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Anticipating students’ solutions to a mathematics taskMonitoring students’ in-class work on the taskSelecting student strategies and students to share themSequencing students’ solutions purposefullyConnecting students’ approaches & the underlying math
Consider how you might plan for a productive mathematical discussion. The template on the right may be helpful in your planning.
Below are some resources for you to access that may be helpful in thinking about each of the practices. There are many resources below. Please take time with to view or choose how you would like to use them at this time. The 5 practices resources are intended to allow you to delve deeper into your thinking at this time.
– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)
Anticipating
Anticipating
Do the Math to Understand the Math
Do the Math to Understand the Math
To think about how students might mathematically approach a problem you will give them. This is more than “who will get the right answer” or “who will be able to access the problem” (both still important planning considerations).
The teacher thinks about the range of mathematical strategies and approaches that may be seen, both correct and incorrect, and how these might relate to the mathematical goal of the lesson. This is a step in building an effective consolidation of learning. As part of this the teacher should also solve the problem in as many ways as possible, also exploring incorrect solutions. Asking themselves, what will I do/say/question if I see this solution/misconception/error. This will provide a much more valuable consolidation than simply "share your solution" or "show and tell" approach without recognizing the depth of some of the strategies in moving mathematical understanding further.
The Ribbon Problem (4:06)
The Ribbon Problem (4:06)
Watch this video on the right about anticipating gr. 7 student thinking with a fractions problem.
Think about what the added value is in asking students to use rods and other visualization tools.
After viewing: What is the relationship between visualizing the spatial relationships between numbers and students having a strong number sense?
- A Guide to Effective Instruction in Mathematics 4-6, Number Sense and Numeration, Vol 3, Multiplication: Developing a Variety of Computational Strategies, pp. 18-23
- A Guide to Effective Instruction in Mathematics K-6, Vol 5: Teaching Basic Facts and Multidigit Computations
different_math.pdfDocument.pdfMonitoring
Monitoring
Begin Where Students Are: Fraction Example
Begin Where Students Are: Fraction Example
This is another classroom example for you.
- What comes to mind when you think about how a specific task impacts learning?
- What would an educator be thinking about, doing, modelling and observing with students throughout the learning process?
Estimation and Benchmarks-
Estimation and Benchmarks-
Gr 6 Assessment (5:55). Please play the beginning of this video and stop at 3:46.
While viewing the video, think about
- what do you notice the teacher doing to introduce the task? How does she monitor for student thinking? What questions are asked?
- What are the students doing to get started? How do they share their thinking?
- After viewing: You will continue this video on the "Sequencing" tab to watch this demonstration for Selecting, Sequencing and Connecting. At this point, discuss the questioning and prompting that you noticed. Check out the resources below and share others you may have found helpful as you assess for student thinking.
What might you be seeing as students problem solve? What might be helpful in making thinking visible? See the 3 resources below:
These descriptions of elements of effective math classrooms come from Marian Small.Please note these are possible indicators - it is not expected that all will be evident all the time.
While Monitoring, the educator is observing as students:
Interact with each other and in response to questioning or prompts for thinking
- Rich Math Talk - Students are provided with opportunities to engage in rich math talk, e.g. debates, question and answer
-There is more student talk than teacher talk
-The math talk is real math conversation
- Collaboration - Students regularly collaborate
-Students seem comfortable when they are collaborating
-Students have been taught what collaboration looks like
- Questions Asked by Students - The questions students ask are mostly to clarify, justify and challenge thinking, and not organizational
Use Learning Tools
- Using manipulatives or technology- Students are using manipulatives or technology in a rich way and not just procedurally
How students engage with the math
- Enthusiasm and Task Completion - Students seem enthusiastic about what they are doing because the tasks are engaging
- Thinking and Communicating - Students regularly seek to make sense of what is going on and do not ask for quick, easy rules just to be done with it
- Students comfortably explain their thinking
How confident students are:
- Self-directed - Students feel confident trying things and do not feel the need to always seek teacher direction and/or approval
- Persistence - Students show perseverance in situations where perseverance is appropriate
- Creative - Students seem comfortable and proud of being creative and do not feel the need to “please” or conform in terms of their math thinking.
Student Interactions in the Math Classroom: Stealing Ideas or Building Understanding – What Works
The following resources are available to purchase that support the implementation of Number Talks.
Further, the book Teaching Math With Meaning: Cultivating Self-Efficacy through Learning Competencies, Grades K-8 by Cathy Marks Krpan is an invaluable resource that will support our elementary educators in creating the conditions for learning, establishing a culture of accountable talk (similar to the strategies in The 5 Practices), and so much more to empower students to become deep mathematical thinkers.
Selecting
Selecting
What would an educator be thinking about as s/he is revealing student strategies?
Continue to watch the Estimation & Benchmarks video, starting at 3:47 to the end.
While viewing the video,
- Who is selected in sharing their thinking?
- What are the students doing?
- After viewing: What key ideas emerged for you? How might the ideas shared further inform or influence practice and impact student learning in your classroom or across your school community? What further questions do you have? What additional information, resources and supports are needed? What are some specific next steps that can be taken based on what has been learned from this video?
Sequencing
Sequencing
The order of student solutions that are discussed matters.
The order of student solutions that are discussed matters.
Highlights, Summary and Independent Practice: The Turkey Problem (4:16 )
Highlights, Summary and Independent Practice: The Turkey Problem (4:16 )
Facilitative Prompts
- Prior to viewing: What strategies come to mind when you think about effective consolidation? What would an educator be thinking about, doing, or modelling with students?
- While viewing the video, what do you notice the teacher doing? What are the students doing?
- After viewing: What key ideas regarding consolidation emerged for you? What further learning might you and your school community engage in regarding effective consolidation strategies or processes?
Connecting
Connecting
After students share their solutions, engage the class in a discussion about those solutions and connect them to the math goals of this lesson. Encourage students to make connections between the mathematical ideas shared and deepen their understanding following their experience in this work.
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