Welcome• Enjoy breakfast• Use three post-its to answer these

questions:– What does it mean to DO mathematics?– What does it mean to LEARN mathematics?– What does it mean to UNDERSTAND mathematics?

• Post answers on appropriate poster• Discover patterns within the Banner

Numbers

Success In Algebra

March 22, 2013Leitchfield, KY

Facilitated by the P12 Math and Science Outreach Unit of PIMSER, UKFunding provided by Council on Post Secondary Ed

Reflection and Feedback

Agenda !/? Card

Survey

One UpOne Down

Math Practice Standards1. Make sense of problems and persevere in solving

them2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

• Don’t forget to reflect…

Exploring What It Means to Know and Do Mathematics

Chapter 2“… about the learning theory of teaching

developmentally and the knowledge necessary for students to learn mathematics with

understanding.” (p 13 Van de Walle)

• What does it mean to DO mathematics?– Pages 13 – 15

• What does it mean to LEARN mathematics?– Pages 19 – 23

• What does it mean to UNDERSTAND mathematics?– Pages 23 – 29

• An invitation to DO mathematics– Pages 15 – 19

Verbs of Math

Compare Explain Predict

Conjecture Explore Represent

Construct Formulate Solve

Describe Investigate Use

Develop Justify Verify

Classroom Environment for Doing Mathematics

1. Persistence, effort and concentration are important in learning mathematics

2. Students share their ideas3. Students listen to each other4. Errors or strategies that didn’t work are

opportunities for learning5. Students look for and discuss connections

Implications for Teaching Mathematics

• Provide opportunities to talk about mathematics

• Build in opportunities for reflective thought• Encourage multiple approaches• Engage students in productive struggle• Treat errors as opportunities for learning• Scaffold new content• Honor diversity

Intertwined Strands of Proficiency

• Conceptual understanding: comprehension of mathematical concepts, operations, and relations

• Procedural fluency: skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

• Strategic competence: ability to formulate, represent, and solve mathematics problems

• Adaptive reasoning: capacity for logical thought, reflection, explanation and justification

• Productive disposition: habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

Connecting the Dots

• Between theory and practice…• Students develop their own

networks of blue dots…

• “As you … design instruction, you should constantly reflect on how to elicit prior knowledge by designing tasks that reflect the social and cultural backgrounds of students, to challenge students to think critically and creatively, and to include a comprehensive treatment of mathematics.” (p 29 Van de Walle)

© 2012, EDC

Math Accessibility Framework

17

Align StrategiesPlan and Implement Evaluate and Revise as Needed

Identify Barriers

Consider theMath Student

Lunch

Student Engagement Strategies

Chapter 9Discussion

Games to Build Fluency

• Revisit–Bowl-a-Fact– Salute–War

• New– MangaHigh– Integer Capture

Feedback and Homework• Turn in !/? Card• Accessibility Framework (by April 30, 2013)– Plan an accessible lesson for your focal student– Implement lesson– Reflect on lesson– Email Karen a copy of completed Accessibility

Framework and your reflection on the lesson• Set Coaching Date via email