This month’s curricular competency focus is connect mathematical concepts to each other, to other areas and to personal interests. This curricular competency is the same across grades K-12.
This competency falls under the organizer of ”Connecting and Reflecting” and is linked to metacognition, synthesizing concepts and ideas, reflective thinking and self-assessment. There are links with this curricular competency to the Core Competencies of Communication and Positive Personal and Social Identity.
Elaborations are suggestions for educators to consider as they plan for developing this curricular competency:
Drawing on the literacy research of David Pearson, one framework for thinking about mathematical connections is to consider creating opportunities for students to make:
- math to math connections
- math to self connections
- math to world connections
Many teachers have seen classroom-based evidence of learning when students demonstrate an ability to make math to math connections and feel students who can connect and see relationships between concepts have strong number or spatial sense and a stronger understanding of the mathematical ideas involved. Instead of learning about fractions in grade 4 for three weeks and maybe not encountering formally again at school until grade 5, teachers weave math concepts together throughout the year to help nurture math-to-math connections. After being introduced to both concepts of fractions and decimal numbers during focused studies, students are asked questions such as “How are fractions and decimal numbers connected?” These types of questions are included in the elaborations for the Big Ideas in our BC Mathematics curriculum.
Other examples include:
“How are addition and subtraction related?”
“How are multiplication and division related?”
“What is the relationship between area and perimeter?”
“What is the connection between patterning and algebra?”
Math-to-math connections can also be considered across grades (how did learning about fractions with pattern blocks last year help you think about fractions with Cuisenaire rods this year?) or across forms (concrete, pictorial, symbolic) or across problem types.
Math-to-self and math-to-world connections enhance understanding of personal, social and cultural identity as well as an understanding of issues in the world around us. A student might make a connection to skip counting or multiples to scoring in basketball or a student might see an infographic or graph on a website and use proportional reasoning to make sense of the information. When making connections, students see how mathematics can be used as a language to both receive and express information about themselves and the world around them. We often ask students: “Where does math live here?” as a way for them to make connections to different places and contexts or areas of study.
Where does math live…
in the game of basketball?
at the beach?
in the study of biology?
at the grocery store?
in the weather?
at the playground?
in cooking and baking?
in the newspaper?
Related to the idea of connection-making is transfer and application. Students may learn facts or skills but they need to be able to transfer, apply or build on that learning in other areas. This is the essence of numeracy – to be able to apply mathematical understanding in new contexts, situations or with new problems.
Some questions to prompt students to make connection include:
What does this remind you of?
When have you done a problem like this before?
What do you already know about this?
What materials have you used to think about this concept?
Where else have you experienced this idea?
Where can you find or use this concept in the world around you?
Some questions to consider as you plan for learning opportunities to develop the competency of connecting mathematical concepts to each other, to other areas and to personal interests:
How can we plan for mathematical connections in different learning contexts such as the gym, music class, art room, library or learning outdoors or in the community?
What opportunities do we create to intentionally nurture students’ connection-making across math topics and across disciplines?
How is connection-making in reading comprehension connected to connection-making in mathematics?
How might we capture and curate mathematical connections that students make to make this learning visible?
*Please note: This is the last in this year’s series of monthly blog posts on BC’s curricular competencies for mathematics.