SQ3R in the Math Classroom When will we ever use this in the real world?

Why incorporate reading techniques into math?

1. The product of three, and a number decreased by two, is forty two. Find the number 2. The product of three and a number, decreased by two is forty two. Find the number. 2. The product of 3 and a number, decreased by 2 is 42. Find the number

The Importance of Reading and Writing in the Math Classroom NCTM (2000) stated students learn math more efficiently and more deeply when reading and writing is directed at learning mathematics Students who have the opportunity, encouragement, and support for speaking, writing, reading and listening in math classes reap dual benefits: they communicate to learn math and they learn to communicate mathematically

Learn to use the language to focus on and work through problems Communicate ideas coherently and clearly Organize ideas and structure arguments Extend their thinking and knowledge to encompass other perspectives and experiences Understand their own problem solving and thinking process as well as those of others The Importance of Reading and Writing in the Math Classroom

Develops flexibility in representing and interpreting ideas Stamps information into their minds Ability to put the math concepts into their own words and understanding Modify their reading behaviors when faced with difficulty Construct meaning as they read by monitoring comprehension, evaluating new information, connecting new information with existing ideas, and organizing information in ways that make sense

SQ3R Applied to Math Associated with George Polya’s Four Steps to Problem Solving (Understand, devise plan, carry out plan, look back) 1957 In 1965 L. Fay developed the SQRQCQ for Math (survey, question, read, question, compute, question) Use this technique every time you are tackling a problem to not only demonstrate your thought process out loud but also to give the students an example of how to approach problems in a logical manner, determine what strategy to use, and construct a plan Then have students model and practice this technique on their own through group work

Survey First we need to get a general understanding or nature of the problem (you don’t have to have it solved by the time you are done reading it!) Read through the entire problem, pausing at end of each sentence so they don’t all just run together and become meaningless Identify/look up any math vocabulary or terms that you don’t understand

Question What is the main goal? What are we trying to find? Assign variable(s) to these right away When I think out loud, I try to use natural curiosity to turn the problem into a puzzle we are trying to solve (change the wording of the problem into a question) What information are we going to need to solve it? What information is actually given to us already?

Read Go back through problem and break it down into pieces: what information is given, what do you need (read actively) Make sure to use and understand proper vocabulary and math symbols How does this problem relate to the math concepts we have been using? What math will we need to use to solve it? Draw pictures, use charts - show given information and missing information in a different way

Recite/Compute analyze what we have just read, always keeping in mind what the main goal is, the variables we are using, use charts or drawings if needed Discuss the strategy of actually solving the problem (show different methods to use) put the abstract formulas and equations into your own words (very important to do because this is what the students will mimic during group work) notice any patterns to previous problems? solve the problem

Review Verbalize, verbalize, verbalize! (put the problem solving into their own words) Did we actually answer the problem and find our main goal? Does our answer make sense and is it in the correct context? Can we go back and describe the steps we took to finding the answer and how we tackled the problem? Did it compare to other problems we have done? How did we know we needed to use that math concept to solve it?

Problem Solved! Increases student’s confidence Put thought process and problem solving into their own words (sense of ownership) Leads to increased conceptual understanding, ability to retain information, and apply and demonstrate knowledge Become independent learners and use critical thinking skills

Example Problem #1 You are flying to Chicago for a trip. The flight over took three hours and you overheard the pilot saying that the average plane speed was 600 mph and there was a tailwind on the way over. You noticed while you were waiting at the gate for your return flight back, the return flight was scheduled to be five hours due to the fact that you would then be traveling against the wind. How far is your one way flight to Chicago and how did the wind affect the speed of the plane (assuming the avg plane speed stayed constant in both directions)?

You are flying to Chicago for a trip. The flight over took three hours and you overheard the pilot saying that the average plane speed was 600 mph and there was a tailwind on the way over. You noticed while you were waiting at the gate for your return flight back, that the return flight was scheduled to be 5 hours due to the fact that you would then be traveling against the wind. How far is your one way flight to Chicago and how did the wind affect the speed of the plane? DistanceRateTime Over Back

Example Problem #2 The flight to New York is 3000 miles and it takes six hours to fly there when there is no wind speed at all to affect the speed of the plane (either with the wind or without). Before you were getting ready to take off for your return flight home, you overheard the pilot say that there is a tailwind speed of 100 mph for the flight back and therefore, you should land early, assuming that the plane speed remains constant. If your flight is leaving at 11:30 (AZ time), what time should you tell your ride to expect you at the airport to pick you up?