As the focus on standards-readiness grows, we need reassurance that we’re not just teaching students how to pass a test, but also supporting their exploration, creativity and deep understanding of applied knowledge. In this webinar for the edWeb.net Adaptive Math Learning community, Joe Trahan and Kelly Urlacher, former Middle School teachers and current Curriculum Designers at DreamBox Learning, discussed the pedagogical approach to preparing students for formal algebra. They shared opportunities educators have to introduce abstract concepts at an early age – at a time when students are more focused on concrete mathematical concepts. Kelly and Joe discussed opportunities to foster mathematical exploration at an early age, digital tools to support concrete and abstract mathematical manipulations, and insights around how to engage middle school students and cultivate math confidence. View the webinar to learn how to prepare your students for pre-algebraic concepts.

1. A Common Model for Elementary
Classes
Middle School Classes?

2. Elementary Class
vs.
Secondary
Class

3. What is Algebra?
Grant Wiggins, 2013
“Algebra, as we teach it, is a death march
through endless disconnected technical tools
and tips, out of context.”
“Our student surveys
consistently rank HS math as
their least favorite course, by a
wide margin – though 22% list it
as their favorite. 46% don’t
merely like it least: they hate it.”

4. Can Middle to High School Math
become Accessible to All
MSantyu stdudeentns sttasrt? struggling with math as they venture into Algebra
and Calculus.
But what will engage them?

5. Manipulatives in Math
• Research supports the
use of manipulatives
• Students gain deep
understanding by using
manipulatives in their
math learning.
• Exploration comes to life.
• Manipulatives
are a means,
not an end.

6. Concrete Manipulatives
What does concrete mean?
Sensory-Concrete
Using materials to make sense of an idea
Integrated-Concrete
Built through learning (interconnected)
Thinking like a mathematician, ideas are made integrated-concrete
through meaning.

7. The Power of Digital Manipulatives
Digital materials can be just as meaningful as real objects!
Concrete and Symbolic
Link the concrete and symbolic with
feedback and representations
Cleaner
No management of physical tools.
More Flexible
No restriction of physical objects, limits of size, scale, material.
Thoughtful Assessment and Reporting
Specific and fast communication to teacher and student
Cleverly Restrictive
Restrictions CAN be set for targeted learning

8. Rate of Change
The long road through this “big idea” in Algebra

9. Checking Ourselves…
How are we avoiding the trap of “disconnected Algebra”?
Are we forcing
students through
context-less
practice?
Or giving them tools
to have rich
conversations?

10. How do we create context and connections for Algebra?
A Word Problem:
An Introduction or a
Conclusion?
What is Context?
Commonly these are used
as one-off challenges to
practice new skills or give
context for learning a new
skill.

11. What is Context?
Models vs. Stories
Look for the contexts that
can be used through
learning.
Extend investigations over
multiple lessons to explore
many facets of a
mathematical context.
Does it have to be “real
life” to be accessible?

12. What is Context?
What does it take to be rigorous? Or perplexing?
Are students challenged?
Are they encouraged to be
persistent and to try out
their own strategies?

13. Critical Math Practices using
Standards
Using technology to align to the Standards of
Mathematical Practice.
Important to focus
purposefully on the
Standards for
Mathematical Practice.

14. Quadratic Expressions
Multiplication with Arrays & Landmarks in 4th grade
Building squared bases
Using the tool to create an array to represent the
expression

15. Tips for Developing Lessons
Strategies for making engaging, connected experiences, either in the class, or on
desktop.
1. Think big picture.
2. Use research.
3. Collaborate.

16. DreamBox Learning K-8 Math
Intelligent Adaptive Learning™
Engine
• Millions of personalized learning paths
• Tailored to a student’s unique needs
Motivating Learning
Environments
• Student Directed, Empowering
• Leverages Gaming Protocols
Rigorous Mathematics
Curriculum
• Reporting Aligned to CCSS,
Texas TEKS, Virginia SOL,
Canada WNCP, & Canada
Ontario Curriculum Reports
• Standards for Mathematical
Practice
Seeing is believing! dreambox.com/request-a-demo

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

18. Progress Monitoring Reporting

19. Strong Support for Differentiation

20. FREE Interactive Whiteboard Lessons
DreamBox supports small group and whole class instructional
resources.
www.dreambox.com/teachertools

21. We value your feedback, compliments,
suggestions, and complaints!
Let us know how we’re doing:
https://www.surveymonkey.com/s/MD8J6Z7
Also, join us for a 15 minute Tweet-Up Session
immediately following this webinar: #edwebchat