Action Research: Effects of Number Sense and Fact Fluency in 2nd Grade

CALLIE BROUGHTONE D U 6 9 7 9 AC T I O N R E S E A R C H I N S C H O O L S E T T I N G SW I N T E R 2 0 1 5

Focus and Rationale Statement

Focus Question: Does student number sense and fact fluency increase when explicit number sense strategies are implemented in a second grade classroom?

Rationale Statement: This action research study will apply effective research-based instructional techniques to increase student number sense and math fact fluency in a second grade classroom.

Why Number Sense and Fact Fluency?

Significance for teachers and learners: -Number Sense is the foundation of mathematical understanding. -Fact Fluency is a crucial factor in primary elementary student success as it affects mathematical comprehension. -Teachers are responsible for preparing students with these core skills.

Number Sense: refers to a person’s general understanding of numbers and operations, along with the ability and inclination to use this understanding in flexible ways (Muir, 2012, p. 21)

Why Number Sense and Fact Fluency?

Potential for change or improvement: -Second grade students may improve their fact fluency based on the current standard (fluency of number equations up to 20) -Better grasp of basic number sense skills which will help in future math context and practice

Fact Fluency: answering basic math facts with efficiency, accuracy, and flexibility. It requires solving problems with automaticity and understanding.

Factors Impacting This Issue/Study:-Common Core State Standards do not match with each area of the school’s math curriculum in terms of number sense. Consideration of how to incorporate the standards and research-based strategies was necessary.

-The current math curriculum at the sample elementary school is not associated with fact fluency instruction.

-Common misconception: Memorization is not the overall goal of fact fluency.

-Number Sense is a wide-ranging mathematical focus so it was narrowed by its major components for this study.

Literature Review Findings

Researchers found that the most valid means of predicting mathematics difficulties in young children involves some of the basic principles of number sense. (Witzel, Ferguson & Mink, 2012, p. 90)

Developing automaticity with basic facts may enhance student ability to acquire and master more complex math objectives and increase the probability of students choosing to engage in math activities. (Windingstad, Skinner, Rowland, Cardin, & Fearrington, 2009, p. 365)

Research suggests students who can fluently complete math facts are better able to fluently complete advanced math tasks. (Poncy, McCallum & Schmitt, 2010, p. 917)

Literature Review Patterns:

Strong Number Sense and Fact Fluency leads to…

Retention of more

information

Performance of tasks

quickly and accurately

Higher confidence

Ability to perform

more complex tasks

Students that think of

math in flexible ways

Increased attentiveness and ability to stay on-

task for longer periods

Interest in math that could determine

future actions

When comparing dysfluent students,

fluent students experience less math-

related…

frustration

anxiety

avoidance

negative perceptions

(Poncy, McCallum & Schmitt, 2010, p. 917)

Implementation Plan

-Add a 20 minute Number Sense/ Fact Fluency block to daily math instruction time

-Use researched strategies for 11 instructional days in a row

-Monitor student progress through data collection, daily journaling, and anecdotal notes

-Use proven resources as well as teacher-made materials during math block

Math Block Implementation

Decomposition of Numbers Number Lines Number BondsMake the Next Ten

Data Collection Plan

Research Question:

Data Source 1:

Data Source 2:

Data Source 3:

What did I actually do?

Fact Fluency Baseline Assessment and End-of-Research

Assessment (same as baseline)

Weekly Exit Tickets

Student Survey based on math

fluency/skills

What changes occurred with

my priority achievement targets?

Twenty minutes of number sense

instruction at the beginning of my math block

Lesson plan editing- inclusion of

mental number lines, daily number bonds, tens frames,

etc…

Sort through surveys and exit

tickets to monitor student levels

What was the relationship between the actions taken

and changes in performance on the achievement targets?

Compare the Baseline

Assessment data with the End-of-Research Assessment to look

at score differences.

Evaluate weekly exit tickets to

gauge student performance and mastery.

Compare student survey to exit

tickets and assessment data

Student Survey ResultsMATH FACT FLUENCY RESULTS: MATH SKILLS RESULTS:

Needs Work

Feel ok about it

Feel great about it!

0% 10% 20% 30% 40% 50% 60%

Needs Work

Feel ok about it

Feel great about it!

0% 10% 20% 30% 40% 50% 60%

What did 2nd grade

students do during

the 11 research

days?

Composition and Decomposition of

Numbers by Adding or

Subtracting

Number Bonds to

break numbers apart

Equal Balancing with

Numbers

Mental and Concrete

Number Lines

Tens Frames/ Making the

Next Ten

Number Patterns and

Equal Intervals

Ways to Represent Numbers

(Place Value)

Weekly Exit Tickets

Decompostion of Numbers Practice

Decomposition Worksheets courtesy of GregTangMath.com

Number Lines to Build Spatial Relationship

Awareness

Number line practice completed during

math block

Data Analysis Findings

Number Sense:

-Class average increased from 74.6% to 86.9%

-Percentage of students with increased or same score: 85%

-1 student with mastery (100%) → 8 students with mastery

Fact Fluency:

-Class average increased slightly from 72.5% to 75.8%

-Percentage of students with increased or same score: 73%

-2 students with mastery (100%) → 3 students with mastery

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

End-of-Research Scatt erplot

Number Sense End-of-Research ResultsFact Fluency End-of-Research Data

Data Analysis

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 260

10

20

30

40

50

60

70

80

90

100

NUMBER SENSE RESULTS

Number Sense BaselineNumber Sense End-of-Research Results

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 260

10

20

30

40

50

60

70

80

90

100

FACT FLUENCY RESULTS

Fact Fluency BaselineFact Fluency End-of-Research Data

Limitations and Extraneous or Intervening Variables

-Different adults administered the Fact Fluency Assessment-More student absences occurred as an effect of mid-winter break weekend-Testing anxiety/avoidance was observed during fluency assessment-Sample group of students have access to the Reflex Math website (fact fluency resource)

Action Plan *The added math skills block caused an overall increase in student performance. However, with a limited research window, results would be solidified over a longer period of time.

-Plan to implement the researched strategies into my normal classroom routines and math instruction (no longer keep it as a separate portion of math)

-Integrate into day-to-day lessons or math workshop opening/closing -Reattempt process from the beginning of the year to the end of a school year (track results and build on methods/skills as the year progresses)

Action Plan continued

-Share Literature Review/Research summary with K-2nd grade colleagues -Offer effective strategies to build number sense and fact fluency -Confirm to 3rd-5th grade teachers the strong focus on these areas -Greg Tang's website for continuance of composition and decomposition of numbers (materials and games) -Number line use for spatial awareness

How will this research affect my current instructional

environment?

*This research project caused me to realize the large math responsibility I have with my primary elementary students. Primary teachers must ingrain strong number sense and fact fluency early on in their students’ education.

*Success in this matter will in turn benefit students in their future academic careers and will aid their perception and attitudes toward mathematics.

*This will also be beneficial to future teachers because it will stop them from having to fill basic gaps in student foundational skills.

End-of-Research

*Fact Fluency mastery does not happen "overnight." It takes persistence, consistency, and prolonged exposure and application.

*Fact Fluency is not about memorization (it is about fully knowing and understanding numbers and number relationships)

*Would appreciate my data results more if the process didn't feel so rushed. I think more time is necessary in order to know the true effectiveness of these strategies of math instruction.

*I look forward to continuing my learning!

End-of-Research