*By* *David Petersen, Lead Curriculum Writer and **Kate Nowak, Director of K–12 Curriculum Strategy*

This school year has been strange and stressful, and there is uncertainty about what next year will look like. Due to school closures in 2019–20, students will have missed important learning opportunities, and existing inequities may have become more pronounced. On top of that, it’s likely that many schools will not be back to normal in the fall. We may face shortened or fewer school days, more distance learning or hybrid face-to-face and distance learning, and ongoing school disruptions.

IM is looking ahead to the next school year. Last week, we published our initial thoughts about support and guidance in K–5. This blog post will show how those ideas extend to 6–12.

Educators want to provide a welcoming, coherent instructional experience for students, yet we hear the anxiety about the impact of the unfinished learning 2019–20 school year. One reaction may be to jam in more topics and cover both the grade-level content and what may have been missed in the previous year. But we know that speeding up instruction to cover more topics doesn’t lead to lasting understanding—there is a reason that “mile wide and inch deep” has a long history as an unflattering way to describe a curriculum. Another response may be to use diagnostic testing to place students in remediation, but we also know the importance of spending as much time as possible accessing grade-level mathematics.

Or, without good alternatives, educators may end up constrained into focusing on procedural skills, because procedural practice is more straightforward to implement using digital tools than instruction for conceptual understanding. But we know we need to protect time for students to do the work of learning mathematics: making and justifying claims, making sense of and solving problems that advance their mathematical understanding, and hearing and critiquing the reasoning of others. Kamau Mposi, one of the teachers who piloted the Algebra 2 materials, once described the IM curriculum as “rigorous and patient.”* Without the patience, so many opportunities for learning mathematics evaporate.

#### Inviting Every Learner to the Mathematics

In the fall, in places where students return to a school building at least part of the time, it will be important for students to reconnect with one another and the adults in school. They will need to readjust to routines and the new structures of school. IM Math curricula already offer some built-in features across K–12 to help teachers facilitate that process. The first unit in each course is designed to be invitational and accessible to every student, no matter what experiences they had the previous year. Students ease into learning while gaining familiarity with routines such as Which One Doesn’t Belong and Notice and Wonder. This is a time to establish norms, and to get every learner engaging in discourse on the same topic.

We have always advocated for beginning the year with the first grade-level instructional unit rather than assessments or lots of review of materials from previous years. For the 2020–21 school year, this recommendation stands firm. Grouping students at the beginning of the year can have many unintended and lingering impacts on their learning and mathematical identity. We believe that, even though more students than ever will have unfinished learning from previous grades, it is better to start with the first unit of each course as originally designed and insert lessons and activities to address missed learning as needed throughout the school year.

#### Making Strategic Decisions about Content

Coherence and major work of the grade informs what we do. To decide what to emphasize, we would use our curriculum dependency chart, the purpose of a given activity (such as introducing a concept, defining a term, practicing fluency, or applying understanding), and whether activities or lessons address major work of the grade and widely applicable prerequisites.

It would be inefficient to teach everything that was missed in the previous grade before starting grade-level work. For example, the 8th unit from our grade 6 course (6.8) is about understanding statistical questions, examining displays of data, and describing distributions. Due to its placement late in the course, most rising seventh graders likely missed this material. It is not essential that students begin their grade 7 course understanding that material, but it will be needed before the grade 7 unit (7.8) on sampling data from a population and comparing two related data sets. We suggest waiting until students are nearer that statistical unit to visit the material they’ll need to understand those concepts.

View the full dependency chart

#### “Just in Time” Assessments

Another advantage of waiting to introduce ideas from missed learning is a greater opportunity to get to know your students and their needs—without overtesting. The embedded formative assessments and focus on student-generated solutions in IM materials are designed to illuminate what students need. That way, any remediation can serve accessing the grade-level topic, an approach to remediation that is sometimes described as “just in time” rather than “just in case.” Each unit’s diagnostic Check Your Readiness assessment is also intended to provide information about where it’s necessary to weave in material from earlier courses.

Impacts from the schooling disruptions will likely be felt for several years, necessitating some adjustments. Missing the introduction to the Pythagorean Theorem from grade 8 may not be noticed in Algebra 1, but will certainly impact students when they get to Geometry. Similarly, Algebra 2 teachers may recognize unusual gaps in understanding quadratic functions and irrational numbers from students missing the introduction of this content during Algebra 1 in 2019–20.

#### What Next?

This post represents our current thinking. Rest assured that our values and beliefs about learning mathematics haven’t changed, it’s figuring out how to apply them to the current situation that is a work in progress. We still have many questions and a lot to learn about the challenges communities face next year. We want to do our thing—apply our deep knowledge of the materials to develop actionable ways to adapt them for unfinished learning and continuing disruptions, so that teachers have more time to do what only they can do—respond to the needs of the learners in their charge. Adapting to these different conditions is an intimidating challenge, but the IM community is more than up to the task. Thank you for everything you do.

**Next Steps**

We would love to hear from you. What are some of your current challenges? What challenges do you envision moving forward? What questions or ideas do you have? Use the hashtag #LearnWithIM on twitter, or comment below.

*An earlier version of this post misattributed this quote. Our apologies.

I am a math coach and we are going to pilot the K-5 beta this fall. The 6th grade already uses the IM work. Is there a bridge between 5th and 6th grade for teachers to use to prepare for this fall? Thank you!

We are working on it!

Your dependency chart is an amazing tool. Do you have anything that can show the dependency between 5th grade skills and 6th grade learning? There seems to be a gap between those grades; but, we know learning is continuous.

Yep we will certainly have that available once the K–5 materials are completed. Thank you for letting us know that you are looking for this information. It helps us prioritize.

(In the meantime, perhaps check out the coherence map at Student Achievement Partners?)

Great post! I was wondering how we can support 6th grade teachers whose students may be missing essential understanding necessary for earlier units like Unit 2: Introducing Ratios. Thanks!

Hi Adina,

It’s coming! We’re working on a plan for for every unit in 6–12. We’ll have a post soon explaining what it will look like.

Hi everyone! I just wanted to make sure the description of IM as “rigorous and patient” is properly attributed. This apt description is courtesy of Kamau Mposi, one of the teachers who piloted the Algebra 2 materials. He shared that description with me when reflecting on the curriculum as a whole at the end of the pilot year, and I loved the description so I passed it along to the team at IM.

Thank you! My fault for misremembering it from when you told us about it. I’ve corrected the post.

Appreciate your recommendation to start the year with on-grade instruction and fill in gaps when needed (Just in Time) and relevant.

Still looking forward to when you (or someone) will create a rigorous and current 9-12 Integrated Mathematics curriculum that is truly integrated and not just the typical re-chunking of unrelated topics from Algebra and Geometry.

Will you be publishing materials or ideas for how to adapt your curriculum to fully online learning? Much of this curriculum relies on discourse and interactions between students and students and students and teachers. This spring our district moved to online instruction in a modified format and most students did not turn on their cameras or microphones. This made it impossible to have the interactions, discoveries, and brainstorming sessions that make this curriculum work. This is something that my colleagues and myself are concerned about as we head into the possibility of school starting online next year. For context, I teach at the high school level.

A question more than a comment: The IM Curriculum is well represented in Khan Academy online materials (looking forward to possible NTI). Is there a plan in place to do the same with the 9-12 curriculum and, if so, when?