Best Practices: Problem Solving and Reasoning

Best Practices: Problem Solving and Reasoning : Best Practices: Problem Solving and Reasoning Paula McPhee Math Helping Corps 2002

Problem Solving : Problem Solving A situation that confronts an individual or group that requires resolution, and for which the individual sees not apparent or obvious means or path to obtaining a solution. (Stephen Krulik and Jesse Rudnick)

Math Reasoning : Math Reasoning The part of thinking that goes beyond the recall level. It includes basic, critical, and creative thinking. It does not include recall.

Research on Problem Solving and Reasoning : Research on Problem Solving and Reasoning 1. Math reasoning is both nurtured and natural in collaborative communities 2. Math reasoning needs to occur in real contexts 3. Reasoning and higher order thinking often yield multiple solutions 4. Young children and lower-ability students can learn and use the same reasoning strategies and higher-order thinking skills that are used by high-ability students 5. Teachers’ emphasis on specific problem solving strategies as an integral part of instruction does significantly impact their students’ problem solving performance 6. Students solving a math problem in small groups use cognitive behaviors and processes that are essentially similar to those of expert math problem solvers 7. A reasonable amount of of tension and discomfort improves the problem solving performance of students

Elements of Problem Solving and Reasoning : Elements of Problem Solving and Reasoning 1. Students need to work the 5 steps of problems solving 2. George Polya's 10 problems solving strategies 3. Math reasoning skills for problems that contain too much information or not enough information 4. Open-ended problem experience 5. Students need to see examples of actual student work so they understand rubrics and standards (“Why I did what I did.” Not “What I did.” 6. Problem solving in groups a majority of the time

What’s Out There? : What’s Out There? NCS Mentor The Exemplars The Problem Solver Problem Solving and Reasoning in the Elementary Classroom K-4 and 5-7 Math Toolkit “Minute Math” from Everyday Math Teacher to Teacher Materials Internet Sites

NCS Mentor : NCS Mentor Computer-based application for WASL questions in math, reading, and writing Advantages Students and teachers learn exactly what WASL questions look like. Sample papers are available to practice rubric grading and thus students understand what a “4” looks like. Disadvantages Many school servers have a difficult time running the program smoothly. There is a limited bank of questions. If you want to give instruction, you need an overhead projection system for the computer.

Slide8 : Advantages Math Problems for Kindergarten Rubrics and sample papers to assist in grading Problems are organized by grade level and math strand New problems come out twice a year Disadvantages Problems need to be placed on the school server (many of CD-ROM’s have been lost by individuals) The grading rubric does not align exactly with the Washington State EALR’s

Slide9 : Advantages Teaches the 10 problem solving strategies Has blackline masters for students to practice Provides solutions Disadvantages Provided problems do not include ones with superfluous information amd not enough information (does not teach reasoning) There is too much flowery language which make it difficult for students, especially ESL students, to read Too teacher directed The Problem Solver

Slide10 : Disadvantages Requires more time to understand lessons and concepts than other resources Advantages Teaches reasoning skills like superfluous information or not enough information Has open-ended Problems Provides blackline masters for students Lessons for grades 1-6

K-4 and 5-7 Toolkits : K-4 and 5-7 Toolkits Advantages Classroom-based assessments aligned with EALR’s and Kent School District SLO’s Gives a good picture of how students are doing to meet Washington State benchmarks Has activities from all math strands Includes teacher directions Good Preparation for the WASL Disadvantages Activities are not presented by grade level

Slide12 : Advantages Takes very little time Builds number sense and concepts by providing real world applications Included in Everyday Math Kits grades K-3 Disadvantages Only available for lower grades

Teacher to Teacher : Teacher to Teacher Advantages Contains warm-up activities Sample papers for assessment Aligns with Washington State EALR’s and Benchmarks Similar format to WASL Disadvantages Contains only about 15 total problems

Internet Sites : Internet Sites www.mathforum.org/pow www.pasd.wednet.edu/school/mathWASL/ www.kent.k12.wa.us/staff/pmcphee