Problem Solving Strategies: Intro

By: Autumn Portillo

Letter to Student

This course in intended for the mathematical class that may differ from other math classes you've encountered. In this course you'll be asked to solve some equations, but mostly you'll be asked to think about problems, solve them, then write about your solutions. You may know some students, who have gotten through math classes without understanding the material, but that will not happen in this course. My goal for you is that when you finish this course, you are able to understand the mathematical you are doing and explain your reasoning in writing or to other students. This course is based on the idea that you'll learn the strategies people in the real world use to solve problems. You will develop specific in the real world use to solve problems. You will develop specific problem-solving strategies, communication skills, and attitudes. Learning problem-solving strategies will help you on the Scholastic Aptitude Test (SAT) and other standardized tests, which often tests problem-solving strategies skills more than the ability to solve equations. In this course you will also learn to to have fun doing equations. For centuries many people have considered challenging problems, often called puzzles or brain teasers, to be a source of entertainment. In this course you will also be asked to solve some tough problems. You will be able to solve most of them by being persistent and by talking to other people around you. When you come across an especially difficult problem, don't give up. Remember the techniques you've already learned in the course, such as drawing diagrams, asking other people for help, looking at your notes, trying other approaches, and so on. You will be expected to communicate with me!


Answers to Questions That Students Usually Ask

Some people have said that America is not ready for a math course with the word dog in the title, but we think the country can handle it. This course is different from most mathematical courses, from the introduction to the final chapter. For one thing, this course is meant to be enjoyable to do. It is also meant to teach problem-solving strategies, and it incorporates research on how students best learn mathematics. This course is written to take advantage of the strength of cooperative learning and the benefits of communicating your math work with others. You've probably attended classes in which your teacher encouraged you to work with others. Your teacher used this approach because research shows that students learn more when they work together. Roughly one-third of the learning in this course will come from teacher explainations, one-third from this course, and one-third from any student on the face of this planet. In addition to working with the people around you, working through this course, and learning from your teacher, you will also be expected to communicate about your mathematical thinking. You will do this by presenting your solutions to the entire class and by writing up complete solutions to problems. You will do presentations and write-ups, because talking and writing allow you to show your thinking. These communication processes will further develop your thinking skills.

What is Problem Solving?

Problem solving has been defined as what to do when you don't know what to do. In some of your math classes, you probably learned about mathematical ideas by first working on an example and then practicing with exercises. An exercise asks you to repeat a method you learned from a similar example. A problem is usually more complex that an exercise, so it is harder to solve because you don't have a preconceived notion about how to solve it.

Some Comments on Answers

When you turn in written work, please express your answer to each problem in the form of a sentence. Don't expect the teacher to dig through your work to find your answer. Think carefully about what your answer means, and make sure that the form of the answer makes sense and is reasonable given the circumstances of the problem. For example, if the answer to a question is a certain number of people and your answer is a fraction or a decimal, think carefully about what the questions answer should be. Does it make sense to round your answer up or down, or to leave it the way it is?


For each of theses question please send me an email at the answer you get and I will email yes, or email no and why you got it wrong and explain how to get the right answer. Please do not hesitate to email me with your questions. Again please be specific with your questions. Throughout the course you will need yo use Google Documents, and Google Presentation so make sure you have those things on Google.