Focus on Fluency Bridging the Gaps

FOCUS ON FLUENCY BRIDGING THE GAPS

Regional Educational Laboratory (REL) Midwest and the Great Lakes West Comprehensive Center presentMaking Connections:Improving Mathematics Instruction and InterventionsWithin a Response to Intervention Framework

Cathy Shide, [email protected]

1Developed by Cathy Shide, Consultant

http://www.movingtocommoncore.com/

Goals for the Session

• 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 how to apply the research to develop fluency


What is fluency?


• ABalancedApproach:Fluencyhttp://www.youtube.com/watch?v=ZFUAV00bTwA

Video of Authors of CCSSM


http://www.youtube.com/watch?v=ZFUAV00bTwA



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.


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.


Fluencies from Listserv question• Computational fluencies – mental recall

of facts and beyond!• Procedural fluencies – algorithms and

properties of arithmetic• Conceptual fluencies – vocabulary!• Representational fluencies• Algebraic fluencies


Grade Required Fluency - http://engageny.org/wp-content/uploads/2011/07/CCSSFluencies.pdf

K Add/subtract within 5 K.OA.5

1 Add/subtract within 10 1.OA.6

2 Add/subtract within 20 2.OA.2Add/subtract within 100 (pencil and paper) 2.NBT.5

3 Multiply/divide within 100 3.OA.7Add/subtract within 1000 3.NBT.2

4 Add/subtract within 1,000,000 4.NBT.4Multi-digit multiplication 4.NBT.5

5 Addition/subtraction of fractions 5.NF.1Whole number and decimal operations 5.NBT.5

6 Multi-digit division 6.NS.1Multi-digit decimal operations 6.NS.3

7 Operations with rational numbers 7.NS.1Solve equations px + q = r, p(x + q) = r 7.EE.4a

8 Solve linear equations in one variable 8.EE.7Solve pairs of simultaneous linear equations 8.EE.8 8

http://engageny.org/wp-content/uploads/2011/07/CCSSFluencies.pdf

High School Required Fluency PARCC Content Frameworks

Computing fluently with positive and negative fractions and decimals.

Applying ratio reasoning in real-world and mathematical problems

Solve real-world and mathematical problems involving angle measure, area, surface area, and volume

Because important standards for college and career readiness are distributed across grades and courses, systems for evaluating college and career readiness should reach as far back in the standards as Grades 6-8

A.REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 9

Computational Fluency

• Multiply 16 x 35 mentally• Only write an answer• Share your strategies in your

table• 384/16


Strategies vs Procedures

• Counting on• Patterns–Fact families–Doubles–Times 5, times 9,

square numbers

• Composing and decomposing numbers to . . .–Make a ten–Make a double–Make a known fact–Make friendly

numbers11Developed by Cathy Shide, Consultant

Fact fluency development

• Follows the progression of learning – concrete, representations or pictures, abstract.• Teacher needs to choose problems

strategically• Time spent with strategies in

different context12Developed by Cathy Shide, Consultant

Flash Cards & Games

• Look at the games that are described in the handout

• What fluency would the game help to build in your students?

• How could this game be used or modified to help struggling learners.


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!


“If a child can't learn the way we teach, maybe we should teach the way they learn.”

Ignacio Estrada15Developed by Cathy Shide, Consultant


• Number Talks – Helping Children Build Mental Math and Computation Strategies, Grades K-5, Sherry Parrish author, from Math Solutions

• Number Talks - http://www.insidemathematics.org/index.php/classroom-video-visits/number-talks

17

Resources

Developed by Cathy Shide, Consultant

High School Strategies

• Increasing Decreasing Quantities lesson http://map.mathshell.org.uk/materials/lessons.php?taskid=210&subpage=concept

• Pre-Assessment Probes – Uncovering Student Thinking in Mathematics, Grades 6-12: 30 Formative Assessment Probes for the Secondary Classroom

• Secondary Number Talks - http://www.sandi.net/cms/lib/CA01001235/Centricity/Domain/217/middle_level_bank.pdf


http://map.mathshell.org.uk/materials/lessons.php?taskid=210&subpage=concept



Recommendation 2

• Instructional materials should focus on whole numbers in K-5 and rational numbers grades 4-8


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


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.


Recommendation 6

• 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.

• 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

Documents

Focus on Fluency Bridging the Gaps