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)
- 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
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
An ebook examining four important number relationships and how they connect to build students' number sense
Consider using instructional frames, such as “notice and wonder” about these connections and “compare and contrast” mathematical ideas and concepts
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.
A kindergarten teacher intentionally "mashes up" two mathematical ideas to support students in making math to math connections.