## Mathematician’s Workshop or Framework^{1}

This instructional framework guides teachers to provide opportunities for whole class, small group, partner, and individual learning. Students are more engaged, grow in their mathematical understanding and see themselves as mathematicians when they collaborate in their learning.

Mathematician’s workshop is based on the following beliefs:

- All students can improve upon their proficiencies when engaged;
- Growth mindset can be fostered and developed;
- Understanding takes time – speed is not the main goal;
- Students can construct their own understandings individually and with others. Both are important; and
- There is more than one way to solve a problem and all ways need to be respected, and inspected. (Boaler, 2017),

Foundational Elements:

Mathematically Rich Environment

A mathematically rich environment is where you can see, hear, feel and experience math within the math block and beyond the scheduled minutes in any given day. In this environment students have access to the tools they need to have success in an engaging manner. It is a place where risks can be taken, vocabulary is used and ideas are listened to in a community that learns and grows together.

Responsive Instruction

Responsive instruction requires teachers to know where their students are at in their understanding, and skills so that they can respond with intentional instruction. To be responsive, teachers need to be flexible, know a variety of instructional strategies to meet different learning styles, be able to provide individual, small group and large group opportunities, and target instruction.

Formative Assessment

Formative assessment is the ongoing gathering of information about student learning through conversations, observations and products in order to highlight progress and guide instruction. It includes a variety of strategies both formal and informal that can occur before, during, and after instruction. In mathematics, formative assessment can lead to targeted wrap ups of Mathematician’s Workshop and informed instruction for the whole class, small groups, and individuals.

Community of Mathematicians

A community of mathematicians involves all learners (students and teachers) engaged in mathematics, celebrating mistakes, and viewing themselves as mathematicians. This community is a safe space where mathematicians feel welcome to take risks, share ideas, and to support one another in their shared learning experiences. Teachers within the community plan opportunities carefully to meet all learning needs as they model collaboration, mathematical language, and cultural competence.

Cultural Competence

An effective culturally competent mathematics classroom approaches learning using a holistic worldview. Instruction is planned, facilitated and assessed in ways that honour all learners and learning styles. In these classrooms all mathematicians can see themselves in the learning and can show their learning in different ways.

Relationships, student voice and choice, respectful interactions, and shared power structures are not only valued but explicitly fostered.

Structural Elements:

Part 1: Minds On

The Minds On section of the workshop model is designed to activate, prepare, and excite students about math. These purposeful activities engage mathematical thinking, are accessible to all, and provide a transition for learners from previous activities to mathematical ones. In this way, Minds On serves as a soft landing routine for mathematicians.

- Minds On Activities might include:
- Using a guiding strategy to have students share and compare reasoning (i.e. Number Talks);
- Sharing and creating open-ended problems/tasks;
- Showing pictures of mathematical situations;
- Highlighting books or stories;
- Using purposefully chosen games or activities; or
- Use routines (such as “Today’s Number”, “Mystery Number”, “KenKen”, “Beat the Teacher”, or “16 boxes).

Evidence points to the need to engage learners actively toward both their understanding of mathematics and for their forging identities and relationships with mathematics.

^{2}

Part 2: The Lesson

An effective math lesson has a clear curricular goal and purpose that supports all students through differentiation. Math lessons are designed by teachers to meet student needs through guided discovery, and engaging activities that support conceptual understanding, procedural fluency, logical reasoning, and a positive mathematical mindset.

- Some examples of Lesson ideas might include:
- Identify lesson goal(s) (may or may not be disclosed depending on where you are at in the instructional sequence) ;
- Identifying potential misconceptions;
- Using math vocabulary;
- Modelling examples by teachers and students
- Presenting in a logical order;
- Linking and building on previous knowledge;
- Using manipulatives;
- Building differentiated lessons and follow-up activities;
- Creating real-world connections;
- Modelling and encouraging multiple strategies;;
- Fostering conversation between students;
- Designing tasks to be culturally responsive;
- Including First Nations and Métis content;
- Using Number Talks;
- Utilizing continuous formative assessment;
- Making thinking visible;
- Connecting previous learning; and
- Targeting instruction based on student needs.

Part 3: Mathematician’s Learning Time

Mathematician’s Learning Time is a time where mathematicians are actively engaging in the inclusive exploration, learning, and practice of mathematics. This flexible learning time is fostered by a safe environment that encourages creativity, conversation, and reasoning. Mathematician’s Learning Time can take many forms including large group, small group, partner, and individual work. At least half of the mathematics block should be devoted to this learning time. During this time, teachers can create opportunities for differentiated small group instruction, and conferring with individual students.

- Some examples of activities to support Mathematician’s Learning Time:
- Playing games;
- Reflecting in a journal;
- Problem solving;
- Engaging in conversations where everyone has a voice;
- Practicing skills;
- Experiencing mathematics stations;
- Utilizing manipulatives
- Allowing for choice;
- Connecting literature with concepts in math;
- Ensuring that the mathematics is accessible for all students (differentiation);
- Using mathematical vocabulary;
- Co-creating expectations;
- Using co-created anchor charts to foster independence;
- Collaborating with others;
- Enriching and extending learning;
- Creating opportunities for land-based learning and connections to real life;
- Conferring with students.

Part 4: Wrap Up

The wrap up portion of the Mathematician’s Workshop Framework serves an important purpose. This brief period at the end of the learning time provides an opportunity for students to reflect on their learning, reground in the goal of the lesson, and consolidate thinking. During this time teachers may choose to call upon mathematicians to share discoveries made during the learning time. Through this carefully facilitated sharing, students can hear and analyze mathematical thinking and identify similarities and differences between the methods and strategies shared. These whole class conversations can provoke connections and deeper thinking. Methods or strategies highlighted during this time can be recorded on an anchor chart in order to be revisited the next day.

Other options for this time may include reflecting in a math journal, completing an exit slip, or answering questions such as: What did you learn? What surprised you? What connections did you make today?

- Some ideas from teachers to support Wrap Up:
- Looking for students during Mathematician’s Learning Time who have made an interesting discovery or have a method of reasoning that you want to highlight;
- Establishing a community where sharing is expected as is the inspection of methods;
- Saving thinking on anchor charts so that it can be revisited. Be sure to title the thinking with the student’s name;
- Consolidating and summarizing essential concepts
- Collecting formative assessment data.

^{1}Adapted from Saskatoon Public Mathematician’s Workshop Framework, 2017

See also https://jenniferbrokofsky.wordpress.com/2015/09/30/getting-started-with-mathematicians-workshop/ [2015]; https://www.youtube.com/watch?v=JsFZ19CbIdA [Video, 2019]

^{2}Adapted from Boaler, J., & Selling, S. (2017). Psychological imprisonment or intellectual freedom? A longitudinal study of contrasting school mathematics approaches and their impact on adults’ lives. *Journal for Research in Mathematics Education, 48*(1), 78-105. p. 79.

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