Want to Engage Your Students? Engage Them in the Math Practices

Want to EngageYour Students?

Engage Them in the Math Practices

Zachary ChampagneFlorida Center for Research in Science, Technology, Engineering, and Mathematics (FCR-STEM)Email: [email protected] Twitter: @zakchamp

Julie BenayPrincipal, Malletts Bay School, Colchester VT Email: [email protected]: @CSDCommunity

Moderator: Tim HudsonSenior Director of Curriculum Design, DreamBox LearningEmail: [email protected]: @DocHudsonMath

Exit Slip on the First &Last Day of School:

What is Mathematics?

What do Mathematicians Do?

From a 5th grade teacher in NY:“I had a lot of good people teaching me

math when I was a student – earnest and funny and caring. But the math they taught me wasn’t good math. Every class was the

same for eight years:

‘Get out your homework, go over the homework, here’s the

new set of exercises, here’s how to do them. Now get

started. I’ll be around.’p. 55, Teaching What Matters Most, Strong, Silver, & Perini,

©2001

Design Limitation“They were so concerned with

making sure we knew how to do every single procedure we never

learned how to think mathematically. I did well in math but I never understood what I was doing. I remember hundreds of procedures but not one single

mathematical idea.”

p. 55, Teaching What Matters Most, Strong, Silver, & Perini, ©2001

Common Core State Standards

for Mathematical Practice

MFAS-CCSS Project • Approximately 1300 K – Geometry Tasks and

Rubrics developed between 2011 – 2013 and are now available via CPALMS http://www.cpalms.org/Resource/mfas.aspx

• K – 3; Algebra and Geometry Lesson Study Toolkits developed between 2011 – 2013 are now available via CPALMS

http://www.cpalms.org/Resource/mfas.aspx



Mathematics Practice Standards

“These standards describe the varieties of expertise that mathematics educators at all levels should seek to develop in their students.”

“[They] describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise [K-12]”

Elaborations

The Elaboration Document can be downloaded at the following link:

http://commoncoretools.me/2014/02/12/k-5-elaborations-of-the-practice-standards/




Math Practice OneMake sense of problems andpersevere in solving them.

What does laying ceramic tile have to do with

making sense of mathematics?

3 inches

4 inches

5 inches

Why Mathematics?

What is Sense Makingin Mathematics?

198 + 37 = ?

Consider This Problem…

How a fourth grade student may solve it…

What About the Content Standards?

1.OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.• Use strategies such as counting on;• making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 =

14);• decomposing a number leading to a ten (e.g.,

13 – 4 = 13 – 3 – 1 = 10 – 1 = 9);• using the relationship between addition and

subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4);

• and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Consider This Context..

At one very lucky elementary school there were exactly 15 students in every

class. At the school there were 19 classrooms. How many students

attended the school?

Standard Algorithm

Partial Product Algorithm

The Standard to Achieve is “Make Sense”

Which Makes More Sense?

Standard Algorithm

PartialProducts

© DreamBox Learning

Partial Products on the Number Line

Composing Partial Product Arrays


Multiplying with Partial Products


Optimal Partial Products


Making Sense of the Algorithm Visually


Algorithm with Estimate First


Distributive Property with Variables


Math Practice SixAttend to Precision

What Does Precision Look and Sound Like in Mathematics?

“[Students] state the meaning of the symbols they choose, including using the equal sign

consistently and appropriately.”

The Equal Sign

• Children in the elementary grades generally think that the equal sign means that they should carry out the calculation that precedes it and that the number after the equals sign is the answer to the calculation.

• Children must understand that equality is a relationship that expresses the idea that two mathematical expressions hold the same value.

Faulkner, K., Levi, L., & Carpenter, T. 1999

A Research Study

Faulkner, K., Levi, L., & Carpenter, T. 1999

Common Core - Equality in K- 2

1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?.

K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way,

e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

EqualityRead each equation aloud and say whether it is true or not true. Then say why you think so.

8 = 4 + 4

3 + 2 = 4 + 1

7 = 7

3 + 3 = 8

A First Grader’s View on Equality (Take 1 and 2)

http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/36526

Equality with Virtual Manipulatives


Thanks For Your Time!


Formative Assessment Tasks: www.cpalms.org/Resources/mfas.aspx

http://www.cpalms.org/Resources/mfas.aspx

Using Adaptive Learning Technology to Support

Mathematical Development

Julie BenayPrincipal

Malletts Bay SchoolColchester Vermont Email: [email protected]: @CSDCommunity

About Malletts Bay School• On the shores of Lake Champlain, minutes from

Burlington• Public school district of about 2,000 students• Five Buildings

• Two K-2 Schools• Malletts Bay School (PreK and 3-5)• 1 Middle School• 1 High School.

• Malletts Bay divides the community into distinct areas.

• District Hallmark• Leadership in implementing differentiated

instruction

Malletts Bay Students

• Many of our families live in Colchester & work elsewhere

• High percentage of divided or single parent families• Over the past 10 years, grown to nearly 40% of

students who qualify for Free or Reduced Price Lunch• Small, but growing, population of English Learners

because Colchester is close to the Vermont Refugee Resettlement Center

• ~17% of our students qualify for special education or a Section 504 plan.

• Majority of our families have Internet access

Math at Malletts Bay School• CCSS-based Curriculum• Core program: Everyday Math (EDM)• All teachers follow a District pacing guide for EDM• Each unit of EDM focused on a “big idea” aligned with

standards and using supplemental resources• Locally designed assessments determine the focus of

instructional planning in each classroom• “Workshop” model enables teachers to focus on instructing

small groups of students based on learning needs• Our District employs one math coach who works across the

three elementary settings with 45 teachers.• When we began using an adaptive math program

(DreamBox), we did not have a Title I funded math intervention program.

Math Achievement• For the past three years, we have exceeded

Vermont state average• Vermont’s No Child Left Behind (NCLB) test has been the

New England Common Assessment (NECAP).• We meet Adequate Yearly Progress for “All”

students• We are “Identified” for:

• subgroups of students with disabilities• particularly concerning, with only about 1/3 of students

meeting the standard

• Subgroups of students from lower income homes

Access to Technology At MBS• All classrooms have at least four devices:

• laptops• netbooks• desktops• Students access DreamBox in the classroom

during independent practice or skills time.• Small dedicated “mini-lab” reserved for students

on IEPs to access specialized programs• 21 Classrooms share 1 laptop cart and 1 ipad cart• WiFi throughout the building.• All classrooms have an interactive whiteboard.

Sample Daily SchedulesTIME Teacher A TIME Teacher B

8:30-8:40 Attendance and announcements

8:30-8:40 Attendance and announcements

8:45-9:30 Unified Arts (PE, Music, Art, etc)

8:40-9:10 Math Intervention

9:30 – 10:25 Writing/Word Study

9:10-10:10 Math Instruction

10:25-11:25 Math 10:10-11:05 Writing/Word Study

11:25-11:45 Math Intervention

11:10-11:50 Lunch/Recess

11:50-12:30 Lunch/recess 11:50-12:40 Science or Social Studies

12:30 – 1:25 Science or Social Studies

12:40-1:40 Reading Instruction

1:25-2:25 Reading Instruction

1:40-2:10 Reading Intervention

2:25-2:55 Reading Intervention

2:10-2:55 Unified Arts

3:00 Dismissal 3:00 Dismissal

Adaptive Learning at MBS

• We learned about DreamBox through a workshop attended by one of our special educators

• After exploring the program (playing in the “sandbox”) and talking with DreamBox, we purchased a limited number of seats for students with disabilities in grades K-5

• All special educators attended a free training session to learn how to:• manage rosters• utilize and interpret the rich data provided by the software.

• Parents were engaged through DreamBox parent letters• All students assigned a “seat” in the program had access

both at home and at school

Early Feedback• We saw results immediately

• The process of placing students in the program:

• gave us good information about critical gaps in the learning progression

• helped us tailor instructional support in the classroom and in special education instructional sessions.

• Students really enjoyed DreamBox.

• Other programs we used required a great deal of practice and repetition, and students resisted being assigned to use them

• Conversely, students looked forward to using DreamBox and did not want to sign off when their sessions ended!

• DreamBox provided learning experiences well matched to students development of mathematical thinking.

• Students are provided with just enough challenge to keep the sessions interesting, and subtle prompts and direction for strategies when they were “stuck.”

• Students are engaged by the games personalizing their “rooms.”

Adaptive Learning in the Math Workshop• Once other students in the classroom observed their peers

using DreamBox, they asked if they could have access!• Our K-5 team considered the results of DreamBox• We are now working to implement a math workshop model

that will allow teachers time to balance whole group instruction with small guided math groups.

• Our workshop model encourages the use of the eight Math Practices so key to the Common Core math standards.

• We have expectations for instruction to ensure that the adaptive learning program supplemented instruction, not replacing it

• Ongoing data updates are shared among teachers, special educators, and parents to ensure coordinated efforts to help students grow in their mathematical thinking and achievement.

Math Workshop Model: Malletts Bay SchoolPart I: Mini-lesson (Full Class)

• Post learning target• Warm up: Mental Math, Math Message• Direction Instruction: Big Ideas • Guided practice and gradual release (modeling, partner work, small groups)

Part II: Small groups and Independent Practice (connected to Big Idea) May include:

• Teacher led small groups• Planned, differentiated stations (games, problem solving)• Pairs, student-led groups• Seatwork and independent practice (Everyday Math “math boxes”)

Part III: Summary and Closing (Full Class)• Questions, comments, observations• Reflections, exit tickets• Homework explanation

Part IV: Intervention (Additional Dedicated Practice) May include:• Additional practice related to this lesson’s Big Idea• Practice with basic facts and skills• Enrichment• Dedicated time for students to leave for supplemental or specialized instruction

Tiers of Support & Universal Access• Our school uses a tiered model of support. A key feature is to

ensure that all students benefit from “first instruction” in grade level standards.

• To accomplish this, we set aside a specific time in the daily schedule for supplemental instruction.

• Students who leave the classroom for Tier II or Tier III instructional support leave during these periods.

• We see the potential for DreamBox to serve as an engaging and perfectly tailored “anchor activity” within our workshop model.

• With an eye toward prevention, we used DreamBox with students who were having difficulties in math but who were not identified as needing special education.

• Beginning in 2014, all students K-5 will have access to this adaptive learning program.

Julie BenayPrincipal, Malletts Bay School, Colchester VT Email: [email protected]: @CSDCommunity

Thank you!

[email protected]@DocHudsonMath

www.dreambox.com

DreamBox Combines Three Essential Elements to Accelerate Student Learning

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DreamBox Lessons & Virtual Manipulatives

Intelligently adapt & individualize to:

• Students’ own intuitive strategies

• Kinds of mistakes

• Efficiency of strategy

• Scaffolding needed

• Response time

Robust Reporting

Strong Support for Differentiation

DreamBox supports small group and whole class instructional resources

Interactive white-board lessonswww.dreambox.com/teachertools

http://www.dreambox.com/teachertools

http://www.dreambox.com/teachertools

Free School-wide Trial!www.dreambox.com

http://www.ffennell.com/

Want to Engage Your Students? Engage Them in the Math Practices

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