FOCUS ON FLUENCY BRIDGING THE GAPS Regional Educational Laboratory (REL) Midwest and the Great Lakes West Comprehensive Center present Making Connections: Improving Mathematics Instruction and Interventions Within a Response to Intervention Framework Cathy Shide, 1Developed by Cathy Shide, Consultant

Goals for the Session Introduce the fluencies required at each grade level in grades K-12 as specified in the CCSSM Introduce the fluencies required at each grade level in grades K-12 as specified in the CCSSM Understand that balanced emphasis requires that teachers create opportunities for students to develop fluencies Understand that balanced emphasis requires that teachers create opportunities for students to develop fluencies Understand how to apply the research to develop fluency Understand how to apply the research to develop fluency 2Developed by Cathy Shide, Consultant

What is fluency? 3Developed by Cathy Shide, Consultant

ABalancedApproach:Fluencyhttp://ww w.youtube.com/watch?v=ZFUAV00bTw A ABalancedApproach:Fluencyhttp://ww w.youtube.com/watch?v=ZFUAV00bTw A ABalancedApproach:Fluencyhttp://ww w.youtube.com/watch?v=ZFUAV00bTw A ABalancedApproach:Fluencyhttp://ww w.youtube.com/watch?v=ZFUAV00bTw A Video of Authors of CCSSM Video of Authors of CCSSM 4Developed by Cathy Shide, Consultant

What is fluency? Fluent in the Standards means “fast and accurate.” It might also help to think of fluency as meaning the same thing as when we say that somebody is fluent in a foreign language: when you’re fluent, you flow. Fluent isn’t halting, stumbling, or reversing oneself. Fluent in the Standards means “fast and accurate.” It might also help to think of fluency as meaning the same thing as when we say that somebody is fluent in a foreign language: when you’re fluent, you flow. Fluent isn’t halting, stumbling, or reversing oneself. 5Developed by Cathy Shide, Consultant

Fluency is related to “quickness”, but it is not just about time. It is about ease of use and confidence in proceeding. For fact fluency, it is about remembering facts with automaticity. Procedural fluency is related to things you do “without having to stop repeatedly to determine next steps.” It enables students to get to application, problem solving, and increased complexity much faster. It facilitates the development of deeper understanding. Fluency helps students access their answers through different vantage points. 6Developed by Cathy Shide, Consultant

Fluencies from Listserv question Computational fluencies – mental recall of facts and beyond! Computational fluencies – mental recall of facts and beyond! Procedural fluencies – algorithms and properties of arithmetic Procedural fluencies – algorithms and properties of arithmetic Conceptual fluencies – vocabulary! Conceptual fluencies – vocabulary! Representational fluencies Representational fluencies Algebraic fluencies Algebraic fluencies 7Developed by Cathy Shide, Consultant

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Computational Fluency Multiply 16 x 35 mentally Multiply 16 x 35 mentally Only write an answer Only write an answer Share your strategies in your table Share your strategies in your table 384/16 384/16 10Developed by Cathy Shide, Consultant

Strategies vs Procedures Counting on Counting on Patterns Patterns – Fact families – Doubles – Times 5, times 9, square numbers Composing and decomposing numbers to... Composing and decomposing numbers to... – Make a ten – Make a double – Make a known fact – Make friendly numbers 11Developed by Cathy Shide, Consultant

Fact fluency development Follows the progression of learning – concrete, representations or pictures, abstract. Follows the progression of learning – concrete, representations or pictures, abstract. Teacher needs to choose problems strategically Teacher needs to choose problems strategically Time spent with strategies in different context Time spent with strategies in different context 12Developed by Cathy Shide, Consultant

Flash Cards & Games Look at the games that are described in the handout Look at the games that are described in the handout What fluency would the game help to build in your students? What fluency would the game help to build in your students? How could this game be used or modified to help struggling learners. How could this game be used or modified to help struggling learners. 13Developed by Cathy Shide, Consultant

Math Wars A player takes two cards and adds the numbers and records the sum. Next player repeats this process during his turn The player with the highest sum gets the cards. Continue play until all cards are done. See which player has the most cards. Make Adjustments to this game! 14Developed by Cathy Shide, Consultant

“If a child can't learn the way we teach, maybe we should teach the way they learn.” Ignacio Estrada 15Developed by Cathy Shide, Consultant

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Number Talks – Helping Children Build Mental Math and Computation Strategies, Grades K-5, Sherry Parrish author, from Math Solutions Number Talks – Helping Children Build Mental Math and Computation Strategies, Grades K-5, Sherry Parrish author, from Math Solutions Number Talks - p/classroom-video-visits/number-talks Number Talks - p/classroom-video-visits/number-talks 17 Resources Developed by Cathy Shide, Consultant

High School Strategies Increasing Decreasing Quantities lesson ?taskid=210&subpage=concept Increasing Decreasing Quantities lesson ?taskid=210&subpage=concept ?taskid=210&subpage=concept ?taskid=210&subpage=concept Pre-Assessment Probes – Uncovering Student Thinking in Mathematics, Grades 6-12: 30 Formative Assessment Probes for the Secondary Classroom Pre-Assessment Probes – Uncovering Student Thinking in Mathematics, Grades 6-12: 30 Formative Assessment Probes for the Secondary Classroom Secondary Number Talks - city/Domain/217/middle_level_bank.pdf Secondary Number Talks - city/Domain/217/middle_level_bank.pdf 18Developed by Cathy Shide, Consultant

Recommendation 2 Instructional materials should focus on whole numbers in K-5 and rational numbers grades 4-8 Instructional materials should focus on whole numbers in K-5 and rational numbers grades Developed by Cathy Shide, Consultant

Recommendation 3 Instruction during the intervention should be explicit and systematic.... Models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review Instruction during the intervention should be explicit and systematic.... Models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review 20Developed by Cathy Shide, Consultant

Recommendation 5 Intervention materials should include opportunities for students to work with visual representations of mathematic ideas and interventions should be proficient in the use of visual representations of mathematical ideas. Intervention materials should include opportunities for students to work with visual representations of mathematic ideas and interventions should be proficient in the use of visual representations of mathematical ideas. 21Developed by Cathy Shide, Consultant

Recommendation 6 Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts. Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts. – K-2 efficient counting – 2-8 = knowledge of properties of arithmetic (page 90 of CCSSM) 22Developed by Cathy Shide, Consultant

Recommendation 7 & 8 Monitor the progress of students receiving supplemental instruction and other students who are at risk. Monitor the progress of students receiving supplemental instruction and other students who are at risk. Include motivational strategies in tier 2 and tier 3 interventions Include motivational strategies in tier 2 and tier 3 interventions – Allow students to chart their progress and to set goals for improvement. 23Developed by Cathy Shide, Consultant