Welcome! August 3, 2015

Achievement Gap vs. Opportunity Gap ”… all students need the opportunity to learn challenging mathematics from a well-qualified teacher who will make connections to the background, needs, and cultures of all learners " (NCTM, 2005).

Increasing Cognitive Demand: Strategies for creating strong tasks through Math Workshop “ Thinking is the hardest work there is, which is probably the reason why so few engage in it. ~ Henry Ford

Analyzing a Mathematical Task Mrs. B.’s class wants to get a pet rabbit for their classroom. They have enough space to build a pen that is 24 square feet. How many different ways can they build the pen? Kelley wants to recarpet her bedroom. Her room is 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

Analyzing a Mathematical Task Mrs. B.’s class will raise rabbits for their spring science fair. They need to build a pen that provides 24 square feet of space in which the rabbits can live. How many different ways can they build the pen? Kelley wants to recarpet her bedroom. Her room is 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

LAUNCH EXPLORE EXTEND* SUMMARIZE

Whole Class “Mini-Lesson” Launch Stimulate existing knowledge Introduce topic (content and context) Explore Student-centered investigation Manipulatives and technology Student Centers: Extension* Elaborate/Extend: Meet with teacher in small groups—Guided Practice Engage in independent practice of concept Math Stations—extend content Debrief Big Ideas: Summarize content Share solution strategies and representations Connect to standards and objectives Emphasize key vocabulary How do you format your lesson plans?

ORCHESTRATING PRODUCTIVE MATHEMATICAL DISCUSSIONS: Five practices for helping teachers move beyond “show and tell” (Stein, M., Engle, R. A., Smith, M. S., & Hughes, E., 2008) Anticipate student responses Learning trajectories; common obstacles Monitor and Select solutions to share Varied representations or solutions Strategically sequence sharing Progression of efficient strategies Common mistakes Interesting responses Connect representations Not C-R-A, Lesh Translation Model

Kindergarten Workshop Model: Example “Time must be allocated not only for the more formal parts of mathematics instruction and discussions, but also for children to elaborate and extend their mathematical thinking by exploring, creating, and playing” (NRC, 2009, p. 124).  LAUNCH  Engage: Read “Rooster’s Off to See the World”  EXPLORE:  How many animals went off to see the world?  SUMMARIZE  Explain: Debriefing Counting/Adding strategies  ELABORATE: MATH CENTERS

Kindergarten Workshop Model:  Standards met:  Mathematical Process Standards (MPS)  Make sense of problems and persevere in solving them (MSP 1)  “might rely on using concrete objects or pictures to help conceptualize and solve a problem” (CCSS, p. 6)  Look for and make use of structure (MSP 7)  Building around tens

 LAUNCH  Read Story  Represent new animals on each page—Discussion Questions  How do you know it’s (insert number)?  How did we make this number?  What other numbers do you see “inside”? Rooster’s OFF!

 EXPLORE:  How many animals did we meet in the book?  Look for evidence of:  1 – 1 correspondence  Writing numbers  Matching numeral to quantity  Cardinality  Number sequence  Place Value  Combinations of 5 or 10  Skip counting Rooster and Friends

 SUMMARIZE  Key concepts of counting during strategy share  Reiterate big ideas from standards  Discuss making counting within the ten frame  Expose students to “making tens”—teens are “ten and some more” Rooster and Friends

Center Time: Building on the Daily 5

CENTERS: LESSON EXTENSION  Read to self  Read to someone  Listen to reading  Work on writing  Spelling/Word Work  Independent Practice  Guided Focus Groups  Number Songs/Stories  Writing About Math  Vocabulary/Fact Fluency ELA—DAILY 5MATH CENTERS*

Independent Practice

8 is… 2 less than 10 3 more than 5 double four four “twos”

Tiered Example— Guided Practice  Quantity, Number, and Subitizing—Learning Progressions  TIER 3: Maker of Small Collections—Make Groups Cover, Copy, Compare (RtI—Tier 3)  TIER 2: Perceptual Subitizing—Dot Flash (RtI—Tier 2 through 5)  TIER 1: Conceptual Subitizing—Dot Flash, Matching (RtI—Tier 1 through 10)  TIER 4: Conceptual Subitizer with PV and Multiplication Counting Towers Game (RtI—Tier 4_Gifted/Extension) Tier 4 Special Education or ESOL

Songs and Stories

“The question is not whether all students can succeed in math, but whether the adults organizing math learning opportunities can alter traditional beliefs and practices to promote success for all” (NCTM, 2014, p. 61). Problem Based Learning

Benefits of workshop model  Students receive focused instruction  Small group format  Work caters to individual needs  Open, parallel, and tiered tasks  Evidence-based practices  Students are tiered, not tracked  Allows for rotations to by lesson or unit

Kelley Buchheister, Ph.D. University of South Carolina Instruction and Teacher Education