This blog post is a work in progress! Be sure to come back and visit in a few weeks, as I will be adding to it over time…
It can sometimes feel overwhelming when we look at all of the individual and group needs of our mathematics learners. Building readiness to learn, along with ensuring that we meet the individual needs of students might give us the impression that we need to create an individual lesson plan for each and every person in our classrooms. That sounds exhausting…
But what if we can create structures and use a variety of math instructional strategies within those structures? What if we can create diverse learning experiences that encourage mathematical thinking and growth over key concepts? This is an idea worth investigating!
Our elementary and middle years math curricula in Saskatchewan cover a number of topics, from number to patterns to shape and space and statistics. Ironically, when you look at the skills needed for students to be READY to engage in these grade-level concepts, there are only a handful of pre-skills. These pre-skills are the math concepts that are applied and used in new learning.
For example, when we are learning about adding and subtracting fractions, we need to know about:
addition and subtraction
multiplication and division, multiples and factors
what a fraction is, finding equivalent fractions, improper fractions
So, how do we teach and reteach each of these key concepts in our classrooms? You can find a large number of curated resources in this Google Drive which contains folders of resources
We can also pull out specific concepts and see how they grow. The following concept trajectories were created by a province-wide math leadership group a number of years ago, and show the language, strategies and concepts over time. Each continuum has four instructional strategies listed.
In their book, Reclaiming Youth at Risk, Brendtro, Brokenleg and Van Bockern (1990) proposed a model of youth empowerment and resiliency. This model is called the Circle of Courage, and it is based on research of First Nations philosophy of child rearing. The Circle of Courage is a holistic approach that is described by Dr. Martin Brokenleg in his video.
Dr. Brokenleg’s research shows that every human being has four basic needs: significance, competence, power and virtue. The Circle of Courage makes the following connections:
Dr. Brokenleg has identified what it looks like in someone whose spirit is in a state of weakness, a state of strength, and what might happen if their spirit has been distorted. The following are ideas to support a state of strength by helping to mend a broken spirit.
Belonging: Right now, I belong here.
Belonging is our most basic need. Maslow’s hierarchy (McLeod, 2018) recognizes that a child needs to belong before they can move towards building self-confidence and self-actualization (Peterson & Taylor, 2009). To feel that we belong, we must build relationships with others. Complex kinship systems have existed within First Nations communities for thousands of years (Learn Alberta, 2019). By building a sense of kinship within your classroom, you can ensure that students feel a sense of belonging, culturally socially and physically.
Weak Spirit of Belonging
Distorted Spirit of Belonging
Spirit of Belonging
Distrust
Overly Dependent
Trust
Exclusion
Cult Vulnerable
Inclusion
Detachment
Gang Loyalty
Warmth
Rejection
Craves Acceptance
Friendship
Antagonism
Craves Affection
Cooperation
To build a sense of belonging, create physical spaces for all. The arrangement of the classroom should reflect the need to serve whole group, small group and individual work needs through:
Desk arrangements
How large furniture allow for student movement
If possible, have a quiet space for those who need it
Include all students in time to learn together. Have all students of different abilities, ethnicities and backgrounds working in the same classroom. They can cooperate, communicate and care for one another. By engaging in heterogeneous groupings frequently, students can know one another deeply. Assistive technologies can help to support students who have mild or severe disabilities and help them to contribute the learning of the whole.
Provide opportunities for students to know each other, such as an Interview and Share activity. Provide positive encouragement to try new activities and recognize individuality and creative talents.
Mastery: I may not be perfect at everything, but I will always try to get better.
Mastery is not only of the cognitive domain, but it is also a holistic view of learning that includes physical, social and spiritual competencies. Giving children the opportunity to develop all parts of self can help to grow a strong spirit of mastery.
Using Outcomes-based assessment and tracking progress towards a set standard can help students and teachers know where learning is at and respond accordingly. Dylan Wiliam has identified that clarifying learning targets is key to improving achievement and mastery (2011). When the criteria for success is visible and understood, students can strive for it. Teaching students to set learning goals and solve problems through collaboration can help them to build a spirit of mastery. Communicate teacher expectations clearly and provide specific feedback on student behaviour.
Independence – Earning independence by building trust.
One of the goals of education is for students to own their own learning. Dylan Wiliam (2011) has identified that goal setting and strategies for students to direct their learning path and destination. It is important that if students are pulled out of the classroom for additional support, they understand that it is to help them become independent when they rejoin their classmates. Student empowerment is important to build intrinsic motivation and confidence to persist through learning experiences.
Weak Spirit of Independence
Distorted Spirit of Independence
Spirit of Independence
Impotent
Manipulative
Powerful
Coerced
Dictatorial
Assertive
Unassured
Defies Authority
Confident
Misled
Rebellious
Self-Control
Futility
Reckless
Optimism
Building a democratic classroom can occur through classroom meetings to make decisions, offering choices within curriculum, and co-constructing classroom rules and norms. This can be done through the Circle of Courage itself, with groups brainstorming what it looks like when we work together to build a sense of belonging, mastery, independence and generosity within our community of learners.
By teaching self-regulation, we encourage and build independence and self-control. This can assist students in maintaining focus and personal responsibility.
Generosity – Giving to others makes you feel good.
The virtue of generosity is one of the most valued within Indigenous communities. There is a responsibility to care for others within our community. By being generous, learners can develop a sense of pride and joy. Service projects and creating spaces that allow for generosity to occur can help to strengthen students’ spirit of generosity.
Weak Spirit of Generosity
Distorted Spirit of Generosity
Spirit of Generosity
Emptiness
Driven
Purpose
Rancour
Over Involvement
Empathy
Exploiting
Servitude
Kindness
Vengeance
Co-Dependent
Forgiving
Disrespectful
Plays Martyr
Respectful
Citizenship education can help us to build a caring community within and outside of our classrooms. At the beginning of the school year, create opportunities for students to know each others’ stories. Activities such as collaborative writing, field trips together, assigned student jobs contributing to the well being of the class, and collaborative problem-solving activities can help students experience giving and receiving support. By watching slide shows of classmates completing tasks can all build a sense of care.
Introducing and teaching the Circle of Courage can help your students understand how they are building their own and their classmate’s resilience and spirit.
Peterson, J. M., & Taylor, P. D. (2009). Whole Schooling and the Circle of Courage. Retrieved May 8, 2019, from Whole Schooling Consortium: http://www.wholeschooling.net/