Big Ideas consist of a comprehensive list of mathematical knowledge and concepts that provide a basis for developing more complex thinking and acquiring a deeper understanding of big mathematical ideas. The linkages and connections between math concepts are made explicit by linking previously learned big ideas to new concepts and problem solving situations. By emphasizing the big ideas in each lesson, teachers can build students' acquisition and use of key conceptual knowledge across lesson plans.
The Bigs Ideas are (Marian Small 2005)
- Number Sense
- Operations
- Measurement
- Geometry
- Patterning and Algebra
- Data Management
- Probability
5 Mathematical Processes To Consider When Planning (Based on the Ontario Curriculum of Mathematics (revised 2005)
- Problem solving
- Reasoning and proving
- Reflecting
- Selecting tools and computational strategies
- Connecting
- Representing
- Communicating
Benefits of Planning With The Big Ideas in Mind (Marian Small 2010)
- Facilitates long range/unit and day planning, and assessment when we understand how various mathematical concepts are interconnected and which concepts are more broader and encompassing than others
- Helps teacher set better learning objectives
- Allows you to create more opportunities for more meaningful teaching and learning experiences by continuously using the same key concepts to teach a variety of math skills and processes
- Builds students' acquisition and use of key conceptual knowledge across lesson plans
- Helps students gain a better understanding of the connections between all mathematical big ideas
- Increases the joy of learning Math
- Develops problem-solving and critical thinking skills
- Assesses more accurately the consolidation of knowledge of various Math concepts
A New Way of Teaching: The Three-Part Lesson Approach
Reference to The Magazine Of The Ontario College of Teachers
http://professionallyspeaking.oct.ca/march_2010/features/lesson_study/three-part.aspx
Before: Getting Started: 10-15minutes
The purpose of this lesson is to activate prior knowledge. Using an activation questions, get students are cognitively preparing themselves for the lesson problem by thinking about ideas and strategies they have learned and used before. The teacher reviews concepts and/or strategies learned through large group class discussion or think/pair/share activities. Then, expectations will be communicated to the students.
During: Working on It: 30–40 minutes
At this time, students are actively solving the problem. During this part of the lesson, students work in pairs or individually. Students are encouraged to use manipulatives. Students are encouraged to persevere and find a solution to the problem.During this part of the lesson, the teacher is walking around the classroom, observing, listening to students' train of thoughts and assessing their reasoning. The teacher may also use prompts to help weaker students get started. Nearing the end of this part of the lesson, the teacher will carefully choose several Math work to show various key concepts and clarify misconceptions if any.
After: Consolidation and Practice: 10–15 minutes
In this phase, the teacher strategically places student solutions, using a mathematical instructional strategy like bansho (http://dl.dropbox.com/u/22184571/Bansho%20with%20annotations.pdf) or math congress or a gallery walk. The teacher will then draw out the math from the students' work and facilitate a whole-class discussion that will provoke students to make connections between their math ideas and those of their peers. This is where students consolidate their understanding of the learning goal of the lesson. The teacher can also make an anchor chart with all the connections made, as well as the strategies explored by the class. What the teacher learns from students about their understanding is directly related to the types of questions asked. What the teacher learns from this discussion will guide the direction of future lessons or activities.Great videos outlining the 3 part math lesson:
Before:
http://dl.dropbox.com/u/22184571/The%20Three%20Part%20Lesson-Part%201-Before%20copy.wmv
During:
http://dl.dropbox.com/u/22184571/The%20Three%20Part%20Lesson-Part%202-During%20copy.wmv
After:
http://dl.dropbox.com/u/22184571/The%20Three%20Part%20Lesson-Part%203-After%20copy.wmv
Effective Planning Tips
- Use the Ontario Curriculum to guide your planning
- Use and order the big ideas based on which expectations come first and/or encompass others
- Ensure a clear progression of difficulty in your lessons
- Encourage the use of manipulatives
- Have a clear learning goal
- Begin planning with the end goal in mind
- Assess prior knowledge
- Plan engaging and meaningful lessons that students can relate to
- Choose good problem-solving questions that are conducive to good math discussions
- Choose various assessment strategies to check for all mathematical processes
- Choose a culminating task that relates back to the expectation that you are assessing
- Share your plans with a colleague
- Team up with an experienced colleague when planning
- Always look for ways to integrate other subject areas in your planning
- Use technology to reinforce your lessons
Helpful Resources
Ministry Documents
Ontario - Early Math Strategy (2003) http://www.eworkshop.on.ca/edu/resources/guides/ExpPanel_K-3_Math.pdf
- Teaching and Learning Math Expert Panel (2004) http://www.eworkshop.on.ca/edu/resources/guides/ExpPanel_456_Numeracy.pdf
- Guides to Effective Instruction in Mathematics (2006)
ð Vol. 1 - Foundations of Mathematics Instruction
ð Vol. 2 - Problem Solving and Communication
ð Vol. 3 - Classroom Resources and Management
ð Vol. 4 - Assessment and Home Connections
ð Vol. 5 - Teaching Basic Facts and Multidigit Computations
- Guide to Effective Instruction in Mathematics, 4 to 6
ð Number Sense and Numeration (2006)
ð Vol. 1- The Big Ideas
ð Vol. 2 - Addition and Subtraction
ð Vol. 3 - Multiplication
ð Vol. 4 - Division
ð Vol. 5 - Fractions
ð Vol. 6 - Decimal Numbers
ð Geometry and Spatial Sense (2008)
ð Data Management and Probability (2008)
ð Measurement (2008)
ð Patterning and Algebra (2008)
Other resources/websites
- Math Make Sense textbook
- Nelson textbook (check out the various websites in the textbook)
- Various resources from Scholar’s choice that are “concept” based
- Teaching Student-Centered Mathematics by Van De Walle (Grade 3-5)
- Math Grade 4
Ontario - Math Question Puddle Question books (Grade 4) or for a sample question http://www.mcgrawhill.ca/school/imprints/wright+group/mathematics/puddle+questions/index.php
Ontario - Online Teaching Resources http://www.eworkshop.on.ca/edu/core.cfm
- Ontario Curriculum Web Resources http://schools.tdsb.on.ca/asit/standards/4start/OntWeb.pdf
Ontario - Smart Board Resources http://www.ldcsb.on.ca/board/cirt/training/SmartBoards.htm
- Illumination: Resource for Teaching Math http://illuminations.nctm.org/ActivitySearch.aspx
- Link of activities that support the
Ontario
Mathematics Sites Categorized To The Ontario Curriculum
- Mathematics WebQuests - From the WebQuest Locator
- Mathematics Links - From Doug Peterson's Diigo Site
- GECDSB 100th Day of School Resources
Links to Internet Resources to help you celebrate the 100th day of school. - The Math Forum
Resources, Lesson Plans, Issues, all related to math education - Mathville Homepage
The homepage for the Mathville products. Includes excellent offline mathematics activities. - Mrs. Glosser's Math Goodies
Interesting site with lots of online manipulative mathematics activities for all grades. - Web Math
Your own personal online Mathematics tutor. - Mr. Pitonyak's Pyramid Puzzle
What would an Egyptian Pyramid cost to build today? - Tangrams
The Chinese called this centuries-old game the "Seven-Board of Cunning" because only an exceptionally determined player would attempt its amazing and challenging puzzles. - Puzzles
The name says it all! - Puzzles with polyhedra and numbers
In this site one can print copies of polyhedron puzzles (for non-commercial purposes only) and one can read several mathematical articles on the subject. - Currency Converter
Use this site to get up to date information on currency exchange rates and foreign investment advice! - Computing Technology for Math Excellence
Computing Technology for Math Excellence is devoted to resources for teaching and learning mathematics (K-12 and calculus) and the standards movement in education. - ABCs to Excel
Resource for spreadsheet modelling. - Fido
Can you determine how Fido reads your mind? - Virtual Pythagorean Theorem
Interactively work with Java applets to discover the theorem and more. - Hubbin'
Check out the various educational hubs at this site - Geometry Step by Step from the Land of the Incas
This interactive web site uses a variety of techniques to introduce geometry to the user. Mathematics, music, visual displays, quizzes, puzzles, science, history, and geography are integrated in this web site. A very visual and engaging site which brings geometry to life. - Currency Conversion
From the Bank of Canada, convert Canadian currency to and from others. Also provides great data for Fathom activities. - Mathematics Learning Objects
Manipulate objects on the screen to learn various mathematical concepts. - Squigly's Playhouse
If you're a primary teacher and looking for some art ideas, activity sheets, or online activities, you've got to pay this site a visit. - mathFROG
Collection of mathematics activities for students in Grades 4, 5, and 6. - Virtual Manipulatives
Go online and solve mathematics problems with web-based manipulatives. - Math and Reading Help for Kids
Math and Reading Help for Kids is a directory of hundreds of original articles, tips and resources centered on the topic of children's learning. - Internet Math Walk
Take a wander around the internet and see Mathematics in action. - Kindersite
Searchable database of activities for language, music, mathematics, and age appropriate games. - Mathville 1
Now, for the youngest of grades, there's Mathville 1.
