oltman's action research report

7/28/2019 Oltman's Action Research Report

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Increasing Basic Math Skills to Improve Solving Word

Problems for Seventh Graders

Anne OltmanFall 2012

University of Colorado Denver


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Introduction and Problem Statement

Keller Middle School* (KMS) hosts sixth through eighth grade students. KMStraditionally has had low standardized test scores and a low graduation rate. Many students entermiddle school math classes without knowing multiple concepts from their elementary math

classes. Also, over half the students do not read at grade level and the majority of students areEnglish Language Learners (English is not their primary language).

As a seventh grade math teacher at Keller Middle School, I realize the importance of astudents ability to recall material he/she had previously learned. I am on the math committee inmy district and we are always working to develop critical thinking skills in our students. It is myfourth year teaching and the students that remember concepts from their elementary years tend tohave better-developed critical thinking skills and are able to solve more real world mathproblems. We are trying to find a way to help students remember content they previouslylearned without taking away too much time from grade level instruction. Our intervention tohelp solve this problem is implementing the first step of The Five Easy Steps to a Balanced

Math Program.

Having taught at this school for the past three years, I inevitably brought some bias to thisresearch. In the past, I had tried giving students multiple practice problems of the same skill andthey still did not remember the steps. Even though this method is different than what I had tried,I was still skeptical. Also, this does not provide much real world application (of which I am astrong believer). Throughout my research, I was constantly aware of any potential bias so it hadlittle effect on my research.

Purpose and Intended Audience

The purpose of this research was to figure out if using the first step of The Five EasySteps to a Balanced Math Program helped 7th grade students retain concepts learned in theirelementary years in order to apply those skills to real world math problems. The first stepincludes students solving a daily warm up consisting of six problems. The six problems aredivided into categories: data, geometry, percentages, number sense, fractions, and decimals.These categories can change as needed; however, they did not change during my research. Fortwo weeks, the question in each category was similar every day. For example, in the datacategory, students answered questions daily about line graphs for two weeks. Students had tenminutes to complete the problems and then we spent five minutes going over the questions andanswers. At the end of the two weeks, students took a quiz with questions taken from those theyhad completed for the past two weeks. Our school is currently only implementing the first step

of the five step program.

Currently, students are entering high school a few grade levels below where they shouldbe in math. This makes higher math classes more difficult to pass and instead of trying to getcaught up, they get frustrated and stop trying. This means students miss out on learning basicmath skills that will help them in all areas of life.

*For privacy reasons, some names have been changed.


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The intended audience of this report will include many people in my district: the mathcommittee, principals, and other math teachers. This research will help my district decide if thisprogram should continue to be implemented in middle school math classrooms. It will also beread by peers in my research class, my professor, and the portfolio reviewers at the University ofColorado Denver.

Research Questions

The purpose of this research was to figure out if using the first step of The Five EasySteps to a Balanced Math Program will help 7th grade students retain concepts learned in theirelementary years. I expected to answer the following questions:

1. How will students performance solving real world problems be affected by theirparticipation in the first step of The Five Easy Steps to a Balanced Math Program?"

2. To what extent will the students retention of previously learned math concepts increase

by participating in the first step of "The Five Easy Steps to a Balanced Math Program?"

I originally had a third research question: To what extent will the students speed at solvingword problems in math class be affected by participating in the first step of The Five Easy Stepsto a Balanced Math Approach? After talking with math teachers at a professional development,I decided the absolute pace at which students solve word problems is not necessarily a goodmetric to be compared with their peers. Not only do students learn differently, they solveproblems at different paces. If two students solve a math problem correctly, it does not matter ifone student took twice as long to get the right answer. Therefore, I decided to remove thatquestion from my research.

Context of Study

KMS opened in the early 1950s. Originally, it had seventh through ninth gradestudents. It was not until the late 1970s that it changed to sixth through eighth grade. KMS is aTitle I school and is part of a Title I district. The entire school qualifies for free or reducedlunch. Students are also served breakfast in the classroom and, if they are part of the Boys andGirls Club, can receive dinner as well. KMS offers a gifted and talented program and bilingualeducation. There are over 600 students at KMS with an ethnic distribution as follows: 0%Asian, 6.67% African American, 77.9% Hispanic, 1.14% Native American, and 13.9%Caucasian.

As of 2010, according to the U.S. Census, 44,913 people live in the city in which KMSresides; 19.8% of the people 25 or older have bachelors degrees and the median householdincome is $56,635. In 2012, the students took the state standardized test. 33% of students wereproficient in math, 38.3% in reading, and 27.3% in writing. According to the Great SchoolsRating, KMS receives a two on a scale of ten. The graduation rate for students on time and infour years is about 65%.


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The teacher turnover rate at KMS is approximately 50% each year. The district is knownas being one of the toughest to work for in the area and many teachers avoid applying to thedistrict. The mean age of the staff at KMS is 31 and the average amount of experience is fiveyears. There are many students that have had over half of their teachers be first year teachers.Students at KMS live in a community where there is not a high value put on education.

Literature Review

I conducted a literature review because teachers need to know what research says aresuccessful instructional strategies for teaching students to solve word problems. They also needto know what the effects are of being able to utilize previously learned math concepts in problemsolving. A literature review provided research to help answer the question: How will studentsperformance solving real world problems be affected by their participation in the first step ofThe Five Easy Steps to a Balanced Math Approach?

Literature Review Questions

1. What are the best methods to help students learn how to solve word problems in math?a. How important is it that students are taught strategies to solve word problems?b. How important is it that students know their basic math facts for them to correctly

solve word problems?2. To what extent does the process of having students complete repeated practice problems help

them retain information on previously learned material?

Literature Search Procedures

My initial search began with the Auraria Library with key terms such as solving math

word problems + middle school students and importance of middle school students knowingbasic math facts. I got frustrated because I did not find anything as specific as what I washoping to locate and nothing was directly related to the research I planned on completing. So Itried using Google Scholar (not through Auraria Library), but the articles were only availablethrough purchase.

After I watched a live session held by my professor and read chapter 3 from GaryThomas, I realized I needed to change my key terms. I wanted to stay specific with basic factsand word problems but realized the literature will not be exactly like the research I planned oncompleting. I also found out that I could get free articles from Google Scholar if I went throughthe Auraria Library.

I continued my search by changing my key terms to math word problems andinstructional strategies word problems. I used the Auraria Library and Google Scholar to findall my articles. I found quite a few articles that researched the benefits of teaching variousproblem solving strategies to help students solve word problems. I went through about the first500 articles, reading titles and abstracts to choose ones I wanted to read more in depth. Afterreading about eight more in depth, I chose four to fully peruse. Of those four, I used three.


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I realized all the research I was finding dealt with teaching problem solving strategies asopposed to students knowing their basic facts to help them solve word problems. So I entered inthe key terms basic math skills and word problems, math drills, and practicing math facts.I was only able to find two articles that fit what I was looking for. Both articles were studiesdone on elementary students. Finally, I wanted to find some research based on students doing

repeated problems to retain basic facts. There was not nearly as much research on this as Ithought there would be. I found two articles which both involved elementary students.

Literature Review Findings

Teaching Problem Solving Strategies

At every grade level in math, students are given word problems to solve. In response tothe study done by Ku, This finding echoes Marshalls research (1995) that stated that wordproblems are strongly disliked by both children and adults because they find the problems aredifficult to solve even when they have adequate computational skills (Ku, Harter, Liu,

Thompson, & Cheng, 2004, p.1208). Not only do students dislike world problems, theysimply grab for numbers rather than trying to understand the nature of the problems that theyare being asked to solve (Jitendra & Kameenui, 1993, p.305). Students need strategies to helpthem approach word problems so they do not feel as intimated by them.

In a study conducted by Cohen and Stover, they looked at teaching specific strategies forcertain word problems. This study explicitly taught groups of middle school students how to useone of the following three strategies: create a diagram, cross off extraneous information, andorder the numbers in an appropriate order. These strategies were chosen based off of gifted andtalented sixth and eighth grade students rewriting math problems to be simpler. Similarly,research done by Jitendra and Kameenul focused on teaching strategies such as drawing apicture, questioning, and crossing off extraneous information. However, this research focusedmore on the use of dynamic assessment to help guide students in their problem solving and thestrategies were chosen by the teachers. Both studies found the use of problem solving strategiesincreased student performance on math word problems. These strategies are one resource forstudents to draw upon when solving a word problem.

Additionally, research was done on the effects of a problem solving strategy thatpersonalized word problems to the individual. According to Mayer (1984), personalizationseems to increase the meaningfulness or external connectedness of the problem text with existingschemata (Ku, Harter, Liu, Thompson, & Cheng, 2004, p.1196). Like the other two researchstudies on problem solving strategies, participants that had personalized word problems out-scored the students that did not. Research shows that teaching strategies helps increase studentsability to correctly solve word problems.

Teaching Basic Facts with Repetition

Woodward states, Without the ability to retrieve facts directly or automatically, studentsare likely to experience a high cognitive load as they perform a range of complex tasks (2006,p.269). The belief behind research done with automaticity of basic facts deals with students


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being able to focus on the more difficult parts of a problem; computation should be the easy part.Woodwards research found that students who were taught the process behind multiplicationincorporated with timed tests performed better on the timed tests than students who were justinstructed to memorize the facts. Likewise, research proved that a computer program that hadstudents repeatedly practice addition facts increased students automaticity of being able to recall

addition facts.

Students who are able to have these facts memorized will be able to spend more timeconcentrating on the steps of more advanced math. They will not need to worry about countingon their fingers or doing repeated addition to figure out a basic fact. The Rasch analysessuggest that the observed improvements in solving word problems should be attributed to gainsin computation skills (Schoppek & Tulis, 2010, p.247). These studies showed that repeatedpractice helped students learn their basic math facts.

Teaching Basic Facts and Problem Solving Strategies

Research has proven the need for problem solving strategies and for learning basic facts.Students need to have problem solving strategies to know what the problem is asking but theyalso need to compute correctly to get the right answer.

Research done by Powell, Fuchs, and Fuchs showed that students did just as well on acomputational test if they had only computational instruction compared to integrated instructionof computation skills and strategies for solving word problems (2010). This research shows thatstudents are able to succeed with an integrated approach. An integrated approach allowsstudents to learn strategies to set up the correct problem and to learn their basic skills to computethe right answer. Additionally, research done on a computer program called Merlins Math Millhelped determine which types of problems were in a students associative phase. This phase iswhere students know the steps to solve problems but need more practice to get to automaticity.Once again, this research showed improvement in students word problem solving abilities basedupon instruction with basic skills and word problem strategies (Schoppek & Tulis, 2010). Thesestudies show the benefit of incorporating instruction of basic facts with problem solvingstrategies to improve word problem solving.

Quality of Literature

Each article followed high standards of conducting and reporting research. All thestudies I read gave pretests and post-tests to show the difference in the knowledge of eachstudent after the implementation of instruction. Also, most of the articles I read had a controlgroup with which the research group was compared. The articles all gave background, methodsused, participants, data collection procedures, and results. Based on the specifics given in eachresearch article I read, I trusted the stated facts of what I was reading. However, I did not trustthe reliability and/or repeatability of the articles. Each article had parts that could have beenexpanded on to make the research more reliable. The articles did not give statistics on theparticipants reading abilities, how many of the participants were English Language Learners, orthe type of math instruction they previously had.


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Each of these articles had research completed on only one or two grades of students. Afew of the articles could only be done on certain grades because of the skills being researched.However, the studies that were done on teaching strategies to solve word problems could havebeen done on multiple grades. They could have looked at whether these strategies would workacross multiple grade levels. None of these studies looked at the long term effects of the

instruction. The studies did not look to see whether students retained the knowledge of the basicfacts or if they were able to use the problem solving strategies a year or two after learning them.Also, the studies often had very small sample sizes (between 6 and 71 participants).

Most of the research was completed at the elementary level. Also, the majority of theresearch focused on teaching strategies. Research proves students must be able to decode theword problem and know what it is asking in order to set up the problem. However, students alsoneed to get the problem correct. The research I found that incorporated strategies and knowingbasic facts was only done with very basic facts such as addition, subtraction, and single digitmultiplication. However, students must learn math concepts beyond these very basic facts.

Gap in Literature

I was able to find enough literature during my search but there was definitely a gap wheremy action research provides some new findings. My research addresses the question: If middleschool students have repeated practice with skills not mastered in previous grades, will theyretain the skills to complete those types of problems and be able to correctly solve more wordproblems?

Middle school math becomes much more difficult for students because they learn morenew, advanced concepts and it becomes more abstract. For example, in middle school, studentsbegin learning surface area, volume, and solving algebraic equations. . . . practicing skills inorder to automatize them is an important condition for reducing working memory load, which inturn is necessary for the construction of new conceptual knowledge (Schoppek & Tulis, 2010,p.239). My research looked at whether students were able to focus more of their brain power onthe newly learned concepts which they are asked to do in word problems if they werecomfortable with previously learned material.

Word problems become more difficult in each grade level with the way they are wordedand by the math needed to solve them. The earlier students are able to grasp the ability tocorrectly solve word problems, the better off they will be in higher math classes. My researchgives insight to secondary teachers on which instructional strategies are best to help theirstudents improve their retention of previously learned material and with solving word problems.

Methods

I followed the methods of design inquiry research. The following describes the steps Itook to collect and analyze data in order to answer my research questions.


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Site Selection and Sampling

I conducted all of my research at KMS because it is the school where I currently work. Ianalyzed the work of 100 seventh grade students. I chose my participants as the students Icurrently have because I am presently impacting their lives. I also included three other seventh

grade math teachers from my district. I chose these teachers because they are the same gradelevel and implementing the same program in a similar environment.

Data Collection Methods

In order to collect sufficient data, I conducted teacher questionnaires, gave surveys to allmy students, collected students scores on bi-weekly warm up quizzes, and collected studentsscores on two word problem quizzes. I decided on teacher questionnaires rather than interviewsbecause that is what my participants decided they wanted to do. Also, I had planned on givingfour word problem quizzes. I changed that to only two. I had a word problem quiz the weekafter the first warm up quiz and then one more a week before the fourth warm up quiz. I decided

to do this because it seemed like my students were being quizzed daily and they were missingtoo much instruction time.

Teacher Questionnaires

I conducted teacher questionnaires with three other seventh grade math teachers in mydistrict. Interviews provide opportunities for participants to describe the situation in their ownterms (Stringer, 2007, p.69). Even though I did not ask the questions in an interview format, Ibelieve a questionnaire provided the same opportunities to participants. The questionnaires gaveme insight to how their students were responding to the first step of The Five Easy Steps to aBalanced Math Program. I realized teachers are very busy and I want to respect their time. Formy participants, that meant filling out a questionnaire was best.

I asked nine questions that required my colleagues to state their opinion based onobservations of their students. Each teacher completed a consent form (found in appendix A)indicating their willingness to participate in the study. The questionnaire that each teacher filledout is in appendix C.

Surveys

I gave students surveys. The survey can be found in appendix B. I decided on surveysinstead of interviews or focus groups because I wanted to hear thoughts from all my students.Each student is unique and learns differently. Each student provided a different perspective ontheir participation in the first step of The Five Easy Steps to a Balanced Math Program.


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Quizzes

Students were given bi-weekly warm up quizzes on questions similar to the questions ontheir daily warm ups. I tracked each students scores by logging them in a spreadsheet (examplein appendix D). The students were given two word problem quizzes. One was administered a

week after the first warm up quiz and the other was given a week before the last warm up quiz.

Data Analysis Procedures

I analyzed the teacher questionnaires using a qualitative approach. First, I created anExcel table for each question with three columns (see appendix E): teacher (represented by aletter), their response, and themes. For each question, I read the responses and made a list of allthe themes. For most questions I had quite a long list of themes and had to think about how tocollapse some of them. For example, one question had the themes of giving up, frustratedbecause of computation mistakes, and took students too long. So I collapsed all of those themesinto lacking number sense. Then I gave each theme a different color and highlighted that theme

within each response. Most responses had multiple themes within them and the color codinghelped me see the themes.

For the three open-ended questions on the student survey, I used a similar approach as Iused for the teacher questionnaire. However, since I had 92 surveys to go through, I did notcreate an Excel sheet of each response. For each question, I read all the responses and made alist of the themes. Then I went back through the surveys and made a mark for each response thatfit the theme. If a response had multiple themes I made a mark for each theme represented. Forthe eight quantitative questions on the survey, I counted the number of yes responses and noresponses and created circle graphs. See appendix F.

I quantitatively analyzed the quiz results. The warm up quizzes focused on six skills butI decided to analyze three of the skills: add/subtract decimals, long division, and add/subtractfractions. Each warm up quiz had two questions for each skill. For each quiz, I recorded whichquestions students answered correctly. The word problem quizzes were given a week after thefirst warm up quiz and a week before the fourth warm up quiz. The warm up quiz had threequestions on it, one question for each skill. I recorded which questions each student answeredcorrectly.

Schedule

Milestone Completed by

Complete draft of Action Research Proposal September 18thComplete final Action Research Proposal

September 22ndCreate interview questions for teachers

Create surveys for students

Conduct interviews October 19th

Analyze interviews October 25th

Distribute surveys October 26th

Analyze surveys November 1st


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All quiz data must be recorded November 2nd

Analyze quiz dataNovember 6th

Complete draft of data analysis

Complete draft of final action research report November 27th

Complete final action research report December 1st

Checks for Rigor

Rigor in action research is based on checks to ensure that the outcomes of research aretrustworthythat they do not merely reflect the particular perspectives, biases, or worldview ofthe researcher (Stringer, 2007, p.57). In addition to the questionnaire I had three 7th grademath teachers fill out, I made sure the research was credible by talking with them on threeseparate occasions at professional development sessions. I also gave students an opportunity tovoice their opinions on the use of math warm ups. If students had questions, I asked them tocome in at lunch to discuss them.

My data is transferable because I explained the Five Steps to a Balanced Math Programin my paper and I made sure to include the teachers reasons as to why or why not this helpedstudents. My data is also more transferable because it was part of my masters degree classwhere my classmates and peers discussed and provided feedback with each part of my researchproject. My literature review will help people find reliability within my research. To ensure thedependability and conformability, I showed the results of my analysis to students. Also, Icreated graphs based upon their answers to the survey questions as well as graphs that representtheir quiz data as a whole.

Findings

How will students performance solving real world problems be affected by their participation

in the first step of The Five Easy Steps to a Balanced Math Program?"

By comparing the results of quiz 1 to the results of quiz 2, I was able to see there was anincrease of students solving word problems correctly after they participated in The Five EasySteps to a Balanced Math Program. The percentage of students solving two to three wordproblems correctly increased by 13% from the first word problem quiz to the second. The bargraph below compares the percentage of students answering zero, one, two, or three wordproblems correctly on quiz 1 and quiz 2. The graph shows that the number of students thatanswered zero word problems correctly decreased by 5% from quiz 1 to quiz 2. It also showsthat the number of students that answered three word problems correctly increased by 10% from

quiz 1 to quiz 2.


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When looking closely at which students improved on solving more word problemscorrectly, I noticed it was mostly my higher students. In response to the question on the teacher

questionnaire,Do you think this program helps students correctly solve more real worldproblems? Why or why not? one teacher said, Yes, for students who can dissect the problemenough to know what they need to do to solve the problem (what strategy or steps to use). Shebelieves if students are able to correctly set the problem up, having better computation skills willhelp the student.

In response to the same question, another teacher said, Ive been having decent successwith transferring the situations we use in the problems to other situations in life that the kids canapply to their lives. This teacher has been able to take the skill-based problems and apply themto real life situations so students can see the purpose of knowing these skills. This connectionhelps students build their own strategies for solving word problems.

The research also shows that using this program is not enough to help students improvesolving world problems. The bar graph shows that there are 65 % of students getting zero oronly one word problem correct. This is a very large percentage of students that are notimproving their word solving ability. The question, What difficulties do your students facewhen they are solving real world story problems? was asked on the teacher questionnaire. Allthree teachers listed knowing what the problem is asking. One teacher wrote, The students havea difficult time knowing what information is important and what they need to do to solve theproblems.


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The word problem results and teacher responses show that this program does not reach allstudents and there are still many students struggling with solving word problems. However thedata also shows that some students did improve while participating in this program.

To what extent will the students retention of previously learned math concepts increase by

participating in the first step of "The Five Easy Steps to a Balanced Math Program?"

This question can be answered by looking at the student surveys, warm up quiz data, and

teacher questionnaires. The students were given a survey a week before the fourth warm up

quiz. The students were asked to answer yes or no to if they believed they improved

adding/subtracting decimals, long division, and adding/subtracting fractions. The surveysshowed 100% of students believed they improved in at least one of these areas. On each warm

up quiz, students were given two questions for each of the following skills: adding/subtracting

decimals, long division, and adding/subtracting fractions.

Below is a circle graph that shows the percentage of students who believe they improved

adding/subtracting decimals. On the survey, I separated the questions into adding and

subtracting but for the circle graph I found the average from those two responses. The graph

shows that 88% of students said yes and 12% said no. The bar graph shows the comparison ofstudents correctly answering zero, one, and two questions for adding/subtracting decimals for

quiz one and quiz four. Students answering zero questions correctly decreased by 18% and

students answering two questions correct increased by 27%.


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Looking at both of these graphs, it shows that students believe they improved and, basedon the quiz results, many actually did. On the survey, many students explained the reason theybelieve they improved was because they were able to practice lining up the decimals daily. Onestudent said, Yes, because I learned you have to line up the decimals and [I am now] starting toget my answers right. However, the graphs also show that more students believe they improved

than actually did according to the fourth warm up quiz. Also, not all students believe theyimproved. One student said on the survey, Because it is kind of confusing subtracting decimals[and] knowing what to do with the decimal.


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The graphs below show the results from the survey and the data quizzes foradding/subtracting fractions. There were similar results to adding/subtracting decimals. For thisskill, 22% of students believed they did not improve and 78% of students believed they didimprove. Students answering zero questions correctly decreased by 22% and students answeringtwo questions correct increased by 36%.

The graphs below show the results from the survey and the data quizzes for long division.Students answering zero questions correctly decreased by 28% and students answering twoquestions correct increased by 21%.

These graphs show that manystudents believe the warm ups are helping them with these skills and the quiz results back upthose beliefs. The research also shows that the program did not help all students improve theirskills in these three areas because for each skill there were at least 7% of students without any

correct answers. The teachers were able to provide some insight on the questionnaires as to whythis might be.

One teacher said, Most of the students get to work quickly on the math review whenthey come to class. The students that struggle with math need more prompting and help instarting their review. This teacher pointed out that not all students benefit from this mathreview. They have always struggled in math and these students may not benefit from practicingthe same skill in the same way over and over. Another teacher had a similar belief that some


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students are not motivated to practice the same problems over and over. She said, Most kidswho do not fully understand concepts (specifically, decimals and fractions) and struggle toremember the rules of these operations/concepts seem to continue to get the problems wrong andmost dont appear to want to change that outcome. Theres about 30% of my kids who onproblems like top dog division, fractions, and decimals will not even start the problem until I

give them time to work together or Im standing next to them coaching or pressuring. Thesequotes show that teachers are still not convinced this program is the best for all students.

Even if this program does not help every individual, the warm up quizzes show that manystudents increased their retention of basic math skills by their participation in The Five EasySteps to a Balanced Math Program. These graphs show that for each skill, the percentage ofstudents answering zero questions decreased by at least 18% between the first and fourthquizzes. The graphs also show the number of students answering two questions correctincreased by at least 21% between the first and fourth quizzes.

Comparison of the Research to the Literature Review

The literature review showed students improved on solving word problems if they knewsome problem solving strategies to use. In response to the study done by Ku, This findingechoes Marshalls research (1995) that stated that word problems are strongly disliked by bothchildren and adults because they find the problems are difficult to solve even when they haveadequate computational skills (Ku, Harter, Liu, Thompson, & Cheng, 2004, p.1208). Theresearch findings support this because most of the students that increased their word problemsolving were my higher students. These are the students who I know have more mathematicalthinking and problem solving strategies to pull from.

The literature review also discussed that just teaching computational skills will help

students solve word problems. The Rasch analyses suggest that the observed improvements insolving word problems should be attributed to gains in computation skills (Schoppek & Tulis,2010, p.247). The research shows students improved solving word problems based on justcomputational instruction. However, the research only shows 13% of students increasing fromgetting zero or one problems right to correctly solving two or three problems. This is a smallpercentage of students that I do not believe contributes to the idea that just teachingcomputational skills will improve correctly solving word problems.

A difference between the findings in the literature review and the research findings dealswith students remembering basic math facts from repetition. Woodwards research found thatstudents who were taught the process behind multiplication incorporated with timed tests

perform better on the timed tests than students just instructed to memorize the facts (2006). Mystudents were taught the process behind each of these basic skills in elementary school and in 6thgrade. However, after repetition of practicing these skills, 100% of the students believed theyimproved on at least one of the skills. Another important difference is that this research wasconducted at a middle school rather than an elementary school.

Limitations


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The most obvious limitation was time. I was only able to collect data on four warm upquizzes and two word problem quizzes. The time limitation did not allow my research to showthe lasting impact of the math warm ups. I only gave two word problem quizzes because mystudents were being tested so often and missing too much instruction time. Time also limited meto collecting data on a smaller sample of students.

Another limitation was students moving in and out of my district. I decided to not use thedata of any of the students that moved out of the district before the fourth warm up quiz becauseI would not have final data on them. I did decide to use students that moved to my district in themiddle of my research because I would have baseline and final data for them. One morelimitation was with the word problems. I chose the word problems from a Colorado StudentAssessment Program prep book but I did not have input from other teachers on whether thesewere the best word problems for my research.

Even with the limitations, my research is still valuable because it shows baseline andfinal data for 96 students. This research was done in a Title I school where 100% of students

receive free and reduced lunch and only 34% of the students were proficient on last yearsTransitional Colorado Assessment Program (TCAP). My research was conducted on a veryspecific population and will be helpful to others working with a similar demographic set. Myresearch is valuable to all types of schools because the strategies used to help lower achievingstudents can also help higher achieving students.

Implications for Practice

The research showed a positive impact on students because for each skill, the percentageof students answering zero questions decreased by at least 18% between the first and fourthwarm up quizzes. The instruction time spent on this was fruitful for some students. However,

this type of practice does not work with all students and another intervention would need to beput in place to reach those students. Another positive impact is students confidence in solvingproblems involving long division, adding/subtracting fractions, and adding/subtracting decimals.In the survey I gave students, 100% of students believed they improved in at least one of theseskills. Along the same lines, improving students basic math skills helps students correctlyanswer more word problems if they know problem solving strategies.

The research showed this program helps students and its use should continue. However, Ibelieve something needs to change because it is not helping every student. During the 10minutes students work on this program, teachers could pull a small group to help the studentswho are still struggling.

The research has shown to help some of my students but not all of them. More researchis needed to find out the best way to help students who are still struggling with knowing basicmath skills. Also, there is a need for more research to be completed on how to help studentsincorporate basic math skills with problem solving strategies to solve word problems. Inaddition, the same research I have completed should be continued to the end of the school year.It is important to know whether the first step of The Five Easy Steps to a Balanced MathApproach helps students retain this information for a long period of time.


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Conclusion

The research responds to the gap in the literature because it showed how middle schoolstudents were affected by receiving repeated practice of basic math. The research showed thatsome students improved their computation skills and ability to solve word problems by their

participation in the first step of The Five Easy Steps to a Balanced Math Program. It alsoshowed that not all students improved in both areas because the number of students solving twoto three word problems correctly only increased by 13% from the first to the fourth wordproblem quizzes. Jitendra and Kameenui stated, students simply grab for numbers rather thantrying to understand the nature of the problems that they are being asked to solve (1993, p.305).So the first step of The Five Easy Steps to a Balanced Math Program cannot be the onlycurriculum implemented into a classroom to help students retain basic math skills and solve wordproblems correctly.

Students in my classroom rarely receive math instruction anywhere but my room. Theirparents are unable to help them at home because they may be working or do not themselves

understand seventh grade math. This means it is crucial I use every minute to help my studentsbecome better mathematicians. Finding programs that are successful will help my students bemore successful in life. The Five Easy Steps to a Balanced Math Program has shownimprovement in some of my students which means it has been beneficial. However, it is not theonly tool that my students need to be successful in math.


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References

Jitendra, A. K., & Kameenui, E. J. (1993). An Exploratory Study of Dynamic AssessmentInvolving Two Instructional Strategies on Experts and Novices' Performance in Solving Part-Whole Mathematical Word Problems.Assessment for Effective Intervention, 305-321.

Jones, T. W. (2011). A Comparative Study of Student Math Skills: Perceptions, Validation, andRecommendations.Decision Sciences Journal of Innovative Education, 379-393.

Ku, H.-Y., Harter, C. A., Liu, P.-L., Thompson, L., & Cheng, Y.-C. (2004). The effects ofindvidually personalized computer-based instructional program on solving mathematicsproblems. Computers in Human Behavior, 1196-1209.

Powell, S. R., Fuchs, L. S., & Fuchs, D. (2010). Emedding Number-Combinations PracticeWithin Word-Problem Tutoring.Intervention in School and Clinic, 22-29.

Schnorr, J. M. (1989). Practicing Math Facts on the Computer. Teacher Education and SpecialEducation: The Journal of the Teacher Education Division of the Council for ExceptionalChildren, 65-69.

Schoppek, W., & Tulis, M. (2010). Enhancing Arithmetic and Word-Problem Solving SkillsEfficiently by Individualized Computer-Assisted Practice. The Journal of Education Research,239-251.

Stringer, E. T. (2007).Action Research (3rd ed). Thousand Oaks, CA: Sage Publications, Inc.Cohen, S. A., & Stover, G. (1981). Effects of Teaching Sixth-Grade Students to Modify FormatVariables of Math Word Problems.International Reading Association, 175-200.

Woodward, J. (2006). Developed Automaticity in Multiplication Facts: Integrating StrategyInstruction with Timed Practice Drills.Learning Disability Quarterly, 269-289.


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Appendix A: Teacher Consent

Teacher Consent

Saturday, June 15, 2013

Dear _______________________,

I am conducting some action research on the first step of the Five Steps to a Balanced MathApproach. This research is a requirement for one of the graduate courses in which I haveenrolled. I am enrolled in this course and conducting this research so I can continue to help ourstudents solve real world math problems.

If you decide to participate in this study, you will be asked to participate in a one-on-oneinterview that will take around 15 minutes. There are no right or wrong answers. Yourindividual answers to the questions will not be identified or published. I am not collecting

names. You may discontinue your participation in this study at any time without penalty.

Please complete the form below to indicate your willingness to participate in the action researchproject.

Thank you for your time.

Anne Oltman

I grant my permission for the use of my ideas, work, or words in research. I understand thatevery good faith effort will be made to maintain confidentiality in any reports of this research.

___________________ (Name)___________________ (Signature)___________________ (Date)


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Appendix B: Student Survey

Survey Questions (Read Aloud to Students)

1. Do you believe you have improved converting fractions to decimals?

a. Yes b. No

2. Do you believe you have improved converting decimals to fractions?a. Yes b. No

3. Do you believe you have improved subtracting all types of fractions since completing thedaily warm-ups?

a. Yes b. No

4. Do you believe you have improved adding all types of fractions since completing thedaily warm-ups?

a. Yes b. No

5. Explain why you answered yes or no to question #4.

6. Do you believe you have improved multiplying decimals since completing the dailywarm-ups?

a. Yes b. No

7. Do you believe you have improved dividing decimals since completing the daily warm-ups?

a. Yes b. No

8. Do you believe you have improved adding decimals since completing the daily warm-ups?

a. Yes b. No

9. Do you believe you have improved subtracting decimals since completing the dailywarm-ups?

a. Yes b. No10. Explain why you answered yes or no to question #9.

11. What part of solving a word problem is most difficult?

a. Figuring out what the problem is askingb. Performing the basic math operations to solve itc. Choosing the correct method to solve itd. Reading the problem

12. Do you believe the daily math warm-ups have improved your ability to do well in mathclass? Why or why not?


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Appendix C: Teacher Questionnaire

1. What difficulties do your students face when they are solving real world story problems?2. How does it affect your students learning seventh grade math content when they do not

remember concepts learned in previous years?

3. When we were introduced to the first step of the Five Easy Steps to a Balanced MathProgram, what were your thoughts in regards to the affect it would have on studentsmath ability?

4. Please describe your students behavior when they are working on the warm up problems.5. Please describe your students behavior when you go over the answers to the warm up

problems.6. Do you think this program is helping students better retain previously learned material?

Why or why not?7. Do you think this program allows students to more quickly solve word problems? Why

or why not?8. Do you think this program helps students correctly solve more real world problems?

Why or why not?9. Will you continue using this program in your classroom? Why or why not?


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Appendix D: Quiz Tracking Excel Spreadsheets

Spreadsheet for recording Warm Up Quiz scores. Each class and warm up quiz was filled outseparately on one of these.

StudentName

Add/subtractdecimals


LongDivision

LongDivision

Add/subtractfractions


Spreadsheet for recording Word Problem quizzes.

StudentName


LongDivision



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Appendix E: Analyzing Teacher Questionnaire

1. What difficulties do your students face when they are solving realworld story problems?

Teach

er

Response Theme

A The students have a difficult time knowing whatinformation is important and what they need todo to solve the problems. Some of the studentshave difficulty reading the problem.

ImportantInformationWhat problem isasking them todo/choosing astrategyReading problem

B Figuring out what the problem is truly asking,what operations to do within the problem,

occasionally what information is important andwhat is just filler.

ImportantInformation

What problem isasking them todo/choosing astrategyChoosing theoperations

C Two difficulties our students face aredetermining what the problem is asking them todoand choosing a strategy to use to solve (orlacking strategies to use). Students do notdetermine the question first to see whichinformation is necessary for the problem. Oftentimes they automatically think they take allnumbers given in the problem and either add,subtract, multiply, or divide them, instead oftruly thinking about the question and the bestway to solve the problem. They do not have atoolbox of problem solving strategies that theycan choose from. Another difficulties is not beingable to accurately read the problem to get themeaning of the text.

ImportantInformationWhat problem isasking them todo/choosing astrategyReading problemChoosing theoperations

ImportantInformationWhat problem isasking them todo/choosing astrategyReading problem


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Choosing theoperations


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2. How does it affect your students learning seventh grade math contentwhen they do not remember concepts learned in previous years?

Teacher

Response Theme

A Many of my students do not have number sense

which is important when students are learningseventh grade concepts. For example, theyneed to use these skills when solving forproportions, finding surface area and volume andsolving equations. I need to go back and reviewthose skills for the students who dont rememberwhich takes time.

Lacking number

sense (stop/giveuplong time tosolvecomputationmistakes)Instruction Time

B A good portion of my students can understandand grasp higher level/7th grade concepts butnot knowing concepts or having basic

computation skills from previous years eithermakes them stop/give up, take an incredibly longtime to solve basic problems, or makecomputation mistakes which lead to wronganswers.

Lacking numbersense (stop/giveuplong time to

solvecomputationmistakes)

C Seventh grade content builds upon and is anextension of what students learn in previousyears. When they lack concepts, I often have totake instruction time to re-teach the studentswhat they have previously learned so that they

have a basis for 7th grade concepts. This takesaway classroom time from 7th grade standards,and often forces us to rush concepts thatstudents need to have a lot of exposure to.

Instruction Time

Lacking numbersense (stop/giveuplong time tosolvecomputationmistakes)Instruction Time

3. When we were introduced to the first step of the Five Easy Steps to aBalanced Math Program, what were your thoughts in regards to theaffect it would have on students math ability?

Teacher

Response Theme


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A After I read about the Math Review, I was veryexcited and was hopefulthat it would help thestudents retain the concepts they did notremember from the previous years.

Retain conceptsHopeful/excited/helpful

B I thought it would be incredibly helpful;frommy experience last year a lot of our studentsdo struggle with retention, especially withbasic rules (fractions, decimals). I thoughthaving a time and space to work on these sortsof problems would give them the opportunityto recall those skills and master or re-masterthem.


C My hope was that it would improve their mathability because it is a review of previouslylearned concepts. It is designed as a way to

incorporate spiral review into class to keepstudents thinking about lots of differentconcepts and keep them fresh in their minds.



4. Please describe your students behavior when they are working on thewarm up problems.

Teacher

Response Theme

A Most of the students get to work quickly on theMath Review when they come to class.Thestudents that struggle with math need moreprompting and help in starting their Review. Butafter a few days in the 2 week cycle, they aremore apt to try the problems on their own sincethey have examples on how to solve theproblems.

Start quickly andmotivated tofinish allproblemsStrugglingstudents needmore prompting

B Most work well throughout the problems. Theycan get most done by themselves and then check

answers and thoughts with neighbors.There aremaybe 10 20% of kids who will not try anythingbecause theyve gotten them wrong for so longthat they dont give much effort when working onthe same problems now.

Start quickly andmotivated to

finish allproblemsStrugglingstudents needmore promptingCheck Answers


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C There are a lot of different behaviors, which havechanged throughout the year so far. In thebeginning most students were talkative, but stillanswered all of the questions because a lot of theproblems were very easy for them. After doing

the math review for a few weeks, most started toget bored and I had a lot of students who had adifficult time completing their problems becausethey were talking too much, playing, day-dreaming, etc. Now that we have been doing themath review for a few weeks, students have avariety of behaviors. Motivated students get theproblems completed and were causing otherproblems, which is why we started doingchallenge problems or encouraging students toread if they finished early. A majority of the

students realized that it is impacting their gradesand started trying all of the problems again (thiswas also the case when I pointed out these are5th and 6th grade problems). Some studentswork when I am circling the room and stampingpapers that are complete andother times aredistracted or are being distracting (talking,playing, drawing, etc.). Students who have adifficult time focusing are typically talking ordoing other things to avoid the work.

Start quickly andmotivated tofinish allproblemsStruggling

students needmore promptingTalkative

Start quickly and

motivated tofinish allproblemsStrugglingstudents needmore promptingTalkativeCheck Answers

5. Please describe your students behavior when you go over the answers

to the warm up problems.Teacher

Response Theme

A We review the answers to the Math Reviewproblems as a class. The students areinvolved by explaining the problems to theclass or showing how to do the problems onthe Smart board. I usually ask the students

Studentsdemonstrating/explainingImmediate response(excitement, why?)


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which problems they answered correctly andthe students are excited when they are right.

B Almost all of my students have an immediatereaction. I hear things like I told you so,

Oooooh, I get it now, I still dontunderstand that, why are you doing it likethat.

Immediate response(excitement, why?)

C I ask students to explain the answers to theclass. The student who gets to explain is veryexcited and wants to share. Most studentsare either trying to talk to neighbors, sittingquietly (day dreaming or drawing), or shoutout the answer. All students check their work(not always when the problem is beingexplained), which is good, but causes other

issues, such as students shouting out to askwhy their answer is incorrect.

Studentsdemonstrating/explainingImmediate response(excitement, why?)Talking to neighborsChecking work

Studentsdemonstrating/explainingImmediate response(excitement, why?)Talking to neighborsChecking work

6. Do you think this program is helping students better retain previouslylearned material? Why or why not?

Teacher

Response Theme

A Since we are continually reviewing the skills thatthe students struggle with and have a difficulttime remembering, I feel this program is helpingthe students to be successful and have a positiveexperience with math.

Reviewing withrepetition skillsstudents strugglewithHelps studentsbe successfulwith math

B Yes and no. I think the extra practice really doeshelp some students who are aware of their gapsin their math learning and want to fill them, butId say that is the minority of my kids.Most kidswho do not fully understand concepts (decimalsand fractions specifically) and struggle to

Reviewing withrepetition skillsstudents strugglewithHelps studentsbe successful


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remember the rules of these operations/conceptsseem to continue to get the problems wrong andmost dont appear to want to change thatoutcome. Theres about 30% of my kids who onproblems like top dog division, fractions and

decimals will not even start the problem until Igive them time to work together or Im standingnext to them coaching or pressuring.

with mathUnmotivatedstudents are notimprovingNot sure

C I think so, but I think it is also too early to give asolid answer. I think the program helps becauseit is a spiral review of different concepts, but in away that allows students to get repetition insolving problems (doing the same types ofproblems each day, but still mixed concepts).They know their scores and which problems theystruggle with, and I ask them to set goals for

their quizzes each week so they are working toremember the concepts.Tracking data, thepercents of students getting problems correcthas increased in each category. It has no impacton students who are not working and they thinkit is a time to play. Im hesitant to say yesthough because the real question will be whenwe truly test them on a variety of different skills(for example all operations with mixed numbers)and not one specific skill (such asadding/subtracting mixed numbers).

Reviewing withrepetition skillsstudents strugglewithHelps studentsbe successfulwith mathUnmotivated

students are notimprovingNot sure

Reviewing withrepetition skillsstudents strugglewithHelps studentsbe successfulwith mathUnmotivatedstudents are notimprovingNot sure

7. Do you think this program allows students to more quickly solve wordproblems? Why or why not?

Teacher

Response Theme


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A I am not sure if this is helping students solveword problems more quicklysince they strugglewith how to start and set up the word problem.But we are working on this issue, also. After thestudents decide how to solve the problem, the

students are remembering what they worked onin the Review and are able to solve the problemsquicker.

Not sureStruggle withsetting up theproblemSolve

computationfaster

B Yes and no again.I think it helps withcomputational skills on some level, especiallythose who see it as a tool to help them fill gaps,but I think a lot of our students problems withword problems is finding what the question istruly asking and how to manipulate the numbersin the problem to get that answer. I dont believe

the Math Review process helps that in any way.

Not sureStruggle withsetting up theproblemSolvecomputationfaster

C In theory, yes,because if students can solvebasic computation faster, which is a lot of whatmath review is, then they can do thecomputation of a word problem faster. Mystudents have the barrier of reading theproblem, understanding what it is about, andpicking a strategy that restricts many studentsfrom getting to the computing part.

Not sureStruggle withsetting up theproblemSolvecomputationfaster

Not sure

Struggle withsetting up theproblemSolvecomputationfaster

8. Do you think this program helps students correctly solve more realworld problems? Why or why not?

Teacher

Response Theme

A I feel that the Math Review is helping thestudents solve the real world problems correctlybecause we are continually using the numbersense skill throughout every class period multipletimes.

Yes-Usingnumber sensedaily

B Almost the same answer as above, though I did Yes and No-some


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like the data section since kids seemed to besuccessful at it and it could spark decentconversations about real world things. I think thepercent problems weve been working with helpwith real world situations too. Ive been having

decent success with transferring the situationswe use in the problems to other situations in lifethat the kids can apply to their lives. (spending5/7 days in school what percentage of the weekare you in school)

problems

C Yes, for students who can dissect the problemenough to know what they need to do to solvethe problem (what strategy or steps to use).

Yes-if they canset up problemcorrectlyYes-Usingnumber sensedaily

Yes and No-someproblemsYes-if they canset up problemcorrectly

9. Will you continue using this program in your classroom? Why or whynot?

Teacher

Response Theme

A I will continue using the Math Review during my

classroom this year andthen I will look at thedata and see how the Math Review has impactedmy students. As I have reviewed the data so farthis year, the students have been improving withtheir math skills so the program is working withmy students and I will continue to use thisprogram next year. We will also have theworksheets and quizzes created this year andwill be able to improve them for next year.

Yes

Review dataMore deliberateplanning

B I think so. Im happy with the changes were

making, I think if we progress towards moredeliberate planning and delivery of certain topicslike ACMS it will look more useful in my own mindand I might work harder at certain topics. I dontthink it can stand alone though, we do need tohave those anchor charts in our room and dowhat we can to incorporate these concepts intoreal world and word problems were using in

Yes

Review dataMore deliberateplanningIncorporate skillsinto classroomcontent


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class,but I like the stability of it, and it doesseem to be slowly helping a larger group ofstudents. It might be helping too that I keepreiterating that these are 6th grade skills and itseems like most of our students WANT to be at a

7th grade level, they just dont know how to andwill hopefully start taking it a bit more seriously.C Yes: partially because we have to, but also

because I think we need a longer time period tosee if it is truly impacting our students in apositive way.

YesReview data

YesReview dataMore deliberateplanningIncorporate skills

into classroomcontent


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Appendix F: Student Survey questions

Explain why you answered yes or no to question #4. Question #4 stated, Do you believe youhave improved adding all types of fractions since completing the daily warm ups?


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Theme Number of responses Quotes

Daily practice 1111111111111111111111(22)

I have improved on addingbecause I do it every day so Iremember.I answered yes because theextra practice helps meimprove on the steps. It alsohelps me because I get thingscorrect because of the extrapractice.I gives me good practiceevery day so now Im gotbetter.

Practice at home 11111(5) I have improved adding alltypes of fractions sincecompleting the daily warm upsbecause I practice at home.

Getting them all right/its easy 111111111111 (12)

Following the steps 1111111111111111111(19) I believe Ive improvedadding fractions because Ilook in my notes and I knowthe steps.

Go over answers/Askquestions after

111111111(9) I answered yes because whenwe answer the problem andthen we go over it we startunderstanding how to do theproblems.

Still dont understand/Getconfused 111111111111 (12) I have not improved addingfractions because Im stillweak on that subject and cantdo it rightI have not improved becauseI dont understandI sometimes dont get it. Iam still confused about thesteps/processesI answered no because I dontunderstand math that very welland I get mixed up

Student noticed he improved 1111111111 (10) I answered yes because I sawon my tracking sheet and I gotthem wrong and I haventlately

Paid attention/didnt knowhow to do it before/trying hard

111111 (6) I answered yes to number 4because I had bad grades in 6grade because I did notunderstand it and know I feelthat I can solve fractions.I said yes because I practiceevery day and I try reallyhard

Dont pay attention 1 (1)


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Explain why you answered yes or no to question #9. Question #9 stated, Do you believe youhave improved subtracting decimals since completing the daily warm ups?


Know to line up thedecimals

1111111111111111111111111(25)

I answered yes because Ilearned how to line them upYes, because I learned youhave to line up the decimalsand starting to get myanswers rightI answered yes because Ilearned better how to set itup properly


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Daily practice 11111111111111111(17) I picked yes on #9 becausethe practice we have beendoing helped me understandmoreI picked yes because all the

extra practice has gotten mefaster and I gotten better

Study 111(3) I said yes to question #9because I go home and studyblue notes so I start tounderstand

Just like subtracting wholenumbers

111(3) I answered yes on #9because subtracting decimalis exactly like subtractingregular number

Notice improvement 11111 (5) I believe I have improved

subtracting decimalsbecause I have done betterthan I did before.

Easy to do/get right answers 111111111111 (12) I have been improvingbecause Im really good atit

Go over answers 11111(5) Yes I have improvedbecause by going over ithelps meYes because we go overthem and check what I did

wrongGet confused (forget to lineup decimals, get a lot wrong

111111111111(12) Because it is kind of confusing subtractingdecimals of knowing what todo with the decimal.

Answered question formultiplying decimals

1(1)


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Do you believe the daily math warm ups have improved your ability to do well in math class.Why or why not?

Yes No Not Sure/Sort of

71 5 6


Never understand math 5 No I dont think the dailywarm ups help me in mathclass because some of thisstuff is hard to understand.I do not like math

Depends on the problem 6 Yes and no because itdepends on what theproblem is asking


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I improve/Know how to doit now

111111111111111111111 Yes because I learn newthings and it helps memore with math learningYes because I have gottenbetter

I think it does helpbecause you can see if youimprove or not

Give me practice 1111111111111111111111111111111111

Yes because we havepractice and we get betterthroughout the day becausewe wake up at mathbecause we practiceyes because its a goodway to practiceI think the daily warm ups

have improved my abilityin math because I get morepracticeYes because its givingme a chance to practiceYes because its prettymuch all practice

Better math grade this year 1111111111 Yes because last year Ihad an F in math and thisyear I have a B

Going over answers 11111111 Yes because it shows me

steps when we go over it

oltman's action research report

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