Co-plan and co-teach a 3-Act Task to promote the mathematical process skills. How will engaging in 3-Act Tasks about estimation support students in effectively demonstrating math content knowledge alongside the mathematical processes?
“On its own, a rich task is not rich – it is only what is made of it that allows it to fulfill its potential. In essence, rich tasks encourage children to think creatively, work logically, communicate ideas, synthesize their results, analyse different viewpoints, look for commonalities and evaluate findings.”
(Jennifer Piggott, retrieved from http://nrich.maths.org/5662)
Teachers will have an opportunity to engage in co-learning around 3-Act Tasks. Originally developed by Graham Fletcher, but has since been created by many other educators and shared online. The PowerPoint attached guides the discussions and learning around 3-Act tasks in estimation and allows the educators to ‘experience’ a task prior to planning their own.
See Powerpoint & Notes
The norms will be discussed, and agreed on, by all members during the first session. Team members, with facilitator guidance, will develop norms of interaction to build trust among the group. The following are suggested norms adapted from http://www.edugains.ca/resourcesPLC/PLF/2015_Module/HO4_CBSPrincipalsCoLearners.pdf
1. Be a co-learner – Engage in the inquiry by being present for the learning and discussions
2. Allow yourself to be vulnerable – Let go of your insecurities, it is ok not to have all the answers!
3. Student learning and well-being is at the heart of all discussions and decision-making
4. Embrace challenges – It is a journey, sometimes a bumpy one, but remaining focused on the goal will ease tensions when challenges arise
5. Value all voices – Each member has a valuable role, their input is instrumental in achieving group goals!
Role of the Facilitator (Facilitation Moves)
Facilitator (me) will support the educator team in the following ways:
• Understand how ‘we’ learn mathematics by preparing content and materials that will engage and challenge current thinking
• Support positive group dynamics through listening, questioning, encouraging discussion and providing feedback (when required)
• Help set goals and establish the process of co-planning and co-teaching
• Provide opportunities for reflection during and after each session
• Empower and encourage others to guide the discussion
Co-Planning and Collaboration (Lesson Planning)
As educators are looking at the variety of 3-Act Tasks available, they would need to consider which tasks would support students in demonstrating the mathematical process skills. The tool provided on The Learning Exchange is an excellent reflection tool as teachers consider the task and its purpose. It has been adapted to suit the needs of this session.
Task Features Attributes
What is the mathematical learning that students will achieve with this task? – Has a clear connection to the curriculum (for both content and processes, namely in estimation)
– Enables students to develop a deeper understanding of mathematical concepts, skills and processes
– Broadens students’ skills and mathematical proficiencies
Is the task problematic for students?
(i.e. something they need to think about, not simply a disguised way of practising already demonstrated algorithms) – Necessitates the use of a range of higher-level thinking skills in mathematical processes
– Allows students to develop, select and apply problem solving strategies
– Requires explanation, justification or proof, and thinking time
– Allows for developing and applying reasoning, hypothesis making and the testing of various strategies
– Provides students opportunities to reflect on and demonstrate that they are monitoring their thinking to help clarify their understanding
High Cognitive Demand and Understanding
Does the task provide opportunities to “press for understanding”? – Requires students to explore and understand the nature of mathematical concepts, processes, or relationships
– Has the potential to develop students’ mathematical processes and/or their proficiencies
– Provides appropriate level of challenge for every student, encouraging students to address their misconceptions
– Has an element of complexity and academic press, encouraging students to see mathematics as sense making
– Is visually structured so as not to obscure the inherent mathematical thinking and reasoning required
Tools and Representations
Does the task allow for the use of multiple tools and representations? – Allows students to select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems
– Promotes the creation of a variety of representations of mathematical ideas
– Encourages the communication of thinking either orally, visually, or in writing
Does the task allow for multiple entry points for students? – Is open, encouraging multiple approaches to its solution
– Has a low floor for entry and a high ceiling for exit; thus is accessible to a wide range of learners
– Provides opportunity for “mathematical play”, i.e. involves investigation, conjecturing and problem extensions
Intellectual and Social Engagement
Does the task have the potential to engage students in mathematical thinking? – Has the potential to spark students’ curiosity (there is an element of perplexity)
– Considers the use of concise questions, visuals, video and other approaches that appeal to the intended audience
– Allows for student choice and voice; students must make decisions about what to do and how to do it
– Can be solved in a reasonable amount of time
– Provides opportunities for students to have their thinking valued, share their thinking, inquire, build on the ideas of others and reconstruct or confirm their thinking
Educators will need to negotiate roles in the classroom as they plan to co-teach. How many educators will facilitate? What roles will we take; observer? Questioner? Who will present the problem? How long will we spend in each Act? What types of questions will we ask to extend student learning?
Planning for Classroom Instruction (Co-Teach)
The sample lesson plan below will help in planning the lesson and the roles each educator will take. This organizational tool will support the co-teaching process, as educators will know how they will support student learning and assessment.
Mathematical Processes Overall Expectations
Materials Required Educator Role(s)
_____ Documenter (both visual and written)
Consolidation (intentionally choose student samples based on common misconceptions, representation)
According to John A. Van de Walle, a math education researcher, estimation is a higher-level skill that requires students to be able to conceptualize and mentally manipulate numbers. In real life, estimation will be part of everyday experiences whether children realize it or not. From shopping in the grocery store and trying to stay within a budget, to paying for a dinner between 6 friends, the skills and foundations the students build in elementary school will remain with them forever. In planning for classroom instruction, it is vital to remember the importance of this co-teaching process.
Assessing Student Learning (Co-Debrief)
The process used to reflect on student learning will rely on the evidence educators documented during their co-teaching session. The following chart will guide the discussion around the evidence of student learning. Guiding questions in the chart will support them in focusing their conversation.
What data story have we collected to help us monitor our progress?
(i.e., triangulation) Data Sources What are students doing well? What learning Challenges are emerging?
Reflection Tool (Co-Reflect)
The greatest impact on learning and teacher efficacy is reflection. The reflection process when done collaboratively is powerful when educators adopt a growth mindset. Conversations about the impact on student learning are challenging but essential for progress. Teachers need to honestly evaluate and hold each other accountable. If we monitor and discuss the effectiveness of the strategies used in the classroom based on the evidence, then we can influence change.
There are so many tools available for reflection; I have opted to use the following because it fits the criteria of this collaborative learning session. It is adapted from Making Thinking Visible by Ron Ritchhart.
Connect – How is what you learned during our co-teach/co-plan CONNECTED to what you already know about how students learn?
Extend – What did you learn through co-planning and co-teaching that EXTENDED or pushed your thinking in new direction?
Challenge – What is still challenging or confusing for you about this process? What questions or wonderings do you now have?
Further Resource Exploration/Tools to Support Learning
I am a firm believer that teachers need time and support to change their practice. Providing too much, too soon, can be discouraging. With that said, I would focus our energy on the following resources and tools to support estimation. It would be discussed, shared and revisited throughout the year with multiple opportunities to co-plan co-teach and reflect along the way.
If there is extra time, there could be a chance to explore the following tools during the session. These tools can be adapted for any grade. During this portion of the collaborative learning session, the educators (in pairs) will explore the online resources and share back with the group using the chart below as a guideline.
**There is a wealth of resources online but I chose only 2 at this time
What is the tool? How does it work? What activities can I use it with? Why is it an effective tool?
(ie., what does it teach my students?)