Spiraling in Mathematics - Dawn Butson @DL_Buts #spiraling

Spiraling in Mathematics

       Dawn Butson

         @DL_Buts
         #spiraling

Your questions:
Go to the Google Form below to send me your questions:

https://goo.gl/forms/nmHtJ1DTEgi3Nq1q1

Have you ever heard...?

“We never learned that last year!”
               or
    “I forget how to do that.”

    Solution = Spiraling

What is Spiralling?
• Learning spread out over time
• Not teaching units in isolation
• Teaching concepts in small doses
  throughout the year
• Revisiting concepts
• Building on knowledge each time a
  concept is revisited

The Ontario Mathematics Curriculum:
When developing their mathematics program and units of study from this document,
teachers are expected to weave together related expectations from different strands,
as well as the relevant mathematical process expectations, in order to create an
overall program that integrates and balances concept development, skill acquisition,
the use of processes, and applications (pg. 7).

Effective instructional approaches and learning activities draw on students’ prior
knowledge, capture their interest, and encourage meaningful practice both inside and
outside the classroom. Students’ interest will be engaged when they are able to see
the connections between the mathematical concepts they are learning and their
application in the world around them and in real-life situations (pg 25).

The Guide to Effective Instruction:
Students are better able to see the connections in mathematics, and thus to learn
mathematics, when it is organized in big, coherent “chunks”. In organizing a
mathematics program, teachers should concentrate on the big ideas in mathematics
and view the expectations in the curriculum policy documents for Grades 4 to 6 as
being clustered around those big ideas.

Why Spiral?
• Students have more opportunities to
  learn and understand a concept
• Retention of concepts is increased
• It reaches all learners
• Students can see a variety of math
  concepts in one learning cycle
• Students make deeper connections
  between math strands and concepts

Planning Process
• Cut out curriculum expectations
• Colour code expectations by strand

• Decide upon BIG IDEAS – Do you teach
  to the big ideas? PollEv.com/dawnbutson725
• Connect expectations to a BIG idea

• Choose a real world activity, project or
  provocation to use (optional)
• Create three part lessons

Note:
   Highlighted
     parts of
  expectations
   will NOT be
  addressed in
this spiral. They
will be covered
   when these
  concepts are
  revisited in a
 future learning
      cycle.

Example of unit teaching:
       September / October:
Unit         Expectations
Integers     - identify and compare integers found in real-life
             contexts
             - represent and order integers, using a variety of tools
             - add and subtract integers, using a variety of tools

Example of spiral teaching:
Big Idea:                 Expectation
There are many ways to    - represent: integers, decimals, fractions, perfect
represent a number.       squares, square roots in a variety of ways, select
                          and justify the most appropriate representation of a
                          quantity

Numbers can be            - Order and compare: integers, decimals, and
compared by their value   fractions
and also to benchmark
numbers.
Operational Sense         - Adding and subtracting: integers, fractions,
(meanings &               decimals.
relationships)

fraction mind map from CLC

Assessment
• Every 1-2 weeks – assessment for
  learning along the way.
• Observation
• Conversation
• Summative at end of learning cycle
• Assessing multiple strands at a time

Examples:

My personal reflections and observations
 Students have more surface level knowledge about a
 wide range of topics earlier in the school year and build
 on that base knowledge as the year progresses.

 Recalling and applying prior knowledge is easier for
 students when concepts are revisited.

 Students are more successful at rich/robust tasks
 because they have more confidence and a greater
 understanding of skills and concepts.

 Students make connections and see relationships
 between math strands and concepts.

Challenges of Spiraling
•   Finding time to create a learning cycle
•   Deciding on big ideas
•   Envisioning what the whole year will look like
•   Letting go of the textbook
•   Not knowing if you are “doing it right”

FAQ: How do you spiral with a combined grade or division?

     Are there any other challenges you can think of?
                  (Comment in the chat box)

FAQs
1. What do parents and administrators think?
2. What do the students say about spiraling?
3. How do you do long range plans with spiraling?
4. How do you keep track of the expectations?
5. What is the best way for students to track/record
   their efforts & understanding? Log sheet / notebook
   / other?
6. Where can I find resources for spiraling?

               Questions or comments?

FAQ: What are my “must haves”?

How do I keep tasks rich and engaging?

What is the best way for students to
    track/record their efforts &
understanding? Log sheet / notebook /
               other?

Next steps: I challenge you to
take a step towards spiraling!

Choose one foundational concept that you
 want to revisit through the year. See what
other areas that concept can be connected
 to and build on it each time you revisit it.

Thank you!!

  @DL_Buts
  #spiraling

Other Resources to Learn about
             Spiral:
Kristin Phillips
https://www.youtube.com/watch?v=4jLANkgniSM

Jon Orr
http://mrorr-isageek.com/a-peek-into-my-classroom/

Alex Overwijk
http://slamdunkmath.blogspot.ca/

Jonathan So
https://mrsoclassroom.wordpress.com/