“BIG IDEAS” & “PROBLEM SOLVING” IN
JUNIOR MATH INSTRUCTION
Ms. Teighlor Marin
BIG IDEAS
•
Programs that emphasize the big ideas allow students to make connections, to see
that mathematics is an integrated whole, and to gain a deeper understanding of the
key concepts
• Big Ideas represent the key mathematical concepts
• Effective math programs demonstrate understandings of the Big Ideas and or
key concepts
• The “Big Idea’s” or “Strands” within Mathematics are:
• Number Sense & Numeration
• Measurement
• Geometry & Spatial Sense
• Patterning & Algebra
• Data Management & Probability
BIG IDEAS
The “Big Ideas” demonstrates concepts found in
each strand. The “Big Ideas” act as a lens for:
• Making instructional decisions
• Identifying prior learning
• Looking at students’ thinking & understanding
in relation to the mathematical concepts
addressed in the curriculum
• Collecting observations and making anecdotal
records
• Providing feedback to students
• Determining next steps
• Communicating concepts & providing
feedback on students’ achievement to parents
BIG IDEAS
• Mathematical processes that help aid in effective learning are:
• Problem Solving
• Reasoning & Proving
• Reflecting
• Selecting Tools & Computational Strategies
• Connecting
• Representing & Communicating
*******Mathematical processes are all interconnected and
help students acquire and apply math skills with
knowledge.
PROBLEM SOLVING APPROACHES
Creating a
Learning
Environment
Using
Manipulatives
Promoting
Communication
Teaching
Through
Problem
Solving
Assessing
Effectively
Central
Themes
Big Ideas of
Mathematics
PROBLEM SOLVING APPROACHES
•
Problem Solving is “the process of applying prior knowledge, experience, skills, &
understandings to new and unfamiliar situations in order to complete tasks, make
decisions, or achieve goals.”
•
Individuals in todays society need to be able to think critically
•
To prepare students for the real world, teachers are responsible to promote problem
solving processes into their classroom
•
When students are taught math concepts through problem solving, they are exposed to
problems and problem solving on a daily basis, even though the problem might not be
formally identified
•
Problem solving is an integral part of the mathematics curriculum because it:
• Helps students become more confident mathematicians
• Allows students to use the knowledge they bring to school and helps them connect
mathematics with situations outside of the classroom
• Allows students to reason, communication ideas, make connections, and apply
knowledge and skill
CORRELATION BETWEEN PROBLEM SOLVING & BIG
IDEAS
• Students who are able to problem
solve are more likely to understand
the “BIG IDEAS” because they can
use prior knowledge, skills, and
understandings to figure out
solutions
• When teachers use Problem Solving
to teach mathematics they make
math make sense. They allow the
students to make sense of what they
are learning and focus on the Big
Ideas
•
•
•
•
The 4 Step Problem
Solving Model
Understand the Problem
Make A Plan
Carry out the Plan
Look Back & Reflect on
Solution
PROBLEM SOLVING & CLASSROOM
•
Key concepts are introduced & explored through problem solving
•
There is no formal problem solving, instead students develop &
share their own problem solving processes
•
Teachers model problem solving with the class and walk through
the mental processes that happen while solving a problem
•
Students solve problems together
•
Problem solving solutions are shared as a class during
discussions or sharing times
•
Perseverance in problem solving is modeled by the teacher and
encouraged in students
•
Students explore math ideas in a way to developing their own
understanding of concepts
“Helping students become good problem solvers is like helping
them learn how to ride a bike; tips can be helpful, but its
impossible to master the process without actually trying it”
(Baroody, 1998)
Classroom Opportunities
for Problem Solving:
• Daily Challenges
• Problem Solving Corner
• Activity Centre
Questioning
Computation
Collaboration
Classroom
Structures
that Support
Problem
Solving
Daily
Challenges
Manipulative
Scaffolding
PROBLEM SOLVING & COMMUNICATION
• Oral communication is integrated into all mathematical learning
concepts and ideas
• Class discussion are incorporated throughout lesson to encourage
students to talk about strategies, solutions, and growing
understandings
• Teacher Prompt Questions are used throughout the lesson
• Teacher should constantly be asking “How do you know?” or
“What’s your reasoning?”
• Encourage students to think aloud
• Different strategies are incorporated to promote communication
• Think/Pair/Share
• Word Wall
• Journals
• Class Discussions
Nonverbal
Speaking
Thinking
Listening
RESOURCES & STRATEGIES
• Ontario Curriculum Grades 1-8: Mathematics
http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
• Leading the Way: Instructional Leadership in Elementary Mathematics
http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/pdfs/e6.pdf
• Teach Using Big Ideas
http://fcit.usf.edu/mathvids/strategies/tubi.html
• A guide to Effective Instruction in Mathematics
https://faculty.nipissingu.ca/danj/DOCUMENTS/MATHEMATICS/GUIDES/GR
ADES%20K-6/GEIM%20K-6.pdf