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Algebra Readiness for Every Student
NCTM Interac:ve Ins:tute for Grades 6-‐8 July 20-‐22, 2015
Trena L. Wilkerson Professor, Mathema:cs Educa:on
Baylor University [email protected]
NCTM Board of Directors
Post Cards with a View!
• As you enter look through the postcards and find one that indicates how you view yourself as a mathema9cs teacher leader.
AND THEN • Select another that describes something fun about yourself as an individual!
• Have fun geCng to know one another! • We will start at 9 a.m.
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Algebra Readiness for Every Student
NCTM Interac:ve Ins:tute for Grades 6-‐8 July 20-‐22, 2015
Trena L. Wilkerson Professor, Mathema:cs Educa:on
Baylor University [email protected]
NCTM Board of Directors
Schedule Overview
• Welcome & Goals • Focused ½ day on professional development • Daily Reflec9on Sessions
– Monday: Immediately following the Ins9tute • 4:30-‐5:30 p.m.
– Tuesday: Immediately following the Ins9tute • 4:30-‐5:15 p.m.
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Who we are!
• Briefly introduce yourselves at your tables. – Name, role, Purpose in being here
• Share both postcards with group at your table. • As a group—be prepared to share one observa9on (interes9ng thing) with the whole group
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Algebra Ins:tute’s Goals 1. gain strategies to build the founda:on of knowledge and skills that lead to
students' future success in algebra; 2. use Principles to Ac.ons as a tool for learning new instruc:onal techniques for
posing purposeful ques9ons, engaging students in produc9ve discourse, and building student responsibility within the community of learners;
3. learn strategies for implemen9ng tasks that promote reasoning and problem solving and provide all students with opportuni9es to develop strong algebraic reasoning skills, including the development of conjectures and generaliza9ons;
4. determine the role of the Standards for Mathema:cal Prac:ce in instruc9onal strategies and assessments; and
5. understand how concepts within mul9ple domains of the Common Core State Standards support algebraic reasoning.
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PD Strand Goals
• Examine models of professional development that support teachers as learners, teachers as teachers, and teachers as reflec9ve prac99oners
• Develop lens for Ins9tute par9cipa9on for professional development focus
• Make plans for developing professional development to address the Algebra Ins9tute’s focus
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PD Strand Ac:vi:es
• Engage in non-‐rou9ne mathema9cal problem(s) • Examine student work and role in PD • Discuss evidence of mathema9cal prac9ces • Iden9fy student and teacher misconcep9ons • Analyze various professional development models for implementa9on
• Consider lens for par9cipa9ng in the ins9tute to support development of PD
• Develop PD plan 8
Content Progression
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! ! ! !!6th!Grade!
!Writing!expressions!with!!a!focus!on!variable!
!
!Solving!equations!using!!multiple!techniques!
!
!Graphing!relationships:!focus!!on!multiple!representations!
!7th!Grade!
!Writing!expressions!with!a!focus!!
on!variable!behavior!and!quantitative!relationships!
!Solving!equations!using!!multiple!techniques!
Graphing!relationships:!focus!!on!multiple!representations,!
proportional!and!!non?proportional!contexts!
!8th!Grade!
!Writing!expressions!and!equations!
!
!Solving!systems!of!equations!using!multiple!strategies!
!!!
!Graphing!relationships!with!a!focus!on!slope!and!transformations!
!
Ques:ons to Consider
• How do you lead teachers to engage in Algebraic Readiness?
• What type of professional development will work best in your situa9on?
• What type of leadership model will be beneficial to implement?
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Brainstorming!
• Small Group Discussion – What types of professional development models do you currently use and/or have some knowledge of?
– List on paper at table • Share with whole group
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Types of PD Models
• Lesson Study • Ac9on Research • Analysis of Student Work • Coaching • PLCs • Grade Level Teams • Co-‐Teaching • Train-‐the-‐Trainer
• Workshop Model • Partnership (ex. HE) • Mathema9cs Teacher Circle • Book Study • On-‐line Op9ons • Problem Solving • Case Study Analysis
– “Studio” Time
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Iden:fying Considera:ons
• What are specific considera9ons that you believe you have to address or think about as you begin to consider professional development planning (i.e. dura9on and 9ming)
• Discuss in small groups then share whole group
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Iden:fy their Considera:ons
• Type & Dura9on (Long term & On-‐going)
• Timing (Amer school, summer, during school day)
• Suppor9ng tools • Grade level configura9ons • Par9cipants (resource teachers, others) • Resources needed • Administra9ve Support needed • Assessing need and impact • Effec9ve Facilita9on 14
CCSS-‐M Mathema:cal Prac:ces Represent what students are doing as they learn mathema:cs
• Make sense of problems and persevere in solving them. • Reason abstractly and quan9ta9vely. • Construct viable arguments and cri9que the reasoning of • others. • Model with mathema9cs. • Use appropriate tools strategically. • Apend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.
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Mathema:cs Teaching Prac:ces (NCTM, PtA 2014, p. 10)
1. Establish mathema9cs goals to focus learning. 2. Implement tasks that promote reasoning and problem
solving. 3. Use and connect mathema9cal representa9ons. 4. Facilitate meaningful mathema9cal discourse. 5. Pose purposeful ques9ons. 6. Build procedural fluency from conceptual understanding. 7. Support produc9ve struggle in learning mathema9cs. 8. Elicit and use evidence of student thinking.
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Candy Jar Problem
17 Principles to Actions: Ensuring Mathematical Success for All, NCTM 201, p. 314
1. 5 minutes to work individually 2. 8 minutes to share at table (various approaches) 3. 8 minutes to record different strategies to post on wall
Candy Jar Problem-‐Sample Student Answers
• 260 • 360 • 40 • 26 • 340 • 50 • 240 • 270 • I do not know
• 2600 • 65 • 100 • 38.14 • 82.3 • 30 • 87 • 250 • I do not understand 18
• 108 • 325 • 35
• 61 • 6.9
• 38 • 160 • 13
• 20 • 36 • 7 R 9
• 50/50 • Less than 78
but more than
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Examining Mathema:cal Teaching Prac:ces (MTP)
• Small group ac:vity • A Lens for Viewing the Algebra Readiness Ins.tute Ac.vi.es
• Considera9ons for Professional Development • Each table is assigned 2 of 4 targeted MTPs to analyze around two areas – Iden:fy the key elements or considera:ons of your assigned MTP
– Analysis of the Mathema:cal Task 19
Mathema:cs Teaching Prac:ces (NCTM, PtA 2014, p. 10)
• #1 Establish mathema9cs goals to focus learning.
• #3 Use and connect mathema9cal representa9ons.
• #6 Build procedural fluency from conceptual understanding.
• #8 Elicit and use evidence of student thinking.
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Gallery Walk-‐Focus
• In what way is this MTP important to you when considering the focus of professional development for your teachers around the Algebra Ins9tute ideas? – Take post it notes, one copy of PtA per group, way to record group’s ideas
– 3 minutes at each MTP – Brief whole group sharing follows
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• hpp://www.nctm.org/Conferences-‐and-‐Professional-‐Development/Professional-‐Development-‐Resources/
• hpp://www.nctm.org/PtAToolkit/
NCTM New PD Resources-‐MTPs
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Planning PD-‐Planning Sheet
• Algebra Readiness Goal(s)-‐Content & Process
• Type(s) of PD • Audience/Par9cipants • Timeline/Time Allotment • Support Needed • Resources & Funding needed
• Assessment & Evalua9on Process
• Poten9al Obstacles, Barriers, or challenges
• Ways to Address (above) • Targeted Principle(s) (from PtA)
• Targeted MTP (from PtA) • BACK PAGE: Next steps & other thoughts
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PD Strand Goals-‐Revisited
• Examine models of professional development that support teachers as learners, teachers as teachers, and teachers as reflec9ve prac99oners
• Develop lens for Ins9tute par9cipa9on for professional development focus
• Make plans for developing professional development to address the Algebra Ins9tute’s focus
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Disclaimer The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring equitable mathematics learning of the highest quality for all students. NCTM’s Institutes, an official professional development offering of the National Council of Teachers of Mathematics, supports the improvement of pre-K-6 mathematics education by serving as a resource for teachers so as to provide more and better mathematics for all students. It is a forum for the exchange of mathematics ideas, activities, and pedagogical strategies, and for sharing and interpreting research. The Institutes presented by the Council present a variety of viewpoints. The views expressed or implied in the Institutes, unless otherwise noted, should not be interpreted as official positions of the Council.
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Algebra Readiness Ins:tute
• Thank you! Enjoy the ins9tute! • Keep your PD plan in mind.
– See you at 4:30 today and tomorrow as well!
• Access the electronic resources – Bibliography of resources for different types of PD – TCM & MTMS ar9cles – PowerPoint and handouts
• Feel free to ask ques9ons any9me! – [email protected]
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Facilitate Meaningful Mathema9cal Discourse
Effec9ve teaching of mathema9cs facilitates discourse among students to build shared understanding of mathema9cal ideas by analyzing and comparing student approaches and arguments.
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5 Prac:ces for Facilita:ng Mathema:cal Discourse (Smith & Stein 2011)
1. An9cipa9ng student responses prior to the lesson 2. Monitoring students’ work on and engagement
with the tasks 3. Selec9ng par9cular students to present their
mathema9cal work 4. Sequencing students’ responses in a specific order
for discussion 5. Connec9ng different students’ responses and
connec9ng the responses to key mathema9cal ideas
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Student Work Analysis
• Using the student work sample(s) provided determine what order you would sequence them for Meaningful Mathema.cal Discourse (MTP #4 pages 29-‐35 in PtA 2014) in the classroom and why. – 14 Different Student Work Samples – May not necessarily use all
• If 9me permits, discuss how you would guide students during their work 9me—par9cularly those that seemed to struggle-‐incorrect answers
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