives

1. When presented with a function in y = mx + b format, students will recognize it as a

linear function and accurately summarize what each variable represents.

2. When given a linear function as well as a specific point, students will describe the

relationship between the point and its x and y values within the y = mx + b format,

including the variables’ independent and dependent natures in their explanation.

3. When provided with a list of functions, students will identify the independent and

dependent variables in 4 out of 5 attempts.

4. Students will be presented with a table of values representing a linear function and will

be able to infer the x and y intercepts of the equation.

5. When given a linear equation as well as a pair of points, students will diagram the related

line on a graph and label the key elements, including the x intercept, y intercept, the

related line, and the given points in appropriate formatting.

6. Students will orally compare a pair of functions, given one represented by a table of

values as well as one represented by algebraic expression. In their comparison, students

will include acknowledgement of the functions as linear and identification of the function

that has a greater rate of change (slope).

7. Given a table of values representing a linear function, students will generate the related

equation in y = mx + b format.

8. When presented with a vertical line, students will write a short paragraph relating why a

vertical line does not represent a linear function, describing the concepts of inputs and

outputs in their account.


9. Students will orally support the rule of functions that mandates there can be only one

output for every input, including at least one of the following pieces of language in their

defense: X and Y variables, independent and dependent variables, or y = mx + b.


Discussion

Once the standards were chosen, vetted for suitability, and added to the draft, it came

time to create the learning objectives that would ensure those standards were met. These

learning objectives would be a critical piece of the overall assessment plan, as they would serve

as the building blocks upon which all assessments, activities, rubrics, and analysis would be

based. It was tremendously important that I develop these learning objectives in a way that not

only covered the content found within the standards chosen, but also ensured my students would

engage in multiple levels of thinking while the learning occurred.

Before beginning the process, I reread the standards chosen in order to acquire a deeper

understanding of the curriculum that my students would need to learn and retain, and what

objectives would ensure those activities occurred. To get started, I created a list that included the

key pieces of information found in each standard. Next, I was able to mold those core elements

into a set of instructional desires. I had my fundamental goals in place, but knew that

transforming those goals into legitimate learning objectives would require a review of their

strengths and weaknesses.

I reviewed my notes taken during our classroom discussion as well as the readings given

to assist in the task. From these readings, I knew that each learning objective must contain four

parts, represented by the mnemonic device ABCD; standing for Audience, Behavior, Condition,

and Degree. Any learning objective that contains anything less than all four ABCD elements

would be incomplete and therefore would not fully support its related standard. In addition, the

readings introduced me to the concept of Bloom’s Taxonomy, which breaks down learning into

six categories: remembering, understanding, applying, analyzing, evaluating, and creating.

These six learning types form a pyramid that represents the increasing level of thinking they


allow a student to use, with “creating” being the most complex, specific, and valuable form of

thinking for students. Using this newfound knowledge, I developed eight learning objectives for

my chosen set of standards.

After receiving feedback from both my instructor and a fellow classmate, I concluded

that there was room for improvement within my learning objectives. Though I had incorporated

Bloom’s Taxonomy principles into my original set of objectives, my word choice focused

primarily on only two of the six learning types. This limited the diversity of knowledge my

students could hope to obtain. In addition, I realized that my objectives restricted my students by

only offering them opportunities to share their knowledge in written form. It is extremely

important to allow for multiple means of knowledge sharing within a unit, as it provides students

with learning disabilities additional ways to prove their understanding. As a result of this

realization, I varied my objectives to allow for oral behaviors in addition to the written ones.

Through a final piece of feedback, I learned that the ABCD elements within my

objectives could also use further development. I had particularly struggled with the “degree” of

each objective, as I found the concept to be slightly ambiguous and difficult to understand. As a

result of this uncertainty, I had added unnecessary qualifiers in my original set of objectives that

caused considerable confusion. As a result of the feedback, I was able to significantly improve

my objectives, allowing them to appropriately reflect the standards, while also ensuring my

students would be exposed to the full spectrum of learning levels.


Rubric: Authentic Assessment

Rubric

The following rubric will be provided to both students and parents prior to the start of the

authentic assessment, Kids Sports Research, Inc.:

Learning Category Areas that Need

Work Project Standards

Evidence of Exceeding Standard Pts.

Generation of y = mx + b equation from a Table of

Values

Interpreted data and generated two linear equations in y = mx + b format.

2

Analysis of y = mx + b Function

Recognized the equations as linear and explained how they know this to be true.

2

Summarized what each variable represents within the context of the task.

2

Graphing of a Linear Equation and its Key

Elements

Diagrammed two linear equations on separate graphs, labeling all key elements including the x and y intercepts, the equations, and the given points.

2

Understanding the Relationship between a Linear Equation and its

Points

Described how given variables affect one another, noting their relative dependence within the equation.

2

Identified the given data points and interpreted their coordinates by explaining their relationship to the linear equations.

2

Comparing a Pair of Functions Given in Different Formats

Calculated the slope of each linear equation, using the assigned methods.

2

Identified the function with a greater rate of change (slope), and explained what that means in the context of the task.

2

Group Work, Presentation Quality, and Effort

Was an engaged member of their group and exhibited effort throughout the project

2

Spoke clearly during their presentation while using proper mathematical terminology.

2

Total Score: 20


Discussion

A quality rubric is a vital component of the assessment process for numerous reasons.

With an effective rubric, students can understand exactly what their teacher expects of them,

which allows them to achieve the best possible grade, while also producing their best possible

work. This knowledge can eventually help students develop their ability to self-assess. By

empowering students and increasing their confidence levels, this skill can enable them to

independently recognize areas within their work that are in need of improvement, without any

assistance from instructors (Andrade, 1997, p. 2). With a proper rubric, a teacher can give their

students complete ownership of the grades they receive as well as full comprehension of how

they were determined. In addition, a teacher can use a rubric to provide their children’s parents

with the same knowledge, giving them critical insight into what must take place in order for their

children to be successful (p. 2).

The rubric I developed for my CAAP is designed to convey precisely what is expected of

my students in their authentic assessment, and to serve as a uniform set of standards upon which

to grade the class. Within the rubric, I individually addressed each of the learning objectives I

had incorporated into the authentic assessment and specifically identified what actions must take

place for my students to gain full or partial credit. I made sure that each description included

both measurable and identifiable elements in an effort to give the students a clear understanding

of what they needed to accomplish (Moskal, 2003, p. 2). In addition, I used the rubric to list my

expectations for each student’s effort, presentation skills, and ability to work within a group. It

was particularly important to me that I provide an opportunity for students to gain points for hard

work and positive group activity, as I believed this could help offset any struggles that my

students might have in meeting the requirements of the learning objectives themselves.


As has become a recurring theme in my CAAP process, feedback was a vital component

in creating a rubric of good quality and completeness. The original rubric I produced for my first

draft was of a completely different format than the final version. I designed my first rubric with

grading options of zero through four and included significantly longer descriptions of what I

required, with extensive repetition within my language. After speaking with my instructor, I

determined that the rubric was considerably verbose, which could confuse and discourage my

students during their initial review. As a result, I decreased the description lengths in my final

draft, while maintaining clarity in regards to what was expected. In addition, I reduced the

scoring complexity and switched to a zero through two format. I believed this would result in

more consistency of grading if multiple evaluators were to use the rubric, as it would allow them

to award zero points for no attempt, one point for partial completion, and a full two points for

meeting or surpassing expectations.

Upon further personal reflection, I became concerned that there was no place on my

rubric for descriptive feedback, as detailed commentary is an essential component when helping

students get the most from their learning (Garrison, 2004, p. 2). When individualized written

feedback is included within a rubric, a student can become more aware of their potential, which

can help them succeed in future units and assessments (p. 2). Also, should a student exceed (or

fall short of) the expectations set forth in the rubric, I believe it is important that they receive a

proper explanation of how exactly that was determined. As a result, I converted my rubric into

the single criteria format, which offers opportunity to provide feedback both when the students

underperform and when they exceed expectations. An additional advantage of this type of rubric

is it can easily be adapted to better support students with special needs, as it allows specific and

individual feedback that can be tailored to the particular student being evaluated.


Authentic Assessment: Kids Sports Research, Inc.

Part 1: Description

The authentic assessment for this unit is a research and analysis assignment that students

will complete as “employees” of a mock sports research company. The students will work in

teams to complete the required research and related calculations, which they will submit in a

written report. In addition, they will orally present their findings as a group to an adult

participant. This adult will be taking the role of a “Sports Agent,” in the mock scenario, a part

which will be played by a fellow faculty member. During their presentation, students will

demonstrate their understanding of the topic being covered within the unit, specifically their

ability to define, evaluate and compare functions in a real-life situation.


Part 2: Script and Materials

KIDS SPORTS RESEARCH, INC

MONDAY MEMO:

Happy Monday team! Thank you for reading our weekly company memo. Exciting

news everyone! We have a new client who needs your help! Our client is a sports agent and he

represents a number of athletes that are looking for new work contracts. Before agreeing to any

deals with the various teams, the agent would like to know exactly how much money his players

deserve. He would like us to look at how much money similar players have received in the past

and use that information to figure out how much he should demand for each player.

Our client has asked us to calculate these amounts using last year’s statistics for each

player and has provided us with a list of similar players to use in our comparisons. He has even

given us all of the data that we need, but it is up to you to create some linear equations to help us

get the answers we need! I will be assigning you to teams, and each group will be assigned one

athlete. Your team will be provided with step by step instructions, and I will be available to help

as well. Make sure to follow all of the steps on the worksheet, answer all the required questions,

and show your work. Each member of your team will be handing in a copy of your calculations

and a completed worksheet at the end of the task.

After all of our research is complete and we have figured out a fair salary for each of the

athletes, our client has asked that we present the results to him directly, including a full

explanation of the math we have used, so he can be absolutely sure his players get the money

they deserve. All groups will need to create posters which graph their results and equations.

These will be presented and explained to the client. During the presentation, each member of

your team must participate and show their understanding of the work completed. This is a big

job for the company, so I’d like to thank all of you in advance for your hard work!


Worksheet:

Kids Sports Research, Inc. - Assessment

Team #: ___

Athlete Name: _________________

Student Name: ________________

STEPS

1. Review the data tables provided by the client. Compare the “STAT 1” amounts to the “AMOUNT PAID” totals.

What do you recognize about their relationship? What type of function would represent this relationship accurately?

Repeat this process and compare the “STAT 2” amounts to the “AMOUNT PAID” totals. Do you see a similar

relationship as with “STAT 1?” Why or why not?

2. Identify the variables in the equation you recognized in step 1. Which set of data represents the independent

variable? Which represents the dependent variable? Explain your reasoning.

3. Determine the slope of the "STAT 1" equation using point slope format. Determine the slope of the "STAT 2"

equation using the table of values method. Which slope is greater, and what does that mean in the context of your

assignment? Show your work.

4. Using the slopes you determined in step 3, as well as the variables you identified in step 2, develop the two

equations that represent the relationships being shown in the data tables given. Use the point slope formula to

determine your equations and then restate both in the y = mx + b format.

5. Now that you have your two equations, plug the stats of your assigned athlete into their related equation to

determine the salary your player deserves. Do the two amounts match? Does that make sense in the context of the

problem? Why or why not?

6. On two large posters, which will be provided for you by your teacher, graph the two equations you generated.

Keep in mind these will be used when you present your results to the sports agent. Make sure to label all key

elements of your graph, the function itself, and your player. Be prepared to explain what the position of those points

means in the context of the problem.

7. With your team, prepare to present your results to the Sports Agent. Make sure you are ready to answer any of

the questions on this worksheet during your presentation, and to explain how you know that the results, the amount

of money you think the player deserves, is the right amount. In your explanation, be sure to use all of the

mathematical language that you have learned in this unit.

Good Luck!


Sample data:

CLIENT'S PLAYER: RUSSELL WILSON, QB

2015 PASSING YARDS: 5,500

2015 TOUCHDOWNS: 47

STAT 1 STAT 2 AMOUNT PAID

QUARTERBACKSPASSING

YARDS

TOUCH-

DOWNSSALARY

TOM BRADY 5,000 42 25,500,000$

AARON RODGERS 4,000 32 20,500,000$

ELI MANNING 4,500 37 23,000,000$

CAM NEWTON 3,500 27 18,000,000$

ALEX SMITH 3,000 22 15,500,000$

SIMILAR NFL PLAYERS


Part 3: Learning Objectives Incorporated

Below, I have stated the relevant learning objectives along with a description of how each will be

incorporated into the planned authentic assessment:

1. Given a table of values representing a linear function, students will generate the related

equation in y = mx + b format.

• Students will be given data sets that include the relevant sports statistics to

be used in the required comparison. They will be expected to interpret those

sets of data in order to develop two linear equations in y = mx + b format.

2. When presented with a function in y = mx + b format, students will recognize it as a

linear function and accurately summarize what each variable represents.

• After using the research data to generate the relevant linear functions, the

students will explain to the sports agent what each of the variables within the

functions represent in the context of their assignment.

3. When given a linear equation as well as a pair of points, students will diagram the related

line on a graph and label the key elements, including the x intercept, y intercept, the

related line, and the given points in appropriate formatting.

• Once the students have determined their linear functions, they will diagram

them on two separate graphs for the sports agent, labeling all key

elements. He will then ask them to identify and compare two different

players using the graph, at which point the students will conduct the

comparison in a manner that shows understanding of what the two points

represent within the context of the situation.


4. When given a linear function as well as a specific point, students will describe the

relationship between the point and its x and y values within the y = mx + b format,

including the variables’ independent and dependent natures in their explanation.

• After the students present the linear function to the sports agent, they will

explain the relationship between the two variables, including in their

explanation the relative dependencies. The students will discuss a specific

point on the line, in order to offer an example of this relationship in action.

5. Students will orally compare a pair of functions, given one represented by a table of

values as well as one represented by algebraic expression. In their comparison, students

will include acknowledgement of the functions as linear and identification of the function

that has a greater rate of change (slope).

• Once the students have generated both of the linear equations required for

their comparison, they will calculate the slope of each using the table of

values method for one, and the algebraic expression method for the

other. During their presentation, the sports agent will ask them to explain

which factor has a greater rate of change, and what that means in the context

of their assignment.


Discussion

The authentic assessment is an important piece of the CAAP, as it is used to measure

student understanding of some key learning objectives. With the results from an authentic

assessment, an instructor is able to learn two important pieces of information: how well their

students performed, and how effective their teaching methods were in guiding student learning.

Specifically, it lets a teacher know where exactly the students have a clear understanding within

the learning objectives as well as where gaps exist in their knowledge (Garrison, 2004, p. 1).

With all of this in mind, for my summative assessment within this CAAP, I created a fictitious

scenario that could exist in the real world, to which the students could apply what they had

learned within the functions unit.

My students will be assigned a task from their “boss” at a mock sports research company

called Kids Sports Research, Inc. This boss will inform the students that they have a new client

who has a particular research need. After explaining in detail what will be required, he will

instruct them in how to go about fulfilling his request. In order to do so, they will need to apply

the concepts they will have learned on functions, slope, variables, and graphs. The students will

need to explain their understanding of these items through writing, and will also be required to

present their knowledge orally to an adult in a presentation setting. The students will work in

groups to complete this assignment and will be graded according to a rubric provided to them

prior to its commencement. The presentation portion will be filmed and stored in their digital

portfolio.

When designing this authentic assessment, I hoped to develop a relatable, realistic

scenario that the students could one day find themselves in. Having worked in the business

world for ten years, I had some valuable, personal experience to draw from, and I was able to


translate my knowledge of common company practices into a believable mock activity.

Furthermore, I designed the assessment to prove that the students possess the ability to produce

their own content using the knowledge they acquired during the unit, and to eliminate any

possibility that they are simply mimicking the mathematical procedures they observed (Scott,

2000, p. 33). In other words, I wanted my assessment to guarantee that the transfer of

knowledge took place. The statistics that I will provide to the students were determined using

actual, real-world data. I felt that this level of detail and authenticity was important to

sufficiently engage the students. As most students love sports, I thought that incorporating them

would help increase their enthusiasm in the assignment as well.

To make sure the students were given some choices within the assignment, I provided a

variety of sports, athletes, and types of data for them to choose from. In addition to increasing

student choice, this variety will allow the students to maintain interest during other groups’

presentations by avoiding repetition. I also wanted to make sure I provided accommodations for

students with different learning styles, as an authentic assessment should provide an opportunity

for every type of learner to succeed. With this in mind, I included both written and oral

components within the assessment. This will give the students an opportunity to show their

understanding in multiple formats. If a student with special needs struggles in one of these two

areas, they can still succeed in the other. Finally, as this is a group assignment, I had to design it

in a way where I could still assess each student individually. At first, I had planned to collect just

one completed worksheet from each group. However, in order to make sure each student is

given an opportunity to prove their understanding, I changed the requirements to be individual,

with each student being required to turn in a completed worksheet. In addition, I added some

language to my materials that made it clear that each student must also participate in the oral


discussion. As they are working on the assessment, I will be rotating from group to group to

make sure all students are participating equally in the discussions and calculations.

Personally, I found this section of the CAAP to be an enjoyable one to create. I think that

the desired benefit of choosing a topic that generates enthusiasm among the students had the

additional effect of increasing my own enthusiasm. As with the previous CAAP sections,

feedback was an important part of the process in making this section as effective as possible.

The original draft of my authentic assessment focused only on one sport and had every group of

students completing the same assignment. I learned through class discussion the problems this

could cause and the potential benefits that increased variety could bring. Overall, I was very

satisfied with my results, and I firmly believe that this assessment would enable me to determine

which students in my future classroom truly understand the learning objectives and which

students do not (Wiggins, 2006, p. 1).


Formative Assessments

Formative Assessment 1: Plickers

Format: Hands-On Skill

Procedure: At the appropriate time within their lesson on linear functions, students will

participate together as a class using Plickers cards, in order to show their understanding

of two learning objectives being covered in the functions unit. As their teacher, I will

write five linear equation questions into the Plickers program, and for each equation, the

students will be asked to select the answer choice (of four) that correctly identifies both

the independent and dependent variables. This same process will be repeated in a way

that allows the students to correctly identify the x-intercept and y-intercept of a linear

equation. If less than 75% of the class answers the questions correctly, I will revisit the

lesson and adjust my teaching methods. The six sets of answers given will be saved in

the Plickers database for further analysis. This assessment will be used as for class

analysis only, and no individual grades will result from student performance, a fact they

will be informed of before commencing.

Learning Objectives:

When provided with a list of functions, students will identify the independent and

dependent variables in 4 out of 5 attempts.

Students will be presented with a table of values representing a linear function and

will be able to infer the x and y intercepts of the equation.


Example

www.plickers.com

https://www.plickers.com/PlickersCards_2up.pdf


Formative Assessment 2: Exit Slips

Format: Written

Procedure: At the end of their lesson on linear functions, students will be presented with

a worksheet displaying a vertical line graphed upon the x and y axes. They will be asked

to answer the following question written below the graph: “Briefly explain why the graph

above does not represent a linear function, noting in your explanation the role of inputs

and outputs.” Students will place their names on their worksheets and hand them to me

as they exit the classroom. I will grade them on a scale of zero through two points,

depending on the understanding the student shows in their explanation (0 – no

understanding, 1 – some understanding, 3 – complete understanding). After grading, I

will determine the class average. If the class average score is less than one, I will review

the lesson concerning vertical lines further in the proceeding class period. Any student

who receives a zero will be required to resubmit the worksheet at a later date.


When presented with a vertical line, students will write a short paragraph relating

why a vertical line does not represent a linear function, describing the concepts of

inputs and outputs in their account.


Example

In the space below, briefly explain why 'line a' in the graph

above does not represent a linear function, noting in your

explanation the role of inputs and outputs.

EXIT TICKET - LINEAR FUNCTIONS

x

y line a


Formative Assessment 3: Oral Questioning

Format: Oral

Procedure: Midway through their lesson on linear functions, students will be taken aside

one by one to speak to me individually. While I speak to the individual students, the rest

of the class will be given a practice worksheet to focus on. I will ask each student to

orally explain the rule of functions that mandates there can be one and only one output

for every input and will take note of the key language they use in their response

(including mentions of X and Y variables, independent and dependent variables, and y =

mx + b), as well as the accuracy of their explanation. I will grade each student on a scale

of zero through two, with zero points awarded for showing no understanding, one point

awarded for showing some understanding, and two points awarded for showing complete

understanding. All scores will be stored in an Excel worksheet, which I will use to

calculate the class average. If the class average is less than one, I will review the rule of

inputs and outputs with all of my students in the class period immediately following the

day when oral questioning takes place.


Students will orally support the rule of functions that mandates there can be only one

output for every input, including at least one of the following pieces of language in

their defense: X and Y variables, independent and dependent variables, or y = mx + b.


Discussion

Chappius (2009) defines formative assessments as “formal and informal processes

teachers and students use to gather evidence for the purpose of improving learning” (p. 5). When

reading this definition, I was initially given pause by her inclusion of the words “and students.”

Up until that moment, I had considered formative assessments to be a tool that is used almost

exclusively to assist a teacher. I certainly believed the students could benefit from formative

assessments, but I believed that benefit to be indirect and acquired through the actions a teacher

takes once they are able to collect their new data. Recognizing that students can gain an equal

amount of instantaneous benefit from formative assessments was a critical realization for me,

and it shaped the decisions I made from that point forward in this section of the CAAP.

To begin the process of choosing my formative assessments, I first re-examined my

learning objectives, attempting to think of any activities that fit with them in the most natural

fashion possible. I identified which objectives would work best with oral, written, and hands-on

assessments and let those identities guide me in choosing how to assess each. In fact, through

this process, I discovered that my learning objectives lacked balance in terms of the learning

styles involved. As a result, I changed the behavior for one of my learning objectives to oral

from its original written format. I felt it was important to design my assessments around a varied

set of learning styles, because of the critical role that plays in accommodating students with

special needs. If I had left my learning objectives as they were, a student that best shows their

knowledge and understanding through oral activities would have been unfairly disadvantaged.

Lastly, I had to determine what kinds of data I would want to gather from the learning objectives

I selected and what activities would be useful in that context (Popham, 2008, p. 53).


Once I knew what considerations would shape my formative assessment choices, I began

to look for interesting, engaging ideas to use as inspiration. Through a slide show on

Slideshare.net, I observed some incredibly clever ways to assess students in a formative manner.

Some I recognized from my own educational experiences, while others were new, intelligent

takes on the assessment experience.

One such idea that was new to me, was the use of mini white-boards. With this

assessment, the teacher could ask a number of questions and get immediate answers from the

class, as each student would be able to write their answer on a personal white-board and hold it

up for the teacher to view. It seemed to be a great way for students to utilize their hands-on skills

in order to show their knowledge and understanding, and the activity was an appropriate fit for

the particular learning objective I had in mind, as it required a measured success rate for a given

number of questions. I was ready to move forward with this idea, until a peer pointed out how

difficult the data collection would be in real-time, and consequently cast doubt on how realistic

the activity would be for a large classroom setting.

Upon hearing this feedback, I was reminded of something James Popham (2008) wrote in

his journal “Transformative Assessment in Action: An Inside Look at Applying the Process”, in

which he stated, “The third question to ask at choice-point is one that, frankly, should trump the

instructional and assessment considerations raised by the first two questions. That question is,

‘How willing am I to do this?’” (p. 54). I quickly realized that I was setting myself up for failure

with such a cumbersome data collection process. Luckily, I found an ideal alternative in

Plickers.com, which accomplishes the same process as mini white-boards but with the efficiency

of technology and automatic data collection. This adjustment served dual purposes, as I had


been searching for a way to incorporate new technology into my assessments, since they have the

potential to increase engagement and employ students’ high order skills (Looney, 2004, p. 15).

For my remaining two formative assessments, I decided to use a few more traditional

activities which I have personal experience with: “Exit Tickets” and “Oral Questioning.” The

idea of an exit ticket appealed to me because it serves as a quick way for students to show their

understanding of a key learning objective, while also giving them a chance to engage in

descriptive writing. All too often in mathematics, written skills are neglected, and it is

tremendously important to me that I not advance that trend in my future classroom. With the

testing standards currently in place in schools, students will need strong written skills in order to

succeed. Furthermore, it is quite difficult to prosper in the real world without the ability to share

one’s thoughts through written word.

My final formative assessment, “Oral Questioning,” would enable students not proficient

in written or group activities to exhibit their knowledge and understanding of the unit through

direct conversation with me, their teacher. I felt this activity lined up quite well with the learning

objective that asked them to explain the outputs and inputs of a function, as it would prove to me

that they truly understand what is transpiring within a linear equation. While other types of

assessments might give students an opportunity to simply replicate a mathematical process that

they learned from an instructor, a direct, oral conversation with myself would require in-depth

knowledge and understanding, giving me the most accurate data possible for measuring student

comprehension.


Data Collection and Use



Brief description

Students will use individual Plickers cards to answer questions posed

to them. As their teacher, I will use their scores to gauge the

students’ understanding as a whole, and no individual grades will be

given.

How will you collect

the data?

The Plickers software will immediately determine which students

answered the question correctly and which did not. It will then

automatically store the information within its system.

In what form and in

what location will

you store the data?

After the class has ended, I will enter the information into an Excel

spreadsheet listing the questions, student responses, and their

accuracy. The spreadsheet will be saved on my work computer.

How will you analyze

the data?

-

-

How will you use

that analysis in

making decisions

about instruction?

After all questions have been asked and answered, I will check the

Plickers.com results to determine whether or not the class answered

75% or more of the questions correctly. If I discover this is not the

case, I will immediately review the portion of the unit being assessed.

After the class has ended, I will enter the results into a table in Excel.

Next, I will utilize the bar graph tool within Excel to analyze the

relative success my class was able to achieve for each question.

Additionally, I will apply conditional formatting to my table of data

in order to determine which students are struggling individually

(Conditional Formatting will color students scoring under 75% in red,

and students scoring over 75% in green).

If I determine that a particular question challenged more than 75% of

their students, I will review that question with the class during the

next period. If I observe that an individual student answered less than

50% of the questions correctly, I will meet with that student

individually to determine if further instruction is needed.

How will you share

the data with your

students?

If, after the initial calculation, it is determined that under 75% of the

questions were answered correctly by the class, I will inform the class

immediately that this occurred, and that further review is required. In

the class period immediately following the formative assessment, I

will share the bar graph I created with the students. Finally, all

students will receive their individual results via email.


How will you give

your students

feedback?

-

What kind of

feedback will you

give them?

-

When will they be

able to apply it?

The bar graph will be shown to the class in order to help them

understand how they are performing as a group within the lesson. I

will also email the students their individual results, with explanations

given for any incorrect responses. Any student that is struggling

(scores under 50%) will be asked to reply with the correct answer, in

their own words, for any questions they answered incorrectly. All

students will be given a chance to apply what they have learned

during further assessments within this lesson, including the

summative one at its conclusion.

Learning Objectives

When provided with a list of functions, students will identify

the independent and dependent variables in 4 out of 5 attempts.

Students will be presented with a table of values representing a

linear function and will be able to infer the x and y intercepts of the

equation.


Data Sample & Analysis

StudentQuestion

1

Question

2

Question

3

Question

4

Question

5

Question

6

Total

Score

Total

Score %

Joe Schmo YES YES YES YES YES YES 6 100%

Jim Slim NO YES NO YES YES YES 4 67%

Jane Plain YES NO NO YES YES YES 4 67%

Bill Thrill YES YES YES NO NO YES 4 67%

Kate Late YES YES YES YES NO YES 5 83%

TOTAL 4 4 3 4 3 5

TOTAL % 80% 80% 60% 80% 60% 100%

4.6 77%

Formative Assessment 1 - Plickers

CLASS AVERAGE




Brief description

Students will be presented with a worksheet before leaving class

displaying a vertical line graphed upon the x and y axes. They will

be asked to write a one paragraph response to a question referencing

that graph. The assignment will be assessed using a 2-point scale and

the students’ scores will be included in their participation grades.


the data? I will collect the worksheets as the students leave class.

In what form and in

what location will

you store the data?

After the class has ended, I will review and grade the student

worksheets, giving each a grade of 0 to 2, depending on how satisfied

I am with their explanation. I will award 0 points for no

understanding, 1 point for some understanding, and 2 points for

complete understanding. Those scores will be recorded in my teacher

gradebook.


the data?

-

How will you use

that analysis in

making decisions

about instruction?

After grading the worksheets, I will determine how many of my

students were able to answer the question correctly by calculating the

class average score using a calculator. If the class average is 1 or

lower, I will review the lesson further in the following class period.

Additionally, I will re-examine the lesson plan I used with

consideration given for future classes.

How will you share

the data with your

students?

The students will receive the worksheets back once they have been

graded.

How will you give

your students

feedback?

-

What kind of

feedback will you

give them?

-

When will they be

able to apply it?

Feedback will be given on the worksheets in the form of comments

from myself, their teacher. If the student answers a question

correctly, I will note the key elements of their correct response. If the

student answers the question incorrectly, I will indicate what was

inaccurate about their response. All students will be given the

opportunity to improve their score by resubmitting their worksheet

with a corrected response. Any student receiving a 0 as their initial

score will be required to resubmit their worksheet.

Learning Objectives

When presented with a vertical line, students will write a short

paragraph relating why a vertical line does not represent a linear

function, describing the concepts of inputs and outputs in their

account.






Brief description

Students will be taken aside, one by one, to speak to me, their

teacher, individually. I will ask the students to orally explain a

mathematical concept. Students will be assessed on a 2-point scale,

and their score will be included as part of their participation grade.


the data?

After hearing each student's answer, I will record a grade of 0 to 2 in

my grade book, depending on how satisfied I am with a student's

response. I will award 0 points for no understanding, 1 point for

some understanding, and 2 points for complete understanding.

In what form and in

what location will

you store the data?

After class has ended, I will input all of the students’ grades into an

Excel file, which will be stored on my school computer.


the data?

-

How will you use

that analysis in

making decisions

about instruction?

I will calculate the classroom average for the assessment using the

Excel table and Excel formulas. If the class average score is 1 or

lower, I will review the lesson further in the class period immediately

following the assessment. In addition, I will re-examine the lesson

plan used with consideration for future classes given.

How will you share

the data with your

students?

Each student will be informed of their score at the end of their oral

questioning session.

How will you give

your students

feedback?

-

What kind of

feedback will you

give them?

-

When will they be

able to apply it?

When given their score, students will immediately receive an oral

explanation from me that informs them of what they did right, what

was inaccurate, and/or what was missing from their answer. All

students will be given the opportunity to retake the oral assessment at

a later date to improve their grade. If a student receives an initial

grade of 0, they will be required to retake the oral assessment at a

later date.

Learning Objectives

Students will orally support the rule of functions that mandates

there can be only one output for every input, including at least one of

the following pieces of language in their defense: X and Y variables,

independent and dependent variables, or y = mx + b.



StudentOral Questioning

Scores

Joe Schmo 2

Jim Slim 2

Jane Plain 1

Bill Thrill 1

Kate Late 2

Average 1.6


Summative Assessment – Kids Sports Research, Inc.

Summative Assessment: Kids Sports Research, Inc.

Brief description

Students will complete a task for a mock sports research company.

The students will work in teams to complete the required research

and related calculations and will then present their findings as a group

to an adult participant. During their presentation, students will

demonstrate their ability to define, evaluate and compare functions in

a real life situation. The assessment score will be included in the

students’ quiz grades for the unit.


the data?

All students will give a presentation, at which point the teacher will

be present and taking notes. The presentation will also be video

recorded for further review and storage. Students will also submit a

completed written worksheet showing their calculations and results.

The presentation and worksheet will be graded using a rubric, and the

students’ grades will be entered into an Excel table for analysis.

In what form and in

what location will

you store the data?

The data will be entered into an Excel file and stored on my work

computer. The worksheets will be given back to students, and they

will be required to include them in their portfolios. In addition, the

video recordings will be stored in a folder on my computer.


the data?

-

-

How will you use

that analysis in

making decisions

about instruction?

The presentations will be graded according to a rubric that enables

the students to score anywhere from 0 to 20 points, with scores

ranging over 6 categories. Each student's scores will be entered, by

category, into an Excel table. I will analyze this data using the line

graph tool found in Excel in conjunction with an average formula in

order to determine the lesson's success rate both for the group and for

individuals. The data will be analyzed on a category-by-category

basis to ensure all learning objectives are being assessed. If after

review, I see a category that the class is struggling to understand (has

an average score of 50% or less), I will review that further before

moving on to the next lesson. If any individual student has an overall

score of 10 or less, I will meet with them individually before moving

on to the next lesson.

How will you share

the data with your

students?

The students will receive a graded rubric including both their score

and any comments or notes deemed appropriate. It will note both the

areas that need improvement as well as the areas in which the student

exceeded expectations.


How will you give

your students

feedback?

-

What kind of

feedback will you

give them?

-

When will they be

able to apply it?

All students will be given feedback via the graded rubric. The

students will receive a grade for each of the 6 categories and will

receive comments where appropriate, noting areas for improvement

as well as areas in which the students excelled. If any student

receives a score of 10 or below, they will meet with me individually

to discuss the areas in which the student struggled. All students will

be given the opportunity to improve their score by submitting a

written explanation that shows understanding of the learning

objectives/categories in which the student scored less than 100%.

Learning Objectives

Given a table of values representing a linear function, students

will generate the related equation in y = mx + b format.

When presented with a function in y = mx + b format, students

will recognize it as a linear function and accurately summarize what

each variable represents.

When given a linear equation as well as a pair of points,

students will diagram the related line on a graph and label the key

elements, including the x intercept, y intercept, the related line, and

the given points in appropriate formatting.

When given a linear function as well as a specific point,

students will describe the relationship between the point and its x and

y values within the y = mx + b format, including the variables’

independent and dependent natures in their explanation.

Students will orally compare a pair of functions, given one

represented by a table of values as well as one represented by

algebraic expression. In their comparison, students will include

acknowledgement of the functions as linear and identification of the

function that has a greater rate of change (slope).



Student

Generation of

y = mx + b

equation from

a Table of

Values

Analysis of

y = mx + b

Function.

Graphing of a

Linear

Equation and

its Key

Elements

Understanding

the

Relationship

between a

Linear Equation

and its Points

Comparing a

Pair of

Functions

Given in

Different

Formats

Group Work,

Presentation

Quality, and

Effort

Total

Score

Score

%

Joe Schmo 2 4 2 4 3 4 19 95%

Jim Slim 1 3 1 2 3 4 14 70%

Jane Plain 2 4 2 3 4 3 18 90%

Bill Thrill 1 4 2 4 3 2 16 80%

Kate Late 2 3 1 2 2 4 14 70%

Class Average 1.6 3.6 1.6 3 3 3.4 16.2 81%

Possible Pts. 2 4 2 4 4 4 20

Class % Score 80% 90% 80% 75% 75% 85% 81%


Discussion

This section of the CAAP, “Data Collection and Feedback”, deals with an area in which I

feel somewhat comfortable. Before deciding to be a teacher, I spent ten years in the finance

industry, and data collection and analysis constituted most of my days. On more than one

occasion, I have uttered the phrase, “I live in Excel,” so I was excited to put that prior knowledge

to good use. The feedback portion of this section was an area in which I stood on less solid

ground, so for that portion, I relied heavily on the class discussions and readings to help guide

my work.

To begin the process of determining what feedback and data collection would take place

for each assessment, I answered the questions given by our instructor using knowledge I gained

from the readings. Once I had my initial thoughts in place, I decided on five key inclusions that

each of my four tables must contain, and I re-assessed my work to ensure they were present in

each one. These inclusions were as follows: a description of the analysis technique to be used, a

precise metric with which to judge success or failure, specific tools which would be utilized

during analysis, opportunity for both individual and group feedback to students, and opportunity

for students to apply the feedback they receive.

Of the five key inclusions, the latter two points concerning feedback were what I

concluded to be most important, as without quality feedback, plus the opportunity to apply it, a

student’s learning is incomplete. In her journal “Advancing Formative Assessment in Every

Classroom,” Connie Moss (2009) states, “Feedback supports cognition because it helps students

realize which knowledge and skills are strong and which are weak.” (p. 45). It is through that

increased cognition that students are able to develop the skill to ‘self-assess’ which is critical to

not just their success in the classroom, but in their lives as a whole (p. 45). Moss goes on to


discuss the nature of feedback, and I agree with her when she acknowledges that feedback must

be both descriptive and evaluative (p. 52). These considerations are what led me to choose the

type of rubric I did, as with a single criteria format, I will be able to leave descriptive

commentary for the students any time I feel they fall short of, or exceed, my expectations.

Many times, teachers do not include feedback when the students exceed expectations, as

they feel that their feedback is only necessary when a student falls short of the learning standard.

I disagree with this sentiment, especially when considering that psychological studies have

shown that students perceive negative feedback as “punishment” and positive feedback as

“positive reinforcement.” (Brookhart, 2008, p. 3). If that is indeed the case, only giving

feedback to students when they are incorrect would mean providing them exclusively with

feedback that they interpret as punishment. This philosophy could result in a student’s avoidance

of feedback altogether, as they might fail to see the positive effects it can provide. I want my

students to embrace feedback, and therefore, I made sure to include opportunities for just as

much acknowledgement of success as failure within my data collection and feedback tables.

When considering my data collection and feedback choices within the CAAP, the final

aspect I needed to examine was their ability to serve my students with special needs. With this in

mind, I made sure to vary the method in which my students would receive their feedback, so that

students who only understand or respond to certain types of criticism would have an opportunity

to improve their learning. With the choices I made, the students that will strongly prefer (or

specifically require) oral, written, or visual forms of feedback will all have an opportunity to

succeed.


Self-Regulation Strategies

Performance Strategy: Memory Devices for Algebra

Content Area: Math, Algebra

Grade Level: 8th Grade

Stage Name Application

Stage 1: Develop and

Activate

Background

Knowledge

During preparation for the first assessment in our linear algebra unit, I will ask

the class what kind of memory devices they have used in the past, and discuss

examples (PEMDAS, FOIL, etc.) that review the concept and exhibit the value

of using this type of performance strategy.

Stage 2: Discuss and

“Sell” the

Strategy

I will explain to students that during our unit we will be using memory and

mnemonic devices similar to ones they have used in the past, and will be doing

this in order to help them remember various behaviors of algebraic functions. I

will ask the class to give me some reasons why these types of devices might be

helpful during an exam or assessment. Finally, I will provide them with some

examples of various devices that clearly show the value of this strategy.

Stage 3:

Model the

Strategy

During this stage, I will show them how to go about developing a memory

device, including the mnemonic process. I will identify some basic algebraic

behaviors and with the participation of the class, develop some new devices

together, in order to show them just how creative they can be.

Stage 4: Memorize the

Strategy

Now that the students understand the process, I will ask them to form small

groups in order to develop their own devices. After each group is finished, they

will present their brand new devices to the class for review and discussion.

Stage 5: Support the

Strategy

Students will be given a homework assignment in which they will need to create

a colorful, creative diagram of a device that they have come up with on their

own or discovered online and find useful. In the following class, the students

will pair up and be responsible for teaching a partner the device they created

and diagrammed. After this activity is complete, all of the diagrams will be

displayed on the classroom wall for further use and reference throughout the

unit. The devices I find particularly valuable for performance enhancement will

be identified for the class to note.

Stage 6: Independent

Performance

After finishing the lesson, I will ask the students what they like and/or dislike

about the strategy. Upon completion of the next assessment, I will poll the class

to see how many of them employed the strategy and ask for examples of usage.

Throughout the rest of the school year I will check with the students to see

whether or not they are developing new devices and reiterate the value this

strategy would add to their learning. I will strongly encourage students to

include the devices they created in their portfolios.


Examples


Performance Strategy: Flashcards

Content Area: Math, Functions




Activate

Background

Knowledge

As we prepare for our first assessment in our algebra unit, I will ask the

students how many of them have used flashcards in the past, and what their

experiences were like. If there are students without experience in this self-

regulation strategy, I will explain how flashcards work and what will be

required of them.


“Sell” the

Strategy

To show the students the value of flashcards, I will provide some examples

of times I have used them myself when I had trouble remembering various

formulas. I will explain that like the rest of our body, our brain requires

practice to increase its usefulness, and that flashcards provide a great

opportunity in that regard. Finally, I will ask the students what they like

about flashcards in order to have them sell the strategy to each other.

Stage 3:

Model the

Strategy

During this stage, I will first help students identify the type of data and

information that is best suited for flashcards by reviewing the previous

lesson and identifying examples. Next, I will provide them with a physical

example of a flashcard as well as a demonstration of how I think they can be

best used.


Strategy

After all students have exhibited that they understand the strategy and all

students have seen the example, I will ask students to form groups in order

to collaborate and create some flashcards of their own. After they are

finished I will ask each group to share one flashcard that they think the rest

of the class would benefit from seeing.


Strategy

After the activity in Stage 4 is complete, I will inform the students that there

will be a formative assessment the next day in which they will need to orally

identify a list of formulas from memory. I will require them all to create

flashcards in order to assist in the memorization. The next day I will collect

the flashcards and conduct the formative assessment, sharing the overall

results with the class. Finally, I will review the flashcards individually and

give feedback where appropriate.


Performance

After completing the formative assessment, I will ask the students if any of

them found the strategy helpful. I will ask if there is any confusion or

concern regarding the strategy and attempt to clear up any remaining

questions. Before moving forward, I will informally poll the class on

whether or not they plan to use the strategy of flashcards going forward.

Throughout the rest of the school year I will monitor whether flashcards are

being utilized by the students and what effect they are having on their

success.


Example

FRONT:

BACK:


Reflection Strategy: SWOT Analysis

Content Area: Math, Functions




Activate

Background

Knowledge

At the end of the Functions unit, I will ask students to complete a SWOT

analysis for their portfolios in which they analyze their strengths,

weaknesses, opportunities, and threats with regard to the completed lesson

and their future work in our class. I will ask they students if they have

ever completed a SWOT analysis before, and if they have not will briefly

explain what the process will entail.


“Sell” the

Strategy

I will explain to my students that a SWOT analysis is an extremely

common form of reflection and analysis used in both colleges and the

business world, providing examples of times I have had to complete one

myself. I will ask the class to tell me in their own words what they believe

each of the four categories means in the context of a math class, and

correct or support their interpretations as needed.

Stage 3:

Model the

Strategy

To introduce the strategy steps, I will take them through an example

SWOT analysis which focuses on a fictional set of notes that a student has

taken for personal reflection. I will ask the class to categorize each point

raised by the student into one of the four categories and help them

understand why each belongs where they do.


Strategy

To help the students become even more familiar with the strategy, I will

rotate between the four categories and ask the class to provide me with

examples that fit each one from their lives within any context inside or

outside the classroom. I will repeat this step until it is clear the students

have a good understanding of each category.


Strategy

Once proper understanding has been exhibited, the students will be

assigned to create their own SWOT analyses with the subjects being their

own performances within the unit just completed. Each student will be

required to include reflections in each category. After they are complete,

students will include their reflections in their digital portfolio, where I will

review each submission for accuracy and completeness.


Performance

After the students have completed their analysis, I will ask whether or not

they found the strategy to be a useful form of reflection. I will address

any concerns or confusion that arises and offer any further support needed

to ensure they are able to use the strategy going forward. Finally, I will

inform them that this is an accepted method of reflection for any future

such requirements and will monitor whether or not any students choose to

use this strategy throughout the rest of the school year.


Example


Discussion

Self-Regulation strategies play an integral role in increasing the level of learning a

student can ultimately reach, and can also help engage students through fun and creative methods

of study. Zimmerman (1996a) states: “When self-regulatory processes play an integral role in

the development and use of study skills, students become more acutely aware of improvements

in their academic achievement and experience a heightened sense of personal efficacy.” (p. 10).

That efficacy is a vital step in the student learning process, as it enables a student to transition

from a dependent learner to an independent one.

The dependence transition, and the ability of a student to transform their understanding

into successful performance, planning, or reflection, are reliant on the strategies a teacher

chooses to provide. As Zimmerman (1996a) points out, "When students are given no explicit

training in homework and studying strategies, they are often unable to devise techniques

personally to improve their success or self-monitoring, and their self-evaluations inevitably

suffer.” (p. 10). I think that teachers often instruct their students to study without stopping to ask

the students if they know how to do so. To many students, that endeavor is too daunting, as the

vast amount of knowledge within a particular unit can overwhelm them. With this in mind, I

developed two performance strategies that are designed to assist my students in their desire to

make studying a more manageable process.

The first performance strategy I included in my CAAP deals with memory devices and

their usefulness within a mathematics unit. In order to sell this strategy to my students, I plan to

remind them that they have all used these types of devices before, and will also provide them

with some humorous examples, in order to show them that developing the devices can be fun.

Furthermore, I want to transfer the knowledge of how to create these devices to my students,


rather than just make them aware of existing memory devices, so I will require them to at least

attempt using their own creativity within the lesson. When first designing this lesson, I planned

to focus solely on mnemonic devices, but I became concerned that this might put my students

with special needs at a disadvantage. Mnemonic devices tend to appeal to a particular type of

learner, so I decided to alter my lesson to accommodate all learners equally. To do so, I

expanded the lesson to include memory devices of all kinds, and included examples of strategies

that I created, in order to show that the devices do not have to be based in written word, but can

be visual or audial, instead.

In order to further equip my students with tools for studying, I also plan to introduce the

concept of flashcards. To sell the strategy, I will give them examples of times when I used them

myself, and explain just how effective they can be. In addition, I will ask my students to share

any positive experiences they have had with flashcards in the past with the class. In doing so,

they will help sell the strategy to each other. It is important that I get the students to buy in,

because developing a students’ efficient use of study time allows them to become a better self-

regulator in all aspects of their learning (Zimmerman, 1996b, p.26).

My final self-regulation strategy was included to give my students some guidance in

completing a self-reflection. From personal experience, I know how hard it can be for a student

to decide what to include, so I decided that a SWOT analysis would give them a perfect

framework with which to start. SWOT analyses are incredibly common in the business world, so

giving the students experience with that type of reflection could be beneficial to them in their

future lives. The categories can be a little confusing at first, so I will make sure to explain them

thoroughly, go over examples with the class, and ask them to prove they understand each one

before moving forward from the lesson.


Student Portfolio

Description

What kind of portfolio is this and why have you chosen this format?

I have chosen to make the portfolio for my class a working one, which will contain all of

their work in progress within the unit on Functions that contributes to their ability to meet the

learning objectives. I feel this format works best for my classroom and unit, as it allows the

students to collect items in many formats, giving a greater range of material for reflection and

analysis. It will also give the students more time to review their work and determine what pieces

they feel are worthy of selection within a more permanent portfolio.

How is this portfolio stored?

The portfolios will be digital and will be stored online in Google Classroom. They will

be kept in the students’ names within the school’s Google Classroom account until the student

graduates or leaves the school district, at which point the student will have the option of having

the portfolio transferred to another school’s Google Classroom or their personal Google account.

The classroom will be relying on Google’s security measures, but the students will also receive a

brief training on how to protect their privacy online.

Who is the audience for the portfolio? How will it be ‘published’?

The primary audience for the working portfolios will be the students themselves, and they

will have full access to them throughout the unit. The students will be strongly encouraged to

consistently review and evaluate their portfolios, in order to self-assess and reflect on their own

progress. When needed, the portfolio can also be shared with parents in order to show the level


of progress their child is making (or not making) within the unit. Lastly, the teacher will be able

to review the portfolio as well, in order to monitor and guide the students’ self-reflection and

self-assessment. At the completion of the unit the portfolio will be locked and published in its

final form, at which point the student will no longer be able to edit the work but will continue to

be able to review it. Students will also still retain the ability to transfer any pieces into other

types of portfolios for later use.

What are the contents of the portfolio?

Because each portfolio is a working one, its contents will be numerous and wide ranging.

The student portfolios will contain worksheets, homework, classroom activities, reflections, and

any summative and formative assessments completed during the unit. The authentic assessment

will be a mandatory inclusion and I will strongly encourage students to include their Exit Slips as

well. Any guidance given will be to ensure all of the unit’s learning objectives have

representation within the portfolios. Since those learning objectives were constructed keeping in

mind Bloom’s Taxonomy, their inclusion also ensures the portfolios contain a full range of

complexity and specificity. In regards to the rest of the items, I will ask the students to choose at

least three other pieces of work that they think should be included and I will help guide them in

their choices. I will remind the students to maintain enough variety in their selections to exhibit

their ability to learn in different ways. The final piece they will include in their portfolios will be

reflections, which will focus on intermittent works throughout the unit. In addition, they will

complete a final reflection for the unit in the form of a SWOT analysis as detailed in the Self-

Regulation portion of this CAAP.


What is the purpose of the portfolio?

The purpose of this working portfolio will be two-fold. It will be used to diagnose

students and their progress throughout the unit and as an opportunity for students to reflect on

their work. These two distinct forms of review will allow teachers and students to independently

analyze the work within the portfolio, identify the student’s strengths and weaknesses, and then

collaborate on their findings. This portfolio will not be graded, but students will be reminded

that its contents may later be moved to more permanent portfolios that would indeed be subject

to grading at a later date.

When and how does the reflection by students take place?

Students will be given various reflections throughout the learning unit and each of these

will be submitted into their portfolio. The work chosen for reflections will be varied so as to get

a full understanding of how the students feel about the different forms of work and the specific

learning objectives. A reflection for the authentic assessment will be mandatory, while three

others will be student chosen, with a total of five reflections required by the end of the unit. The

fifth and final reflection will be in the form of a SWOT analysis, which will be completed as part

of their self-regulation instruction.


Table of Contents

I. Learning Objectives

II. Formative Assessments

A. Exit Slip

B. Oral Questioning (Teacher Evaluation)

III. Summative Assessment

A. Kids Research Inc.

1. Research Tables and Data.

2. Digital Video of Presentation

3. Graded Rubric

4. Reflection

IV. Student Choice Items

A. Student Choice #1

1. Reflection

B. Student Choice #2

1. Reflection

C. Student Choice #3

1. Reflection

V. Final Reflection - Unit

A. SWOT Analysis


Student Reflection Sheet

Example:

UNIT REFLECTION SHEETIn which part of the unit do you feel you were most successful? Why?

In which part of the unit do you feel you were least successful? Why?

If given a chance, what would you do differently within this unit? Why?

Any final thoughts/questions/lessons learned?


Discussion

When considering what type of portfolio to use in my future classroom, I first had to

determine exactly what I wanted my students to gain from the compilation of their work. Math

is a particularly difficult subject to develop a portfolio for, as so little of the work completed is of

a creative nature. As a result, most of the work is assignment- or assessment-based, and has

therefore already been factored into the students’ final grades. I wanted my portfolio to help the

students improve their mathematical skills, and I had no desire to create yet another high-stakes

grading scenario for them to agonize over. As a result, I chose a working portfolio, which would

allow the students to self-diagnose their progress without any threat being posed to their

respective GPAs (Danielson, 1997, p. 1).

A second consideration when choosing the appropriate portfolio plan for my future

classroom was its format; specifically, whether it would be digital or physical in nature. This

decision did not take me long, as I am a firm believer that technology, when used appropriately,

can greatly enhance the educational process. A digital portfolio also appealed to me for its

versatility, as it can transition seamlessly between audio, video, and written content. I felt this

was a perfect fit with my classroom, as it will provide students of all different learning types an

opportunity to show their best work. A physical portfolio could prove challenging for a student

with special needs, and the accommodations that are added by utilizing technology are endless. I

researched Google Classroom, and was amazed by the different tools and learning opportunities

it can provide students, so I decided that my classroom would employ the software.

Math does not lend itself to much natural reflection, so it was important that I use the

portfolio section of my CAAP to enable my students in this area. Lundy (2004) states that

"Portfolios allow students to feel ownership. Students can see their work not as a series of


assignments that need to be handed in and marked, but as a process that is engaging, informative,

thoughtful, negotiable, and self-affirming for all,” and I personally feel that a large portion of

that ownership comes from realizations made during reflections (“What is a Portfolio?” para. 2).

As a result, I will ask my students to include five pieces of reflection within the unit. Student

choice is important, so I plan to dictate the theme for only two of those five pieces of reflection,

and will ask my students to choose the other three subjects on their own.

When deciding on the audience for the portfolio, I knew that the focus must be on the

students themselves. As the goal of the working portfolio is self-assessment and self-reflection, I

will make clear to the students that they are their own primary audience. However, I will let

them know that I will be observing their work as well, and will offer guidance where I see fit, but

only in an effort to help them come to their own conclusions. Finally, I will allow for the

possibility that the portfolios could be shared with parents. This stipulation will be made with

the understanding that there are certain parents that have a misguided view of their children’s

skillset, either positively or negatively, and a working portfolio can do a great deal towards

helping them accept the reality of their child’s actual progress (Danielson, 1997, p. 2).


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Documents

Content Area Assessment Plan - Functions Unit – 8th Grade