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Learner Thinking V.1
Transcript of Learner Thinking V.1
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. Why Start With the Mathematical Practice Standards? Standards for Mathematical Practice
FOR STUDENTS http://www.corestandards.org/ 1. Make sense of complex problems and persevere in solving them.
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning. Grouping the SMPs What not to do... Problem solving Friday
Enrichment for the few
Just give the answer
Isolate content from process Might lead to this: What is learning? Is it this? The mathematical practices give teachers a foundation for effective student learning.
However, we are asking many teachers to fundamentally change the way they teach. Where should teachers begin? Read the standards. or this? or worse, this: Discuss what they mean. Have contentious discourse. Do the math. Questions? The mathematical practices
of the classroom contract. 3 Major Shifts:
Teachers cannot create learning-only learners can do that.
Increased student responsibility- from receptive to active learner
Teacher/student relationship shift- from adversarial to collaborative
Black and Wiliam, 2006 Where can you start?
Look at "Inside Mathematics" “The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.” Separating the practices from the content is not helpful and is not what the Standards require.
The practices do not exist in isolation; when students engage in the practices, what they are “practicing with” is mathematical content.
The SMPs are inherently interconnected with the content. An example:
Wikipedia reports that 8% of all Americans eat at McDonalds every day. In the US, there are approximately 310 million Americans and 12,800 McDonalds.
Do you believe the Wikipedia report to be true? Create a mathematical argument to justify your position.
(Briars, Feb 2011)
Traditional U.S. Problem
Which fraction is closer to 1: 4/5 or 5/4 ?
Same Problem with SMP integration
4/5 is closer to 1 than is 5/4 . Using a number line,
explain why this is so. Ideas to consider:
Focus instruction on the big ideas at a grade level.
Understand the learning progressions.
Use previous mathematics in service of new ideas.
Develop support structures for struggling students.
Avail yourself of the resources provided by GaDOE, NCTM, NCSM and PARCC. http://www.insidemathematics.org/index.php/standard-1 http://www.insidemathematics.org/index.php/standard-2 http://www.insidemathematics.org/index.php/standard-3 http://www.insidemathematics.org/index.php/standard-4 http://www.insidemathematics.org/index.php/standard-5 http://www.insidemathematics.org/index.php/standard-6 http://www.insidemathematics.org/index.php/standard-7 http://www.insidemathematics.org/index.php/standard-8 http://www.insidemathematics.org/index.php/math-standards-together