MATH UNIT ASSESSMENT PLAN - STUDENT TEACHING

PRE-TEACHING PHASE

McClellan Elementary School is a Pre-K–8 neighborhood Chicago Public School

in the Bridgeport neighborhood on the South Side of Chicago. Bridgeport is a very

diverse neighborhood. Demographics show that it is about 35% white, 35% Asian and

28% Hispanic with a median household income of $35,000. McClellan is near the heart

of Bridgeport at the intersection of 35th Street and Wallace.

It is a smaller school of 301 students with only one class per grade, and has a

corresponding smaller budget. It is a Level 1 school with strong leadership and a

dedicated staff. Progress reports available at cps.edu show that student growth for all

grades on the NWEA is “far above average,” however actual attainment levels are

“average” with most grades’ NWEA test scores falling below the national average

(except 4th and 6th grades). From my experience as a student teacher, I have seen that

much of the staff and administration are very dedicated to providing the best learning

environment for the students. The principal is especially approachable and always seen

talking with students and staff. My CT also says he makes the teachers work very hard

and he cares very much about the school and the children.

 The school building is over 100 years old. The first-grade classroom is on the 2nd

floor and has a very high ceilings and tall windows. It has its own coatroom. Because

the building may predate electricity, outlets are few and the use of extension cords is

necessary to run the computers. Ms. S.’s desk is at the side of the room, perpendicular

to the way the students desk faces. It is only used during attendance.

The students desks are arranged mostly in pairs, but because of space issues, the

grouping furthest from the door forms a large “E.” For the most part, students are

grouped boy/girl, except in cases where students are switched to pair “talkers” with

quieter ones. There are several student work tables around the perimeter of the

classroom for “centers.” There is also a kidney shaped guided reading table. A

classroom library is in the back corner and two student computers are against the

window, which are used only during centers because there is no computer projector.

There is also an older overhead projector though. Word walls, literary theme posters,

math charts, and student work adorn every inch of reachable space on the walls and

two bulletin boards. The classroom is very crowded and becomes easily disorganized

because there is not enough shelf space.

First grade has 31 students, 16 girls and 15 boys. There are two parent

volunteers, a teacher’s aide and a student volunteer who comes weekly. The aide

comes three times a week for a couple hours in the morning and a couple in the

afternoon. The parent volunteers come several times a week for a couple hours a day.

Ms. S. has them help out with instruction and classroom tasks, such as making copies,

grading tests and homework. They also read and practice sight words with students or

monitor student behavior.

The diversity of the first-grade students is representative of the Bridgeport

neighborhood. Out of the 31 students about 17 are Hispanic or part Hispanic and white,

9 are white, 4 are African American and 1 is Arabic. Six students are English learners.

Until recently all six were meeting with the ESL teacher, however, now only 4 receive

ESL teaching outside their regular classroom. There is much differentiated instruction

designed to accommodate students’ needs. The class is divided into math and reading

groups tiered by ability.

Low-level learners and whose Attention Deficit Disorder causes them learning

difficulty are accommodated in all instruction. Ms. S. spends much extra effort to ensure

that they are paying attention and are learning, so thus does not let them fall behind.

The children are encouraged to treat each other kindly through positive

affirmation of good behavior and discipline when not treating each other well. There is

also a program called Second Step designed to teach skills such as compassion,

empathy and focusing their attention. They have not yet started to form cliques

according to ethnicities or race as they do when they get older.

   There is a variety of instructional methods used in the classroom, though it errs

on traditional and rarely is there hands-on and or inquiry-based learning. For reading

and language arts, there is small group and whole group instruction. The teacher meets

with guided reading groups according to reading levels. There are 8 different levels in

this classroom. Besides having students read leveled readers aloud to the teacher,

each group works on different skills. Lower groups focus on phonics skills, whereas

higher groups focus on reading comprehension and will be asked higher-order thinking

questions about what they read. The EL guided reading group involves more discussion

in an effort to build both reading and spoken language skills. Whole group instruction for

reading includes language arts, where phonics, grammar, shared writing and shared

reading. During shared writing and shared reading, students will participate in paired

and whole group discussions. Reading instruction accounts for at least half the day.

Math involves whole group presentation using the overhead projector and

whiteboard and some discussion. Students work in groups according to ability levels.

When appropriate, manipulatives are provided to help student comprehension. Most

instruction closely follows the math textbook and is kept simple and to the point in order

to accommodate the lowest level students by not confusing them with too much

information.

Science and social studies is whole group and involves reading the textbook and

whole group discussion. After whole group presentation and discussion, students write

about what they learned. Unfortunately content-area learning is not enhanced by access

to technology, hand-on or other inquiry activities. The teacher prefers that students use

science and social studies to build writing skills rather than explore the content more

deeply through more student-centered activities.

Different types assessment are conducted very often and regularly in the

classroom. Reading comprehension and spelling tests are done every week and follow

the basal reader program tests and spelling words. The tests are provided by the

reading program and are tiered into three levels. Lower level students are given a one-

minute fluency test as well. Student writing assignments are graded according to

organization, sound-spelling correlation, amount written and punctuation, grammar and

capitalization that was explicitly taught.

Reading levels are also tested with the Dibbels test at least twice a year. Lower

level students are tested more often. These are done one on one with the iPad. They do

not take the ISAT or NWEA.

Math tests are done every week, regardless of it is in a middle of a chapter.

Chapter tests are also provided by the McGraw-Hill math program. Pretests are usually

not done. Exit slips are also done at the end of most lessons to assess comprehension

and to inform lesson planning.

Science and social studies assignments are also graded on a less rigorous scale

to check comprehension of content and to assess clarity and structure of writing. There

are never social studies or science tests that test content knowledge.

For this assessment project I decided to do a math unit. I looked ahead in their

textbook and saw the upcoming graphs and tables chapter. They had learned a little

about graphs and tables in their science and social studies books. Reading and making

charts and graphs is both a valuable and “fun” skill for them. They will focus on making

and reading tally charts, picture graphs and bar graphs. To test their prior knowledge I

used the pretest and an alternate version of the chapter test provided by the book as a

pretest. More specifically, the test assessed the following skills: reading bar graphs,

reading picture graphs, reading tally charts, interpreting tally charts, and answering

“How many fewer” and recognizing what “survey” means.

The students’ average score on the pretest was 58%. Here is the breakdown of

how many questions students answered wrong. 25.9% of the class answered only one

question incorrectly and nearly 15% of the class answered 6 out of 8 questions

incorrectly. This shows that there is a broad range of prior knowledge about the subject.

PERCENT OF STUDENTS BY HOW MANY QUESTIONS THEY ANSWERED WRONG

In general, students were able to answer the easy “reading” questions, while

questions that made them interpret the graph proved to be more difficult for them. Out

of 8 questions given, no students answered all correctly. (See sample test attached.)

The breakdown of the number of questions students answered correctly were as

follows:

PRETEST

 SKILL

Students answering question correctly

Picture graph reading - easy 96%Tally chart reading - easy 59%Reading tally marks showing "5" 56%Reading bar graph - easy 48%Understanding meaning of "surveyed" 33%Answering the question asked 56%Understanding "How many fewer" 0%

Of these questions, most students answered the easy level reading picture graph

skill correctly - 96%. For the easy-level reading tally chart skill, 59% of students

answered the questions correctly. 56% of students knew how to read tally marks, i.e.

that on every fifth tally mark, a diagonal mark crosses over the set. For the reading bar

graph skill, 48% students answered the question correctly, while only 33% of students

understood what “surveyed” means. Also, 44% of students answered a question

beginning with “Which” with a number. For instance, “Which toy is the most like?” these

44% answered “6” from the chart, instead of “train.”

The most difficult question was the question phrased as follows: “How many

fewer students chose dogs than cats?” Three students answered this question correctly,

but it appears that these may have been lucky guesses as demonstrated on incorrect

answers on related questions and that the students in the high-level math group all

answered this incorrectly. Discounting the three guesses, 0% of students understood

this question.

Based on this data, it appears that reading picture graphs is an intuitive skill that

most students already know. More time will be needed on explaining how to make and

read tally marks. I will make time to demonstrate how to count them, and be explicit

about drawing a diagonal line over four marks to indicate the fifth. I would have thought

this skill would be more evident in this class since it is demonstrated every day as part

of a behavior reward system. Student groups receive tally marks for being the first

group to be organized and sitting quiet at their desk after lunch and centers. This data

shows that I should never assume that students learn things without explicit

explanation.

I will also give simple, direct instruction on how bar graphs and tally charts can

be used with their textbook providing the backbone of their lessons. I will also make

sure to stress vocabulary and whenever possible go over what a survey is and how it

can be used to create data for charts and graphs. When possible I will try to get

students to see how to distinguish between bar graphs, tally charts and picture graphs.

However, I will explain how they can be just different ways to show the same

information or data.

From their test results it seems like the most difficult skill is understanding how to

answer a question that asks “how many more…” or “how many fewer…” These are

“abstract” phrases that seem like they could easily confuse the students who may not

be mature enough to grasp phrases such as these. This skill should be taught as a drill

to the lower students and the higher students may be taught the reasoning behind it. It

will be easier to teach the lower level students just that they should “take away” or

“subtract” when they see or hear these “how many more” or “how many fewer”

beginning a question.

TEACHING PHASE

After showing the results of the test to my cooperating teacher, she agreed with how I

read the results and how I planned to teach the unit. We have been working very closely

on how I teach math, so I have come to know how she prefers math to be taught. This

includes keeping whole group presentation short, keeping an eye on the students with

attention problems, and using simple direct language so as to keep the lowest students

engaged. Also because of the large class size, use of resources outside the textbook

and worksheet is difficult, so this unit will be taught as the children are used to. She

made no suggestions except help me create a fun activity for them to do at the end of

the unit. It involves making up their own survey. They will go around and ask their

classmate survey questions. They will record their answers on a tally chart, which they

will in turn use to create a bar graph. I thought this sounded like something very fun and

engaging for the children as well, as long as it is properly modeled and structured.

POST-TEACHING PHASE

After teaching six lessons, I gave the post-test to students during their usual

science time. The students posttest average score was 86%. Thus, my instruction

resulted in about a 28% gain overall.

Pre-test Post-test0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Average Test Score

I would have liked to have seen a bigger difference. The biggest gain was in

student comprehension of a question asking, “How many fewer” and the skill “How

many more.” Originally none of the students understood the question. The next biggest

gain was in students understanding of what surveyed meant, in the question that asks

how many students were surveyed. Also there was notable improvement in reading a

bar graph and answering the question asked, i.e. Giving the answer “train.” instead of

“6” when asked which toy is most liked. The picture graph reading stayed the same. I

think this is a very intuitive skill. Only one student answered it wrong on both tests,

though it was not the same student. Here is the breakdown of pretest and posttest

scores by skill and percent of students by how many questions they answered wrong.

Picture graph reading - easy

Tally chart reading - easy

Reading tally marks showing "5"

Reading bar graph - easy

Understanding meaning of "surveyed"

Answering the question asked

Understanding "How many fewer"

0% 20% 40% 60% 80% 100% 120%

Specific Skills - percent answered correctly

Post-test Pretest

66.7%3.7%

7.4%

3.7%

11.1%

7.4%

0 wrong1 wrong2 wrong 3 wrong 4 wrong5 wrong 

Before their chapter test I will review all the skills again. I think some students

may not have been paying attention or became confused during the instruction of

certain skills. The ones I would be sure to cover first are reading tally marks in sets of 5

and how to answer questions beginning “how many more” or “how many fewer.”

There were significant differences in both pretest and posttest scores between

the struggling, on-level and advanced level students. The average scores for each

group were as follows:

pretest postteststruggling 29% 54%on-level 58% 84%advanced 77% 100%

AVERAGE SCORES BY GROUP

PERCENT OF STUDENTS BY HOW MANY QUESTIONS THEY ANSWERED WRONG

struggling on-level advanced0%

20%

40%

60%

80%

100%

120%

pretestposttest

There was not as much improvement as I would have liked. I am pleased that the

high group all received 100 percent, but that seems to be the case with all their

assessments. Although the low and middle groups improved I would have liked to have

seen more. Included with the on-level group are two English learners who I think have

trouble with math in general. Both of these students received poor scores on both the

pretest and the posttest. I will need to work on teaching strategies to better reach them.

This distribution of test results has happened in my teaching before. The

advanced learners perform extremely well. The on-level students reach around 80%

and the lowest group do poorly. Again, from the posttest it is evident that the lowest

students still cannot perform the skills or comprehend the concepts I taught. I believe

that I need to change my instructional style. Because the low group has a pattern of

failing tests I think I need to attend to these children even more. They are a difficult

group that seem to have a low motivation for learning, unlike most of the other children,

or have severe attention problems. Although they sit right in front of me, their attention

often wanders, even though I am constantly redirecting it. I am glad to see that my focus

on keeping their attention has not affected the comprehension of the on-level and

advanced-level children too much. Often while I am teaching to the lower ability children

I feel like the rest are bored and restless and may not be learning.

I will be more diligent in keeping the low group’s attention during whole group

presentation. Also, instead of sitting with them as they do their remedial worksheets I

will sit them in a circle around me to repeat the presentation again. Because there are

so many of them and they are so hard to control, I think location is important. It might be

a good idea to take them to the guided reading table so that they can see that I can see

all of them at once and will know that they have to pay attention. Also repeating the

lesson may provide the extra scaffolding they need in order to work on their own.

REFLECTION

Although there was improvement for most students I think I could have done a

better job. Some areas I would focus on are developing and implementing a plan to

reach the lowest level children, taking more care to reach EL children, and reviewing

concepts more carefully in general.

The lowest-ability children are always the most difficult to teach for me. There are

so many of them and several of them have attention difficulties as well. One child likes

to spend all of math instruction time making faces and giving thumbs down to the other

children who have difficulty paying attention, thus making keeping their attention even

more difficult. He is skilled in doing it when the teacher is not looking. If available an

adult is usually sitting next to him, but now I think I will have any other adult sit on the

other side of the room, watching him instead. I think if he know is being watched, it will

keep him from distracting the other low-level students. I think he is the first major step to

address in improving the low group’s attention.

Also, although I have made the effort, I need to continue on keeping my

sentences short and direct and less wordy when I am speaking to the class. This will

also help maintain the attention of the low-level children and also the English learners.

Children who are confused are likely to tune out. I will also try to be more conscientious

in repeating things and pointing to things so that the EL students will understand better.

Also I will make sure they are paying attention. I would like to ask them questions during

whole group, but one is painfully shy and refuses to talk in front of the whole class.

After whole-group presentation I think I should provide more formal scaffolding

for the low-level students and maybe EL students as well. It is evident that they need

the extra support. I think they would benefit from additional time for the skills to be

modeled and time to process and internalize it.

This group, along with the rest of the class, would also benefit from more

frequent mini-lessons of review. These math concepts are all brand new to them and

review can only help reinforce their knowledge and comprehension, and help them

make connections. For the advanced children I would like to make learning more

interesting for them as well, but because of the logistics of the large size and the

number of students who need extra guidance it is difficult. However I will try to

implement some more interactive learning activities. One way I may be able to

accomplish this is by having them create charts and tables for social studies and

science assignments. Applying a skill across the curriculum makes for a deeper and

more impactful learning experience.

Overall, I thought this assessment process was very informative and would like to

apply it again. I really enjoyed getting measurable feedback on my instruction. I found

that giving pretests is a valuable way to learn what students already know. Being

informed about their prior knowledge let me know in what areas I would have to spend

extra time and where they already were good (such as knowing how to read picture

graphs). This was a very fun subject to teach and they haven’t yet taken the chapter

test. I will use this information to review the areas where they did not succeed and

speak with my CT about extending modeling math time at the guided reading table. I am

very excited about implementing these changes.