Problem-Solving, Critical Thinking and Estimation Basics
On Fridays we will be working on developing students' perseverance and teamwork skills through a variety of critical thinking and problem solving activities. Problem solving activities are from John A. Van De Walde. See your notebook for individual activities. Dates and lesson titles are listed below.
Strategy and Process Goals:
· Develop problem analysis skills- to improve students’ ability to analyze an unfamiliar problem, identify wanted and needed information, ignore nonessential information, and clearly state the goal of the problem or task
· Develop and select strategies-to help students acquire a collection of problem-solving strategies that are useful in a variety of problem-solving settings and to select and use those strategies appropriately
· Justify Solutions-to improve students’ ability to assess the validity of answers
· Extend or generalize problems-to help students learn to go beyond the solution to problems; to consider results or processes applied in other situations or used to from rules or general procedures
Metacognitive Goal:
· Monitor and regulate actions-to help students develop the habit and ability to monitor and regulate their strategies and progress as they solve problems
Attitudinal Goals:
· Gain confidence and belief in abilities-to develop students’ confidence in their ability to do mathematics and to confront unfamiliar tasks
· Be willing to try and persevere-to improve students’ willingness to attempt unfamiliar problems and to develop their perseverance in solving problems without being discouraged by initial setbacks
· Enjoy doing mathematics-to help students learn to enjoy and sense personal reward in the process of thinking searching for patterns, and solving problems.
Almost every problem or activity is organized in a lesson that contains the following four parts:
- Before: Do the problem yourself!! Try to get “inside” the task or activity to see how it is done and what thinking might go on. The focus is as much on the thinking (if not more) than on the actual solution.
- Getting Ready: Make sure kids understand the task and their responsibilities, get students mentally ready to work on the task, be sure all expectations are clear.
- Students Work: The first agenda item here is to LET GO! Students need a chance to work without your constant guidance. Give them an opportunity to use their ideas and not simply follow directions. Find out how different groups are thinking, what ideas they are using, and how they are approaching the problem
- Class Discourse: Accept student solutions without evaluation. Conduct discussion as students justify and evaluate results and methods and evaluate results and methods. It’s sooooo hard, but please, DO NOT EVALUATE!
Promoting discourse:
The value of classroom discussion of ideas cannot be overemphasized. As students describe and evaluate solutions to tasks, share approaches, and make conjectures as members of a community of learners, learning will occur in ways that are impossible otherwise. Students begin to take ownership of ideas and develop a sense of power in making sense of mathematics. Students should understand when given a task that one of their responsibilities is to prepare for discussion that will occur after they have had an opportunity to work on the problem. For every task students should be able to answer the following questions:
- How did you solve the problem (What did you do to get the answer)?
- Why did you solve it this way?
- Why do you think your solution is correct and makes sense?
John A. Van De Walle Elementary and Middle School Mathematics
Dates and Lessons
September 14th
Introduction to Problem Solving Activities
September 21st
Acrobats, Grandmas, and Ivan
September 28th
Over or Under
October 5th
The Truck Problem
October 19th
Estimation Front-end Methods
October 26th
Estimation Rounding
November 2nd
Estimation Using Compatible Numbers
November 9th
Pizza-Small, Medium, and Large
November 16th
Ron's Recycle Shop
November 30th
