Mathematical+Practices

= Standards for Mathematical Practices =

|| * Explain meaning || * Work in groups with assigned roles || * Justify their answers || * Apply what they know to make assumptions & approximations || * Select the best tool to use in a given situation || * Use clear definitions || * Look for patterns || * Look for patterns/shortcuts/generalizations Click HERE for more information on the Standards for Mathematical Practices. Click HERE for classroom videos of the Standards for Mathematical Practices.
 * ~ Best Practices  ||~ A Secondary Math teacher will... ||~ A Secondary Math student will... ||
 * ~ Make sense of problems and persevere || * Circulate around the classroom
 * Start discussions
 * Ask "Does it makes sense?" "Why?"
 * "How did you come to that conclusion?"
 * Suggest alternatives
 * Figure out problem solving diagrams
 * Drawings
 * Discussions with peers
 * Various solutions
 * Ask themselves "Does it make sense?"
 * Ask themselves "What is important and why is it important?" ||
 * ~ Reason abstractly and quantitatively || * Use different approaches for problem solving
 * Look for generalizations of what makes sense
 * Represent the situations symbolically and allow for manipulatives
 * Allow students to come up with activities related to the pie
 * Ask the students "What does the number represent?"
 * Represent the problems in varied ways
 * Learn symbolical signs and meanings
 * Describe meaning of values and relationships between values
 * Use units appropriately ||
 * ~ Construct viable arguments and critique reasoning of others || * Teach students to appropriately critique others
 * Facilitate discussions
 * Redirect when appropriate
 * Provide problems that encourage multiple types of reasoning
 * Teach critical thinking skills
 * Teach vocabulary
 * Provide materials
 * Serve as a guide/facilitator
 * Provide sentence starters to help students agreeably disagree
 * Ask for explanations
 * Monitor student discussions
 * Provide positive feedback
 * Use prior knowledge
 * Apply content related info to problem solving
 * Accept or refute situations
 * Improve vocabulary
 * Maintain appropriate behavior
 * Defend answers
 * Think about, talk about and write about their thinking
 * Contribute to the discussion/argument with substance (not just "I agree")
 * Find logical reasoning for response
 * Provide positive feedback ||
 * ~ Model with mathematics || * Research NCTM process standards & strands of math proficiency
 * Complete a pre-assessment to identify what students know/don't know
 * Apply vocabulary and application strategies to real life math situations based on pre-assessment data
 * Provide real life problems
 * Include the use of technology
 * Be involved in meaningful conversations
 * Students will explore real life problems/situations
 * Check/verify their model for effectiveness
 * Do outside research to find info not already given
 * Use graphics/multimedia ||
 * ~ Use appropriate tools strategically || * Provide instruction on all tools available
 * Allow multiple uses of each tools
 * Provide access to a variety of tools
 * Decide when to use/not use a tool
 * Look for errors
 * Use estimates
 * Use/read tools accurately ||
 * ~ Attend to precision || * Monitor students' precision with vocabulary and use of correct symbols and units
 * Model in conversation, correct/consistent use & expectation of correct units and symbols
 * Calculate accurately and efficiently
 * Use carefully formulated explanations of terms and processes
 * Use proper units/labels
 * Check whether their answers make sense in context of the problem
 * verbally communicate responses
 * Know/use common vocabulary
 * Specify units of measure ||
 * ~ Look for and make use of structure || * Monitor
 * Question
 * Encourage
 * Provide instruction on use of appropriate tools
 * Model the structural vocabulary and the use of structure
 * Discuss findings with classmates
 * Work through a large set of problems
 * Test patterns
 * Make drawings/tables
 * Collaborate in groups to identify, analyze and explain structure ||
 * ~ Look for and express regularity in repeated reasoning || * Emphasize paying attention to the details/pattern while remember to "zoom out to the BIG picture"
 * Always evaluate the result obtained for reasonableness
 * Ask the students "is there a pattern?"
 * Creates activities that promote conversations that reveal repeated patterns
 * Remember to check if their answers make sense in the context of the problem
 * Ask "what is the pattern?"
 * Ask "does that always work?"
 * Try different numbers
 * Apply pattern to different situations. ||