ahealeyksumed.weebly.com · web viewthe purpose of this research is to identify the conditions for...

1Action Research Paper

Ashley Healey

Kennesaw State University

Spring 2015

What are the effects of weekly timed math assessments, games, and number relationships

on student's fact fluency knowledge within 20?


Abstract

The purpose of this research is to identify the conditions for students to fluently add and

subtract within 20 and the effects of weekly timed fact assessments. The Common Core

Standards for 2nd grade specifies that students should be able to fluently add and subtract within

20 using mental strategies. By end of Grade 2, students should know all sums of two one-digit

numbers from memory. If students do not know their basic addition and subtraction facts, then

more complex mathematical procedures will prove to be difficult in the future. Therefore, the

focus of my research is:

1. What effects do weekly timed assessments based on fact fluency knowledge from 0-

20 have on students?

2. Under what conditions can students fluently add and subtract within 20 using number

relationships, mental strategies, and games?


Table of Contents

Abstract...........................................................................................................Page 2

Introduction.....................................................................................................Page 4

Professional Research.....................................................................................Page 7

Demographics.................................................................................................Page 8

Statement of the Problem................................................................................Page 8

Research Design..............................................................................................Page 10

Methodology....................................................................................................Page 11

Conclusion.......................................................................................................Page 13

References.......................................................................................................Page 16

Appendices.......................................................................................................Page 18


Second Grade Fact Fluency

Introduction

Math fact fluency is the ability to recall the answers to basic math facts automatically and

with minimal hesitation. Basic facts would include addition and subtraction facts that involved

adding and subtracting one and two digit numbers. Fact fluency is gained through significant

extensive practice, with mastery of basic math facts being a goal of both teachers and parents.

Automaticity can be defined as an automatic response, without a delay. It can also be described

as students quickly gathering an answer without hesitation.“Everyone knows what automaticity

is. It is the immediate, obligatory way we apprehend the world around us. It is the fluent,

effortless manner in which we perform skilled behaviors. It is the ‘popping into mind’ of familiar

knowledge at the moment we need it (Logan, 1991 a, p. 347).”

As adults, we can all recall to the faint memory of elementary school and learning our

addition and subtraction facts. We can also relate those facts to drills and how we learned these

important facts through practice and time. The same importance still remains imperative;

however, with the new Common Core State Standards for Mathematics, goals for students and

effective strategies for teaching have changed with the importance stress on meeting the needs of

our students to prepare them for the 21st century. The shift also appears to be less on rote

memorization of facts that on recalling facts from memory by using comprehensive strategies.

It's important that young students in grades K-2 have meaningful practice and time to develop

these strategies for solving addition and subtraction problems as well as introducing them to a

variety of ways that an answer can be derived. Student thinking also needs to be supported as

well as modeling specific strategies by teachers. Through addition and subtraction games

involving dice, cards and manipulatives, students are able to practice these skills while they are


having fun and enjoying learning. Teachers also have the ability to observe students playing

games and interviewing their students. Teachers can also select a specific skill or strategy for

students to practice or just a general strategy for students to focus on.

The major strategies used for fluently deriving addition and subtraction facts center

around two main groups of facts: doubles and combinations of ten. Once students have mastered

those two key groups of facts, they are able to derive every other challenging fact (Kling, 2011)

Students begin practicing addition and subtraction to 10 when they are in kindergarten by using

dot cards and ten frames. By the time students enter 2nd grade, they have a basic understanding

of composing and decomposing the number 10. Other strategies that are also important to

conceptual understanding are the following strategies: counting on, counting on from larger,

adding up in chunks, and removal strategies.

For decades, the argument over timed fact assessments has also been debated. Many

researchers indicate that timed math assessments can cause math anxiety in children, while

others believe that timed math assessments are appropriate for assessment purposes. Because

practice enhances speed of accurate responding, interventions that occasion higher rates of

accurate responding are likely to cause greater increases in automaticity and/or fluency

(Codding, Chan-Iannetta, Palmer, & Lukito, 2009; Skinner, 1998; Skinner, Belfiore, Mace,

Williams, & Johns, 1997; Skinner, Bamberg, Smith, & Powell, 1993; Skinner, Belfiore, &

Watson, 1995; Skinner, Fletcher, & Hennington, 1996; Skinner & Shapiro, 1989). In this

research, I selected to use timed math assessments because I wanted my students to be able to

recall their addition and subtraction facts in a quick and timely manner. If students were given

unlimited time, many of them may take anywhere from a few minutes to ten minutes or longer to

solve each problem. However, these are facts that students have been learning since kindergarten


and first grade. In second grade, students are expected to know the sums of all two one- digit

numbers by the end of the year in May.

Professional Journal Research

Research indicates that children typically progress through three phases in learning a

basic combination or a family of related combinations: Phase 1: Counting strategies (using object

or verbal counting to determine answers); Phase 2: Reasoning strategies (using known facts and

relations to deduce the answer of an unknown combination); Phase 3: Mastery [efficiently

producing answers from a memory network; e.g., Kilpatrick et al., 2001].Most authors

suggest that learning the facts in terms of relationships is an intermediate

stage between the stage of conceptual development that involves using a

procedure and the stage of practicing to develop automatic recall.

(Steinberg, 1985; Stein et al., 1997; Suydam, 1984; Thorton, 1978).In second

grade, educators want students to produce their answers from their memory for fact automaticity;

however, there are a wide variety of learning phases that students may stay or move in

throughout the school year.

Students also need to know their basic addition and subtraction facts as they continue on

into 3rd grade, which is a grade level that introduces more complex problem solving such as

multiplication and division. Basic math skills learned throughout the primary years are critical

for students to learn and understand how to complete advanced mathematical concepts (Lerner &

Johns, 2011). Research also shows that memorization of the basic number combinations is

important for success with more advanced school mathematics. By freeing cognitive resources so

that attention can be focused on more complex matters (e.g., looking for patterns), ready access


to number combination knowledge can facilitate problem solving and both mental and written

computation with multi-digit and rational numbers [National Mathematics Advisory Panel,

2008]. Moreover, students who successfully store basic math fact information in memory and

retrieve it easily are more likely to develop the skills necessary for solving a wide variety of

complex problems and interpreting abstract mathematical principles (Patton, Cronin, Bassett, &

Koppel, 1997; Shapiro, 2010; Siegler & Shrager, 1984.)Students who can successfully store their

basic math information can move onto more difficult algorithms and mathematically equations.

Research also points out that application of math facts to solve problems is one of the

most fundamental goals for math education (NMAP, 2008) and is considered a distinct stage of

understanding in cognitive models of learning (Bloom, Engelhart, Furst, Hill, & Krahwohl,

1956; Thurber, Shinn, & Smolkowski, 2002).Furthermore, learning to decompose and

recompose numbers in flexible ways is an important step in students’ development of efficient

computational strategies. (Wheatley and Reynolds 1999). It's also imperative that teachers help

students see the flexible ways in which to compose and decompose numbers, and that there is not

solely one way in doing such.

Students who struggle with basic math facts regularly struggle to recall the fact fast

enough to successfully use it (Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007). Currently,

many students in second grade are still observed using their fingers and 100's chart to solve basic

addition problems like 7 + 8 or 13-5, which they should already know from memory.“Research

has indicated that helping them [students] to develop thinking strategies is an important step

between the development of concepts with manipulative materials and pictures and the mastery

of the facts with drill-and-practice activities [emphasis added] (Suydam, 1984, p. 15).”

Additional practice activities are needed (after teaching thinking strategies) in order to develop


automatic, direct retrieval of facts. This is why using games and activities in the classroom allow

students extra time for fact retrieval and to practice facts is so highly important. Several studies

have also shown daily time trials to be an effective way to build students' fluency with basic

math skills . Van Houten and Thompson (1976) found that a series of l-minute timed trials

increased the rate with which students answered math problems while maintaining high levels of

accuracy. In this study, one minute trials were not used, but instead four minute timed trials. I

believe that four minutes is an appropriate time frame for students to adequately solve 40

addition and subtraction problems. I feel as if one minute timed assessments would not capture

the overall picture and clarity that I was seeking in this research. Timed practice drills as a

method for developing automaticity offer a clear alternative to strategy instruction for

academically low-achieving students and students with LD (Ashcraft & Christy, 1995; Geary,

1996). Special education research supports time drills that often include pretesting and

systematic review (Burns, 2005; Koscinski & Gast, 1993; Morton & Flynt, 1997; Stein, Silbert,

& Carnine, 1997). Timed math drills are also used as a progress monitoring tool for our students

in second grade who are in the Student Support Team process and are receiving additional math

instruction weekly. Students who are in the Student Support Team process who do not meet

progress monitoring goals may also be looked at for a referral to special education if there are

not responding to math interventions in the classroom.

Demographics

Currently, I am a 2nd grade teacher in Gwinnett County, Georgia. Gwinnett County is the

largest school district in the state of Georgia with a population of over 160,000 students and still

growing. Gwinnett is also very ethnically diverse with many students who come from various

racial backgrounds. The current enrollment at my school is 898 students and my school is a non-


Title-1 school, so we do not receive financial assistance. 6.4% of students enrolled at our school

are ESOL (English to Students of Other Languages), 6.2% are EIP (Early Intervention Program),

and 12.2% are Special Education. 46% of our students receive free and reduced lunch. The

demographics include: 35% Caucasian, 24% Hispanic/Latino, and 19% African American.

Currently in my classroom, I have 21 students, eight students are female and thirteen students are

male. I have six ELL's (English Language Learners) in my classroom. Five students are either in

Tier II or Tier III reading, math, or both in the Student Support Team (SST) process. The Student

Support Team process is a way to identify students who need additional instruction in the areas

of reading, writing, math, or all three. The process involves Administrators, teachers, and

specialists working together to provide a plan for students who need additional support. I also

have two students in Tier III behavior and I implement a daily behavior chart. Four students have

an IEP for speech. Two students qualify for resource pull-out and receives math, reading, and

writing instruction from a resource teacher.

Statement of the Problem and Research Questions

As the 2014-2015 school year started, I realized that many of my students did not know

their basic addition and subtraction facts. I observed many students counting on their fingers,

using a 100 chart, or a number line to solve basic addition and subtraction problems. I also

observed many students who were very confident in the wrong answer for a basic addition and

subtraction problem, i.e. 7 + 5. The number of students in second grade who were receiving extra

interventions in the classroom each week through the Student Support Team process became

alarming to me,. These students were struggling with current classroom content and they were

also still in the process of learning their basic addition and subtraction facts. Mastering basic

addition and subtraction facts became even more concerning after viewing the scores from the


Gwinnett County District Developed Assessment's, which are given in mathematics and

language arts every nine weeks and serve as a benchmark test, that is, an accumulation of what

content students have learned from the current nine weeks of instruction. The 2nd grade

Common Core Standard that directly correlates to fact fluency is 2.OA.B.2, which had a class

section average of 44.1% on the 2nd nine weeks assessment, a school average of 47.8%, a cluster

school average of 44.5%, and a district average of 45.2%. In all four categories, the percentage

of mastery was below 50%. Personally, this was an alarming statistic within my county and

within my classroom and these percentages have been a driving force as to something I wanted

to change within my own classroom.

With the introduction of the Common Core State Standards, fact fluency begins in

kindergarten when our students enter elementary school for the first time at five years old. In the

first year of elementary school, students must be able to add and subtract within five. In first

grade, students should be able to add and subtract within 20 and with fluency to 10. By 2nd

grade students should be able to add and subtract within 20 using mental strategies, and know

from memory all sums of two one-digit numbers. By 3rd grade, students must be able to multiply

and divide within 100. The importance of fact fluency serves as a conceptual purpose that each

grade level grows and expands upon the previous grade level's content and standards. If students

do not have automatic recall of basic addition and subtraction facts, then multiplication, division,

and more complex algorithms will prove to be difficult for our students. The problem with

mastering basic math and additions facts is that these facts cannot just be memorized. Students

need time to practice skills and to see strategies and multiple ways for solving basic math facts.

The problem that I was seeing was classroom-wide fact fluency weaknesses and that many


students could not automatically recall basic addition and subtraction facts. Therefore, my

research questions are the following:

1. What are the effects of weekly timed assessments on students’ fact fluency knowledge

from 0-20?

2. Under what conditions can students fluently add and subtract within 20 using number

relationships, mental strategies, and games?

Design and Methodology

Purpose

The purpose of this study was to identify the effects of weekly timed math fact

assessments with 2nd graders and the conditions in which students can fluently add and subtract

within 20. The purpose was to observe the effects of discussing, modeling, and practicing mental

math strategies and number relationships. An additional purpose of this study was to determine

the effects that playing math and addition games has on students’ abilities to fluently add and

subtract within 20. The rationale of this study was to allow me, the teacher, more valuable

classroom instruction time to emphasize particular facts, that is, addition to 10, subtraction to 10,

mixed facts to 10, addition to 20, subtraction to 20, and mixed facts to 20. The focus had already

been selected as areas that need improvement by our 2nd grade team, and facts that students

needed to know and master before entering 3rd grade.

Setting

This study took place in a second grade class during the spring of 2015. This elementary

school is located in Suwanee, Georgia. This school is part of Georgia's largest school district,

Gwinnett County Public Schools. Gwinnett County Public Schools currently has 77 elementary


schools in addition to two new elementary schools that will open in August 2015. In 2012,

Suwanee had a population of 16,253 people. The estimated median household income for the zip

code 30024 was $77,789, which is upper-middle class. The median residential age was 36.8

years old.

Participants

Participants that were involved in this study were eighteen second grade students; two

students did not participate because they receive math instruction with a special education

resource teacher. There are eight (38%) female and twelve (57% ) male students. Five students

are Hispanic, six students are Caucasian, four students are African American, three students are

Indian, two students are Asian, and one student is Multi-racial. Two students are identified as EIP

(Early Intervention Program) and six students are identified as ESOL (English to Students of

Other Languages), two students are identified as Special Education (speech only). Three

students are in the Student Support Team process and receive extra math instruction weekly.

Research Design and Instruments Used for Data

Research Plan

As a whole school, teachers have come together to discuss the importance of fact fluency

and how each grade level grows upon the previous grade level. Second grade as a whole entity

came up with a plan for timed weekly fact fluency assessments. Most teachers have their own

way and plan of implementing timed assessments within their own classrooms. I decided that

this would be a great way to assess students’ fact fluency; However, I also decided that it was

important to re-cover and re-teach important mental strategies and number relationships. On

Monday and Wednesday of each week, I devoted 20 minutes of our math block to Number Talks


strategies and number relationships. I had students use white boards to practice using and

looking for these specific number relationships, and I used whole class discussions to talk about

what students noticed within an addition or subtraction problem. We also used daily math journal

slips that students complete for their morning work that focuses on solving word problems using

pictures, words, and numbers. On Tuesday and Thursday of each week, I devoted 20 minutes of

our math block for games and to practice skills including friendly 10, doubles, doubles plus 1,

and take away. I would specifically pair a higher-level math student with a lower-level math

student for the duration of the games. I also found many free resources on teacherspayteachers,

which included many game options. This is an online website where teachers create lesson plans,

activities, PowerPoint's, games, etc., and they can sell them for a price for other teachers to use

within their own classroom. I also found many essential addition and subtraction strategy videos

on BrainPop Jr. and LearnZillion. BrainPop Jr. provides videos and activities about certain skills

and their website includes videos for reading, writing, math, social studies, and art. This website

is also aimed at students in lower grades, kindergarten through second. LearnZillion is also a free

website where teachers have created videos and posted them online. Their website has many

videos that are connected to the state Common Core standards.

Qualitative Data

The qualitative data of this research included classroom observations of students

practicing and utilizing number relationships and mental strategies. Observations were also made

when students used their fingers or their 100's chart during the timed math assessments. Other

data included charts of classroom observations of student's problem solving during addition and

subtraction math games. Brief comments were noted and analyzed into a chart or checklist in the

appendices.


Quantitative Data

The quantitative data that was used in this research are scores from the weekly timed

math assessments. There were 6 main foci to adding and subtraction with 20; Addition to 10,

Subtraction to 10, Mixed Facts to 10, Addition to 20, Subtraction to 20, and Mixed Facts to 20.

Each assessment was composed of 40 questions and was timed for 4 minutes. The averages of

the assessments were also calculated. Students needed a copy of the assessment as well as a

pencil. The teacher needed a timer in order to time the assessment. These assessments proved to

be important data collection for groups of facts that needed remediation and enrichment

purposes.

Results

The following section includes graphs and data from each of the six timed math

assessments given on Friday of each week. There were three different copies of the same

assessment for each week, meaning students either had Test A, Test B, or Test C. This way,

students could not look at other students’ papers to copy answers. On some weeks, many students

finished before the four minutes elapsed. On other weeks, many students were unable to finish

within the four minute time frame.


Addition to 10

Subtraction to 10

Mixed facts to 10

Addition to 20

Subtraction to 20

Mixed facts to 20

0

10

20

30

40

50

60

70

80

90

100

9894.88

74.33

83.27

63.47

75.72

Weekly Timed Math Fact AssessmentsWhole Class Averages

Whole Class Averages

The above graph shows the weekly results from each timed fact fluency

assessment for the whole class average. Eighteen student scores were calculated into the

averages. Students performed the highest on addition facts to 10 and the lowest on subtraction to

20. Students also performed well on subtraction to 10, and fairly well on addition to 20. Mixed

facts appears to be the assessments where students had mediocre scores. Mixed facts had a

variety of addition and subtraction problems; therefore, students had to think about mental

strategies for both addition and subtraction.


Addition to 10

Subtraction to 10

Mixed Facts to 10

Addition to 20

Subtraction to 20

Mixed Facts to 20

0

10

20

30

40

50

60

70

80

90

100 98

58

44.5

69

46.5

52.5

Weekly Timed Math Fact Assessments ELL Averages

ELL Averages

In the above graph, the ELL (English Language Learner) assessment averages are

displayed. I have six ELL students altogether in my classroom; however, only four out of the six

ELL students participated in this research. The other two ELL students receive math instruction

with an Interrelated Resource teacher. The graph above indicates that ELL students performed

the highest on addition to 10, and the lowest on mixed facts to 10. The mixed facts assessments

also had low scores in this data analysis as well.


0

10

20

30

40

50

60

70

80

90

100100 100 96 99.33

93.33

100

Gifted Tested Student Averages

Gifted Tested Averages

The graph above shows the averages for tested Gifted students. These students

were identified in January as being referred to the Gifted program based on their CoGAT

(Cognitive Abilities Test) and ITBS (Iowa Test of Basic Skills) scores. These students also had to

take further Gifted ability assessments, motivation and creativity tests, and teacher rating scales.

Even though students may get referred to the Gifted program they do not necessarily always

qualify. There are many factors that determine if a student qualifies for the Gifted program. I had

three students in my classroom who were "flagged" for having test scores that put them into the

Gifted qualification range. However, as of April 2015, none of the three students met the

eligibility requirements. It is very apparent in this graph that these Gifted tested students

performed very well on the fact fluency assessments. One of the three students also scored 100%

on each of the six assessments. These students also finished rather quickly on all of the six


assessments, even with time left over. After analyzing these data, it is apparent that these students

could also benefit from enrichment facts with two and three digit addition and subtraction.

Addition to 10

Subtra

ction to

10

Mixed Fa

cts to

10

Addition to 20

Subtra

ction to

20

Mixed Fa

cts to

200

102030405060708090

100 91.66

52.33 52

82

42

60

Tier II/Tier III Student Support Team Student Averages

Tier II/Tier III SST Student Av-erages

This final graph displays the data from Tier II/Tier III SST (Student Support

Team) student averages. I currently have three students who are in the Student Support Team

process for extra math instruction. I also collected data on these students for progress monitoring

and whether or not they are responding to extra interventions in the classroom. At a Student

Support Team meeting, I meet with an Administrator, our school psychologist, and the student's

parents and we come together as team to discuss how the student is performing in math and what

type of interventions need to take place in order for him or her to be successful. Usually, it may

be an extra math group, or a computer program that focuses on basic math skills, etc. However,

these students are receiving additional support in the classroom and more instruction than the rest

of the class. Students in Tier II receive an extra hour of math instruction weekly; students in Tier

III receive an additional two hours of math instruction weekly. These students have been


struggling with basic addition and subtraction facts and I knew that their data would be very

important to peruse. These students performed the highest on addition to 10, and the lowest on

subtraction to 20. There were also two assessments that were very similar in the average score:

subtraction to 10 and mixed facts to 10 with an average of 52%. It would be fair to say that these

students need support with subtraction facts and strategies.

Conclusion

After 6 weeks of research, the weekly timed math assessments appeared to have mixed

findings. In particular weeks there were dramatic differences in the overall averages, and on

other weeks there were a wide variety of increases in scores. I now know upon which set of facts

students performed the highest and the lowest in the assessments. Students performed the highest

on addition facts to 10, and the lowest on subtraction to 20. I am also able to group my students

based on which facts they need more practice with, which facts could be used for enrichment

purposes, and which students are ready for more practice on two and three digit

addition/subtraction. The timed assessments have also allowed me to look at more data with my

math Tier II and Tier III students who receive extra weekly support. These findings have already

proven to be beneficial at Student Support Team meetings; for example, when a question has

risen regarding whether or not a student should move from Tier II (1 hour of extra instruction

each week) to Tier III (which is an additional 2 hours of instruction each week). The math game

portion of my research also proved to be beneficial as well. Students enjoy playing math games

involving dice, cards, and manipulatives. I believe this had a positive impact because students

appear to enjoy collaborating with their peers and communicating about games. This part of my

research has also allowed me to think about future areas of content in 2nd grade where games

could also be beneficial: measurement, time, two and three dimensional shapes, and fractions.


Focusing on number relationships and mental math strategies also had a positive impact perhaps

due to the fact that students can more frequently identify an addition or subtraction problem that

has a "friendly 10, doubles, doubles plus or minus one, etc." These were all important strategies

that were discussed and taught in the classroom.

Implications

If I decide to take no further action on timed fact fluency assessments, the data from the

assessments would not be readily available. These fact fluency assessments were graded,

graphed into student data binders, and this binder will also continue to serve a purpose in third

grade. The third grade teacher can look at these assessments to see how well students performed

or what concepts they struggled with in regards to fact fluency. If I continue to no longer use

addition and subtraction games, students would miss out on valuable time practicing skills and

collaborating mathematically with partners. It would also not be beneficial to my students to no

longer continue discussing number relationships and mental math strategies. Students need

reminders, time, and practice with solving addition and subtraction equations. They need time for

understanding and using strategies for real life problems and scenarios if we want to prepare our

student's to become 21st century learners.

Recommendations

It is recommended that teachers start reviewing basic addition and subtraction facts in

August and continue throughout the school year until the end of May. By the end of 2nd grade,

students are expected to know from memory all sums of two one-digit numbers. It is also

recommended that teachers spend applicable time teaching addition and subtraction mental math

strategies and number relationships throughout the school year. In 2nd grade, two and three digit

addition and subtraction is also introduced into the curriculum. Students need a solid


understanding of basic addition and subtraction facts in order to move onto more difficult

algorithms that may involve borrowing or regrouping. It is also recommended that teachers have

a grade level plan for fact fluency so each classroom is on board and actively involved in the

process. At my school, fact fluency has been a large focus in grades K-2. Each teacher has his or

her own way or method for what works best in the classroom, but every teacher is participating

in some type of fact fluency plan. It's also beneficial that teachers can collaborate with other

teachers within the county and to see what is working at other schools.


References

Assessing 2.OA.2. (n.d.). Retrieved March 31, 2015, from

https://grade2commoncoremath.wikispaces.hcpss.org/Assessing 2.OA.2

Baroody, Arthur J., Neet Priya Bajwa, and Michael Eiland. "Why can't Johnny remember the

basic facts?." Developmental Disabilities Research Reviews15.1 (2009): 69-79.

Bay-Williams, J. M., & Kling, G. (2014). Enriching addition and subtraction fact mastery

through games. Teaching Children Mathematics, 21(4), 238-247.

Crawford, D. B. (2002). Mastering math facts in your classroom. Eau Claire, W'I: Otter Creek

Institute.

Dowker, A. (2013). Young children's use of derived fact strategies for addition and

subtraction. Frontiers in human neuroscience, 7.

Kling, Gina. "Fluency with basic addition." Teaching Children's Mathematics18.2 (2011): 80-88.

Buchholz, L. (2004). The road to fluency and the license to Think. Teaching Children

Mathematics, 362-367.

Codding, R. S., Chan-Iannetta, L., George, S., Ferreira, K., & Volpe, R. (2011). Early number

skills: examining the effects of class-wide interventions on kindergarten

performance. School Psychology Quarterly, 26(1), 85.

Geary, D. C., Hoard, M. K., Byrd‐Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive

mechanisms underlying achievement deficits in children with mathematical learning

disability. Child development, 78(4), 1343-1359.


Houten, R. V., & Thompson, C. (1976). The effects of explicit timing on math

performance. Journal of Applied Behavior Analysis, 9(2), 227-230.

Jordan, N. C. (2007). The need for number sense. Educational leadership,65(2), 63.

Kilpatrick, J. (2001). Understanding mathematical literacy: The contribution of

research. Educational Studies in Mathematics, 47(1), 101-116.

Lerner, J. W., & Johns, B. (2011). Learning disabilities and related mild disabilities. Cengage

Learning.

Mann, Z., McLaughlin, T. F., Williams, R. L., Derby, K. M., & Everson, M. (2012). The effects

of direct instruction flashcards and rewards with math facts at school and in the home:

acquisition and maintenance. Journal of Special Education Apprenticeship, 1(2).

Math Coach. (n.d.). Retrieved March 31, 2015, from

http://schoolwires.henry.k12.ga.us/Page/21865

Miller, A. D., Hall, S. W., &Heward, W. L. (1995). Effects of sequential 1-minute time trials with

and without inter-trial feedback and self-correction on general and special education

students' fluency with math facts. Journal of Behavioral Education, 5(3), 319-345

O'Malley, P., Jenkins, S., Wesley, B., Donehower, C., Rabuck, D., & Lewis, M. E. B. (2013).

Effectiveness of using iPads to build math fluency. Online Submission.

Parrish, S. (2010). Number Talks: Helping Children Build Mental Math and Computation

Strategies, Grades K-5. Math Solutions.

Patton, J. R., Cronin, M. E., Bassett, D. S., & Koppel, A. E. (1997). A life skills approach to

mathematics instruction preparing students with learning disabilities for the real-life math

demands of adulthood. Journal of Learning Disabilities, 30(2), 178-187.


Ramos-Christian, V., Schleser, R., &Varn, M. E. (2008). Math fluency: accuracy versus speed in

preoperational and concrete operational first and second grade children. Early Childhood

Education Journal, 35(6), 543-549.

Samuelson, H. (2013, January 1). Retrieved March 30, 2015, from

http://secondgradeccssmresources.blogspot.com/p/fluency-to-20.html

Suydam, M. N., Lindquist, M. M., & Smith, N. L. (1984). Helping children learn mathematics.

Prentice-Hall.

Thurber, R. S., Shinn, M. R., & Smolkowski, K. (2002). What is measured in mathematics tests?

Construct validity of curriculum-based mathematics measures. School Psychology

Review, 31(4), 498-513.

Woodward, J. (2006). Developing automaticity in multiplication facts: integrating strategy

instruction with timed practice drills. Learning Disability Quarterly, 29(4), 269-289.

2.OA.B.2. (n.d.). Retrieved March 30, 2015, from

https://www.teacherspayteachers.com/Browse/Core-Standard/2.OA.B.2


Appendix A

Student Knowledge/Application of Basic Facts (Adapted from Cotton Indian Elementary School Math Coach/Henry County

Public Schools)

4

The student mentally calculates accurately. Most/all facts are automatic. The student uses a strategy(ies) and is able to fully explain his/her thinking.

3

The student mentally calculates most examples accurately. Some/most facts are automatic. The student generally uses a strategy(ies) and when asked is able to explain his/her thinking.

2

The student mentally calculates some examples accurately. Few/Some facts are automatic. The student uses relatively inefficient strategies and has limited ability to explain his/her thinking.

1

The student mentally calculates most/all examples inaccurately. Some/No facts are automatic. The student uses inefficient strategies and has poor/no ability to explain his/her thinking.


Student Knowledge/Application of Basic Facts

Students: 1/30/15Addition

to 10

2/6/15Subtraction

to 10

2/20/15Mixed

Facts to 10

2/27/15Addition

to 20

3/6/15Subtractio

n to 20

3/13/15Mixed

Facts to 20

Student 1:Tier II speech/language 4 4 4 2 2 3

Student 2: Tier II Math/ Tier III behavior/Tier III reading

2 3 3 4 3 3

Student 3: ESOL/Tier II Math 3 3 2 2 2 2


Student 4 4 4 4 3 3 3

Student 5 3 2 1 2 2 2

Student 6 3 3 2 4 2 3

Student 7:Gifted testing 4 4 4 4 3 4

Student 8: ESOL/Tier III reading 4 3 2 1 1 1

Student 9 4 4 2 3 2 3

Student 10: Gifted testing 4 4 4 4 4 4

Student 11: IEP 4 4 4 3 3 3

Student 12 4 4 4 4 3

Student 13:ESOL/Tier III Math/ IEP

2 1 2 2 1 2

Student 14:Tier III Behavior 3 4 3 3 2 2

Student 15 3 3 2 3 2 2

Student 16: ESOL/Gifted testing 4 4 4 4 4 4

Student 17 4 4 4 4 3 4

Student 18 4 3 4 4 4 4

Table 1:

Addition & Subtraction Within 204 minute timed assessments-40 questions total

Student:1/30/15Addition to 10

2/6/15Subtraction to 10

2/20/15Mixed facts to 10

2/27/15Additionto 20

3/6/15Subtraction to 20

3/13/15Mixed facts to 20

Student 1 100% 100% 100% 48% 48% 88%

Student 2 80% 100% 93% 95% 78% 95%

Student 3 100% 27% 25% 73% 35% 30%


Student 4 100% 100% 100% 68% 83% 80%

Student 5 100% 63% 40% 83% 40% 53%

Student 6 98% 75% 68% 95% 40% 85%

Student 7 100% 100% 98% 98% 85% 100%

Student 8 100% 75% 25% 25% 43% 25%

Student 9 100% 100% 38% 93% 75% 73%

Student 10 100% 100% 100% 100% 100% 100%

Student 11 100% 90% 100% 78% 65% 38%

Student 12 95% 30% 38% 78% 13% 55%

Student 13 100% 88% 48% 93% 53% 93%

Student 14 100% 100% 90% 78% 35% 48%

Student 15 100% 100% 90% 100% 95% 100%

Student 16 98% 100% 95% 98% 60% 100%

Student 17 93% 85% 90% 98% 98% 100%

Student 18 100% 100% 100% 98% 68% 100%

Mean: 98 85.166666666667

74.333333333333

83.277777777778

61.888888888889

75.722222222222

Chart 1:

Types of Games used during research:

Dice Games: Roll & add Roll & subtract

Card Games: Tens Go Fish Subtraction War

Printable Games: Bump Scoot


Roll 3 dice in a row Roll then double, Roll then double plus 1 Roll then double subtract

1

Salute Color the sum Color the

difference

Chart 2:

Observations of Games (dice, cards, and printables)

Positive Results Negative Results

Students enjoyed playing games with a partner.

Teacher was able to pair a higher achieving students with a lower achieving student.

Students were able to practice number relationships.

Students did not want their game time to end when class time was up.

Some students were off task; talking to other partners, playing with game pieces, etc.

Not all students were collaborating or communicating with their partner consistently.

Chart 3:

Observations of Number Relationships & Mental Math Strategies

Positive Results Negative Results


Students enjoyed using doubles and doubles plus one strategies.

Students were very familiar with making a "friendly 10."

Students had multiple ways of solving an addition and subtraction problem.

Students enjoy using numbers, pictures, and words to solve addition and subtraction problems.

BrainPop Jr. &LearnZillion have an abundance of videos for 2nd graders to view.

Number Talks served as a guiding source for providing ideas for classroom discussions.

Some students appeared to be off task and not engaged when sharing math journal strips about problem solving within 20.

It was harder to find more subtraction strategies versus addition strategies.

A few students said certain strategies were "too easy" or "they already knew it."

Chart 4:

Types of Number Relationships & Mental Math strategies used during Research

Addition: Counting all Making tens Doubles Doubles plus 1

Subtraction: Compensation Counting back Thinking addition

Chart 5:

Action Research ChartSummary of Research Question and Findings

Recommended Actions

Responsibility Data Collection

Permissions Time Line Resources

What are the effects of weekly timed

Daily practice of addition and subtraction facts,

The teacher is responsible for creating

The classroom teacher will need to collect

There is no permission needed from

6 weeks was an adequate time line for

1.Number Talks by


math assessments, games, and number relationships on student's fact fluency knowledge within 20?

My study found that weekly timed assessments resulted in a mixed find. Students scored the highest on addition facts to 10 at 98% and the lowest on subtraction facts to 20 at 63.47%. The scores varied each week even though the assessment time remained the same at four minutes.

the use of Number Talks strategies, and incorporating addition and subtraction games.

Students could also be grouped according to their fact fluency knowledge; there can be a low, middle, and high group to work on remediation and enrichment facts.

classroom discussions using Number Talks strategies and for selecting appropriate problem solving strategies.

The teacher is also responsible for selecting appropriate subtraction and addition games and videos that encourage students to practice their problem solving skills.

his or her own data.

Data collection could also be used as a whole grade level.

the Principal or local school district. However, consulting with a member on the county wide math vertical alignment team or a math specialist may prove to be beneficial for gathering more research ideas and for further suggestions.

gathering data. I will continue to use mental math and number relationships by using daily math journal slips that students glue into their math journal each morning.

Addition and subtraction fact fluency assessments could also be implemented at the beginning of the school year and at the end of the school year to show growth and changes.

Sherry Parrish.

2. Dice, cards, and manipulatives for addition and subtraction games.

3. Internet access for BrainPop Jr. & LearnZillion Videos.

4. Notebook and pencil for observations

4. Copies of fact fluency assessments.

5. Timer.

ahealeyksumed.weebly.com · web viewthe purpose of this research is to identify the conditions for...

Documents