Teaching mathematics is a continuous cycle of identifying where each student is in their learning trajectory and determining meaningful ways in which to build on their current understandings. While we often have little control over students’ mathematical experiences before they walk into our classrooms, we do have complete control of our own learning.
Understanding the mathematics and its progression for ourselves is one of the most valuable tools in understanding where students are in their thinking and determining ways in which to help each student make sense of the mathematics in a connected, coherent way. In support of this work, Jennie Beltramini, Student Achievement Partner’s Professional Learning Math Specialist, and I designed a five-step process teachers and coaches can use in a PLC to help guide collective learning around a mathematical progression.
The process detailed below could be used to better understand any mathematical idea in the Common Core State Standards. Because fractions are such a pivotal point in students’ mathematical journey, we focused this process on the big idea of equivalence in the Grade 3–5 fraction progression.
Step 1: Find appropriate, standards-aligned tasks
To ensure the tasks are aligned to the standards and follow a coherent progression, we recommend using the Coherence Map on Achieve the Core to identify standards-aligned Illustrative Mathematics tasks. For this process, we identified a series of Grade 3, 4, and 5 tasks, along the fraction equivalence progression that you can download here. These tasks will be referenced throughout the steps outlined below, so check them out before you continue reading.
Step 2: Do the math
Doing the math is a critical piece of understanding the progression. Since this process focuses on the progression across three grade levels, it is helpful to think about what happens in the middle first. Each person should independently complete the Grade 4 task and answer the questions on this planning sheet. Independent work time offers each person time to make sense of the math for themselves and reflect on their current understandings. After each person has finished, discuss responses as a group.
Step 3: Read the Progression Documents
When doing math tasks, our strategies are often influenced by how we learned the math or how we how we have previously taught it. For this reason the Progression documents are necessary to help ground our ideas in the mathematical progression itself. These documents can be fairly heavy and time-consuming to read all at once, so it is important to carefully choose the sections that relate to the math tasks at hand when working within limited PLC time.
Since this series of tasks focuses on the big idea of fraction equivalence, each person in the group should read a different piece of that progression. In this case, one person should read Grade 3 pages 5–6, another, Grade 4 pages 7–8, and a third person should read Grade 5 pages 9–10.
Once everyone has finished reading, discuss the following questions:
- What big ideas stood out to you while reading your grade level section of the progression?
- Where do you see similarities or connections between the grade levels?
Step 4: Revisit and revise your Fraction Planning Sheet
Based on what was learned from the group discussion about the fraction progression documents, revisit the original fraction planning sheet. Each person should take a few minutes to individually add to or revise their individual ideas and discuss any changes they made with the group.
Step 5: Complete the 3rd and 5th grade tasks
Now it is time to see what the progression looks like through what the math students will be doing. Look back at the original set of fraction progression tasks, and complete the grade 3 and 5 tasks. As a group, discuss the following questions:
- What connections do you see across the tasks?
- How did your conversations about the math and students’ understandings change after reading the Progression documents?
- How will your new understandings impact the way in which you teach fractions in your classroom?
Investing time in our own learning through these 5 steps can help us not only understand the math better for ourselves, but also help us in building opportunities for students to see mathematics as a meaningful and connected journey.
- If you use this process, I would love to hear about your learning and how it impacted the teaching and learning in your classroom. You can share your ideas here in the comments section, or share with us on Twitter using the #LearnWithIM hashtag.
- If you added steps to this process to make it more meaningful in your PLC work, I would be really interested in making this process more useful for all, so please share!
- To read more about some of the ideas along the fraction progression, check out Bill’s posts on building fractions from unit fractions and fraction equivalence.