Engaging Students in Mathematics:
The link below has a fantastic video and follow up that includes templates, resources, organizers, and a guide for how to plan for and engage your students in mathematics.
Engaging Students in Mathematics - Ontario
Making Math Relevant For Our Students
Friday, April 25, 2014
Sketch of a Three-Part Math Lesson:
Below shows a link and an article that shows how the framework for a three-part math lesson works and is effective.
Source: "Capacity Building Series, The Literacy and Numeracy Secretariat," May 2007
Literacy and Numeracy Secretariat - Capacity Building Series
Two Additional Links:
Professionally Speaking - Three Part Math Lesson
Professionally Speaking - What is Bansho?
Before: Getting Started: 10–15 minutes
The purpose of this preliminary part of the lesson is to get the students to be cognitively prepared for the lesson problem by having them think about ideas and strategies they have learned and used before. The teacher organizes a revisit to a concept, procedure or strategy related to the lesson’s learning goal. The revisit might be a class discussion of the previous lesson problem, students demonstrating methods or strategies that were developed to solve previous problems, or students solving a smaller problem that evokes prior knowledge, skill and strategies.
During: Working on It: 30–40 minutes
For this part of the lesson, the students are actively solving the problem. They work in small groups, in pairs, or individually to solve a problem and record the mathematical thinking they used to develop solutions. Students develop independence and confidence by choosing the methods, strategies and concrete materials they will use, as well as ways to record their solutions. When students are given sufficient time to solve a problem, they learn to develop perseverance and come to expect that solutions will not be immediately apparent and that it takes time to solve a math problem.
While the students are making a plan and carrying it out to solve the lesson problem, the teacher circulates, making observations about the ways students are interacting and taking note of the mathematical models of representation, methods, strategies and mathematical language the students use to develop their solutions. If students are stuck, the teacher might pose questions to provoke further thinking or have other students explain their plan for solving the problem.
After: Consolidation and Practice: 10–15 minutes:
In this phase, the teacher strategically co-ordinates student sharing of solutions to the lesson problem, using a mathematical instructional strategy like Bansho or math congress or a gallery walk. By using such a strategy, the teacher can facilitate a whole-class discussion whereby students explain the mathematics in their solutions, methods, and strategies and discern whether classmates used the same or different strategies.
Through such co-ordinated sharing and discussion, students can hear and analyze their classmates’ mathematical thinking. Also, the students learn to discern similarities and differences in the mathematics, methods and strategies inherent in other students’ solutions. Such discernment provokes students to make connections between their own mathematical ideas and the ideas of others and to understand the mathematics within and across math strands.
Further, through such rich mathematics classroom discourse, students develop and consolidate their understanding of the learning goal of the lesson in terms of making connections to prior knowledge and experiences and making generalizations.
New methods and strategies derived from student solutions are posted on the class’s strategy walls or used to develop a class mathematics anchor chart. 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.
Below shows a link and an article that shows how the framework for a three-part math lesson works and is effective.
Source: "Capacity Building Series, The Literacy and Numeracy Secretariat," May 2007
Literacy and Numeracy Secretariat - Capacity Building Series
Two Additional Links:
Professionally Speaking - Three Part Math Lesson
Professionally Speaking - What is Bansho?
Before: Getting Started: 10–15 minutes
The purpose of this preliminary part of the lesson is to get the students to be cognitively prepared for the lesson problem by having them think about ideas and strategies they have learned and used before. The teacher organizes a revisit to a concept, procedure or strategy related to the lesson’s learning goal. The revisit might be a class discussion of the previous lesson problem, students demonstrating methods or strategies that were developed to solve previous problems, or students solving a smaller problem that evokes prior knowledge, skill and strategies.
During: Working on It: 30–40 minutes
For this part of the lesson, the students are actively solving the problem. They work in small groups, in pairs, or individually to solve a problem and record the mathematical thinking they used to develop solutions. Students develop independence and confidence by choosing the methods, strategies and concrete materials they will use, as well as ways to record their solutions. When students are given sufficient time to solve a problem, they learn to develop perseverance and come to expect that solutions will not be immediately apparent and that it takes time to solve a math problem.
While the students are making a plan and carrying it out to solve the lesson problem, the teacher circulates, making observations about the ways students are interacting and taking note of the mathematical models of representation, methods, strategies and mathematical language the students use to develop their solutions. If students are stuck, the teacher might pose questions to provoke further thinking or have other students explain their plan for solving the problem.
After: Consolidation and Practice: 10–15 minutes:
In this phase, the teacher strategically co-ordinates student sharing of solutions to the lesson problem, using a mathematical instructional strategy like Bansho or math congress or a gallery walk. By using such a strategy, the teacher can facilitate a whole-class discussion whereby students explain the mathematics in their solutions, methods, and strategies and discern whether classmates used the same or different strategies.
Through such co-ordinated sharing and discussion, students can hear and analyze their classmates’ mathematical thinking. Also, the students learn to discern similarities and differences in the mathematics, methods and strategies inherent in other students’ solutions. Such discernment provokes students to make connections between their own mathematical ideas and the ideas of others and to understand the mathematics within and across math strands.
Further, through such rich mathematics classroom discourse, students develop and consolidate their understanding of the learning goal of the lesson in terms of making connections to prior knowledge and experiences and making generalizations.
New methods and strategies derived from student solutions are posted on the class’s strategy walls or used to develop a class mathematics anchor chart. 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.
Three-Part Math Lesson Vs. Traditional Math Lesson
Traditional Math Lesson:
•Teacher directed
•Text books
•Teachers centered with
teachers relaying their learning with teacher talk
•Concepts taught in
isolation
• Only one way to reach
the answer is taught
•Paper pencil tasks
•Students work as
individuals
•Rote learning through
drill and memorization
Three-Part Math Lesson:
•Hands-on activities
•Relevant application
and connections to real life
•Students work in small
groups to complete tasks
•Student talk
•Students can problem
solve and discuss solutions and ways to solve, showing their thinking
•Teacher is facilitator
•Open-ended
Commonalities Between Both Lessons:
•Question and answer
•Student practice
•Whole class
instruction
•Mathematical language
•Students learn symbols
and facts (i.e., addition and subtraction signs etc)
Thursday, April 24, 2014
How is planning a mathematics lesson like dominoes?
How is planning a mathematics lesson like dominoes?
Guinness World Record - Longest / Biggest Domino Line Ever:
When planning for mathematics it is very much like a game of dominoes. Dominoes, like math involves us looking at the big idea and planning ahead. Math and dominoes both take a lot of patience, scaffolding, and effort and thought to ensure things go as planned. Often time’s modifications and accommodations need to be made to ensure that the lesson or plan is successful. Only when we get to the end of the chain of lessons or dominoes do we know if the plan was a successful one. When we are not successful or something fails in our plan, it can be used as a teachable moment to ensure that the outcome is positive and effective the following time.
Big Ideas in Mathematics
Big
Ideas in Mathematics:
Ø Teachers:
As a teacher it is
important to plan for mathematics with the “Big Idea” in mind as it allows the
teacher to cover all of the curriculum expectations and make connections
between math concepts. It also allows for teachers to establish clear goals for
instruction and amalgamate student learning. When using the “big idea,”
teachers are able to determine the prior knowledge that students must have
before the lessons, and it allows teachers not to teach each mathematical
concept in isolation. This focus provides teachers with the opportunity to
provide constructive and relevant feedback to students about the math concepts
being taught.
Ø Students:
Teaching with the “big
idea,” in mind is very effective for students in that it allows students to
connect their mathematical learning to other subjects, worldly experiences and
their own prior knowledge. It also allows for students to begin the lessons at
their own pace and because students know where the lessons are head, they are
more often engaged in the lessons.
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