Week 3 Assignment, Part 3
Draft Action Research Project Progress Report
Building Computational Fluency Through Addition
and Subtraction Strategies
Through
years of classroom observations as a fourth and fifth grade teacher, I’ve watched
my students struggle with their basic facts of addition, subtraction, multiplication,
and division. As a Mathematics Instructional Coach for Kindergarten through fifth
grade, I see the efforts that teachers are putting forth to help students master
their basic facts, however, students are still struggling. Year after year, across
both genders and all lines of ethnicity, students have difficulty learning and retaining
basic facts, understanding reasonableness, and problem solving. I’ve attended several
trainings about number sense and computational fluency this year and the common
thread is all about teaching students the number strategies, such as learning and
applying doubles, doubles plus one, making a ten, and composing and decomposing
numbers, to help them be successful.
The objective
of my Action Research Project is to determine whether or not second grade students’
scores and recall will increase on weekly math fact tests after direct and
intense instruction on fact strategies, such as, but not exclusively, learning
doubles, doubles plus one, making a ten, and composing and decomposing numbers.
In one of the second grade classrooms, the teacher, Mrs. Smith, and I have compiled
the scores from the weekly fast fact tests for the fifth six weeks before we began
working on number strategies. I have been modeling lessons in the classroom with
whole group instruction and small groups for the last month using manipulatives,
ten frames and double ten frames to model addition problems. Using problems such
as 8 + 7 is helping students manipulate the numbers to see that the number eight
is two away from ten and seven is three away from ten. Some students are using the
doubles plue one strategy while others are using doubles minus one. My vision is
ultimately to help students learn how to manipulate numbers and make connections
when adding and subtracting. I am also hoping that we will see increases in student
scores on weekly timed fast fact tests; many of the teachers are leary about teaching
these strategies because it is so ‘different from the way we learned and ever taught’.
Seeing improvement in student scores will be a positive step toward helping teachers
understand the benefits of teaching specific number sense strategies. Students will
continue to take weekly timed fast fact tests and student scores will be compiled.
At the end of the grading period, we are going to compare student scores from ‘before’
learning strategies, ‘during’ learning strategies, and ‘after’ learning strategies
to determine whether or not students benefitted from the direct, intense instruction.
My reasoning behind conducting
this action research about learning math strategies stems from my studies of what
Jon Van de Walle and LouAnn Lovin have found through their research about teaching
mathematics to young children using best practices. Van de Walle and Lovin (2005)
found that
“many children have learned basic facts without
being taught efficient strategies. They develop or learn many of these methods in
spite of the drill they may have endured. The trouble is that far too many students
do not develop strategies without instruction and far too many students in middle
school continue to count on their fingers.”
I’ve looked to Principals and Standards for School Mathematics
(NCTM) for information regarding children developing an understanding of whole
numbers and operations and found that students in grades Pre K-2 should “develop
a sense of whole numbers and represent and use them in flexible ways, including
relating, composing, and decomposing numbers (NCTM). In Texas, our first grade
Texas Essential Knowledge and Skills (TEKS) and state standards do not give
enough support for teaching numeracy and number fluency. Therefore, curriculum
development is left up to the districts to decide where gaps are occurring in
student learning, what does best practice tell us about learning, and how can
we close in the gaps to support student achievement. Case in point, last summer
our district revised the curriculum for our first grade students to include
number fluency, numeracy, and a rich foundation for the conceptual
understanding of numbers. I can’t help but wonder whether or not this change in
the curriculum will indeed increase the level of student understanding and
performance and what long-lasting effects it will have on student achievement
and problem solving skills on my campus. Since these changes have taken place
in the first grade curriculum, it’s going to be ever so important for the second
grade teachers to be prepared for these students with their variety of number
strategies. Although our primary teachers will be the first to tell you their
students have no number sense and a change has been long overdue in the
curriculum, many of them are resistant to spending the amount of time needed on
numeracy, decomposing and composing numbers, and building upon the important
understanding of part-part-whole relationships. Their fear and resistance stems
from a lack of training and staff development for teaching number sense. They
will need a great deal of my support which beautifully lends itself to becoming
my action research plan. It is my hope that our students will have a greater
understanding of numbers with fewer struggles in learning their basic facts. My
principal is completely supportive of my action research plan and is anxious to
view my findings. Since I am new to the campus this year, I couldn’t begin the
project as early as I anticipated because of the time it has taken to build
relationships and trust with classroom teachers. The decision was finally made
that I would work with only one teacher with the hopes that my findings will spark
an interest in more teachers wanting the job-embedded professional development
in their classroom as well.
I have communicated the vision to staff
members and administrators through numerous discussions about the importance of
teaching students how to develop their number sense. Each grade level on my campus
has a copy of Teaching Student–Centered Mathematics.
Before each unit of study, we review what Jon Van de Walle (2005) says about
best practices for introducing and teaching the content at each of the developmental
levels.
I have organized the Action Research Plan with
the help of a second grade classroom teacher, Mrs. Smith. I have been modeling lessons
in her classroom and then helping her implement the activities with me there as
a support if she doesn’t feel comfortable with using the questioning strategies
needed for students to begin to make connections with their learning. With a priority
given to student learning, we’ve been working on finding out from students ‘how
and why’ they know the answer instead of just an answer alone. Burns (1992) explains
that “math instruction should seek to help children learn to think, reason, and
make sense of numbers” which is why I find it so important for students to explain
their thinking. Students explain their thinking through words, pictures, and using
their manipulatives. Van de Walle and Lovin (2005) point out that “as students continue
to attempt to show their thinking, they will improve both from practice and from
seeing the methods using by others.” Money has not been needed for this project;
time, manipulatives, and questioning strategies are all that have been needed to
complete this action research.
First and foremost, the priority from the beginning
has been about helping students be successful in their development of number sense.
The second grade teacher that I’ve been working with, Mrs. Smith, actually approached
me and explained that her students were struggling with learning their basic facts
and she did feel like she had sufficient training for teaching students to be computationally
fluent. Her other teammates are not on-board with teaching these strategies and
believe their methods of ‘drill and kill’ are sufficient. Mrs. Smith asked if I
would model several lessons in her classroom and then watch her teach a small group
using the same activities and strategies. After I model the lessons, we debrief
about the student responses, my questioning strategies and discuss observations
about formative assessments on each student and their level of understanding. Based
on the observations and student responses, we have made changes to our small groups
on several occasions.
Mrs. Smith’s
class has a diverse population with a wide-variety of readiness levels. We are scaffolding
lessons and differentiating to meet the needs of all students. Van de Walle and
Lovin (2005) found that “all children are able to master the basic facts—including
children with learning disabilities. Children simply need to construct efficient
mental tools that will help them.” By conducting this action research, the
students, teachers, parents, and our campus will benefit from determining
whether or not there really are benefits to devoting time to number fluency. In
the short amount of time that we’ve been working on this project, we are already
finding that students are making connections and building a deeper understanding
about numbers in their world.
References
Burns, M., (1992). About teaching mathematics. Sausalito, CA:
Math Solutions Publications.
National Council of Teachers of
Mathemetics (NCTM). Principals and Standards for School
Mathematics. Retrieved from http://www.nctm.org/standards/content.aspx?id=7564#numbers
Van de Walle, J., Lovin, L., (2005).
Teaching student-centered mathematics: grades
K-3.
Boston, MA: Allyn & Bacon.
