Math Instruction for ALL Students

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!

I am still learning

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

When you analyze grade-level outcomes in mathematics, you will often see combinations of the following pr-skills:

  1. Number Sense and Place Value
  2. Addition and Subtraction
  3. Multiplication and Division
  4. Parts of a Whole – Fractions, Decimals and Percent
  5. Algebraic Thinking

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: https://bit.ly/2zrNfqd which contains folders of resources designed to help you to teach through these continuums, as well as:

  • What is an instructional sequence and strategies for teaching each concept?
  • What are some common misconceptions and how might we address them?
  • How might we infuse technology into our mathematics instruction?
  • What are some fun ways to engage in mathematics?
  • How might we use math with a purpose to gain a deeper understanding of social issues?

Concept Continuums

When we look at our Saskatchewan curriculum, we can see how concepts grow over time in these math Curricular Through Lines:

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.

The Circle of Courage: Building Resilience

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:

 

Circle of Courage Stems

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.

Circle of Courage Graphic

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). maslow-5To 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.

Weak Spirit of Mastery

Distorted Spirit of Mastery

Spirit of Mastery

Failure Oriented Arrogant Successful
Unmotivated Workaholic Motivated
Non-Achiever Over Achiever Achiever
Avoids Risks Risk Seeker Creative
Fears Challenges Cheater Problem Solver

To build a sense of mastery, teach students using authentic, relevant, differentiated learning. This includes things such as low floor, high ceiling tasks, open-ended and parallel tasks, and being cognizant of multiple intelligences when planning instruction and assessment.

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.

Brendtro, L., Brokenleg, M., & Van Bockern, S. (1990). Circle of Courage. Retrieved February 14, 2014, from Reclaiming youth international: http://www.reclaiming.com/content/aboutcircleofcourage

Circle of Courage Model – Spaces. (n.d.). Retrieved 05 15, 2019, from Portland Community College: https://spaces.pcc.edu/download/attachments/13337564/Circle+of+Courage+Model.doc

Learn Alberta. (2019). Kinship. Retrieved May 8, 2019, from Walking Together: First Nations, Metis and Inuit Perspectives in Curriculum: http://www.learnalberta.ca/content/aswt/kinship/

McLeod, S. (2018). Maslow’s Hierarchy of Needs. Retrieved May 5, 2019, from Simply Psychology: https://www.simplypsychology.org/maslow.html

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/

Blog at WordPress.com.

Up ↑