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.