Algorithms in Everyday Math 100 - 21 78 + 54 Algorithms in Everyday Math A Parent’s Guide 54 X 36 23)893 Rina Iati South Western School District Math Coach

Top 5 things Parents Say When Helping Their Kids with Math Homework 5. “I don’t understand why your teacher is making you do it this way.” 4. “That’s the most ridiculous thing I’ve ever seen.” 3. “The old way is so much faster.” 2. “The old way worked for hundreds of years, so why are they changing it now?” 1 “That’s not how you do it. I’ll show the right way to do it.”

The Evening's Objectives Why are we changing the way we teach math? What is the purpose of teaching multiple algorithms?

What was wrong with the old way? The traditional, rote approach to teaching algorithms fosters beliefs such as: Math consists mostly of symbols on paper Following the “rules” of math is most important Math is mostly memorizing facts and rules Speed and accuracy are more important than understanding There is one right way to solve any problem Math symbols and rules have little to do with common sense, intuition or the real world.

Why Do We Need New Algorithms? Traditional math instruction isn’t working as well as we might think. our advanced calculus and AP physics students rate last in the world. (Wm. Schmidt, MSU, The Widening Achievement Gap) Our 8th grade advanced students rank in the middle of the pack in the world.(See TIMS and TIMSS-R 1996 and 1999 http://isc.bc.edu/) In one study only 60% of 10 year olds achieved mastery of subtraction using the standard “borrowing” algorithm. A Japanese study found that only 56% of third graders and 74% of fifth graders achieved mastery of this algorithm.

Why Do We Need New Algorithms? Research tells us that between 3rd and 6th grade the equivalent of one year is spent teaching long division. Yet, when 17 year olds were tested for division with a 2 digit divisor, fewer than 50% answered it correctly. Children learn to perform the steps (rules) of the algorithm without thinking about the math behind it

Over-reliance on Algorithms 900 ÷30 = __ 56 -36=___ 30) 900 56 - 36

The Value of Multiple Algorithms Problems can, and should, be solved in more than one way Studying several algorithms for an operation can help students understand the operation Providing several alternative algorithms for an operation affords flexibility Presenting several alternatives gives the message that mathematics is a creative field. The “focus algorithms” were selected because they reveal more about underlying concepts and are less likely to lead to wrong answers

If you consider the traditional instructional model to be handing the kid a shovel and making him expert in using the shovel, then the EM approach is handing the kid a fully-stocked tool shed and training him to select the most appropriate tool from the shed to apply to the math task at hand. The kid who only knows the shovel can only respond if the task is digging, but the kid who owns the tool shed can respond flexibly to any task. Bruce Harrison

Small Group Sessions Learn new algorithms/ methods Analyze the concepts reinforced in the methods Determine what “math thinking” takes place while performing these methods Discuss the advantages of new methods vs. traditional methods

It's not about the algorithm... it's about the math.