Creating Real-WorldProblem Solvers

Brooke PalmerJessica McFarlandJonathan WaltersVictoria Maselli

EDUC 4800Action Research ProjectGeorgia Gwinnet College

School of EducationSpring 2013

Introduction

• Need: Our project studied how exemplars can help students solve real world problems dealing with mathematics.

• Causes:– Alcova Elementary: “Alcova's goal is for every student to improve mathematical computation

and problem solving skills and math achievement.”– Jackson Elementary: “Jackson’s goal is for students to use higher order thinking and processing in

order to enhance their educational experience and demonstrate proficiency…” – Mountain Park Elementary: “Our goal is for all students at Mountain Park Elementary School to

be real-life problem solvers and critical thinkers…”– W.J. Cooper Elementary: Cooper’s goal is to “enhance math learning center ideas for students…

(which) will engage students with math manipulatives, vocabulary, and math reasoning skills,” to increase from 56.6% of students exceeding to 60% or higher exceeding in Mathematics on the CRCT.

• Solution: Best practices for solving exemplars include using a variety of relatable context, models, manipulatives, co-construction of knowledge, and explaining math thinking.

School Improvement Plans: Alcova, Cooper, Jackson, and Mountain Park Elementary Schools

• Analysis of School Improvement Plan: All of our schools have goals relating to increasing problem solving skills in mathematics.

• Topic Selection: Our research and field experience showed the increased support for solving exemplars in schools across all grade levels.

• Benefit: These new best practices promote using the strategies we teach in the classroom and integrate word problems into the curriculum. Students can benefit from this because they will know specific strategies to solving word problems and can apply them on a test or in real-life.

Description of Action Plan

•What can we do? Frameworks•Vocabulary: In order to understand what the questions is asking, students will need to know vocabulary such as, “how many more” or “how many less.” Knowing these phrases will help the student decode the problem to determine what it is asking and which steps they need to take. (Voyer, 2011).•Schema Broadening Instruction: This teaches students to identify the problem type and how to solve it while weeding out superficial features and eliminating confusion (Fuchs et. al., 2008).

Description of Action Plan

•What can we do? Frameworks•Manipulatives and Math Language Prompts: The use of concrete manipulatives and reasoning prompts in RTI for math problem solving can effectively prevent math deficiency from developing and identify students with disabilities affecting Math achievement (Fuchs et. al., 2006).•Schematic Diagrams: The use of diagrams, models, and pictorial representations has been found “to be the single most important means to assist weaker students” in learning problem solving strategies (van Klinken, 2012).

Description of Action Plan

•What can we do? Strategies• Horizontal Math: Students come up with their own math tools to use

while solving problems. The teacher can then help the students put these ideas into math symbols (Heuvel-Panhuizen, 1998).

• Writing in Math: Students can keep a math log where they explain their math ideas and their learning process for math. Also, they can keep a timeline of their new learning. (Burns, 2004).

• Assessment: The teacher can use assessments that are purposeful to the student so that they can both see what they have mastered and where they can improve (Charlesworth & Leali, 2011).

Description of Action Plan

•What can we do? The Teacher’s Role• Scaffolding Strategies: The teacher should be able to use

strategies that are tiered to the students so that they can pick up on what is being displayed. Once the students understand the basic foundations, then they can apply this to real-life situations where they solve problems by working together (Britz, 1993).• Self-monitoring: The teacher can provide prompts to the

students to help them journal what they have learned, what confuses them, or steps to solve the problem (Burns, 2004).

Relevant Literature• Bottge, B. A., Heinrichs, M., Chan, S., & Serlin, R. C. (2001). Anchoring Adolescents' Understanding of Math

Concepts in Rich Problem-Solving Environments.Remedial & Special Education, 22(5), 299.

– This article discusses a study of using problem-solving based math instruction to teach students with 504 plans or diagnosed learning disabilities. The methods and strategies chosen for instruction were not designed for remedial instruction, but were instead intentionally chosen as methods and strategies designed for regular math instruction so that the students would be guaranteed the same instruction as regular math curriculum.

• Britz, Joan (1993). Problem Solving in Early childhood Classrooms, Early Childhood and Parenting(ECAP) Collaborative, online.

– This article discuses how it is important for students to learn problem solving skills at an early age. It also informs the teacher how to plan for incorporating these skills into the classroom. There are strategies that are helpful when planning and how to make it meaningful and beneficial to the students as they are learning the skills.

• Burns, M. (2004). Writing in math. Educational Leadership, 62(2), 30-33.– This article talks mainly about how you can incorporate writing into math. I chose this as one of my

articles because one main factor in solving an exemplar is explaining your work in words. The author discusses four ways to incorporate writing into every day math activities: keep a journal or a log, solving math problems, explaining math ideas, and write about learning processes.

Relevant Literature• Charlesworth, Rosalind and Shirley A. Leali. (2012). Using Problem Solving to Assess Young Children’s

Mathematics. Early Childhood Educ. J, 39, 373-382.– This article talks about different types of assessments to use when it comes to teaching students problem solving skills.

These assessments help teachers monitor students progress as well as the teacher’s strategies used. It provides the teacher with information that is specific to individual students and how they think through math problems and other skills.

• The Education Alliance. (2006). Retrieved from Best Practices in Teaching Mathematics:http://www.educationalliance.org/files/Teaching-Mathematics.pdf

– This article gives many ideas or best practices for the following concepts: curriculum design, professional development, technology, manipulatives, instructional strategies, and assessment for math in elementary grades. Overall, this article uses research to discuss clear, recommended practices that can be used in the classroom. For example, for curriculum design, the teacher should make sure that the content is challenging and standards-based. Clearly identify skills to your students as to what they need to know.

• Fuchs, L. S., Fuchs, D., Hamlett, C. L., Hope, S. K., Hollenbeck, K. N., Capizzi, A. M., & ... Brothers, R. L.(2006). Extending Responsiveness-to-Intervention to Math Problem-Solving at Third Grade.Teaching Exceptional Children, 38(4), 59-63.

– This article describes methods used for Tier 1 and for Tier 2 interventions for Math problem solving instruction. The problem solving methods discussed include identifying what the problem is asking, identifying what kind of change (what mathematical operation) is happening in the problem, labeling important information, and deciding whether the answer makes sense.

Relevant Literature• Fuchs, L. S., Seethaler, P. M., Powell, S. R., Fuchs, D., Hamlett, C. L., & Fletcher, J. M. (2008). Effects of Preventative Tutoring on the

Mathematical Problem Solving of Third- Grade Students With Math and Reading Difficulties. Exceptional Children, 74(2), 155-173.– This article did research using students that had math and reading difficulties and held preventative tutoring sessions using

schema broadening instruction. This helped the students not only learn effective steps in how to solve problems, but also built their schemas to identify similar problems using different stories. This was far more effective than JUST teaching the three steps to breaking a story problem down. Students learned how to identify how to read the problem, figure out what it wanted, as well as understand what the problem was really asking.

• Heuvel-Panhuizen, M. (2008). Realistic Mathematics Education Work In Progress [website]. Retrieved from Lecture Notes Online Website: www.fisme.science.uu.nl.rme– This article is about a computer program that combined problem based learning using Polya’s Mathematical Problem-Solving

Process and Computer Assisted Instruction. Computer Assisted Instruction is used in this computer program because research shows that it aids in learning and increases motivation. It can be a mediator for the learning and create positive attitudes and beliefs. Computer Assisted Instruction in math can be a great way to integrate technology and mathematics that allows students to take more interest in practicing problems, because they look like a computer game.

• Huang, T.-H., Lin, Y.-C., & Chang, H.-C. (2012). Learning achievement in Solving Word-Based Mathematical Questions through a Computer-Assisted Learning System. Educational Technology & Society, 15(1), 248-259.– This article talks about Realistic Mathematics Education (RME). RME is all about taking typical math and how it is taught and

switching it up. Normally in classroom, math is taught using numbers, symbols, and theories- and then moved into word problems and In RME, application problems are given along with manipulates and other strategies to help the students ‘invent’ application, a way to solve it. This article talks about the taking math from the world of symbols and making it a human activity.

Relevant Literature• McLennan Pecaski M. D. (2011). Using Sociodrama to Help Young Chirldre Problem Solve. Early Childhood

Educ. J, 39, 407-412.– This article discusses how to use different methods through other subjects to help teach the students problem

solving skills. This strategy will help students be engaged and use verbal and cognitive skills. This strategy can also be used for all different content areas and incorporate real life issues and problems that the students will face in life at any age.

• van Klinken, E. (2012). Word problem solving: A schema approach in Year 3?. Australian PrimaryMathematics Classroom, 17(1), 3-7.

– This article used methods and strategies for real-world word problems to increase the mathematics achievement of its third grade students. The researcher discovered that students who are “weak problem solvers” can learn the skills needed for solving complex problems, such as converting word sentences into number sentences and drawing models, if the skills are explicitly taught.

• Voyer, D. (2011). PERFORMANCE IN MATHEMATICAL PROBLEM SOLVING AS A FUNCTION OF COMPREHENSION AND ARITHMETIC SKILLS. International Journal Of Science & Mathematics Education, 9(5), 1073-1092.– This article discusses the frameworks of problem solving, and begins by saying problem solving is used all the time. It

is used multiple ways and multiple times throughout a student’s life. For example, the article talks about the comprehension process, which relates to problem solving by saying that in order to problem solve, a student must understand what is going on in the problem.

Presentation of Findings/Artifacts• What did you find out as a result of research?

– Computer Assisted Learning increases motivation, attitudes and beliefs. The students can make “playful” math discoveries (Huang et. al., 2012).

– Long term use of manipulatives increases student’s attitudes, reduces math anxiety, and helps students understand the process of mathematical concepts (The Educational Alliance, 2006).

– Common best practices are teacher modeling, use of manipulatives, continuous use of rigorous math problems.

– Explicit instruction for specific math vocabulary, language demands of problem solving, and identification of critical information in word problems are essential in increasing the depth of learning and student achievement in Mathematics.

– Use of rubrics can improve Mathematics achievement by showing the student what he or she is expected to do.

Presentation of Findings/Artifacts

• What did you choose to display and why?– We chose to make a word splash to highlight the terminology

and phrases which represent the best practices most frequently recommended in our research.

– We provided anchor problems showing successful problem solving strategies used by second and third grade students.

– The purpose of the eraser puzzle is to challenge the audience members to investigate their own problem solving strategies.

– A more extensive representation of our research is displayed in a binder for those with further interest.

Feedback and Conclusions

We Learned THESE Lessons• Lessons Learned:

– We learned that the factors which determine the effectiveness of Mathematics instruction are common practices which we currently see trending in our schools.

– We will continue to increase student achievement by continuing to focus our instruction on these research-based methods.

• Meaning to Us as Educators: – One of the critical components of teacher leadership is the ability and willingness to

implement and share research-based practices with colleagues. The results of our action research project are meaningful to us because they have enabled us to share best Math practices with our schools and future colleagues.

• Things We Would Do Differently Next Time:– One thing that we would add to our project next time would be specific lesson plans

which teachers could then implement in their classrooms after viewing our research.– Our next step would be to record our own data from our classrooms to show the

effectiveness of implementing these best practices.

Executive Summary

• Need Identified: In summary, our schools wanted to improve student achievement in Mathematics, specifically through the use of vocabulary, manipulatives, and problem solving techniques.

• Artifacts Developed: (What did you present to your schools ?)• Feedback: (Summarize the reactions of other Educators)• End Result / Impact:

– The end result of our project provides research to teachers which supports their instructional decisions in the classroom.

Credit; Appreciation; ThanksBottge, B. A., Heinrichs, M., Chan, S., & Serlin, R. C. (2001). Anchoring Adolescents‘

Understanding of Math Concepts in Rich Problem-Solving Environments.Remedial & Special Education, 22(5), 299.

Britz, Joan (1993). Problem Solving in Early Childhood Classrooms, Early Childhood and Parenting (ECAP) Collaborative, online. http://ecap.crc.illinois.edu/eecearchive/digests/1993/britz93.html

Burns, M. (2004). Writing in math. Educational Leadership, 62(2), 30-33.

Charlesworth, Rosalind and Shirley A. Leali. (2012). Using Problem Solving to Assess Young Children’s Mathematics. Early Childhood Educ. J, 39, 373-382.

Credit; Appreciation; ThanksThe Education Alliance. (2006). Retrieved from Best Practices in Teaching Mathematics: http://wwBriBw.educationalliance.org/files/Teaching-Mathematics.pdf

Fuchs, L. S., Fuchs, D., Hamlett, C. L., Hope, S. K., Hollenbeck, K. N., Capizzi, A. M., & ...Brothers, R. L. (2006). Extending Responsiveness-to-Intervention to MathProblem-Solving at Third Grade. Teaching Exceptional Children, 38(4), 59-63.

Fuchs, L. S., Seethaler, P. M., Powell, S. R., Fuchs, D., Hamlett, C. L., & Fletcher, J. M. (2008). Effects of Preventative Tutoring on the Mathematical Problem Solving of Third- Grade Students With Math and Reading Difficulties.Exceptional Children, 74(2), 155-173.

Heuvel-Panhuizen, M. (2008). Realistic Mathematics Education Work In Progress [website]. Retrieved from Lecture Notes Online Website: www.fisme.science.uu.nl.rme

Credit; Appreciation; ThanksHuang, T.-H., Lin, Y.-C., & Chang, H.-C. (2012). Learning achievement in Solving Word-Based

Mathematical Questions through a Computer-Assisted Learning System. Educational Technology & Society, 15(1), 248-259.

McLennan Pecaski M. D. (2011). Using Sociodrama to Help Young Children Problem Solve. Early Childhood Educ. J, 39, 407-412.

van Klinken, E. (2012). Word problem solving: A schema approach in Year 3?.Australian Primary Mathematics Classroom, 17(1), 3-7.

Voyer, D. (2011). PERFORMANCE IN MATHEMATICAL PROBLEM SOLVING AS A FUNCTION OF COMPREHENSION AND ARITHMETIC SKILLS. International Journal Of Science & Mathematics Education, 9(5), 1073-1092.