Broadening Our Defini;on for Student Success DeAnn Huinker - PowerPoint PPT Presentation

Fluency is Not a Simple Idea: Broadening Our Defini;on for Student Success DeAnn Huinker University of Wisconsin-Milwaukee Wisconsin Mathema;cs Council Annual Mee;ng Thursday, May 4, 2017, 1:00-2:00 pm Session #179 (Bauer – Morehouse C) Focus: Grades K-5

Session Goal “To have a conversa;on about fluency and unravel some of its complexi;es.” § What is the meaning of fluency in math? § What are some instruc;onal implica;ons related to fluency?

Fluency . . .

Stop & Jot • Fluency in math means . . . • Concerns I have about what fluency seems to mean to others . . . (e.g., parents, students, administrators, teachers)

25 + 37 = ? Study the student work samples. Assume this is typical of the student. • Is each student fluent with two-digit addi;on? • What observa;ons can you make about each students’ level of fluency?

Student 1 Student 2 Student 3 Student 4

Fluency Having and using efficient and accurate methods for compu;ng. (NCTM, 2000, p. 32, 79, 84, 144 ) Na;onal Council of Teachers of Mathema;cs.(2000). Principles and Standards for School Mathema:cs . Reston, VA: Author.

Message #1 Fluency: accuracy is important, but it isn’t enough.

What fluency is not!

The Story of Ryan, Grade 4 I know all my mul;plica;on facts. I’m the fastest in my class! Do I add or subtract? I hate word problems. I’m good at adding, subtrac;ng, mul;plying, and dividing numbers!

What does it mean to be smart or good in mathema;cs? What would your students say? Featherstone, H., Crespo, S., Jilk, L. M., Oslund, J. A., Parks, A. N., & Wood, M. B. (2011). Smarter together! Collabora:on and equity in the elementary math classroom . Reston, VA: Na;onal Council of Teachers of Mathema;cs..

It means to be smart and know what 6 th graders know. It also means to do problems very fast. You answer problems quickly. You do good on tests. Grade 3 Students

I think it means that all the math problems just come to your mind no maier how big the problem is, even 50 x 50 = 2500. Grade 3 Student

“It’s a widespread belief that to be good at math means to be fast at computa;on. But this belief may in fact do more harm as good.” “Overemphasizing fast fact recall at the expense of problem solving and conceptual experiences give students a distorted experience and they ooen turn away from mathema;cs for years, some;mes forever.” -- Cathy Seeley, NCTM Past-President Seeley, Cathy L. Faster isn't smarter: messages about math, teaching, and learning in the 21st century: a resource for teachers, leaders, policy makers, and families . Sausalito, CA: Math Solu;ons, 2009. (p. 93, 95)

A rush to fluency undermines students’ confidence and interest in mathema:cs and is considered a cause of mathema:cs anxiety. (Ashcrao 2002; Ramirez et al., 2013) Ashcrao, M. H. (2002). Math anxiety: Personal, educa;onal, and cogni;ve consequences. Current Direc:ons in Psychological Science , 11 (5), 181-185 Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2013). Math anxiety, working memory, and math achievement in early elementary school. Journal of Cogni:on and Development, 14(2), 187-202..

Steve Leinwand, American Ins;tutes for Research, Washington, D.C. Sue O’Connell, Quality Teacher Development, Millersville, MD

“Fluency is not instantaneous recall, fluency is not memory. Fluency requires understanding and strategies. And there is a maier of efficiency. Fluency efficiency, not fluency speed.” -- Steve Leinwand

Message #2 Fluency ≠ Speed Fluency ≠ Recall

Efficiency . . .

What does Steve mean by: “Fluency efficiency, not fluency speed.”

Efficiency implies that the student does not get bogged down in too many steps or lose track of the logic of the strategy. An efficient strategy is one that the student can carry out easily, keeping track of subproblems and making use of intermediate results to solve the problem. --Susan Jo Russell, TERC Russell, Susan Jo. "Developing computa;onal fluency with whole numbers." Teaching Children Mathema:cs 7, no. 3 (2000): 154-158. (p. 158)

6 x 12 = ? Javier, Grade 5 ( 1:10 minutes) hip://www.sci.sdsu.edu/CRMSE/sdsu-pdc/nickerson/imap/files/clips/Javier.mov

Message Efficiency ≠ speed #3 Efficiency à strategies Efficiency involves using strategies based on number and opera;on rela;onships while keeping track of the quan;;es and groups.

Let’s work on our own “efficiency” in reasoning. . .

17 x 5= ? 8 x ? = 336 6 x 98 = ? 24 x 25= ? Mental Math Solve in your head. No pencil or paper! Focus: Efficiency

17 x 5= ? 8 x ? = 336 6 x 98 = ? 24 x 25= ? Consider how you used these understandings: n Composing and decomposing n Place value ideas n Proper;es of the opera;ons n Rela;onships among the opera;ons

24 x 25 = ? I thought 25 x 25 = 625 and then I subtracted 25. 625 – 25 = 600. Distribu%ve Property : (25 – 1) x 25 = (25 x 25) – (1 x 25) I figured that there are I thought 4 twenty-fives in 100, 24 x 100 = 2400, and there are 6 fours in and 2400 ÷ 4 = 600. 24, so 6 x 100 = 600. Iden%ty & Inverse Ideas Associa%ve Property : 25 = 4 x 25 ÷ 4 (6 x 4) x 25) = 6 x (4 x 25) (24 x 100) ÷ 4 = 2400 ÷ 4 = 600

24 x 25 = ? 25 x 4 = 100, 6 x 100 = 600, 600 + 100 = 700. “I would try to “Got lost!” mul;ply in my head, but I can't do that.” Well, 10 x 25 = 250, 2(10 x 25) = 500, 500 x 4 = 2000. Trying to use the distribu%ve property .

s e g a 1. Accuracy is important, but not enough. s s e M 2. Fluency ≠ speed (or recall). 3. Efficiency is using strategies based on number and opera;on rela;onships while keeping track of quan;;es and groups (not geyng lost). 4. ...

Mathema;cal Proficiency and the Role of Procedural Fluency

The Strands of Mathema;cal Proficiency Conceptual Understanding Strategic Produc;ve Competence Disposi;on Adap;ve Procedural Reasoning Fluency Na;onal Research Council. (2001). Adding it Up: Helping Children Learn Mathema:cs . Washington, D.C.: Na;onal Academy Press.

The Strands of Mathema;cal Proficiency Grasp concepts, Conceptual opera;ons, & rela;ons. Understanding Strategic Produc;ve Competence Disposi;on Pose, represent, See math as sensible, and solve problems. useful, & doable. Adap;ve Procedural Reasoning Fluency Use logic to explain & jus;fy approaches. Na;onal Research Council. (2001). Adding it Up: Helping Children Learn Mathema:cs . Washington, D.C.: Na;onal Academy Press.

Procedural fluency refers to: • knowledge of procedures, • knowledge of when and how to use them appropriately, and • skill in performing them flexibly, accurately, and efficiently. (NRC, 2001, p. 121) Na;onal Research Council. (2001). Adding it Up: Helping Children Learn Mathema:cs . Washington, D.C.: Na;onal Academy Press.

Procedural fluency refers to: • knowledge of procedures, • knowledge of when and how to use them appropriately, and • skill in performing them flexibly, accurately, and efficiently. (NRC, 2001, p. 121) Na;onal Research Council. (2001). Adding it Up: Helping Children Learn Mathema:cs . Washington, D.C.: Na;onal Academy Press.

Flexibility requires knowing more than one approach to solving a par;cular kind of problem. Students need to be flexible to be able to choose an appropriate strategy for the problem at hand and be able to use another method to double-check the results. --Susan Jo Russell, TERC Russell, Susan Jo. "Developing computa;onal fluency with whole numbers." Teaching Children Mathema:cs 7, no. 3 (2000): 154-158. (p. 158)

Message #4 Flexibility à Good Choices Flexibility involves choosing a strategy appropriate for the numbers in the problem and for the opera;on.

Let’s work on our “flexibility” in compu;ng. . .

564 + 9 = ? 72 – 29 = ? 75 + 78 = ? 2005 – 998 = ? Mental Math Solve in your head. No pencil or paper! Focus: Flexibility

8 + 9 = ? 72 – 29 = ? 25 + 37 = ? 2002 – 998 = ? Consider how you used these understandings: n Composing and decomposing n Place value ideas n Proper;es of the opera;ons n Rela;onships among the opera;ons

72 – 29 = ? Subtract 72 – 30, that’s 42. Removed 1 too many, so I put it back on; answer is 43. ( Use a friendly number, then compensate ) Start at 29, add 1 to I changed the problem get to 30, add 40 to get to 73 - 30, that to 70, add 2 to get to 72, so 1 + 40 + 2 = 43. equals 43. ( Constant difference ) ( Add up in chunks)

s e g a 1. Accuracy is important, but not enough. s s e M 2. Fluency ≠ speed (or recall). 3. Efficiency is using strategies based on number and opera;on rela;onships while keeping track of quan;;es and groups (not geyng lost). 4. Flexibility involves choosing a strategy appropriate for the numbers in the problem and the opera;on.

Stop & Jot Revisit your thoughts about fluency, add addi;onal thoughts or notes. What adjustments did you make to your ini%al defini%on? Which ideas were affirmed or deepened?

Developing Fluency

Steve Leinwand, American Ins;tutes for Research, Washington, D.C. Sue O’Connell, Quality Teacher Development, Millersville, MD Start at 1:13