Exemplary Work Sample
A Unit on Place Value for First Graders.
Exemplary Teacher Work Sample
Teacher Work Sample on Place Value
For First Graders
This work sample in intended to support your efforts in teaching candidates
about connecting teaching and learning. It is one of the better work samples
we have found. It was developed by a veteran teacher completing her
twentieth year in the classroom. It may turn out to be a formidable example
for some candidates.
Appreciation is extended to the Renaissance Group for sharing the original
form of this work sample with Western Oregon University faculty. This
example work sample was developed by an anonymous teacher with support
from faculty associated with a Renaissance Group teacher education
institution.
The teacher work sample shown here was revised and shortened to make it
more efficient for use by teacher educators and their licensure candidates.
We edited the paper to highlight and/or simplify teacher work sample
segments or concepts. For example, we showed only 3 of the 10 lesson plans
the teacher prepared,. Because of the changes made in the work sample
readers should not infer that this example represents the standards of the
Renaissance Group. Rather, the changes made were intended by the authors
to help the learning process of teacher education candidates.
We hope you will find the work sample useful in the education of your teacher
candidates.
Gerald R. Girod (ret.)
Western Oregon University
Mark A. Girod
Assistant Professor
Western Oregon University
Teacher Work Sample
First Grade Thematic Unit on Place Value
Table of Contents
Contextual Factors
Community, District, and School Factors
1-2
Learning Outcomes
Objectives for learning aligned with goals
3
Assessment Plan
4-7
Design for Instruction
Overview, Three example lessons, Instructional Strategies
and materials, In-flight decisions
8-17
Data Presentation and Analysis
18-19
Self-evaluation and Reflection
20-21
Attachments
22-51
Contextual Factors
Community, District, and School Factors
The Umatilla County School Division is located in the small rural town of
Paisley. Paisley is located in the heart of an area rich in history. Paisley
Elementary is a relatively new school built four years ago and nestled in the
rolling acres of Umatilla County. The school division has been involved in
educating the youth of rural Virginia since 1879. Native American,
Revolutionary, and Civil War artifacts abound in the region, Our faculty is
constantly striving to tie the past to the present.
This school division serves a county population of 7,876, which is an
increase of only 51 over the previous census. There are only three schools in the
school division. Approximately 1,350 students attend the one high school, one
middle school, and one elementary school. All three schools are accredited by
the Virginia Department of Education. Their performance report card
accreditation rating summary for last year was “Provisionally accredited/Needs
improvement”.
A five-member board of supervisors governs Umatilla County. The
budget for the upcoming school year proposes additional funding for programs,
teacher pay raises, and much needed support staff for the schools. Presently,
some strain exist between the school board members and the country supervisors
with regard to the upcoming school budget. It has been mandated that the
county build a new courthouse in this fiscal year. Funds are limited which
results in different agendas for the school board members and county
supervisors. The community rallied for our state-of-the-art elementary school
built recently, yet parental support in the school is limited likely because both
parents typically work full-time and there are also many single-parent families.
A county superintendent handles the daily operations of the schools. The school
division annually spends approximately $1700 per student. That cost is high
compared to the $775 each household pays in real estate taxes annually.
Therefore, the county loses money when a new house is built and a student
enrolls in our schools.
The elementary school maintains a 93% average daily attendance and has
a 58% minority population. The three largest racial groups in the elementary
school consist of 369 African Americans, 272 Caucasians, and 16 Hispanic
students. Within the total school population, 64% are on the reduced/free lunch
program. The elementary school is composed of 684 students with 105
employees, of which 56 are licensed personnel. All the teachers are endorsed in
the academic areas they teach, although some hold provisional licenses. The
majority of the teacher live outside the community and have a considerable drive
to work each day. Teachers’ salaries are well below the state average for Virginia
which seems to lead to the 30% turn-over rate among the faculty each year.
1
2
Classroom Factors
The school is designed so each grade level is housed in a pod of five
classrooms connected by one large activity room. These large rooms flow into
parallel halls divided by the large media center, music, art, cafeteria/stage, and
gymnasium classrooms. Upon entering the first grade pod, one encounters a
gallery exhibiting childrens’ art work. My classroom is inviting, colorful, and
richly decorated with childrens’ work. The classroom walls are “print rich” to
symbolize the importance of written work. Centers and small work tables
surround four large tables arranged with five students at each table. Library, art,
and language arts and math games, and a listening center invite students to work
independently about the room. Manipulative and reading materials fill these
centers for children to explore, grow, and develop their minds.
The classroom include one television/VCR, one computer, an overhead
projector, and telephone for internal communications within the building.
Classroom rules are posted and each child has signed his/her name below the
rules signifying agreement to uphold the decisions pledged by all students on
the first day of school. Direct whole group, small group, and individual
instruction are the varied approaches I use for grouping these first grade
students by ability.
Student Characteristics
My classroom contains 20 students—10 African Americans (6 males and 4
females) and 10 Caucasians (2 males and 8 females). Three of the students were
identified as developmentally delayed in kindergarten and looped with their
teacher to first grade. They receive daily services in the core subjects from the
special education teachers. Only one of the remaining 17 students is repeating
first grade. The children in the classroom range in ages from 5 years 7 months to
7 years 2 months.
There is much diversity in the performance levels of the students in this
mathematics class. They range from one gifted, 5 above average, 6 average, and
5 below average based on the results of the Stanford 9 match scores from April.
Prior to the introduction of this unit, the majority of the class had been
accurately adding and subtracting numbers with sums or differences to 10 and
had a strong sense of numbers and their values ranging to 10. They enjoy handson activities engaging them in meaningful practice of the skills being taught.
This group of children enjoy speaking, writing, drawing, and creatively
communicating their ideas about what they have learned. Some of the students
are shy but seem to have opened up during the course of the year because many
opportunities have been given for the development of the communication skills
which support their learning.
3
Learning Outcomes
The goals and objectives outlined below are specific to the unit I plan to
teach on place value. The lesson outcomes are sequenced to support the Virginia
Standards of Learning (SOL) for teaching place value to first graders. Each of the
unit’s objectives is aligned to provide appropriate learning experiences for the
SOLs. Table 1, below, shows the unit objectives and how they support the SOL
content standards.
Table 1: Unit Objectives as Outgrowths of the Virginia SOLs
Virgina Standards of Learning |
TWS Unit Goals
|
Students will count objects in a |Students will link their
given set containing between 10 |models and pictures to the
and 100 objects and write the
|formal symbolic language of
corresponding numeral.
|mathematics and record the
|results.
|
|
|
|
|
|
Students will group concrete
|Students, through the manipobjects by ones and tens to
|ulation of objects, will create
develop an understanding of
|mental images they can use
place value.
|to interpret mathematical
|symbols
|
|
|
|
|
|
| TWS Unit Objectives
|
|Students will count objects to
|interpret pictures and symbols
|for items represented by tens
|and ones.
|
|Students will compare and
|contrast numbers of greater
|and lesser quantity using
|knowledge of place value.
|
|
|Students will group objects
|to develop an understanding
|of the pattern in place value
|from one through 100.
|
|Students will compare groups
| of objects to determine if
|numbers and pictures
|correspond mathematically
|for correct representation.
|
I believe my unit goals flow directly from the state SOLs and my four unit
objectives are aligned with the unit goals.
4
Assessment Plan
In order to create a pre-assessment to determine what the students knew
prior to instruction and a post-assessment to determine what still needs to be
taught, it was necessary to target specific math concepts for this unit. As a first
grade teacher, it is important to take on the role of a coach attempting to
motivate and guide the players to do their best. The directions for any
assessment at this level should be open to rephrasing and providing assistance
for those who need help. The abilities of my students vary more than might be
supposed because each arrived at school with such diverse prior knowledge and
readiness for learning. The early grades leave no room for assuming that
exposure to the most simple concepts has occurred. I face the daily challenge of
adapting my instruction and assessment in a way that is appropriate for learners
with special needs or limited natural ability. It is important to allow students
adequate time to do their best work and they could have done better if they had
been allowed more time. All the students need not proceed through the
assessments at the same rate nor in the same manner. With young children who
are not experienced in test taking practices, other valuable insights can be
collected in samples of their daily work and informal communications the
teacher has acquired throughout the unit. By modifying the ways performance is
measured there is always the chance, however, that assessments may be less than
reliable. Teacher judgments, observations, and communications with the
students, will with tests, will serve as valuable assessment sources in the end.
After reviewing the pre-assessment information (see Table 2, below), I
gained valuable insight into the strategies the students were using to organize
their thoughts as they attempted to solve problems. Their pre-assessment
experience encouraged students to produce their best work in the face of a
challenge. The pretest also directed my instruction, activities, assignments, and
resources for presenting the unit on place value.
•The reader will notice in the bottom three rows of Table 2 that the
pre-assessment mean scores for each objective did not exceed 50%
which I thought indicated the students had clearly not yet mastered
the objectives I intended to teach. On the other hand, because every
student seemed to have at least some information about place value,
they seemed to have demonstrated readiness for these objectives. Two
student may find a bit of this unit very easy. For instance, student #12
may have mastered objectives #1 and #2/ I have prepared some extra
work for students #12 and #7 if they continue to indicate they need
extension in their work.
•There are four fairly distinct groups within the class. The top two
groups
knew a bit more than half of the content assessed on the pretest. The
third group new a bit less than half the content while the fourth group
may not even be ready for the unit content.
5
Student
Number
12
1
7
8
4
2
5
11
9
10
13
15
14
6
3
16
17
Maximum
Mean
%
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Table 2: Student Pretest Performance
Scores for Pretest Objectives
|
#1
#2
#3
#4
|
6
6
3
2
|
6
4
3
3
|
7
5
3
1
|
6
3
3
4
|
5
5
3
2
|
5
3
3
3
|
4
3
5
2
|
3
4
4
1
|
4
2
3
2
|
4
3
1
3
|
2
4
2
3
|
3
3
3
2
|
4
2
2
2
|
0
2
2
1
|
2
1
0
1
|
0
0
2
1
|
0
1
0
2
|
8
6
6
6
|
3.59 3.00 2.47 2.06 |
44.9 50.0 41.2 34.3 |

17
16
16
16
15
14
14
12
11
11
11
11
10
5
4
3
3
26
11.12
42.8
•Because many of the test items were multiple choice, I was a bit
perplexed with the total scores below 6, or less than one-fourth correct.
Those four likely knew little of the content and guessed incorrectly more
than one would have predicted. However, that also means some of the
students with higher scores may have merely guessed more successfully.
My practice items, where we have time to converse about their
understanding of place value, should help to clarify whether my pretest
was a valid measure.
•Additionally, there is not much variability in the scores for objectives 3
and 4 so the content presented to the whole class will likely be adequate
for all the children. In objectives 1 and 2 scores ranged from 0-7 and 0-6,
respectively. I will need to be attentive to the varying needs when those
lessons occur.
My formative assessment data collected (see Table 3) during the
course of the unit helped me to determine if student learning was taking
place for each of my unit’s objectives. As I reviewed the strengths and
weaknesses of my students throughout the lessons, it was necessary to
restructure the learning activities. An initial strategy might have been less
effective than supposed, or my intuition told me the class preferred a
kinesthetic or tactile modality for learning. Sometimes I altered my plans
for the unit because the children were not learning through my
6
Table 3: Assessment Plan
Assessment Type |Unit Objectives
|Assessment Form |Adaptations
Pretest
|All four
|Paper and pencil |None
|
|
|
Formative #1 |Count objects to |Paper and pencil |Additional
|interpret symbols |worksheets. |practice page
|for items
|
|available.
|represented by
|Journal drawing |
|tens and ones.
|activity for
|
|
|regrouping
|
|
|pictures.
|
Formative #2 |Compare and
|Pencil and paper |Repeat oral
|contrast numbers |worksheet.
|directions for
|of greater and
|Partner activity
|students working
|lesser quantity
|with hundreds
|in pairs.
|using knowledge |Teacher
|
|of place value.
|observation of
|
|
|calendar activity. |
Formative #3 |Group objects to |Paper and pencil |None
|develop an under- |worksheet.
|
|standing of the
|Work on place
|
|pattern in place
|value vocabulary |
|value from one
|
|
|through 100.
|
|
Formative #4 |Compare groups |Paper and pencil |Offer additional
Post-test
|of objects to |worksheet.
|modeling of head|determine if
|Make headbands |bands assignment
|numerals and
|with crayons and |to those who need
|and pictures
|paper.
|help.
|correspond math- |Journal drawings. |
|ematically.
|
|
|All four
|Paper and pencil |None
|
|test.
|
presentation. On-going assessment gave me feedback as to how I needed
to proceed with my learning activities.
Table 3 summarizes the steps I took in assessing student
knowledge both formatively and summatively. Table 4 presents the
materials and items I chose for my pretest, for formative and practice
activities, and for my post-test. The page numbers in Table 4 indicate on
which appended page the items are found that immediately follow. Items
which are found in appended tests are preceded by the name of the test;
i.e., P.1 #1-#4.
7
Table 4: Table of Specifications—Assessment Items and Materials
Students will:
test
|Pretest
|Formative
1. ..count objects to interpret
|P. 1 #1-#4
|P. 29 #1-#4
pictures and symbols for items
|P. 69 #1-#4
|P. 32 #1-#4
#1-#4
represented by tens and ones. |
|P. 72 #1-#4
|
=8 |
 = 12
2…compare and contrast
|P. 75 #2-#5
|P. 73 #1-#6
numbers of greater and
|
|P. 214 #1-#5
lesser quantity using
|
|
knowledge of place value.
|
=6 |
 = 11
3…group objects to develop an |Pre #11-#12 |P. 199 #1-#4
understanding of the pattern |P. 70 #1-#4
|P. 229 #1-#6
in place value from one
|
|1P. 76 #1-#12
through 100.
|
=6 |
 = 10
4…compare groups of objects to |Pre #23-#24 |P. 85 #1-#4
1
Use only for those needing additional practice.
|Post|Post #1-#4
|P. 71
|
|
 = 8
|P. 75 #2-#5
|
|
|
=4
|Post #11-#12
|Post #17-#20
|
|
=6
|Post #23-#24
determine if numerals and
pictures correspond mathematically for correct
representation.
=
|P. 74 #1-#4
|
|
|
=6
|26 items
|P. 89 #1-#4
|
|
|
=8
|41 items
|P. 74 #1-#4
|
|
|
=6
|24 items
8
Design for Instruction
As I designed this unit, I wanted to include seven teaching
strategies that I have found important to first graders’ success as they
learn about place value.
•Modalities—I try, whenever possible, to employ not only aural
presentations but I rely also on visual and kinesthetic activities to allow
children to have many ways by which to come to understand place value.
You will find all three used extensively within this unit.
•Grouping—As a rule I try to pattern activities so I initiate topics,
first, with large group activities, second with partner activities, and,
finally, with individual work. Through the first two grouping patterns,
children with a shaky understanding of place value have plenty of
opportunity to receive help from me as well as classmates. Within each
lesson, you will this pattern employed. Students are never expected to
perform a task until they have seen me demonstrate it and practice it with
them, or until they have practiced it with a partner.
•Practice—Children need daily practice with the content they are
learning. I provide small group and individual practice activities daily.
In order to assess the effectiveness of my teaching, I generally conclude
each lesson with some type of formative assessment. The journal activities
and workbook pages (see Table 4) become independent activities that my
students are able to complete with ease. Given the range of pretest scores,
I also need to provide varying amounts of practice for each of the
objectives.
•Sequence—Each concept is taught concretely before we begin to
move into a semi-abstract form to record place value. As lessons occur,
we continue to circle back and bring concepts back from previous lessons.
I try to ensure the students see the connection between what they learned
concretely to what we do days later in a more abstract form. Recalling the
Stanford 9 scores, it should be expected that some student would be
dependent on concrete instruction for their success, while others would
benefit from discussion of place value at an abstract level.
•Duration—Lesson components are short—10 to 20 minutes, with
often 2-4 activities within each component. Children at this age cannot be
expected to learn if the pace is slow. I need to provide regular variation
though it is mandatory that each activity is clearly related to its successor
as well as its predecessors.
•Attentiveness—I try to work with child each day. Even the very
adept children need assurance and attention from the teacher.
9
•Integration—Mathematics is one of my favorite subjects to teach
because it can be integrated with language arts, social studies, music, art,
and science with ease. Three of the lessons in this unit begin with
literature involving math. I purposely read selections such as Too Many
Birds, Numbers, and The Button Box to give my students a sense of how
math is directly related to reading. I think too many first grade teachers
give less attention to math because reading is considered the most
important subject. Anyone can effectively combine the two subjects as I
did in this unit.
These are the seven instructional strategy goals I held for this unit. I
think the reader will find each had been regularly employed.
10
Lesson Plan #1
Topic:
10 objects in a group makes 1 ten
Duration:
60 minutes
Focus:
Explore counting by tens through 50.
Identify and compare numbers 10 through 50 by rods and bean
Sticks.
Ring groups of 10 objects.
Understand that 10 objects in a unit makes 1 ten.
Objective:
The student will be able to count objects to interpret symbols for
items represented by tens and ones.
Materials Needed:
Too Many Birds by Barbara Reeves
Felt board
Felt birds and yarn
Craft sticks and white glue
Blue unifix cubes arranged in ten
rods—5 needed
Unifix cubes, ten rod
Kidney beans (2 bags)
Plastic cups
Large place value chart
Dry erase markers
Worksheets—pretest &
practice
Instructional Procedures:
(20 minutes)
Give children pretest—move around and read directions as needed. Make
sure they don’t do unneeded items on worksheets.
Read Too Many Birds. Have volunteers count how many birds live on each
floor. Help students see that each row contains ten birds.
Put ten blue rods on each page for each row of birds. Show that 10 cubes
makes one rod and each rod is a group of ten.
Count each row of birds and rods by 10s.
(10 minutes)
Arrange 10 felt birds on the felt board and ring them with yearn. “This is
a group of 10 birds.” Continue having students place birds on the
board. Each time 10 birds are on the board ring them with yarn.
“How many group of 10 do you see?”
Continue until 5 groups of ten are reached. Compare to the rods and the
row of birds in the story read earlier.
(10 minutes)
Distribute beans in cups, craft sticks, and white glue.
Have children write their names on the bottom of the craft sticks.
Model placing glue on stick. Arrange 10 beans to make a group of ten on
each stick. “Count aloud as you glue.”
11
Have each child glue five sticks (total of 50) and set aside to dry. When
completed have them count aloud by tens to 50.
Assist students as they arrange beans.
(10 minutes)
Return to blue rods and record the number of rods on the large place
value chart with a dry erase marker.
Hold up 2 rods and ask how many tens there are.
Record on place value chart. Continue to 50.
Count aloud by tens to 50.
(10 minutes)
Practice—use workbook pages 29 and 32 (appended).
Circle groups of ten. Write how many groups there are.
Use craft sticks to provide an accurate count.
Do journal drawings.
For those needing additional practice, use the rest of workbook p. 72.
Can take home.
Evaluation and Reflection
The students enjoyed the story about the birds living in apartment houses
with ten on each floor. The visual stimulation of the colorful birds
sparked their interest from the beginning of the lesson. They asked to
draw their own pictures of birds living in houses with 10 on a floor in
their journals.
They also enjoyed putting one row of unifix cubes on the book pages to
represent a row of birds. I wish I had more felt birds and boards because
things seemed to click for them when they took the yarn and circled 10
birds that way. We could have extended that part of the lesson beyond
50. I told them I would put the board, felt birds, and yarn in the math
center for them to reuse.
12
Lesson Plan #2
Topic:
Develop knowledge of vocabulary for place value.
Duration:
60 minutes
Focus:
Explore tens and ones through 50.
Understand vocabulary of tens and ones.
Place objects on work mat under correct value.
Count and write numbers to 50.
Regroup ones as a ten using exchange method.
Illustrate numbers with pictures of their own.
Objective:
The student will compare groups of objects to determine if
numbers and correspond mathematically for correct
representation.
Materials Needed:
Bean sticks from previous lesson
Loose beans in a cup.
Place value work mats
Pencil and paper.
Individual units of unifix blue
cubes
Word cards (tens, ones, and
hundreds) on magnets
Magnetic blue base ten
rods.
Large place value chart
Dry erase markers
Chalkboard and chalk
Index cards numbered 1150
White construction paper
12X18 plus crayons.
Instructional Procedures
(10 minutes)
Compare 10 beans to one bean stick from yesterday.
“Both show the same number but one shows 10 ones and the other
one ten.”
Place 10 beans on the work mat and exchange them for 1 beanstick.
Record the tens and ones on the place value work mat.
Repeat this procedure using the ten rod and the single unifix cubes.
(20 minutes)
Draw a place value chart on the chalkboard.
Distribute work mats and bean sticks from 1st lesson.
Explain each work table has 20 bean sticks or 20 groups of ten, plus
a cup of beans.
Re-emphasize each group of ten beans is 1 ten.
Display work cards on the chalkboard with a line to separate ones,
tens, and hundreds.
Explain that magnetic cubes, like bean sticks and loose beans, serve
as another way to represent 10s and 1s.
13
(10 minutes)
Guide students through the first example of representing 23 on the
Stick. “Count aloud as you glue.”
Have each child glue five sticks (total of 50) and set aside to dry.
When completed have them count aloud by tens to 50.
Assist students as they arrange beans.
(10 minutes)
Return to blue rods and record the number of rods on the large
place value chart with a dry erase marker.
Hold up 2 rods and ask how many tens there are.
Record on place value chart. Continue to 50.
Count aloud by tens to 50.
(10 minutes)
Practice using workbook pages 29 and 32, appended.
Circle groups of ten. Write how many groups there are.
Use craft sticks to check to provide an accurate count.
Do journal drawing.
For those needing additional practice, use the rest of workbook p.
72. Can take home.
Evaluation and Reflection
The students enjoyed the story about the birds living in the
apartment house with ten on each floor. The visual stimulation
of all the colorful birds sparked their interest from the beginning
of the lesson. They asked to draw their own pictures in their
journals of birds living with 10 on a floor.
They also enjoyed putting one row of unifix cubes on the book
pages to represent a row of birds.
14
Lesson Plan #5
Topic:
Compare and contrast for correct numerical representations.
Duration:
60 minutes
Focus:
Represent two-digit numbers in different ways.
Make connections for two-digit numbers with the use of a
calendar.
Compare numbers of greater and lesser value.
Make place value connections to coins.
Objective:
See Table 1. This lesson is a composite of all four objectives.
Materials Needed:
The Button Box by Margarette Reid
Enlarged magnetic dimes and
8 X 10 page of February
pennies for chalkboard
calendar
A drum and triangle
Red & blue counters one
Plastic dimes and pennies
per student
Place value work mats
Journals, pencil & crayons
Instructional Procedures:
(10 minutes)
Read aloud The Button Box. Revisit each page and have children
use
cubes to represent each button on the page. Ask volunteers
to group and regroup “buttons” by tens and ones; i.e., 22
buttons = 2 tens and 2 ones.
(10 minutes)
Display two musical instruments such as a triangle and drum.
Show them how two beats of the drum and five chimes on
the triangle can represent the numeral 25. Ask for
volunteers to play the instruments while others identify the
number. Then select a number and ask volunteers to play
the music for each numeral.
(15 minutes)
Distribute the February calendar and different colored counters.
Ask them to place the red counter on a specific date. Then
ask them to place the blue counter on any other date.
Children then take turns stating whether their date is greater
or lesser than the date the teacher chose.
After several examples, allow them to work in pairs doing the
same activity. Walk around and monitor their
understanding.
15
(15 minutes)
Display ten pennies and a dime. Review the value of each and
show how they represent tens and ones. Have each child
count out 26 pennies.
Represent the two dimes in the tens place and the six pennies in the
ones place on the chalkboard. Have the students represent
the 26 cents on their work mats.
Have volunteers exchange 10 pennies for 1 dime to reinforce the
value of each. Repeat this value for up to 60 cents.
Continue to repeat this activity and count out money aloud as a
group.
(10 minutes)
Practice using workbook pages 73, 214, 229, and 76. Assign to
individuals as needed.
Journal drawings of dimes and pennies represented by circles with
a 10 or a 1 written inside. Include a drawing of what they
would buy with the money.
Evaluation and Reflection
The visual and auditory elements of this lesson continued to help
my students make connections to the elements of place value. I tried to
vary the presentation of materials as much as possible so they did not
become bored. Over the years I have found it becomes easier for my
students to understand mathematical concepts when I relate them to real
life use as with the calendar and money activities.
I walked around with my grade book and made notations of their
understanding by recording a minus (-), plus (+), or double plus (++). I
made entries when they completed their journal drawings of money and
also when they were working in pairs on the calendar activity.
The central theme of all the lessons in this unit was built on place
value. The actual post assessment test was administered after five more
lessons. The results are shown in the assessment portion of this work
sample.
16
In-flight Decisions
During the first days of presenting this unit, it became clear that five of the
seventeen students could easily recognize tens and ones and identify the
corresponding numerals through 100. They began to ask questions about the
hundreds place and how they could model 100. Because first grade is the
foundation for math as well as language arts, I had to be certain my students
understood the vocabulary as well as the mechanics of what we were learning.
For example, some of them knew how to add and subtract but did not know the
meaning of the words “sum” and “difference”. For this reason, I directly taught
the whole group when we were learning new concepts and then individualized
in small group instruction when it was appropriate.
On the third day of this unit, I met with the five advanced students and
showed them how to model 100. We grouped ten bean sticks into a bundle to
represent 100. Upon completion of their journal activity. They were given
workshop games involving three—digit numbers and corresponding computer
games which included place value to the hundreds place. They were excited and
shared some of the information with the other students during center time. It
always encourages me to challenge students when they know they are to be a
tremendous resource for teaching other students.
Following math each day we have center time. During this time I was
able to challenge my accelerated students and modify instruction for my
students having trouble, I have accumulated over 100 match activity folders that
I use to enhance instruction or to re-teach concepts with which my students are
struggling.
The group of advanced students engaged in more comparison activities
involving numbers than the rest of the class. At one point they were writing
three-digit numbers in their journals and illustrating them with pictures. Those
illustrations were quite involved.
One students had been taught how to add two-digit numbers by her
grandfather. She took it upon herself to show the others in the small group. At
one point there was a need to regroup numbers for addition. I gave a minilesson to the small group but only my gifted student grasped the concept. The
following day I had some worksheets for her on grouping and a computer stepby-step regrouping game in the pod of our classroom. I had not planned to
explore place value to this extent. My students seemed to sense I would run with
instruction if they were willing to work hard toward learning. They perceived
each day at school as one more step in learning more, getting smarter, and going
further.
Another group of learners in my class required several repetitions and
additional help on a one-to-one basis before they grasped new concepts.
Knowing this, I carefully planned the transitions of my lessons. Ringing groups
of ten birds was difficult for them at the onset of this unit. I provided extra help
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for them working with manipulatives and did not exceed numbers to 30 in the
first week of the unit. Every lesson gave them an opportunity to model place
value with bean sticks, unifix cubes, or base ten rods. I also allowed them to
count ten popsicle sticks and then rubber band them to form one group of ten.
These students were not doing as well on my daily formative assessments within
their journal entries. I decided to send some extra worksheets home with notes
to the parents for additional practice. I also copied some examples of journal
drawings other students had completed (without names) and asked the parents
to work with their children to represent tens and ones.
In the past, I have had great support from parents when I gave them a tool
to use. Simply writing a note and asking for help does not seem to work as well
as giving them the actual activity their child needs to complete.
In the days that followed, I tried to give my students many opportunities
to communicate their learning orally so I could assess which pieces of knowledge
they grasped and what I needed to address next in my teaching. One thing was
certain; they were having more trouble referring to a group of ten objects as 1
ten. Once they had counted 10 objects, they could no longer see it as 1 of
anything. Once they understood that 10 ants could live in one hill, it clicked.
Their journal drawings that day showed a better understanding. One child did,
however, draw 2 aquariums and 3 fish for 23. No fish were in the aquariums.
My greatest challenges as a teacher were the ongoing modifications
which I needed to make to ensure my students were developing the needed
skills. Each day I had to decide what time allotments to provide for each
component. My experience has been that sometimes math cannot be confined to
the one-hour allotment per day. Being flexible and restructuring lessons was
sometimes needed in order to achieve the learning objectives.
18
Data Presentation and Analysis
The gain score data in Table 5, on the next page, provides an
opportunity to draw several conclusions:
•Each of the children improved their performance from the pretest to the
post-test. The gain scores in the two far right columns show that
everyone learned. I was worried the top cluster would make only a
minimal gain. Because their entry scores were high, I thought
improvement might be small.
•In the two rows at bottom, called Avg., improvement from the pretest
to the post-test seems to have occurred. I was particularly pleased
because there were fewer points available on the post-test. That
difference made it hard to compare the results of the two tests for
objective #2. I wish I had made the tests so both had the same totals.
•I wanted to know, in more concrete terms, how much the class had
learned. I made up the number in the last row called “Points Added to
Knowledge”. I was trying to provide something I could show parents to
demonstrate concretely how much the class had learned.
•I thought the change in percent correct scores for each objective from
pretest to formative (practice), to post-test was consistent in growth
across all three measurements. That likely means my assessments
measured the students’ place value knowledge reliably.
•In summary, I think these data mean I helped the children meet each of
the instructional objectives I set for this work sample. Though several
students (the bottom cluster, in particular) are still shaky, their consistent
improvement gives me great hope that as we continue discussing place
value in future units on addition and subtraction, their knowledge will
increase and solidify.
I am not sure why these gains occurred. It is likely the students found the
strategies upon which I focused (see pages 8 and 9) helpful. Moving back and
forth between skills and concepts, moving from concrete to abstract, and
providing consistent practice with feedback undoubtedly aided their progress. I
mentioned also in my daily evaluations and reflection that the use of modalities
in my instruction likely encouraged, particularly, the less adept. I would also
like to think my consistent encouragement was of value to all the children.
20
Self-evaluation and Reflection
This teacher work sample was an exciting way for me to consider some of
the instructional strategies that emanate from my beliefs and philosophy and
reflect my performance as a teacher over the past twenty years. Without a doubt,
having to revisit the days of defining the specific goals and objectives for every
lesson made we wonder initially if I wanted to pursue writing up this unit.
When I began to look upon writing it as a way of enabling oneself and others to
see how to evaluate with more precision the desired outcomes for learning, then
I was sold on the idea. This work sample methodology is most effective in
guiding a new teacher through the process of being an effective planner,
instructor, and decision maker based on childrens’ learning responses.
Additionally, the work sample offered valuable analysis into how well my
students achieved the targeted outcomes I set for this unit. The work sample
offered meaningful feedback for reflection about student learning and my
effectiveness as a teacher, Many of the decisions I make in a split second as a
seasoned teacher come from predictions and hypotheses I have formed across
many years.
An analysis of how well the students have achieved the goals of this unit
are reflected in the post assessment scores, but also in my formative observations
of the students’ progress throughout the unit. Regardless of the avenue chosen
for assessment, you must always evaluate your teaching by how well the
students understand the learning objectives and can apply the knowledge they
have gained to other mathematical and language experiences. For example, it is
very important to me to introduce dimes and pennies following the presentation
of this unit on place value in order to see if my students can relate the concepts
presented to money.
I also evaluate my performance based on childrens work. If I am clear in
my instruction, the product is better. When I am vague or less enthusiastic about
what we are doing, it shows in their work. This teacher work sample activity
offered continuous opportunities for self-evaluation through targeted assessment
and planning. It allows teachers to recognize their responsibility as decision
makers in the process of teachers teaching and students learning. The script is
ever changing and always in need of evaluation.
When I first started planning this unit it became quite clear I would need
to modify my original plans to use the math workbook as the only source of
formative assessment. In the past I found that students could make judgments
about base ten rods and cubes that were accurate in terms of the mathematical
representation, but they had not reached full understanding of one ten being ten
ones. For this reason, I felt there were advantages to alternative assessment
procedures over relying exclusively on paper and pencil assessment.
21
I felt a high percentage of my students were contributing to the class
discussions on place values and when they wee asked to work independently or
with partners they showed a good understanding of modeling place value. Their
journal drawings, as opposed to formal tests, conveyed how well the students
had internalized the learning.
The formative evaluations throughout the unit steered the course for my
self-evaluation. If half my students failed to produce work that showed an
understanding of the materials presented, then I sought to find an alternative
way to enhance greater understanding. After twenty years of teaching place
value to first graders, I have found their direct involvement in manipulating
objects is the best approach. Drawing their own objects in groups of ten gives
ownership of the concept. Once I give them opportunity to relate what they have
learned in a familiar language, such as the words they use to describe their
drawings, then I have achieved my goal. I spent a great deal of time observing
their attentiveness to the lessons and involvement in class activities. Their time
on task and length of engagement in the activity gave me the necessary feedback
for evaluating my teaching.
I just completed a graduate class in Inclusive and Collaborative Education.
The purpose in taking the class was to further my understanding of ways to
reach special education students being mainstreamed in the general education
classroom. The emphasis in the class was the importance of creating a classroom
atmosphere where students help one another learn concepts as a community of
learners. The objectives and goals for the special education students in my group
should have been different than those for my general education students. My
work sample did not include nor address the individual differences a teacher
will face when special education students are mainstreamed. In light of recent
research showing inclusive education resulting in higher performance by special
students, it may be beneficial to new teachers to take a closer look at this
dimension of the classroom in their work samples than I did.
22
Attachments
24
Attachments
Pretest Pages
32
Attachments
Formative/Practice Materials
43
Attachments
Post-test Pages
51
Attachments
Example Journal Drawings
54
References for Workbook Pages