CGI & The Common Core: A Perfect Match

CGI & The Common Core: A Perfect Match Educators Summer Symposium June 8, 2011 Sue McAdaragh

"To teach means scarcely anything more than to show how things differ from one another in their different purposes, forms, and origins...therefore, he who differentiates well teaches well." - John Amos Comenius (17th Century Educator)

Cognitively Guided Instruction Is… • A research-based way of teaching mathematics that embraces and/or encompasses the following concepts: • Problem solving in meaningful context with flexible solution strategies • Building mathematical understanding through questioning • Integration of mathematical concepts *CGI is also a Professional Development program.

CGI as Professional Development The way that teachers’ knowledge, beliefs and practices are influenced by their understanding of students’ mathematical thinking; Instruction that influences that development; Teachers’ knowledge and beliefs that influence their instructional practices;

Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

CGI* 8 Standards • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision • Look for and make use of structure. • Look for and express regularity in repeated reasoning • A research-based way of teaching mathematics that embraces and/or encompasses the following concepts: • Problem solving in meaningful context with flexible solution strategies • Building mathematical understanding through questioning • Integration of mathematical concepts

How are they alike/different?

Tools for the Common Core Standards http://commoncoretools.wordpress.com/about/ Bill McCallum, University of Arizona

Cognitively Guided Instruction

Standards for Mathematical Content • Understanding • Procedures "Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to . . . deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices."

Students with Number Sense… …understand relationships, properties, and procedures …are able to explain and justify one’s actions on numbers …are able to use strategies appropriately and efficiently

Are Our Students Ready? • Marilyn Burns and her colleagues have developed a tool to assess students’ numerical understanding and skills. • These problems and possible solution strategies were shared at NCTM in April of this year. • The following examples for designed for fifth graders. • Be thinking about how this tool could be modified for your grade level.

Which is greater-- 3/5 or 1/2? How did you decide?

Strategy Choices • Which is greater—3/5 or 1/2? • Converted to common denominators • Converted to decimals or percents • Explained that 3 is more than half of 5 • Described a visual or physical model • Gave other reasonable explanation [record] • Guessed, did not explain, or gave faulty explanation

5/6 + 12/13 • Don’t figure out the exact answer. • Without paper and pencil, decide which of these choices is closest to the answer: 1/2, 1, 2, or 8 Why do you think that?

Strategy Choices for 5/6 + 12/13 • Rounded one or both fractions to 1, then added. • Compared to ½ (e.g. both are greater than ½ so the answer is greater than 1) • Analyzed choices and chose one that seemed most reasonable. • Gave another reasonable explanation (record). • Guessed, did not explain or gave faulty explanation

1/2 + 2/3 • Without using pencil or paper, decide if the answer to this problem is greater than one or less than one. Why did you think that?

Strategy choices for 1/2 + 2/3 • Converted to common denominators • Explained that 2/3 is greater than ½ so the answer must be greater than 1 • Converted to decimals or percents • Described a visual or physical model • Gave other reasonable explanation • Guess, did not explain, or gave faulty explanation

School Bus Problem There are 295 students in the school. School buses hold 25 students. How many school buses are needed to fit all the students? How did you figure out the answer?

3.9 x 4.75 5 10 20 30 Don’t figure out the exact answer to this problem. Without using paper and pencil, decide which of the choices is closest to the answer – 5, 10, 20, or 30.

Strategy Choices 3.9 x 4.75 • Used standard algorithm • Rounded then multiplied • Analyzed choices and chose one that seemed most reasonable • Gave other reasonable explanation • Guessed, did not explain, or gave faulty explanation

Could these be modified to fit other grade levels? • Which is greater – 3/5 or 1/2? • Is 5/6 + 12/13 closer to 1/2, 1, 2, or 8? • Is 1/2 + 2/3 greater than or less than 1? • 25 students can fit on one bus; how many buses needed for 295 students? • Is 3.9 x 4.75 closest to 5, 10, 20, or 30?

Cognitively Guided Instruction Is… • A research-based way of teaching mathematics that embraces and/or encompasses the following concepts: • Problem solving in meaningful context with flexible solution strategies • Building mathematical understanding through questioning • Integration of mathematical concepts *

Thanks for attending the Symposium! susan.mcadaragh@k12.sd.us http://2011ess.sfinstructionalresources.wikispaces.net/Sessions

CGI & The Common Core: A Perfect Match