It’s one of the most important questions math teachers ask every day: how do we engage students in meaningful, enjoyable mathematics? In this webinar for the Adaptive Math Learning community, presenters Zachary Champagne, Researcher at the Mathematics Formative Assessment Project at the Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCR-STEM), and Tim Hudson, former Math Curriculum Coordinator for Missouri’s Parkway School District, and DreamBox’s Senior Director of Curriculum Design, shared useful insights about the Mathematical Practices that will help deepen students’ understanding, enjoyment, and success in math class. Zachary and Tim discussed how to stop teaching ‘tricks’ and instead engage students in thinking like a mathematician. They also shared insights about the power of formative assessment, the importance of uncovering students’ intuitive thinking, and how technologies such as adaptive learning can support the Mathematical Practices. Topics included: understanding equality and precision, observing students engaged in sense-making, and designing learning experiences that empower students to “look for” important mathematics. Additionally, Julie Benay, Principal of Malletts Bay School in Vermont, shared how her school implemented DreamBox and the outcomes they experienced. View the webinar to learn how to make math more engaging for your students.

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

2. Zachary Champagne
Florida Center for Research in Science, Technology, Engineering, and
Mathematics (FCR-STEM)
Email: zacharychampagne@gmail.com
Twitter: @zakchamp
Julie Benay
Principal, Malletts Bay School, Colchester VT
Email: BenayJ@csdvt.org
Twitter: @CSDCommunity
Moderator: Tim Hudson
Senior Director of Curriculum Design, DreamBox Learning
Email: timh@dreambox.com
Twitter: @DocHudsonMath

3. Exit Slip on the First &
Last Day of School:
What is Mathematics?
What do Mathematicians Do?

4. 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

5. 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

6. Common
Core State
Standards
for
Mathematical
Practice

7. Zachary Champagne
Florida Center for Research in Science, Technology, Engineering, and
Mathematics (FCR-STEM)
Email: zacharychampagne@gmail.com
Twitter: @zakchamp

8. 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

9. 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]”

10. Elaborations
The Elaboration Document can be downloaded
at the following link:
http://commoncoretools.me/2014/02/12/k-5-
elaborations-of-the-practice-standards/

11. Math Practice One
Make sense of problems and
persevere in solving them.

12. What does laying ceramic tile
have to do with
making sense of mathematics?

13. 3 inches
4 inches
5 inches

14. Why Mathematics?

15. What is Sense Making
in Mathematics?

16. 198 + 37 = ?
Consider This Problem…

17. How a fourth grade student may solve it…

18. 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).

19. 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?

20. Standard Algorithm
4
1 9
x 1 5
1 9 5
+ 1 9 0
2 8 5

21. Partial Product Algorithm
1 9
x 1 5
(9 x 5) = 4 5
(10 x 5) = 5 0
(9 x 10) = 9 0
(10 x 10) = 1 0 0
2 8 5

22. The Standard to Achieve is “Make Sense”
Which Makes More Sense?
1 9
x 1 5
(9 x 5) = 4 5
(10 x 5) = 5 0
(9 x 10) = 9 0
(10 x 10) = 1 0 0
2 8 5
4
1 9
x 1 5
1 9 5
+ 1 9 0
2 8 5
Standard
Algorithm
Partial
Products

23. © DreamBox Learning
Partial Products on the Number Line

24. Composing Partial Product Arrays
© DreamBox Learning

25. Multiplying with Partial Products
© DreamBox Learning

26. Optimal Partial Products
© DreamBox Learning

27. Making Sense of the Algorithm Visually
© DreamBox Learning

28. Algorithm with Estimate First
© DreamBox Learning

29. Distributive Property with Variables
© DreamBox Learning

30. Math Practice Six
Attend to Precision

31. 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.”

32. 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

33. A Research Study
Faulkner, K., Levi, L., & Carpenter, T. 1999

34. 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).

35. Equality
Read 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

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

37. Equality with Virtual Manipulatives
© DreamBox Learning

38. Thanks For Your Time!
Zachary Champagne
Florida Center for Research in Science, Technology,
Engineering, and Mathematics (FCR-STEM)
Email: zacharychampagne@gmail.com
Twitter: @zakchamp
Formative Assessment Tasks:
www.cpalms.org/Resources/mfas.aspx

39. Using Adaptive Learning
Technology to Support
Mathematical Development
Julie Benay
Principal
Malletts Bay School
Colchester Vermont
Email: BenayJ@csdvt.org
Twitter: @CSDCommunity

40. 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

41. 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

42. 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.

43. 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

44. 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.

45. Sample Daily Schedules
TIME 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

46. 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

47. 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.”

48. 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.

49. Math Workshop Model: Malletts Bay School
Part 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

50. 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.

51. Julie Benay
Principal, Malletts Bay School, Colchester VT
Email: BenayJ@csdvt.org
Twitter: @CSDCommunity

52. Q & A

53. Thank you!
timh@dreambox.com
@DocHudsonMath
www.dreambox.com

54. DreamBox Combines Three Essential
Elements to Accelerate Student Learning
54

55. DreamBox Lessons & Virtual Manipulatives
Intelligently adapt & individualize to:
• Students’ own intuitive strategies
• Kinds of mistakes
• Efficiency of strategy
• Scaffolding needed
• Response time

56. Robust Reporting

57. Strong Support for Differentiation

58. DreamBox supports small group and whole
class instructional resources
Interactive white-board lessons
www.dreambox.com/teachertools

59. Free School-wide Trial! www.dreambox.com