BC Numeracy Network - How to foster math-to-math connections?

How do I foster math-to-math connections?

"One of the gaps in many teachers' mathematical backgrounds is an internal map of the subject. They lack a fundamental understanding of how various mathematical topics interconnect, which topics are more important in the long term than others, and which aspects of those topics are most important. As they teach, many teachers often feel like they are going through a checklist, checking off whether students have learned each new discrete concept or skill listed in the curriculum. This is in stark contrast to what we know from research about how much more effective it is for students to learn when connections are explicitly made between new knowledge and ideas that students already know (Borko and Putman, 1995; Schifter, Bastable, and Russell, 1997; Kennedy, 1997)."

(Small, Big Ideas from Dr. Small, 2009, pp. xi, xii)

Considerations

seek and highlight connections among mathematical strands and concepts
consider using instructional frames, such as “notice and wonder” about these connections and “compare and contrast” mathematical ideas and concepts
develop mathematical language
provide rich, open-ended tasks that involve multiple mathematical concepts and strategies
students investigate and create through exploration
deepen my professional understanding of foundational mathematical concepts across the developmental continuum

Resources

Seek and highlight connections among mathematical strands and concepts

Making Sense of Math by Cathy Seeley

Students need to "have a strong enough foundation and confidence to tackle problems that may not look like routine problems they have seen before - problems that may require them to think about relationships, connect mathematical ideas, and extend what they already know." p. 19

Making Mathematical Connections Article

Making mathematical connections by NCTM Past-President Linda Gojak

Math Connections

Questions to promote math-to-self, math-to-world, and math-to-math connections

4 Relationships That Will Increase Your Students Number Sense

Free ebook by Christina Tondevold examining four important number relationships and how they connect to build students' number sense.

number-sense-relationships-ebook (1).pdf

Extending Counting Collections: Making Math to Math Connections

Blog post from Janice Novakowski SD38

makeconnections_soccerlesson.pdf

SD71 Soccer Lesson Plan: Making Math Connections

connections_soccerBLM.pdf

SD71 Soccer Lesson Plan: Recording sheets (English and French)

Consider using instructional frames, such as “notice and wonder” about these connections and “compare and contrast” mathematical ideas and concepts

notice_wonder_one_pager.pdf

notice_wonder_intro.pdf

Notice Wonder

The educators at the Math Forum, Annie Fetter and Max Ray have shared the power of using Notice Wonder as a routine to tap into children's curiosity and show them the importance of asking questions - "What do you notice? What do you wonder?" Check out the one-pager to the right to learn more about what this could look like in your classroom and the learning involved.

Annie Fetter's IGNITE talk "Every Wonder What They'd Notice"

Suggestions for Notice Wonder and Recording Template

Same / Different

This routine, also known by some as "Alike or Different" is a routine in which the teacher presents two numbers, shapes, or objects to be compared. The teacher carefully selects what will be compared to focus student thinking on a desired mathematical concept. This routine is powerful because it fosters so many curricular competencies, including communication, reasoning, constructing arguments, etc in relation to mathematical ideas. Brian Bushart, with the support of several other math educators have created an outstanding website with examples that have been categorized into galleries based on math concepts.

Same and Different.pdf

Which One Doesn't Belong and More CHunter[2919].pdf

"Alike and Different: Which One Doesn't Belong? and More"

Article by Chris Hunter from the British Columbia Association of Math Teachers magazine Vector (Spring 2008).

Chris Hunter explores the instructional routines WODB and Alike and Different, considering how they can be designed and connections to the curricular competencies.

Circles and Patterns Math Provocation

A classroom example: A kindergarten teacher intentionally "mashes up" two mathematical ideas to support students in making math to math connections.

Kindergarten Circles and Patterns Math Provocation.pdf

Develop mathematical language

Language in the Mathematics Classroom

Language in the mathematics classroom.pdf

Article from the Australian Council for Educational Research

This book is filled with alternatives to the shortcuts so prevalent in mathematics education and explains exactly why the tricks are so bad for understanding math.

"90% of math language happens only within the math classroom." - Krpan, 2018

Author Cathy Marks Krpan believes that through competency-based learning, students and teachers alike can deepen their mathematical understanding and share and impart that knowledge in and out of the math classroom. Teaching Math With Meaning takes a practical approach to embedding this deep learning in K to Grade 8 mathematics classrooms.