Kelly Pultorak

Model for Response to Intervention in MathThe Haley Pilot School

Grade One

Study Objectives:

Document strategies for intervention that have already been put into place

Create a toolbox of additional strategies from “Developing Number Concepts”

by Kathy Richardson

Assess students who are receiving interventions on a six-week cycle

Provide interventions for math concepts every Tuesday and Thursday

Create a structural model for implementation of RTI math interventions

Responsibilities at The Haley:

I will be visiting The Haley every Tuesday and Thursday for the math block. I

will choose two concepts from every chapter prior to the chapter beginning to focus

on to provide interventions. I will provide teachers with activities that could be

used for students who are struggling with these concepts on a weekly basis. On my

Tuesday and Thursday visits I will come prepared with activities to implement

intervention that address these concepts in a small group setting. Assessment will

take place on a six-week cycle. The students whom the two first grade teachers

believe need extra tier 2 interventions for the given concepts will be assessed at the

beginning of the six week cycle as well as the end of the six week cycle to track their

progress in order to determine if the intervention is successful in helping the

students. The assessments will be given by myself and will come from the

“Developing Number Concepts” books.

Demonstrating Objectives:

In order to demonstrate that these objectives are met, I will create a binder

documenting the RTI process. This binder will include the chapter objectives with

the concepts that I chose to implement interventions for in each chapter. The

binder will also be used for creating a toolbox of strategies and interventions that

address the chosen concepts. In addition, I will create a section for data collection

and analysis for the assessments that will be given every six weeks. After

collaborating with the first grade team and other faculty at the Haley, I will also

create a structural model for implementation at the completion of my project.

Journal 1Addition up to 10

The beginning of my independent study was a challenge because it was very

difficult for me to narrow down to outcomes that I was aiming for within the huge

topic of Response to Intervention. The first meeting I had with the first grade team

that I was going to be working with was very helpful in giving me ideas with the

direction I could take my project in. I was originally thinking that I would make

interventions myself aiming at the problems that the teachers have found certain

students had. The team was wonderful in providing me with a book that they

believe is the best for extra interventions and advised me to use activities right from

the book rather than recreating the wheel myself. We also decided that my service

while I was in the classroom would be best used if I could take a small group of

students whom were suspected to benefit from tier two interventions to give them

two extra doses of instruction a week. We then discussed how assessment was

going to work so that the students’ progress could be documented and it could be

determined if the intervention were addressing the students needs. We decided

that the best way for them to be tested was to use tests from the “Singapore Math”

assessment book as well as some extra tests that could be created based on the

intervention that was being given. While a six week assessment cycle would be

more ideal, we decided for the purposes of my study and gathering more data that a

three week cycle would be best. After having this meeting with the team, I felt as

though I had a clearer outlook for my project and that I would also be doing

something beneficial for the students, the first grade, and The Haley School.

I began my study with the assessment of six students whom the teachers

have noticed have greatly been struggling with addition facts up to ten. I gave them

a test from the “Singapore Math” assessment book and took notes about the way

they took the test while they did it. I noted things such as the process they used, if

they used their fingers, and if they took a long time on certain problems. I also gave

them a mad minute of addition facts up to ten to gather information about their

fluency in addition problems. After I determined that all six of the students

appeared as though they would benefit from the tier two intervention I had chosen

from the Developing Number Concepts, I was ready to get started.

The first day of the intervention went well with the group. There was a lot of

procedural instruction with how the two games that involved working with addition

facts to ten had to be played. After the students understood how to play the games

with all of the right questions that had to be asked when playing, the process went

much more smoothly. The first game is called bulldozer and required the students

to line up ten cubes in two rows of five. I provided the students with papers that

had dots where the cubes had to be placed. One person in the pair then “knocks” out

or moves away a certain amount of cubes while the other student closes their eyes.

When the student opens their eyes, the “bulldozing” student asks: “How many cubes

did I take away? How many cubes are left? How many all together?” The idea

behind this is the manipulatives are supposed to help the students who have trouble

with visualization to be able to see the combinations of numbers. The repetition of

the game and the questions that are being asked is to help the student internalize

these facts so that they are able to recall them quicker. This is very important

because the way that the curriculum teaches addition up to twenty is by breaking

numbers down into tens. The second game is a similar concept but requires more

visualization. It is called “Grab Bag” and it requires the students to start with ten

cubes in the bag. Any number of cubes is then pulled out of the bag and the students

have to come up with the number of cubes that are still left in the bag. This is

practicing number conservation and giving students lots of extra practice with

combinations up to ten. I also have been drawing these games back to the symbols +

and – to help them develop meaning of what the symbols represent and make the

connections between the activities and addition and subtraction sentences.

One of the challenges with my group was that we did not have a good space

that I could bring them to for instruction. We have been having our group in the

hallway, which has been working out fine but gives lots of opportunities for

distraction. The six children who are in the group have some difficulty with

attention to begin with so I have had to be very strict when working with them.

Each week, the students have become more comfortable and familiar with the game

and they have been enjoying using the manipulatives. My worry about these

children is that they may not have the ability to obtain number conservation and

that the work they do with the manipulatives will not transfer over to assessments

that I will be giving them. By next Tuesday, the student will have received three

weeks of the intervention and I will be assessing their progress again. If they do not

make improvements, I will have a meeting with the teachers to discuss the “why” in

the problem.

Journal 2- Response to Intervention in MathAddition up to 10

When the students were initially assessed for the addition intervention, their

raw scores were not too bad. However, many problems were seen as I observed the

students taking the test. Overall, the students moved fast and relied heavily on their

fingers without being able to do any computations in their heads. They were also

very reliant on me reading and explaining each of the questions. I found that these

observations were the most crucial area of assessment for this intervention. After

the students received the intervention, I assessed them with the exact same test and

once again took observational notes.

The scores were interesting because they did not change very much from

before the interventions. However, the observations that I made while the students

were taking the test did change. With the first student, C, she wanted to fly through

the test without taking instruction from the teacher. She made some computations

in her head and some on her fingers but seemed very careless. I was actually

surprised by the ones that she had gotten correct because she was moving so

quickly. She got two more wrong on the end assessment than the original. It is hard

to exactly nail a conclusion on this one but I think some of the mistakes she made

were careless. While it is not good for her to move so quickly, she did appear more

confident in her fact fluency and was able to do some of the work in her head, which

was not the case in the first assessment. I still believe that she benefitted from the

intervention in her fact fluency with addition up to ten even though her raw score

did not reflect this.

The second student, Jo , was very slow at the first assessment but showed

significant improvement. He got the entire test correct at the end of the

intervention. He used his fingers to count but did it very quickly and kept moving.

He also originally had trouble with number conservation but when I read the

problem a second time for him he was able to draw dots in the box representing

bells that were not visible and corrected his answer. He worked independently for

the most part which showed confidence in his computations. Through the weekly

interventions, Jo was very focused and engaged in the activities which aided to his

improvements.

The third student, Ja, was able to get one more problem correct in the ending

assessment. He still struggled with test taking but he had faster computation on

problems and could complete questions without words on his own. He used less

finger counting than the initial assessment but often checked on his fingers. He had

trouble with word problems even with scaffolding but this is expected due to his

learning disability.

The fourth student, N, moved very quickly and independently through the

end assessment. She did computations in her head but had difficulty with number

conservation. This could also be a result of her not reading the problem close

enough. She has shown improvement in her skills and fact fluency in addition with

numbers up to ten.

The fifth student, A, got the entire test correct. He drew on strategies for test

taking by showing his work and was able to read most directions and compute

independently. He still relied on his fingers for some problems but moved quickly

for the most part. He still needs more confidence with his fact fluency and his

answers need to be more automatic but he is showing improvement.

The last student, S, got points off for one problem that she skipped. She

relied on her fingers for most of the problems but still moved slow. She still has not

reached number conservation and if she loses count she has to start back at one

rather than beginning with the number she ended with. Assessing her is very

challenging because she is highly distracted even working one on one with a

teacher. She does not have automaticity with her facts yet and could still use more

support. She has trouble even in the small group of six for interventions because

she is so easily distracted by the other students in the group. Working in a group in

math is extremely beneficial but Sophia struggles socially to understand how to

work with a partner or in a group. When she is having a good day, she can be

engaged and excited but on other days she is worrying about everything outside of

the group.

Journal 3

Meeting with Grade One Team

After looking at the results from the final assessment, I was left with the following

questions:

1) Is assessment based on observation acceptable?

2) How do we address if intervention did not work but class is moving on?

3) Do we always stay topic based in line with what whole class was doing?

4) Is every intervention appropriate to give for 3 weeks?

I happen to give my intervention on Tuesdays right after the first grade team’s PLT

period, which is very beneficial for me. I have been jumping in during their

meetings to discuss how the intervention is going and to keep up to date with their

schedules. I asked them provide me with some time on their agenda this week to

ensure that I could get some of my questions discussed and share my results with

the team. They were not surprised by any of my results, especially with my

observational notes. A lot of the trends that I saw with the students in the group

were trends that the teachers have seen. They agreed that my observational notes

were the most valuable assessment tool, especially for the students who have

special needs because it gives a more complete depiction of their learning. As I

continue with my interventions, I am going to make sure I always keep strong

observational notes while assessing. For the purpose of my study, I also decided

that I will not longer spend days that I go in just to give a paper assessment to the

students because the observational notes during the interventions are much more

useful. If I was trying to stay strictly in line with RTI, I would have to find a more

specific way to track the students progress but the team suggested for now I just use

my observational notes rather than looking at numbers.

One of my main concerns was that while I saw some improvement in the

students, there were still students in the group who do not have number

conservation and could use even more interventions. However, the class is

continuing to move and they are now on to a new topic and I am starting a new

intervention for that topic. My concern is that I did not just want to leave these

students unaddressed if they still did not get where we wanted them to be. After

discussing this concern with the team, we decided that with math it is important to

keep the intervention in line with what is being taught in the general classroom. In

order to address that the students could still use more help, we decided that I

should compile a toolbox for students so that they can go back to these

interventions when it is appropriate. For example, I will make a booklet for each

student with reminders of what we talked about and the resources that we used so

that when they move on to addition up to twenty and addition up to forty they can

draw these interventions back. In this case, they are able to be refreshed with what

was learned and have access to their “toolbox” when they feel like they need it.

In deciding this, we also decided that each intervention will no longer be on a

three-week cycle but instead by aligned with what is being taught. For example,

addition and subtraction took a longer period of time so three weeks was

appropriate, but weight is only going to be taught for a week and a half so the cycle

will be much shorter. After getting these questions cleared up, as a team we have

come to a clearer picture of what RTI should look like for math in the Haley first

grade.

Journal 4Intervention Video

This week I taped myself giving an intervention to the students on the topic

of weight. I did four total interventions on weight and the session that I video taped

was the second session. The first session was a very basic introduction to weight

talking about things that are heavy and light and talking about when the students

have talked about weight in their lives. The second session that I taped was a little

more in depth and gave the students more of a chance to feel different things and

discuss if they are heavy or light as well as imagining things in their head and

determining whether they were heavy or light. They also compared different

objects and ordered them from heaviest to lightest. The conversations were very

rich and the students were encouraged to explain their thinking which lead to new

discoveries for the students and they even had some moments where they disagreed

and had to explain why.

I was fortunate that I was able to share ten minutes of this video during a

PLT and discuss it with the rest of the first grade team as well as the curriculum

specialist in the school. They felt as though the steps of learning and scaffolding for

weight were very effective and felt the student conversation was very informative

and crucial to the group. One of the biggest concerns that we talked about was the

assessment piece for each individual student. The students may have been able to

respond effectively as a group but it was not very clear the individual

understandings of the students. Part of this had to do with the fact that they only

experienced ten minutes of the video that was twenty minutes and the next part was

when the students broke up into partners and had to work with a partner to

complete tasks. However, students still could have slipped through the cracks even

with a partner if they did not have a full understanding.

We discussed possible solutions to address this problem and had trouble

coming to one. Ultimately, we want to avoid using pencil and paper assessment

because these students are students who need other opportunities to express their

knowledge. We felt that moving one step further from partners to individual work

would help to solve the problem. However, in a group with six children, they still

tend to look at each other and have trouble focusing on just their individual work

when in a group of that size. We thought some variety in the group throughout

interventions may be valuable. For example, maybe the first intervention takes

place with a group of six students, the next two with three students, and another

with just two students. In doing this, the teacher could focus more on individual

student and complete more observational notes when handling a smaller group.

However, this would require more time for the teacher providing the interventions

because instead of covering six children in one group, they would have to hold

multiple groups. For the sake of my study unfortunately, it is not possible for me to

provide that many interventions for the students since I am only there twice a week.

Individual learning is something however, that I need to make sure I pay more close

attention to.

Meeting Plan for 3/27/12- RTI for Math

Overall Study Objectives:

Create a structural model for implementation of RTI math interventions

Provide interventions for math concepts every Tuesday and Thursday

Assess students before and after receiving interventions

Weight Intervention Objectives:

Students will develop a deeper understanding of the vocabulary heavy,

heavier, heaviest, light, lighter, lightest

Students will be able to identify and sort objects based on their weight using

both physical objects and pictures

Video Focus:

Are the students engaged in the activity?

Are the students gaining extra experience and practice that will enhance

their understandings of weight?

Is instruction effective in meeting the needs of ELL students?

RTI for Math Questions:

If students still need more help after intervention is given, how do we

address the students’ needs with the curriculum moving on?

Realistically, how often should students be receiving interventions? Is twice

a week enough?

Journal 5

Addition and Subtraction 20-40

Addition and subtraction from twenty to forty is a very challenging, and

important, chapter for the first grade students. The teachers expressed to me that it

would be a big problem for the student who already did not have a full

understanding of addition and subtraction up to twenty. To continue with what I

had already started a few chapters earlier with addition and subtraction, I tried to

use the same intervention but tweaked it for numbers up to forty and to meet what

was being asks of the students from the textbook. Therefore, I gave each of the

students four ten-frames so that they would be able to represent all of the numbers

on the ten-frame and manipulate them in a way that was already familiar to them.

The students’ ten-frames looked like this:

Each of the students was provided with cubes to build the numbers and manipulate

them. We still worked within the “ten-ness” of numbers and discussed how to use

the ten frames to count totals the easiest way. The students were pretty

comfortable with doing this and it was a good introduction to get them familiar with

the numbers up to twenty before really having to delve deeper into the

computations.

It surprised me how reliant the students were on the cubes because none of

them even attempted simple problems such as minus one in their heads. When they

used the manipulatives to subtract one, they still had to go back to the very

beginning to count up the frames. This indicated to me that they do not have any

number conservation and completely rely on the visual component to complete the

computations that are being asked. This is difficult for me in moving forward

because I am not completely comfortable with moving on to these bigger numbers

when they have not yet mastered the smaller ones; however, they do still need to

move on to the curriculum so they have to be provided with some way to

understand these bigger numbers and have a tool to be able to complete the work.

Journal 6Place Value and Addition and Subtraction to Forty

Moving from the ten frames, I had to provide an intervention for the students

to become more familiar with the place value chart and representing numbers

correctly on it. They were already familiar with it because they had learned it in

class but it was very useful to have the students practice with their own place value

charts in front of them and have the whole process broken down to even discussing

what makes up the ten and the one and recognizing there are ten ones in the ten.

The students enjoyed using the boards and some of them got it right away while

others needed to continue being guided through the process.

We then moved to addition and subtraction without regrouping because it

simply required the students to take away or add ones to the one column. The

students felt good about themselves to be able to do some addition with working

with the larger numbers. These steps took two sessions of interventions to make

the students comfortable with the place value chart and manipulating the numbers

without regrouping.

For the next intervention, I introduced regrouping to the students. I first

introduced regrouping by having the students discover that they could not always

continue just adding and subtracting ones with certain numbers when you do not

have enough ones. We then discussed further the value of the tens and how we

could break the tens down. The students seemed to follow along as I was doing it

and were on occasion able to give me the next step to what I was doing. However,

without the scaffolding, it was evident that the students needed a lot of practice with

this. After recognizing this was going to be very difficult, we spent three

interventions continuing to work with the same concept because they really needed

the extra practice and help with the steps before they could move towards paper

and pencil algorithms. I saw great improvement as we moved through the three

interventions as the students became more confident in their regrouping and even

were able to explain why they were taking the steps that they were taking. It was

very evident through these specific interventions that the students really needed

this concept to be further broken down and extra exposure and practice with the

topic.

Overall Reflection

Throughout my time at the Haley for my Response to Intervention project, I

learned a tremendous amount about the difficulties in providing math interventions

as well as the great benefits. While I originally thought that I would be able to pick

out specific concepts within each chapter, I soon realized that I had to really cover

the concepts as a whole in order to really further the students’ understandings. I

also soon came to the realization that although I was hoping that some of the

interventions I was providing could be further pushed by the teachers, that they

simply did not have any time into their busy schedules, especially with being behind

in math and the end of the school year near approaching. The students became

familiar enough with what we worked on during the interventions on Tuesday and

Thursday, that they were able to carry these skills and use the manipulatives that I

used with them even on their own in their classrooms when I was not with them.

My goal through the whole study was for the students to benefit academically

as much as possible. In keeping to this goal, a lot of my initially objectives had to be

changed. One of the biggest challenges as a person coming in the classroom only

twice a week was that they constantly made changed to the schedule and spent

different amounts of time on every concept. In addition to this, even the two first

grade classrooms got way off schedule with each other, which made the group

dynamic of students from both classes difficult. While in an ideal world I would be

able to provide much more interventions until the students fully understood the

concepts, I had to make sure I kept the students moving with the concepts the way

that their classes were moving so that they would not fall behind. The students may

not have gotten to a point that they had full understanding, but the teachers did

report that the group of students that I took out for interventions had increased

confidence in the classroom when they came back in and felt like they knew how to

do more.

I believe that in order to successfully implement RTI for math, you would

have to have a person who is very available to provide multiple interventions

throughout the week to students. It would be very beneficial for students to benefit

from small group and individual interventions to stick to the model but it would just

be too difficult to do without a person who is assigned to that specific responsibility.

I also believe that classrooms across each grade need to try to stay on track with

each other if they are going to try to work as a team. It hurts the students to be in

groups with other students who may have already learned a topic if their class gets

ahead of the other class. Communication is key in making this possible. Teachers

need to effectively communicate with the person providing interventions with

specific struggles that they see and keep them up to date with the timeline that is

going to occur for each chapter. Ultimately, it can be very beneficial for students to

receive these extra doses of math. I felt it was extremely rewarding when the

teachers expressed to me that the students come back into the classroom after the

interventions with increased confidence and desire to participate in whole class

discussions. I believe that if schools had the appropriate resources in the

implementation of RTI for math, students would make tremendous progress.