Make your own free website on Tripod.com
A Research Project

Devon Radant

| Home | A Research Project | Critique of Education Headlines | ASSURE | Unit of Instruction | Assessment | VFT | Developmental Trends | Curriculum Standards | Curriculum Overview

 

 

 

 

 

 

Improving Problem-Solving Skills in Third Grade Mathematics

 

 

 

 

 

 

 

 

by

Devon L. Radant

ETL Cluster 12

 

 

 

 

 

 

 

A Research Project Presented to

the National Graduate Teacher Education Online Program

in Partial Fulfillment of the Requirements

for the Degree of Master of Science in Education

 

 

 

 

 

 

Nova Southeastern University

2005


Chapter I: Introduction

Description of the Community

            The research project was conducted in a suburban community outside a metropolitan area in a southeastern state.  The county within which this community is located has a population of 673,345 according to the U.S. Census Bureau (2004) for the year 2000.  There are 1,359.9 persons per square mile, and the average family income is $60,537.  One out of every five residents in the county attends public school as reported in the county’s website (2004).  

Writer’s Work Setting

            The writer’s work setting is a public elementary school, one of 63 in the county.  The county school district is the largest in the state. Enrollment at the local school for the 2002-03 was 668, as reported in the school’s accountability report.  Of these 668 students, 3% received services for English Speakers of Other Languages (ESOL) and 20% were serviced in Special Education programs.  Students receiving reduced-priced lunch equaled 10% of the population.   In second through fifth grades, 27% of students qualified for the gifted program. The racial composition of the population is: 71% white, 14% black, 6% Asian, 5% Hispanic, 4% multiracial, and .1% American Indian.   The school has a good reputation in the community and within the county.            

Students’ scores on standardized tests frequently meet or exceed state standards.  On the 2002-03 Grade 4 Criterion-Referenced Competency Tests (CRCTs), 95% of fourth grade students met or exceeded state standards in the area of Reading/English Language Arts.  Students also performed well in Math with 91% of those same students meeting or exceeding state standards.  Along with standardized scores, students also perform well at the local level. 

            Each school within the county also participates in Local School Plans for Improvement (LSPIs).  The objective of this program is to set annual goals for the school as designed by administrators, teachers, and parent advisory groups.  In 2002-03, 89% of students in kindergarten through fifth grade (K-5) performed on or above grade level on Reading Standards.  On Writing Standards, 88% of students K-5 demonstrated at or above grade level ability.  And, in the area of Math Exemplars, 86% of students in K-5 showed improvement of one or more levels by the end of the year. 

            In addition, the staff and parents also add to the school’s success.  There are 53 certified teachers; 70% of those teachers have received a Master’s degree or higher.  School faculty also participates in staff development courses resulting in more than 6,000 hours. Parents support the school by logging more than 5,000 volunteer hours and taking part in more than 1,000 parent-teacher conferences.  The school also boasts 100% Parent Teacher Association (PTA) membership.

Writer’s Role

            The writer is a third-grade teacher certified in Early Childhood Education.  She works with a team of five on her grade level.  As a classroom teacher, she is responsible for teaching math, reading, spelling, writing, grammar, and science.  Students receive social studies and health education from other third-grade teachers. In addition to the regular math curriculum, the writer also teaches an Academic Knowledge and Skills (AKS) Implementation Model class in the area of mathematics. Students receive instruction on specified math skills throughout the year on one of four levels: challenge, enrichment, tutorial, or remedial.   The writer is responsible for planning and implementing instruction within her classroom and assessing student achievement.

The writer also has other roles and responsibilities at the school.  She serves as a mentor teacher to a new teacher on third grade level by advising and participating in mentor-mentee meetings and discussions.  Additionally, the writer works with a Local Leadership Team on a Literacy Committee.  She is a pal to a student with whom she meets periodically throughout the year.  The writer also takes part in various professional leadership opportunities to foster and improve learning in her classroom.

Chapter II: Study of the Problem

Problem Statement

               The problem-solving skills of third-grade
                                    mathematics students are inadequate.
Problem Description

            Third-grade students have problem-solving difficulty in mathematics. Students at this school traditionally score lower on problem-solving questions on standardized tests than in other areas of mathematics.  On the Criterion-Referenced Competency Tests administered in Spring 2004, students in first and second grade received lower scores on the problem-solving section than in the other sections of mathematics.  Seeing this trend in the lower grade levels, teachers in third-grade focus on this skill each year with the goal of improvement. 

            In addition, third-grade teachers continually voice concerns with this area of mathematics.  Teachers state that the problem-solving questions on chapter tests are the most frequently missed.  In observations made by teachers, they have reported that students often show signs of frustration in class when confronted with these types of questions.  Teachers have also noted that students with reading deficiencies often have trouble with problem-solving because most of these problems are presented in written form. 

Problem Documentation

Evidence of this problem can be seen based on students’ performance on exemplars.  On exemplars administered at the beginning of the school year, 26.1% of third-graders performed at the Novice level.  The largest number fall into the Apprentice level with 48.9%.   There were 19.6% of students demonstrating a Practitioner level of knowledge, and only 5.4% scored in the Expert range.  Of a population of 19 students:

        47% feel confident doing problem-solving

        37% have a plan for problem-solving questions

        58% feel like they have a lot of strategies to choose from when problem-solving

        21% are frustrated when they work on problem-solving

        79% believe that computation is much easier than problem-solving

        42% think they are able to express their math reasoning clearly

Relationship of the Problem to Literature

            Problem-solving in mathematics is not a new concern for educators.  This particular area has frustrated teachers and students alike in the past.  Ironically, problem-solving should come naturally to you young children because the world is new to them, and they exhibit curiosity, intelligence, and flexibility as they face new situations. However, this is not always the case.  The challenge lies in building on children's innate problem-solving inclinations with the goal of preserving and encouraging a disposition that values problem-solving.  In recent years, much has been learned about the problem-solving capabilities of elementary school children and their use of strategies in solving problems. Unfortunately though, problem solving has typically existed apart from core curriculum objectives. In many situations, it is addressed only after specific concepts and skills are taught and only then to provide practice for those concepts and skills (Trafton & Midgett, 2001).  Several leading educational institutes, however, recognize the importance of problem-solving.  In fact, the National Council of Teachers of Mathematics has recommended that problem-solving be placed at the center of mathematics education.  Problem-solving has even been called “heart of mathematics.” (Peixotto, 2000, 2).   It should continue to be a core strand of math learning for all grade levels.

            The mathematics community acknowledges the effect that problem-solving can have for students by developing higher-order thinking, promoting confidence in facing life’s challenges, and building understanding that is transferable.  Students who are good problem-solvers also display characteristics of being resourceful, willing to explore, persistent, and tolerant to frustration (Jarrett, 2000).   There is sufficient evidence that problem-solving is beneficial for students; however, most students struggle with this area of mathematics.

            This struggle results from several factors.  One such factor is the relationship between reading and problem-solving.  Many students do not possess a working mathematical vocabulary; they do not know the definitions and therefore have trouble comprehending what they are being asked to do.   In a study done by Blessman and Myszczak in 2001, they discovered that students did not know the necessary vocabulary to express their ideas in mathematics.  They also made a correlation between the lack of reading comprehension and the understanding of mathematical concepts. In a similar study, Schoenberger and Liming (2001) helped students solve multi-step problems and word problems by improving their mathematical vocabulary. Children have to combine reading, thinking, and computational skills to solve math word problems.  For many students, the major problem with word problems is the words.  Solving these problems involves many steps and requires learners to be good readers as well as proficient at thinking critically, computing, and using a process to solve problems all at the same time (Forsten, 2004).   If students know the vocabulary and can communicate mathematics effectively, then their problem solving skills will improve (Fletcher & Santoli, 2003).  Reading ability can affect a student’s ability to problem solve.

            In addition, there is evidence that rote memorization does not necessarily lead to understanding.  James Hiebert has done research over the past 20 years on problem-solving.  He believes that students learn best when they have to “[grapple] with difficult and absorbing problems” (Jarrett, 2000, 4).  Too much time in the classroom is focused on drill and practice of math facts and computation.  Teachers spend more time on memorization and recall instead of critical thinking skills and reasoning necessary for problem solving (Millard, Oaks, & Sanders, 2002).  One problem with the rote memorization that so many mathematics teachers employ is that it doesn’t allow for students to see past the surface features of problems and understand what they are being asked to solve.  Students learn by mimicking.  This mimicking may lead to success on chapter tests, but it does not lead to developing real understanding (Fletcher & Santoli, 2003). O’Brien and Moss (2004) write,

The fact is that an exclusive emphasis on rote memory and rote performance of computational procedures at a time when every desktop computer can do billions of computations in a second is downright foolish. Of course, children should learn to add, subtract, multiply, and divide, and they should do so sensibly and efficiently…[but] children today are facing a world that is shaped by increasingly complex, dynamic, and powerful systems of information in a knowledge-based economy.... Being able to interpret and work with complex systems involves important mathematical processes that are underemphasized in numerous mathematics curricula” (292).

 

 Research investigations have shown that teaching for meaning and understanding has positive effects on student learning (Grouws & Cebulla, 2000). However, many students have a lack of training and strategies necessary to successfully undertake problem-solving. 

            Because students lack training, they have no background or framework when problem solving.  Children simply do not do enough problem solving. Although they can perform mathematical operations, many do not really understand what they are doing. (Miller, 1996). When students are confronted with a problem for which they have no background knowledge to draw on or strategies to employ, they also have no confidence.  They become frustrated with the problem and give up.  Knowing that if they wait long enough, the teacher will provide the answer for them.  The goal of many teachers is for students to simply to get the right answer. They view their role as showing students the proper way to go about solving the problem. Too often, teachers rescue students in the midst of problem-solving by giving them specific hints to guide them to the answer or eventually working the problem for them (Mikusa, 1998).  This may help students get the right answer, but it won’t strengthen their problem-solving skills. 

            Furthermore, teachers have to deal with a lack of resources when it comes to problem-solving.  They have difficulty finding time to include problem-solving strategies in the math curriculum.  A cause for concern is the critical need for daily problem-solving activities in the classroom.  There is a limited amount of time in each school day, yet teachers have seemingly endless demands placed on it.  A lack of teacher training also contributes to the problem (Millard, Oaks & Sander, 2002).  Although many teachers agree that math concepts should be taught through hands-on activities and problem-solving, it’s simply not happening. Even though most elementary teachers are certified to teach all subjects, most are strongest in language arts and very few favor mathematics. Many do not like to teach math because they feel inadequate in the subject area (Shafer, 1998).  Teachers are also asked to use textbooks that might not adequately address the area of problem-solving and when it does, it is often in isolation (Millard, Oaks & Sander, 2002).  The problems are not meaningful to the students because they have no real-life connection; thus, they have no relevance.  Teachers face many obstacles in trying to teach problem-solving skills to students.

Causative Analysis

            Based on the research findings, there appear to be certain causes that contribute to the problem.  Each child is different.  What works for one child will not necessarily work for another.  With this in mind though, one can focus on the deficiencies that impact a student’s ability to problem-solve.  While several causes were stated, the insufficient problem-solving instruction in the classroom seems to be the biggest factor. 

            All of the causes given so far are included in instruction.  Students need to have a better working vocabulary of math. In the classroom, teachers need to focus on problem-solving more frequently and spend less time on “kill and drill” practices.  By providing students with instruction in this area, they will build a background and thus increase their confidence allowing them to work the problems with less frustration.  When teachers are better equipped, the quality of the instruction in their classroom will also be enhanced. 

            Based on the research findings and the opinions of educational professionals, the main cause for the inadequate problem-solving skills in third-grade mathematics students is the ineffective instruction in the classroom.

Chapter III: Anticipated Outcomes and Evaluation

Goals and Expectations

            The goal of this research project is to increase the problem-solving skills of third grade mathematics students.

            As students’ problem-solving skills improve, the work setting will be changed.  Students will become more comfortable in problem-solving situations.  They will approach these problems with more confidence and with less frustration.  With the strategies that students have learned, they will undertake problem-solving with a plan. They will be able to articulate their reasoning by using a strengthened math vocabulary.  Because of their increased understanding, students will perform better on problem-solving exemplars. 

Expected Outcomes

Of a population of 19 students:

    75% of students will increase their exemplar performance by one level

    35% of students will achieve Pracitioner level or higher

    More than 60% will feel confident doing problem-solving

    More than 50% will have a plan for problem-solving questions

    More than 70% will feel like they have a lot of strategies to chose from when problem-solving

    Less than 10% will feel frustrated when they work on problem-solving

    Less than 60% will believe that computation is much easier than problem-solving

    More than 60% will think they are able to express their math reasoning clearly

Measurement of Outcomes

            Outcomes will be measured through the use of the same exemplar that was given at the beginning of the year and from the problem-solving survey from which the baseline data were obtained. 

Chapter IV: Solution Strategy

Discussion of Solutions

            Elementary students struggle with problem-solving in mathematics.  Much has been written about how to improve this inadequacy.  One such way to improve is by stressing reading comprehension in math lessons.  Mathematical vocabulary is also essential.  Students need to have a working vocabulary in math if they are expected to be able to explain their mathematical reasoning (Fletcher & Santoli, 20003).  In addition, educators need to teach students how to read word problems. Students need explicit instruction on how to interpret the mathematical language found in word problems. The text structure, vocabulary, and purpose are unique and quite different from other types of reading.  One suggestion is for students to use graphic organizers, highlighting tape, or self-stick notes to identify key information in the problem (Forsten, 2004).  Once students better understand what the problem asks, then they can go about solving it.  

            Math problem-solving, however,  should go beyond the routine use of operations.  Instead, “problem solving should engage students in rigorous and complex tasks that require them to think, reason, communicate, and apply their understanding” (Peixotto, 2000, p.2). Computation may be required, but more important, imagination, flexibility, logic, and reasoning are needed (Holly, 1999). When using problem-solving as the center of learning, the emphasis moves from "doing" the activity to "thinking" about relationships among mathematical ideas and how they connect to help students make sense of these ideas (Trafton & Midgett, 2001). 

Additionally, classrooms should be organized in such a way that students can think and talk about their work, share ideas, and question other students.  Students must also have time to reflect on their work.  They should be encouraged to think for themselves.  Requiring students to illustrate every problem and then to use the illustration to help solve it is one possible solution. Some problems may also necessitate a written explanation of the solution (Miller, 1996).  Writing is often overlooked in the math curriculum, but it is a reflection for students. All of this leads to problem-solving success (Millard, Oaks, & Sanders, 2002). 

Another possible solution for problem-solving success is the classroom environment.  When students are able to work collaboratively, they are better able to explore a problem and therefore develop a richer understanding.  They leave feeling a sense of learning and achievement (Coad, 2003).  Students should be given the freedom to use their own approach and explore a variety of solutions.  Open-ended problem-solving is effective in promoting deep mathematical understanding (Jarrett, 2000).  Kathy Richardson argues that how a student arrives at an answer is just as important as the actual answer itself (2004).  No solutions should be given so that students will look to themselves as the mathematical authority, thereby developing the confidence to validate their work.  Students should also be encouraged to use alternative approaches in reaching their conclusions (Holly, 1999).  In classrooms that stress sense-making, reflection, and communication in problem-solving, children learn to listen to one another, respect the thinking of others, and become confident in their capabilities as mathematics students.  They develop confidence in themselves as problem solvers and become mathematical risk-takers. (Trafton & Midgett, 2001).  Teachers, then, should make the classroom environment one that encourages problem-solving and finding solutions in a variety of ways. 

            The teacher’s role is also very important in problem-solving.  Along with providing the right environment, she also needs to model positive attitudes about problem-solving so that her students can develop the same.  It is also essential for the teacher to demonstrate a lack of knowledge sometimes.  When a teacher doesn’t know the answer, she can then model the techniques of good questioning and learning behaviors that gives students an understanding of mathematical processing and the value of thinking (Millard, Oaks, & Sanders, 2002). 

            Another area that needs to be enriched is the problems themselves; they lack real-world connections.  Students retain material when it is relevant to them.  In “Going Beyond the Right Answer,” Kathy Richardson writes, “If children are going to be successful in the study of mathematics throughout their schooling, it is vital that the mathematics they learn be meaningful to them” (2004, p. 53).  The problems and tasks that are used in problem-solving are crucial. They need to be mathematically rich and appropriate for the goals of the lesson.  The use of familiar, everyday contexts enables children to connect their informal, out-of-school knowledge with school mathematics (Trafton & Midgett, 2001). Students are often asked to complete isolated problems from a specific page of text that have little or no connection to their lives.  Because many textbooks lack problem-solving questions that relate to the students, Millard, Oaks & Sanders discuss using the newspaper and/or the Internet as a source for real world problems focusing on such topics as averages, ratios, large numbers, and percentages (2002).  Students need to be able to draw on previous experiences when problem-solving. 

            Developing background knowledge will help students with problem-solving too.  Many students lack problem-solving experiences and therefore are at a disadvantage when faced with such problems.  Students needed to be provided a framework for problem solving.  Learning through problems is powerful. As students make sense of mathematics, they develop a deep, connected understanding of content and learn essential skills. This approach also causes them to develop as capable, confident problem solvers (Trafton & Midgett, 2001).

One way to accomplish this is by teaching students the steps to problem-solving.  George Polya is a famous mathematician who developed four steps to help make problem solving easier.  They are: understand the problem, plan a strategy, do the plan, and check your work (Millard, Oaks & Sanders, 2002).  Forsten (2004) also suggests using a step-by-step approach. Word problems can appear overwhelming and difficult to many students. Problem-solving can be made manageable by breaking it into a series of steps. In addition, start with easy problems and gradually increase their complexity. Teaching strategies doesn't work if they are used only now and then. Students must see the need for the strategies and have numerous opportunities to practice using them. 

            Similarly, students need to be provided with instruction on strategies that are available to use when problem-solving.  Teachers need to incorporate specific strategies for problem-solving.  They need to be introduced one at a time.  Examples of strategies employed most frequently in elementary math include:  guess and check, draw a picture, choose an operation, make a chart or table, find a pattern, and work backwards.  Even though these strategies are taught individually, students need to know that problem-solving usually requires a combination of these strategies (Millard, Oaks & Sanders, 2002).             

One final solution requires examining the teaching techniques of Japanese educators.  It is well known that Asian students in general do well in mathematics on knowledge level, conceptual, and problem-solving questions.  Some noteworthy techniques of Japanese teachers include: connecting present problems to previous problems and solutions, teacher functioning as a guide, student contributions determining the content and flow of the lesson, embedding concepts within the lesson, acting out the problem, using manipulative aids, and introducing formulaic statements at the end of a lesson in summary.  One other intriguing aspect of the lesson examined in “Mathematics as Problem Solving: A Japanese Way,” is the time spent on one problem.  Sawada cites that time must be allowed for investigating the nature of the problem, generating several solutions, discussing those solutions, and reflecting on what has been learned (1999).  According to this model, it is acceptable to spend an entire class period on only one problem.

Evaluation of Solutions

            In order to be successful problem-solvers, students need to have a working mathematical vocabulary that they can use when explaining their reasoning.  Students need the opportunity to think, talk, share, question, and even write about the problems they are solving.  Collaboration and reflection are also important practices.  Teachers need to provide both a positive environment and attitude toward problem-solving.  The problems themselves need to be relevant to the student population.  Students need both a plan and strategies for problem-solving.  It is also important for educators to look to the teaching styles of successful teachers and model them.

Selected Solutions

            Solutions for this problem will comprise:

  • Stressing mathematical vocabulary in lessons
  • Use exemplars that have real-world problems and requiring students to explain their problem-solving in a variety of ways
  • Providing weekly opportunities for students to work collaboratively
  • Modeling a positive attitude during problem-solving activities
  • Discussing and posting in the classroom the steps for problem-solving
  • Teaching a different problem-solving strategy each week (guess and check, draw a picture, choose an operation, make a chart or table, find a pattern, and work backwards)
  • Problem-solving strategies posted in the classroom as they are taught

Chapter V: Results

Results

The problem-solving skills of third-grade mathematics students are inadequate.

The following outcomes for a population of 19 students were projected for this research project. 

 

  1. 75% of students will increase their exemplar performance by one level.  This outcome was not met.  57.9% of students increased their exemplar performance by one level.

 

  1. 35% of students will achieve Practitioner level or higher.  This outcome was met.  68.4% of students achieved Practitioner level or higher.

 

3.      More than 60% will feel confident doing problem-solving.  This outcome was not met.  50% feel confident doing problem-solving.

 

4.      More than 50% will have a plan for problem-solving questions.  This outcome was not met.  22% have a plan for problem-solving questions.

 

5.      More than 70% will feel like they have a lot of strategies to chose from when problem-solving.  This outcome was not met.  61% of students feel like they have a lot of strategies to chose from when problem-solving.

 

6.      Less than 10% will feel frustrated when they work on problem-solving.  This outcome was not met.  22% feel frustrated when they work on problem-solving.

 

7.      Less than 60% will believe that computation is much easier than problem-solving.  This outcome was met.  44% believe that computation is much easier than problem-solving.

 

8.      More than 60% will think they are able to express their math reasoning clearly. This outcome was not met. 28% think they can express their math reasoning clearly.

 

Discussion

While only two out of the eight outcomes were actually met, the research could still be called successful.  On the first exemplar, only 19.6% of students demonstrated a Practitioner level of knowledge.  When given the same exemplar again after six weeks of problem-solving instruction and practice, 68.4% were achieving at the Pracitioner level.  The goal had been 35% and it was met exceedingly.  The other area where positive results can be seen in regards to outcomes is students’ views on computation versus problem-solving.  At the onset of this project, 79% of students believed that computation was much easier than problem-solving.  At the culmination of the research project, that number significantly decreased to 44%.  The anticipated outcome was 60% so this goal was surpassed as well.  While students may not “feel” that they are better problem-solvers, the data indicates otherwise.  Even though the other outcomes may not have reached their target numbers, there were small gains in other areas.  In the beginning, 47% felt confident doing problem-solving compared to 50% at the end.  Before instruction, 58% felt like they had a lot of strategies to choose from when problem-solving compared to 61% after instruction. 

Perhaps the biggest hindrance to the implementation was the interruptions in the instructional schedule.  Due to several holiday inconveniences and scheduled school breaks, the instruction was not as consistent planned.  In addition, the final exemplar and problem-solving survey were not administered until after winter break when students had been out of school for two and a half weeks.  However, as a result of the project, students were exposed to more math vocabulary, they were given weekly opportunities to problem-solve using real-life problems and able to work on them individually, with partners, and in groups.  Additionally, they have been taught the steps/plan for problem-solving and are equipped with six specific strategies to utilize when faced with word problems.  Posters of the plan and strategies were posted in the room for students to use as a reference. 

Recommendations

Consistency in incorporating problem-solving into the mathematics curriculum is key.   Give students numerous opportunities to problem-solve each week; students need lots of practice to build their confidence.  Be sure to include problems that are relevant to students and allow them to work alone, with partners, and/or in groups.   Use math vocabulary during instruction and post it in the room or have students keep a math dictionary.  Give students a plan for tackling word problems by teaching them the four steps involved: understand the problem, plan a strategy, do the plan, and check your work.  Also, make sure students understand and practice using the six strategies: guess and check, draw a picture, choose an operation, make a chart or table, find a pattern, and work backwards.  Encourage students to use pictures, words, and numbers to explain their reasoning.  Accept alternative methods for solving the problem too.  Providing students with hints may help them get the right answer now, but it won’t help their problem-solving skills; it will only foster dependence.   Finally, the teacher’s attitude is vital.  Students imitate the teacher; therefore, it is up to the teacher to display a positive attitude about problem-solving for students to emulate. 

References

Coad, J. (2003, December).  Problem-solving exercises [Electronic version].  Mathematics Teaching, 185, 39-40.

Fletcher, M. & Santoli, S. (2003).  Reading to learn concepts in mathematics: An action research project. (Research report, University of South Alabama, 2003).  Educational Resources Information Center, 4-13, ED 482 001. 

 

Forsten, C. (2004) The problem with word problems.  Principal, 84, 20-21, 23.  Retrieved June 20, 2005 from Wilson Web Database. 

Grouws, D.A., & Cebulla, K.J. (2000).  Improving student achievement in mathematics, part 1: Research findings.  ERIC Database.  (ERIC Document Reproduction Service No.  ED 463 952)

Holly, K. (1999)  So you have a problem?  Teaching Children Mathematics, 5, 410-411.  Retrieved June 20, 2005 from Wilson Web Database. 

Jarrett, D. (2000). Open-ended problem solving weaving a web of ideas.  Northwest Teacher, 1, 6-9. 

Mikusa, M.G. (1998) Problem solving is more than solving problems.  Mathematics teaching in middle school, 4, 20-25.  Retrieved June 20, 2005 from Wilson Web Database. 

Millard, E.S., Oaks, T.L., & Sanders, T.M. (2002). Improving student achievement through inclusion of problem solving in the math curriculum.  (Master’s thesis, Saint Xavier University, 2002).  Educational Resources Information Center, 11-31, ED 469 078.

Miller, E. (1996)  Learning to think through reading and mathematics.  Teaching Children Mathematics, 2, 306-07.  Retrieved June 20, 2005 from Wilson Web Database. 

O’Brien, T.C. & Moss, A.  (2004)  Real math? Phi Delta Kappan, 86, 292-96.  Retrieved June 20, 2005 from Wilson Web Database. 

Peixotto, K. (2000).  A word from the director.  Northwest Teacher, 1(1), 5.

Richardson, K. (2004) Going beyond the right answer.  Teaching PreK-8, 34, 52-53.  Retrieved June 20, 2005 from Wilson Web Database. 

Sawada, D.  (1999, September).  Mathematics as problem solving: A Japanese way [Electronic version].  Teaching Children Mathematics, 6, 54-58.

Shafer, P. (1998) Three ways to improve math scores.  Principal, 78, 24.  Retrieved June 20, 2005 from Wilson Web Database. 

Trafton, P.R. & Midgett, C.  (2001)  Learning through problems: a powerful approach to teaching mathematics.  Teaching Children Mathematics, 7, 532-36.  Retrieved June 20, 2005 from Wilson Web Database. 

 


APPENDIX

PROBLEM-SOLVING SURVEY

CALENDAR PLAN


Name___________________


 

 

 

 

 

 


I feel confident when I do problem-solving.  

 

I have a plan for solving problem-solving questions.

 

I feel like I have a lot of strategies to choose from when I problem-solve.

 

I get frustrated when I work on problem-solving.

 

Computation is much easier than problem-solving.

 

I am able to express my math reasoning clearly.  

 

 

On a scale from 1-10 (10 being the highest), I would say that I am a ____ when it comes to problem-solving.

 

 

 

 

 

 

   YES        SOMETIMES      NO

 

J

 

K

 

L

 

J

 

K

 

L

 

J

 

K

 

L

 

J

 

K

 

L

 

J

 

K

 

L

 

J

 

K

 

L

 

 

Circle one:

1   2   3   4   5   6   7   8   9  10


Calendar Plan

Week 1

        Discuss and post the steps for problem-solving in the classroom

        Teach “guess and check” strategy to students

        Post “guess and check” strategy poster

        Model positive attitude during problem-solving activities

        Stress math vocabulary in lessons

        Use an exemplar with real-world problem

        Provide students with an opportunity to work collaboratively

Week 2

        Teach “draw a picture” strategy to students

        Post “draw a picture” strategy poster

        Model positive attitude during problem-solving activities

        Stress math vocabulary in lessons

        Use an exemplar with real-world problem

        Provide students with an opportunity to work collaboratively

Week 3

        Teach “choose an operation” strategy to students

        Post “choose an operation” strategy poster

        Model positive attitude during problem-solving activities

        Stress math vocabulary in lessons

        Use an exemplar with real-world problem

        Provide students with an opportunity to work collaboratively

Week 4

        Teach “make a chart or table” strategy to students

        Post “make a chart or table” strategy poster

        Model positive attitude during problem-solving activities

        Stress math vocabulary in lessons

        Use an exemplar with real-world problem

        Provide students with an opportunity to work collaboratively

Week 5

        Teach “find a pattern” strategy to students

        Post “find a pattern” strategy poster

        Model positive attitude during problem-solving activities

        Stress math vocabulary in lessons

        Use an exemplar with real-world problem

        Provide students with an opportunity to work collaboratively

Week 6

        Teach “work backwards” strategy to students

        Post “work backwards” strategy poster

        Model positive attitude during problem-solving activities

        Stress math vocabulary in lessons

        Use an exemplar with real-world problem

        Provide students with an opportunity to work collaboratively

Week 7

        Model positive attitude during problem-solving activities

        Stress math vocabulary in lessons

        Provide students with an opportunity to work collaboratively

        Give students the problem-solving survey

        Have students complete the exemplar from the beginning of the year