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# Accessible Mathematics

A presentation for the PNW Curriculum Council

by

Tweet## Tim Kaltenecker

on 19 December 2012#### Transcript of Accessible Mathematics

To truly meet the demands of the Common Core State Standards, it is not sufficient to simply revise the list of mathematical content covered in the curriculum.

The Standards' emphasis on Mathematical Practices require students to... Accessible Mathematics 10 Instructional Shifts that Raise Student Achievement What do the SHIFTS look like in practice?

How do the SHIFTS relate to the Common Core Standards?

What leadership is needed to SHIFT in our districts/schools? 6,795,000 9,390,000 5,500,000 3,745,000 2,968,000 11,506,000 16,988,000 South America North America Africa Asia Antarctica Europe Australia Incorporate ongoing cumulative review into every day's lesson. SHIFT 1 Shift 2 Shift 3 Shift 4 Shift 5 Shift 6 Shift 7 Shift 8 Shift 9 Shift 10 Adapt what we know works in our reading programs and apply it to mathematics instruction. Use multiple representations in mathematics. Create language-rich classrooms. Take every available opportunity to support the development of number sense. Build from graphs, charts, and tables. Tie the math to such questions as: How big? How much? How far? to increase the natural use of measurement throughout the curriculum. Minimize what is no longer important. Embed the mathematics in realistic problems and real-world contexts. Make "Why?" "How do you know?" "Can you explain?" classroom mantras. STATE Power Outages Deaths Square Miles Total Population

NY 2,200,000 47 54,566 19.4

CT 625,000 3 5,543 3.5

NJ 2,700,000 23 8,721 8.8

PA 1,200,000 15 46,055 12.7

RI 122,000 0 1,545 1.0

WV 270,000 6 24,229 1.8 Which state was affected the most by Hurricane Sandy? If you were in charge of FEMA, how would you distribute funds between the six states? New York's power company, Con Edison, has been criticized for the extensive power loss.

Compared to other states, do you think this is fair criticism? An effective mathematics classroom would demonstrate:

An abundance of problems drawn from the data presented in tables, charts, and graphs.

Opportunities for students to make conjectures and draw conclusions from data presented in tables, charts, and graphs.

Frequent conversion, with and without technology, of data in tables and charts into various types of graphs, with discussions of their advantages, disadvantages, and appropriateness. Examples of each shift:

http://csdelemmathsupport.wikispaces.com/file/view/10ShiftsOverview!.pdf

Resources Mathematics Assessment Project - video examples in classrooms: http://map.mathshell.org/materials/index.php Dan Meyer video from TED: http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html What other questions might you ask? About how much bigger is NY than NJ? SO WHERE ARE THE LINKS?

COMMON CORE LEARNING STANDARDS

&

ACCESSIBLE MATHEMATICS INSTRUCTIONAL SHIFTS How are the Accessible Math Instructional Shifts embedded within the CCLS? ...be able to think mathematically, and apply the techniques they have learned to rich problems in diverse contexts. Mayor Bloomberg banned 64oz drinks in NYC. Is he justified? What other questions would you ask from this advertisement posted on the Mayor's facebook page? CCLS Math Shift 1: FOCUS - Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards. CCLS Math Shift 2: COHERENCE - Principals and teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. CCLS Math Shift 3: FLUENCY - Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions. CCLS Math Shift 4: DEEP UNDERSTANDING - Students deeply understand and can operate easily within a math concept before moving on. They learn more than the trick to get the answer right. They learn the math. CCLS Math Shift 5: APPLICATION - Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. CCLS Math Shift 6: DUAL INTENSITY - Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. CCLS ELA Shift 2: KNOWLEDGE IN THE DISCIPLINES - Students build knowledge about the world (domains/ content areas) through TEXT rather than the teacher or activities. CCLS ELA Shift 4: TEXT-BASED ANSWERS - Students engage in rich and rigorous evidence based conversations about text. CCLS ELA Shift 6: ACADEMIC VOCABULARY - Students constantly build the transferable vocabulary they need to access grade level complex texts. This can be done effectively by spiraling like content in increasingly complex texts. Shift

Happens! Connections to the Common Core Shifts The Shifts Keep skills and understandings fresh

Reinforce previously taught material

give students time to clarify their understandings Use question prompts that require inferential and evaluative comprehension that we use in reading instruction

Probe for how answers were determined

Ask for justification of responses Frequent use of pictures, number lines, and bar graphs to help students visualize the math they are learning. Allow students to draw and show, and to describe it. Use estimation

and justify it! Focus on place value. Ask lots of questions. Integrate measurement into daily instruction. Deliberately question the appropriateness of the math content. Should we have to simplify: 6

√10-√7 When and where do normal human beings encounter the mathematics I need to teach? Students might offer sound explanations in new ways.

Students might recognized their own errors and self-correct.

You might hear flawed explanations that reveal misconceptions in understanding.

Other students can be asked to offer alternative explanations.

Supports a language-rich classroom. Box of Sweets - VIDEO

http://map.mathshell.org/static/draft/pd/modules/3_Problem_Solving/html/videos_d2.htm What Opportunities exist in your districts to engage teachers and administrators in this work? What barriers exist to doing this work? What next steps will you take? What resources will you access? Achieving this requires changes in the way mathematics is taught and assessed in most schools. - Mathematics Assessment Project, http://map.mathshell.org/materials/index.php

Full transcriptThe Standards' emphasis on Mathematical Practices require students to... Accessible Mathematics 10 Instructional Shifts that Raise Student Achievement What do the SHIFTS look like in practice?

How do the SHIFTS relate to the Common Core Standards?

What leadership is needed to SHIFT in our districts/schools? 6,795,000 9,390,000 5,500,000 3,745,000 2,968,000 11,506,000 16,988,000 South America North America Africa Asia Antarctica Europe Australia Incorporate ongoing cumulative review into every day's lesson. SHIFT 1 Shift 2 Shift 3 Shift 4 Shift 5 Shift 6 Shift 7 Shift 8 Shift 9 Shift 10 Adapt what we know works in our reading programs and apply it to mathematics instruction. Use multiple representations in mathematics. Create language-rich classrooms. Take every available opportunity to support the development of number sense. Build from graphs, charts, and tables. Tie the math to such questions as: How big? How much? How far? to increase the natural use of measurement throughout the curriculum. Minimize what is no longer important. Embed the mathematics in realistic problems and real-world contexts. Make "Why?" "How do you know?" "Can you explain?" classroom mantras. STATE Power Outages Deaths Square Miles Total Population

NY 2,200,000 47 54,566 19.4

CT 625,000 3 5,543 3.5

NJ 2,700,000 23 8,721 8.8

PA 1,200,000 15 46,055 12.7

RI 122,000 0 1,545 1.0

WV 270,000 6 24,229 1.8 Which state was affected the most by Hurricane Sandy? If you were in charge of FEMA, how would you distribute funds between the six states? New York's power company, Con Edison, has been criticized for the extensive power loss.

Compared to other states, do you think this is fair criticism? An effective mathematics classroom would demonstrate:

An abundance of problems drawn from the data presented in tables, charts, and graphs.

Opportunities for students to make conjectures and draw conclusions from data presented in tables, charts, and graphs.

Frequent conversion, with and without technology, of data in tables and charts into various types of graphs, with discussions of their advantages, disadvantages, and appropriateness. Examples of each shift:

http://csdelemmathsupport.wikispaces.com/file/view/10ShiftsOverview!.pdf

Resources Mathematics Assessment Project - video examples in classrooms: http://map.mathshell.org/materials/index.php Dan Meyer video from TED: http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html What other questions might you ask? About how much bigger is NY than NJ? SO WHERE ARE THE LINKS?

COMMON CORE LEARNING STANDARDS

&

ACCESSIBLE MATHEMATICS INSTRUCTIONAL SHIFTS How are the Accessible Math Instructional Shifts embedded within the CCLS? ...be able to think mathematically, and apply the techniques they have learned to rich problems in diverse contexts. Mayor Bloomberg banned 64oz drinks in NYC. Is he justified? What other questions would you ask from this advertisement posted on the Mayor's facebook page? CCLS Math Shift 1: FOCUS - Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards. CCLS Math Shift 2: COHERENCE - Principals and teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. CCLS Math Shift 3: FLUENCY - Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions. CCLS Math Shift 4: DEEP UNDERSTANDING - Students deeply understand and can operate easily within a math concept before moving on. They learn more than the trick to get the answer right. They learn the math. CCLS Math Shift 5: APPLICATION - Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. CCLS Math Shift 6: DUAL INTENSITY - Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. CCLS ELA Shift 2: KNOWLEDGE IN THE DISCIPLINES - Students build knowledge about the world (domains/ content areas) through TEXT rather than the teacher or activities. CCLS ELA Shift 4: TEXT-BASED ANSWERS - Students engage in rich and rigorous evidence based conversations about text. CCLS ELA Shift 6: ACADEMIC VOCABULARY - Students constantly build the transferable vocabulary they need to access grade level complex texts. This can be done effectively by spiraling like content in increasingly complex texts. Shift

Happens! Connections to the Common Core Shifts The Shifts Keep skills and understandings fresh

Reinforce previously taught material

give students time to clarify their understandings Use question prompts that require inferential and evaluative comprehension that we use in reading instruction

Probe for how answers were determined

Ask for justification of responses Frequent use of pictures, number lines, and bar graphs to help students visualize the math they are learning. Allow students to draw and show, and to describe it. Use estimation

and justify it! Focus on place value. Ask lots of questions. Integrate measurement into daily instruction. Deliberately question the appropriateness of the math content. Should we have to simplify: 6

√10-√7 When and where do normal human beings encounter the mathematics I need to teach? Students might offer sound explanations in new ways.

Students might recognized their own errors and self-correct.

You might hear flawed explanations that reveal misconceptions in understanding.

Other students can be asked to offer alternative explanations.

Supports a language-rich classroom. Box of Sweets - VIDEO

http://map.mathshell.org/static/draft/pd/modules/3_Problem_Solving/html/videos_d2.htm What Opportunities exist in your districts to engage teachers and administrators in this work? What barriers exist to doing this work? What next steps will you take? What resources will you access? Achieving this requires changes in the way mathematics is taught and assessed in most schools. - Mathematics Assessment Project, http://map.mathshell.org/materials/index.php