Math Summer Institue 2013
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Summer Institute Math presentation 2013

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  • Chat , chat
  • Survey participants: first timers, math coaches, classroom teachers, central office, principals, etc… This will allow us to modify presentation accordingly.
  • Thumbs up if you agree with these norms. Are there other norms we need to add so that we have the best possible learning experience for all?
  • Share outcomes
  • Share objectives
  • Potential problems in any elementary classroom – focus could be on these versus learning
  • Potential problems in any secondary classroom – focus could be on these versus learning Then allow time for participants to discuss – traditional classroom issues/problems
  • Why change?
  • Think for a minute about your answer to this problem, and what students in 1-6 grade might think the answer is. What goes in the box? What might students say? Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School Carpenter, Franke, & Levi, Heinemann, 2003
  • Across the top you see the various answers students offered: 7, 12, 17, 12 & 17. How did they get each of these responses?
  • We can see that 5 percent of 1-2 graders produced the correct answer. However, 58 percent thought the answer was 12. How did they get that?
  • Now we look at 3-4. 2% more were right. Why do 12 % more students think 17 is correct?
  • Now 5 th -6 th grades. The good news is that very few still think there are 2 answers. The bad news is that we are down to 2 % getting the right answer. Procedures memorized but not understood are getting in the way. Dr. Drew Polly at UNCC replicated this study for 6 th grade, and none of the students got the correct the answer.
  • More research from NAEP
  • More research
  • Research continued Constance Kamii has done extensive research on how young children learn mathematics. Here is a task frequently used to assess understanding of tens and ones. Students usually are successful, and count our 6 blocks.
  • Kamii found that essentially no first graders could correctly complete this task.
  • Many 3-5 graders still do not give the correct answer.
  • Grayson Wheatly’s research with 5,000 middle-school students were given the following task: Some students gave this answer. Others knew the tens had to be in the middle, so….. Many gave this answer, knowing about decimals, and that you could only have 3 digits if a number was in the hundreds. Around 50% of the middle school students gave the correct answer.
  • Think about the practices!
  • What would have happened if ? (wait time, no opinions and value judgments, and not repeating student responses pg. 61) Or use post-it notes to use Formative Assessment type task.
  • Additional problem if needed
  • Share slide
  • Tons or research has told us what students need for success in the future.
  • Again, these standards tell us “what” students need but not “How” Standard III – Teachers Know the Content They Teach Standard IV – Teachers Facilitate Learning for Their Students
  • These standards also tell us ‘What” not “how” Students learn language and culture through meaningful use and interaction. Students develop language proficiency in listening, speaking, reading, and writing interdependently. Students’ development of social, instructional, and academic language is the foundation for their success in school. Students’ access to instructional tasks requiring complex thinking is enhanced when linguistic complexity and instructional support match their levels of language proficiency.
  • UDL - Tells us to make learning accessible to all but not “How” Diversity is the norm within modern classrooms. As educators, it is our responsibility to provide students with an equal opportunity to learn and access education. Every classroom is filled with diverse learners. Every learner is unique and processes information in a different way. As educators, it is our job to take time to get to know our students and understand their individual strengths, needs, and interests
  • Now focus on the “How” Modeled through a math problem.
  • Pass out handout - Test time. Participants take test and share with shoulder partner Pass out books while discussing test results!
  • Look at pages 34-35, talk with your shoulder partner.
  • Look at pages 37, talk with your shoulder partner. The book includes useful guidance on this topic, you can explore this section at a later time.
  • Take a look at some student types. How many do you know? DO they look familiar?
  • Distribute Mathematical Practice Handout
  • Rectangle Problem Model by asking them to reflect on their thinking… Teacher Strategy #9, p.88
  • Fraction Problem Model by using multiple entries Teacher Strategy # 5, p.78
  • Fraction Problem Model by using multiple entries Teacher Strategy # 5, p.78
  • Fraction Problem Model by using multiple entries Teacher Strategy # 5, p.78
  • I believe students meet our expectations, expectations they infer from observing us.
  • Student assessment
  • These are designed for PLC work during which teachers would observe each other. Students from grades 4 and up could also take turns recording. This really builds a community of learners.
  • Here is where you can get more information…
  • This should be included for all instructional content sessions
  • When the system is first rolled out, teachers will have immediate access to content that has been vetted, tagged, and aligned to Common Core and NC Essential Standards. DPI has a team of people reviewing resources and selecting those that are strictly aligned – this process involves a teacher review to ensure that these are resources that teachers will use. At the end of 2012, over 2300 resources had been reviewed and tagged in Math, ELA, Science, Biology, Math I (some Social Studies). This number increases daily. These are some examples of instructional resources that we know we are going to use. You may already know about and use these, but now we will have them all in one place and only include those things that are aligned to NC SCOS.

Math Summer Institue 2013 Math Summer Institue 2013 Presentation Transcript

  • Summer Institutes 2013 Changing Teacher Practice Changing Student Outcomes
  • June’s remodeling 2013 Summer Institutes | Changing Teacher Practice  Changing Student Outcomes Remodeling Session 2013 Mathematics Summer Institute DPI Mathematics Consultants
  • Welcome “Who’s in the Room”
  • Norms • Listen as an Ally • Value Differences • Maintain Professionalism • Participate Actively
  • Learner Outcome With the development of thoughtful classrooms aligned to the Standards for Mathematical Practice, educators will understand and promote complex level thinking in students.
  • Session Objectives • Provide strategies teachers can utilize to increase students’ complex level thinking. • Connect the Strategies for a Thoughtful Classroom to the Standards for Mathematical Practice.
  • Let’s Define the Problem
  • First Grade • The Leader • The Ethics Police • The “I’m Finished First” Winners • The Do-Overs
  • High School Rows of 5, all eyes on cell phones texting Wondering what’s for lunch? Students asleep or praying for a fire drill.
  • Why is change necessary?
  • 8 + 4 = [ ] + 5 Turn and Talk
  • 8 + 4 = [ ] + 5 Percent Responding with Answers Grade 7 12 17 12 & 17 1st - 2nd 3rd - 4th 5th - 6th Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003
  • 8 + 4 = [ ] + 5 Percent Responding with Answers Grade 7 12 17 12 & 17 1st - 2nd 5 58 13 8 3rd - 4th 5th - 6th Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003
  • 8 + 4 = [ ] + 5 Percent Responding with Answers Grade 7 12 17 12 & 17 1st - 2nd 5 58 13 8 3rd - 4th 9 49 25 10 5th - 6th Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003
  • 8 + 4 = [ ] + 5 Percent Responding with Answers Grade 7 12 17 12 & 17 1st - 2nd 5 58 13 8 3rd - 4th 9 49 25 10 5th - 6th 2 76 21 2 Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003
  • Estimate the answer to (12/13) + (7/8) A. 1 B. 2 C. 19 D. 21 Only 24% of 13 year olds answered correctly. Equal numbers of students chose the other answers. NAEP
  • Students were given this problem: ÷168 20 4th grade students in reform math classes solved it with no problem. Sixth graders in traditional classes responded that they hadn’t been taught that yet. Dr. Ben Klein, Mathematics Professor Davidson College
  • Research Students are shown this number. Teacher points to the 6 and says, “Can you show me this many?” 16 Constance Kamii
  • Research When the teacher points to the 1 in the tens place and asks, “Can you show me this many?” 16 Constance Kamii
  • Research By third grade nearly half the students still do not ‘get’ this concept. 16 Constance Kamii
  • More research - It gets worse! A number contains 18 tens, 2 hundreds, and 4 ones. What is that number? 1824 218.4 2824 384 Grayson Wheatly
  • Lesson Comparison United States and Japan The emphasis on skill acquisition is evident in the steps most common in U.S. classrooms The emphasis on understanding is evident in the steps of a typical Japanese lesson •Teacher instructs students in concept or skill •Teacher solves example problems with class •Students practice on their own while teacher assists individual students •Teacher poses a thought provoking problem •Students and teachers explore the problem •Various students present ideas or solutions to the class •Teacher summarizes the class solutions •Students solve similar problems
  • How are you feeling?
  • Let’s Do Some Math!
  • The Famous Horse Problem A farmer buys a horse for $60. How much money did the farmer make or lose? Later he sells it for $70. He buys it back for $80. Finally, he sells it for $90.
  • Feeling Better?
  • Instruction Must Change
  • We know “What” Students Need… 21st Century Skills, critical thinking and problem solving, collaboration and leadership, agility and adaptability, oral and written communication, accessing and analyzing information. Tony Wagner, Rigor Redefined
  • Teacher Evaluation
  • WIDA
  • Universal Design for Learning A universally designed curriculum is developed from the start to be accessible as well as challenging, for ALL students.
  • We Know the “What” But Not “How” to Meet Their Needs Common Core Standards for Mathematical Practice
  • Creating Active Thinkers Do You Value Thinking? “Teacher Test” Turn and Talk with your shoulder partner about your Teacher Test.
  • How do we meet student needs?
  • The First Step “Before all else, a classroom environment that fosters complex thinking must be predictable and safe.” Creating Active Thinkers, page 35 How do you know if a classroom is safe and predictable?
  • Characteristics of a safe and predictable classroom • Shared decision making • Lively exchange of opinions and ideas • Visual evidence of student thinking
  • The Next Step “Complex thinking is developed in students primarily through the careful planning and teaching of lessons.” Creating Active Thinkers, page 37 What do you need to keep in mind when planning a lesson?
  • Jigsaw on Teacher Strategies
  • The Nine Teacher Strategies in the Thoughtful Classroom gives us the
  • Nine Teacher Strategies The teacher will… 1.focus and refocus students on task. (pages 62-67) 2.ask open-ended questions.(pages 67-70) 3.ask extension questions.(pages 70-74) 4.wait for student responses.(pages74-78) 5.accept a variety of student responses.(pages 78-81) 6.encourage student interaction.(pages 81-84) 7.not give opinions or value judgments.(pages 84-86) 8.not repeat student responses.(pages 87-88) 9.ask students to reflect on their thinking.(pages 88-90)
  • Student Responsibilities “The student takes his or her cues from the teacher.” Include your students in the journey. Meet some of your students… Creating Active Thinkers, page 97-100
  • Student Behaviors Read the student behaviors on page 101. Are these student behaviors familiar? Surprise! Standards for Mathematical Practice.
  • Let’s do some math using some of the Strategies for a Thoughtful Classroom
  • Cube Problem A block made of small cubes is dropped in paint. The block has four cubes on each edge as shown below. How many small cubes have paint on them?
  • Nine Teacher Strategies The teacher will… 1.focus and refocus students on task. 2.ask open-ended questions. 3.ask extension questions. 4.wait for student responses. 5.accept a variety of student responses. 6.encourage student interaction. 7.not give opinions or value judgments. 8.not repeat student responses. 9.ask students to reflect on their thinking.
  • Fraction Riddle Using color tiles and grid paper. Riddle 1: A rectangle is 1/2 red, 1/5 green, 1/10 blue, and the rest yellow. How much of the rectangle is yellow? Draw the rectangle on grid paper and record the fraction that tells which part is yellow.
  • Fraction Riddle Using color tiles and grid paper. Riddle 2: A rectangle is 3/5 red. The rest is blue and yellow but not in equal amounts. What could the rectangle look like? Record.
  • Fraction Riddle Using color tiles and grid paper. Riddle 3: A rectangle is 1/2 red and 1/3 blue. Also, it has one green tile and one yellow tile. What could the rectangle look like? What fractional part is green? Yellow? Record. Try to make up your own riddle.
  • Nine Teacher Strategies The teacher will… 1.focus and refocus students on task. 2.ask open-ended questions. 3.ask extension questions. 4.wait for student responses. 5.accept a variety of student responses. 6.encourage student interaction. 7.not give opinions or value judgments. 8.not repeat student responses. 9.ask students to reflect on their thinking.
  • Self Assessment Students are amazingly honest when assessing themselves. Creating Active Thinkers, page 117 – 121; 136-137
  • Self Assessment Doesn’t Always Work The last pages contain Observation Forms, to help identify what your students and others observe in you during instruction. Creating Active Thinkers, Appendix C
  • What questions do you have?
  • • Learning Opportunities • Resources
  • Assessment Student Information and Learner Profile Instructional Design, Practice & Resources Data Analysis and Reporting Information a simpler, better information system to replace NC WISE Integrated Instructional Solution a new standards-aligned tool that connects instructional content with (e.g. lesson plans, unit plans) assessment for better data analysis and decision making Effectiveness a simpler, better online evaluation system Information Instruction Educator Effectiveness: Educator Evaluation OpenClass Collaboration SchoolnetPowerSch ool Truenorthlo gic Available for the start of the 2013-14 School Year
  • Home Base Website and Updates •Home Base website is http://www.ncpublicschools.org/homebase/ •To sign up for Home Base Biweekly Newsletter, please go to http://goo.gl/appdp. •We will continue to email the biweekly updates, but you can also find them archived on the Home Base website at http://www.ncpublicschools.org/homebase/updates/
  • Exploring Instructional Content
  • Open Education Resources (OER) Samples • Home Base NCDPI-Vetted OER Samples Available at http://goo.gl/8sbFX
  • Sample Mathematics Resources Summary: This site comprises six lesson activities including the definition of a fraction, equivalent fractions, addition of fractions, and multiplication of fractions. Students may respond online to get immediate feedback, or they can work the examples on grid paper. Who Wants Pizza? A Fun Way to Learn About Fractions Exploring Linear Data Standards: •CCSS.Math.Content.8.SP.A.1 •CCSS.Math.Content.8.SP.A.2 •CCSS.Math.Content.8.SP.A.3 •CCSS.Math.Content.HSS-ID.B.6c Standards: •CCSS.Math.Content.3.NF.A.3a •CCSS.Math.Content.3.NF.A.3b •CCSS.Math.Content.4.NF.B.3a •CCSS.Math.Content.5.NF.A.1 •CCSS.Math.Content.5.NF.A.2 •CCSS.Math.Content.5.NF.B.4a Summary: Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students work to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
  • DPI Mathematics Section Kitty Rutherford Elementary Mathematics Consultant 919-807-3841 kitty.rutherford@dpi.nc.gov Denise Schulz Elementary Mathematics Consultant 919-807-3839 denise.schulz@dpi.nc.gov Johannah Maynor Secondary Mathematics Consultant 919-807-3842 johannah.maynor@dpi.nc.gov Ashton Megson Secondary Mathematics Consultant 919-807-3934 ashton.megson@dpi.nc.gov Vacant K – 12 Mathematics Section Chief 919-807-3838 Susan Hart Mathematics Program Assistant 919-807-3846 susan.hart@dpi.nc.gov
  • Facilitated Team Time Preparation • To prepare for Facilitated Team Time, complete the brief reflection to identify the “big ideas” gained from this session that you will share with your Summer Institute team. • To access the reflection document, visit http://bit.ly/SIreflection or scan the QR code. • To access the reflection responses during Facilitated Team Time, visit http://bit.ly/SIresponses.
  • For all you do for our students!