I still believe that our math curriculums (as well as other subject curriculums) need an enema. Math should not be restricted to books, standards, fancy online works, or equations to be solved that are meaningless. I feel "learning loss" or "opportunity loss" goes deeper than the pandemic ever caused. In my dream world, math would be discovered and formulas used to solve those discoveries and meaningful opportunities will be presented to the learning then there would no losses.

I will continue what I have done in the past: use my district priority standards, meet my students where they are, and do my best to give them rich learning experiences to get them to meet priority standards we have set. In addition, the vertical planning we do at my building allows us to share how deep we taught in the course and which standards and units may need more remediation. Maybe it is because I have always taught in at risk classrooms, but the challenge of getting kids "math holes" doesn't scare me. What helps my students "catch up" or "fill in gaps" is not so much about the math but my commitment to establish raport between the students and me and create a safe learning space where kids can talk math, learn from each other, and use mistakes as learning opportunities. It would be so much easier to just teach algorithms, especially when the kids beg for an "easy" day. But life isn't easy, and my kids know this. And while they whine, complain, and roll their eyes and sigh, at the end of the year, they come to appreciate my approach and thank me.

Of course, I am privileged to have teachers to collaborate with and a district that has designated priority standards and allows me to teach how I see fit. I am a high school math teacher, 30 years experience, and my current school is at 65% free/reduced lunch. We can do this!

Jodi is absolutely right that "meeting students where they are" is essential and will not be that different next Fall than it has always been. Vertical planning will give us some advance notice of what "gaps" students may have, but more important will be teacher and students searching day-to-day for the "edge" that students bring to each lesson.

Seeing lots of this throughout the comments. Emphasizing continuities with past years and past practices.

"What helps my students 'catch up' or 'fill in gaps' is not so much about the math but my commitment to establish rapport between the students and me and create a safe learning space where kids can talk math, learn from each other, and use mistakes as learning opportunities."

Some resources are precious and finite—like class time. Other resources—like rapport, like an understanding of math as a coherent story across grades—are infinite and available to everybody, and every math teacher probably needs them this year more than ever.

For each grade level, our standard of focus should be the grade level standards. However, we should have always been connecting them to ideas that connect back to previous grade level standards to lower the floor, engage prior knowledge, and make connections between what they have learned and what they will be learning. In addition, we should also be setting our students up for success by setting up opportunities that will enhance future learning. While teaching a 7th grade student order of operations with rational numbers, we can lower the floor by giving them similar problems with whole numbers from the 6th grade standard and raise the bar by asking them to evaluate expressions written in scientific notation and solve operation problems written in scientific notation. Depending on what strengths students bring into the classroom, you can even include the 5th grade standards with whole numbers where the expressions do not have exponents. This not only helps cover some of the loss of opportunities but also helps to accelerate their learning in the long run. The difficult part for teachers is that they cannot teach within the silo of their own grade level. They need to not only master the full breathe of the standards at their grade level but also above and below. No small task by any means. Even more difficult for teachers that do not have proper support from instructional coaches or the support of colleagues that work collaboratively.

I can't even begin to imagine doing this without collaboration. I am privileged to work with colleagues that believe in the strength of collaboration. The building/district does not give us time or compensation. We stay after school to do this because we know it is vital to our own sanity 😊 and to the learning experiences we want our students to have. Implementing a new text series this fall. We have not taught from a text in over 10 years. So big learning curve for our dept. to go along with creating opportunities to bring our kids knowledge base back where it should be. We wont be perfect but we, the staff and kids, will persevere

For too long we've focused (especially in mathematics) on covering particular content rather than truly engaging students in learning. Thus, for some students, we reteach certain concepts every year from 5th grade through a third year high school course. It's no wonder they're disengaged. Rather than a focus on what was "lost," I think we need a greater focus on reimagining what can and should be. I wrote about that in conjunction with NSTA from a science perspective - https://www.nsta.org/blog/rethinking-discussion-learning-loss.

Dan, you know you are opening such a can of worms. You wrote, “'learning loss' isn’t a particularly accurate description of cognition." So you understandably shift to "opportunity loss." I wish to share two brief ideas to refocus the conversation on what is worthwhile -- a deeper interrogation of what happens in math classrooms for far too many (especially secondary) youth in math classrooms. (1) The common conception of "learning" in schools is about the degree and accuracy to which the student knows the curriculum – the thing to me learned. But, because humans are involved, this is really a measure of the degree to which the teacher sees their ways of knowing in the child. A better match to the teacher equates to positive learning for the child. With that sort of definition, learning “loss” can make sense. And I would suggest it may actually be a good thing. (2) Until there is a significant shift in the number of students who have horrible experiences in math classrooms, the “opportunity loss” you name is very likely a gain for the population of secondary-school age children in the US, in identity building and likely logico-mathematical ways of knowing the world.

If the conversations about “learning loss” that occur in districts (and flood district leadership’s email boxes with packaged, costly solutions) would take seriously what we mean by “learning” and interrogate truly whether positive mathematical experiences were “lost,” we might begin to acknowledge what our youth have been saying for decades, and are beginning to fully articulate today, how we teach math is broken. “You’re taking my humanity by telling me I’m wrong all the time, or saying that I failed.” <-- that statement is from a group of youth that are forging a National Math Literacy Corps. https://docs.google.com/presentation/d/1VBA2NOQcR3kYFnfvXg-MpHDgNOFfHFjWeW8sNMW8AnE/edit?usp=sharing Here is a short presentation of their work https://docs.google.com/presentation/d/1_tkuXLD4hQyfffL7ZITOLzuFXM3p-Pm69vCCVzKIFMI/edit?usp=sharing

Good to get an update on your current work, Brian. However, I'm unconvinced these questions are as tightly entwined as you seem to be. We can wonder, "What experiences do we hope students will have in math classes?" and, separately, "What should teachers do next year when students haven't had the experiences we hoped they'd have?" Looking forward to the answers you and your students co-construct for that first one.

Every year we face students who have not had the same opportunities as the majority of our student body. This year that number will likely be larger. As such we will need to be more mindful of activities that have a low floor and high ceiling do everyone can stay engaged.

Hopefully school districts will permit teachers to rely on their experience of working with students and knowledge of their content, to determine what skills the students need to achieve successful learning. Students did miss opportunities, but did have other opportunities. The key is to meet them where they are yet challenge them to go beyond and to grow. There will be gaps, but there always is. I just hope that districts do not try to strip away the meaning of math by teaching rote skills without the context, students need to make connections. If we build bridges and help the students provide them with the opportunity to make connections, but it is key not to try and rush them through things. We must allow them the time they need to build experiences and they will make the connections they need to achieve the standards of mathematics they need to move forward.

I agree opportunity loss is a better description. I plan on using desmos and Peter Liljedahl’s new book Building Thinking Classrooms to bring students into a state of thinking about the math. Give them math headaches and let them create the asprins. The content will come.

First, by assuming that teachers taught “less” because they used fewer lessons is a mistake. This year, I pulled from a variety of helpful online resources to make my math instruction more engaging both online and in-person. The biggest challenges for me were reduced opportunities for social learning when in-person and assessing individual student learning when remote. I taught first grade, so handing in work was harder for them without parent assistance and the available tools for documentation/observation/communication were insufficient. Social learning is so crucial, especially for less confident learners who start to feel “stupid” if they feel they’re asking the teacher for help all the time. We couldn’t let kids work as partners or small groups until restrictions eased to 3 feet apart near the end of the school year. Despite the challenges of teaching under COVID conditions, I taught everything “we were supposed to” based on district priorities and benchmarks. I also taught more because I’m not a fan of the depth not breadth movement and think math learning should meet students practical daily needs, like making change, telling time, keeping score, and estimating space. Many of these skills have been marginalized at the expense of extensive focus on counting, addition and subtraction. I hated the math program my district used so I was actually gleeful when parents neglected to pick up their children’s workbooks when we went remote. I used it as an excuse to teach my own way and either create my own materials or use fun interactive activities I found online. It was a good opportunity for me to explore what’s out there. So, don’t assume teachers taught less because they didn’t use your lessons. We’re not robots, we’re professionals. Published programs are a convenient tool, not a curriculum and certainly not a “how to” when it comes to teaching.

I'll continue to use low floor-high ceiling tasks, such as 3 Act Math or Open Middle problems. These have multiple entry points and can me identify starting points for learning and misunderstandings. Students will continue to be met where they are at in their learning.

The Opportunity Myth goes into some good data on the importance of teaching grade-level content. Gaps continue to widen if we try to address content from previous grades. Moving Forward article talks about the importance of identifying essential understanding and supporting prerequisite knowledge. That will be our focus this year.

Last year, many students spent less time learning about things from the narrow band of "what math teachers teach," and so probably learned less of it. Which means there are more times where we may have to say, "We can't learn some things this year, because we didn't learn the prerequisite things last year, for whatever reason." The more we can minimize the importance of "prerequisite" knowledge in our courses, the less we have to worry about this.

First a follow up question on your data- if you restrict teachers to exclude those using the curriculum for the first time what does that do to your median? My hypothesis is that teachers were learning so many other new things that something had to give for first time users.

In answer to your question- Having used the curriculum for the first time myself this summer with students who had struggled during the school year, the readiness checks were a great guide to what previous topics needed to be woven in. The curriculum is so inviting that there was 100% zero need to teach a unit of missed material. They could all find a way in to that first lesson. But it did find myself going much slower than I had anticipated as I wove in things that showed up in the readiness check to our class discussion and supported social emotionally scarred students who were so afraid to engage deeply. Other teachers from my team plowed through at the originally planned pace and had more mixed feelings about how much they had helped students to recover from the previous year.

I don't have all the answers for next year but I think it starts at grade level with adjusted scaffolds as the needs show themselves.

> The curriculum is so inviting that there was 100% zero need to teach a unit of missed material. They could all find a way in to that first lesson. But it did find myself going much slower than I had anticipated as I wove in things that showed up in the readiness check to our class discussion and supported social emotionally scarred students who were so afraid to engage deeply.

Love to hear the first part. Sad to hear the second. Do you think that scarring was primarily COVID-related or more related to the kinds of math trauma we often see in students in summer school?

It was a mix. A few students with extreme anxiety around people in general, and more whose self worth had taken a beating when they failed 3 or more classes last year.

But there was also alot of joy as students exclaimed out loud "Hey I am smart!" or to a partner "we are so good at this!"

Hopefully, most teachers start the year finding out what their students know and where they are, and then moving them forward from this point. This year will be no different, although the starting points for kids may be very different from what we are used to.

Perhaps we'll find out new things as we move forward - maybe some kids will benefit from being introduced to certain concepts later rather than earlier. Maybe students will have learned to be more independent in their learning. I am looking forward to seeing how this year unfolds, knowing that I will need to be flexible, just as in years past (this past year and a half in particular!). Plus, I have a few more tools in my pocket now as a result of online learning time!

I still believe that our math curriculums (as well as other subject curriculums) need an enema. Math should not be restricted to books, standards, fancy online works, or equations to be solved that are meaningless. I feel "learning loss" or "opportunity loss" goes deeper than the pandemic ever caused. In my dream world, math would be discovered and formulas used to solve those discoveries and meaningful opportunities will be presented to the learning then there would no losses.

I will continue what I have done in the past: use my district priority standards, meet my students where they are, and do my best to give them rich learning experiences to get them to meet priority standards we have set. In addition, the vertical planning we do at my building allows us to share how deep we taught in the course and which standards and units may need more remediation. Maybe it is because I have always taught in at risk classrooms, but the challenge of getting kids "math holes" doesn't scare me. What helps my students "catch up" or "fill in gaps" is not so much about the math but my commitment to establish raport between the students and me and create a safe learning space where kids can talk math, learn from each other, and use mistakes as learning opportunities. It would be so much easier to just teach algorithms, especially when the kids beg for an "easy" day. But life isn't easy, and my kids know this. And while they whine, complain, and roll their eyes and sigh, at the end of the year, they come to appreciate my approach and thank me.

Of course, I am privileged to have teachers to collaborate with and a district that has designated priority standards and allows me to teach how I see fit. I am a high school math teacher, 30 years experience, and my current school is at 65% free/reduced lunch. We can do this!

Jodi is absolutely right that "meeting students where they are" is essential and will not be that different next Fall than it has always been. Vertical planning will give us some advance notice of what "gaps" students may have, but more important will be teacher and students searching day-to-day for the "edge" that students bring to each lesson.

"I will continue what I have done in the past"

Seeing lots of this throughout the comments. Emphasizing continuities with past years and past practices.

"What helps my students 'catch up' or 'fill in gaps' is not so much about the math but my commitment to establish rapport between the students and me and create a safe learning space where kids can talk math, learn from each other, and use mistakes as learning opportunities."

Some resources are precious and finite—like class time. Other resources—like rapport, like an understanding of math as a coherent story across grades—are infinite and available to everybody, and every math teacher probably needs them this year more than ever.

We need to build a classroom culture where formative assessment and prompt feedback are the norm

For each grade level, our standard of focus should be the grade level standards. However, we should have always been connecting them to ideas that connect back to previous grade level standards to lower the floor, engage prior knowledge, and make connections between what they have learned and what they will be learning. In addition, we should also be setting our students up for success by setting up opportunities that will enhance future learning. While teaching a 7th grade student order of operations with rational numbers, we can lower the floor by giving them similar problems with whole numbers from the 6th grade standard and raise the bar by asking them to evaluate expressions written in scientific notation and solve operation problems written in scientific notation. Depending on what strengths students bring into the classroom, you can even include the 5th grade standards with whole numbers where the expressions do not have exponents. This not only helps cover some of the loss of opportunities but also helps to accelerate their learning in the long run. The difficult part for teachers is that they cannot teach within the silo of their own grade level. They need to not only master the full breathe of the standards at their grade level but also above and below. No small task by any means. Even more difficult for teachers that do not have proper support from instructional coaches or the support of colleagues that work collaboratively.

I can't even begin to imagine doing this without collaboration. I am privileged to work with colleagues that believe in the strength of collaboration. The building/district does not give us time or compensation. We stay after school to do this because we know it is vital to our own sanity 😊 and to the learning experiences we want our students to have. Implementing a new text series this fall. We have not taught from a text in over 10 years. So big learning curve for our dept. to go along with creating opportunities to bring our kids knowledge base back where it should be. We wont be perfect but we, the staff and kids, will persevere

I think that the "opportunity loss" is also the area above the bars < 60% completion, too.

Also, love to see the comparable graph for pre-Covid 2018-2019. How much "opportunity loss" then? (Assumes same resources accessible on Desmos.)

For too long we've focused (especially in mathematics) on covering particular content rather than truly engaging students in learning. Thus, for some students, we reteach certain concepts every year from 5th grade through a third year high school course. It's no wonder they're disengaged. Rather than a focus on what was "lost," I think we need a greater focus on reimagining what can and should be. I wrote about that in conjunction with NSTA from a science perspective - https://www.nsta.org/blog/rethinking-discussion-learning-loss.

I agree.

Dan, you know you are opening such a can of worms. You wrote, “'learning loss' isn’t a particularly accurate description of cognition." So you understandably shift to "opportunity loss." I wish to share two brief ideas to refocus the conversation on what is worthwhile -- a deeper interrogation of what happens in math classrooms for far too many (especially secondary) youth in math classrooms. (1) The common conception of "learning" in schools is about the degree and accuracy to which the student knows the curriculum – the thing to me learned. But, because humans are involved, this is really a measure of the degree to which the teacher sees their ways of knowing in the child. A better match to the teacher equates to positive learning for the child. With that sort of definition, learning “loss” can make sense. And I would suggest it may actually be a good thing. (2) Until there is a significant shift in the number of students who have horrible experiences in math classrooms, the “opportunity loss” you name is very likely a gain for the population of secondary-school age children in the US, in identity building and likely logico-mathematical ways of knowing the world.

If the conversations about “learning loss” that occur in districts (and flood district leadership’s email boxes with packaged, costly solutions) would take seriously what we mean by “learning” and interrogate truly whether positive mathematical experiences were “lost,” we might begin to acknowledge what our youth have been saying for decades, and are beginning to fully articulate today, how we teach math is broken. “You’re taking my humanity by telling me I’m wrong all the time, or saying that I failed.” <-- that statement is from a group of youth that are forging a National Math Literacy Corps. https://docs.google.com/presentation/d/1VBA2NOQcR3kYFnfvXg-MpHDgNOFfHFjWeW8sNMW8AnE/edit?usp=sharing Here is a short presentation of their work https://docs.google.com/presentation/d/1_tkuXLD4hQyfffL7ZITOLzuFXM3p-Pm69vCCVzKIFMI/edit?usp=sharing

Good to get an update on your current work, Brian. However, I'm unconvinced these questions are as tightly entwined as you seem to be. We can wonder, "What experiences do we hope students will have in math classes?" and, separately, "What should teachers do next year when students haven't had the experiences we hoped they'd have?" Looking forward to the answers you and your students co-construct for that first one.

Every year we face students who have not had the same opportunities as the majority of our student body. This year that number will likely be larger. As such we will need to be more mindful of activities that have a low floor and high ceiling do everyone can stay engaged.

Hopefully school districts will permit teachers to rely on their experience of working with students and knowledge of their content, to determine what skills the students need to achieve successful learning. Students did miss opportunities, but did have other opportunities. The key is to meet them where they are yet challenge them to go beyond and to grow. There will be gaps, but there always is. I just hope that districts do not try to strip away the meaning of math by teaching rote skills without the context, students need to make connections. If we build bridges and help the students provide them with the opportunity to make connections, but it is key not to try and rush them through things. We must allow them the time they need to build experiences and they will make the connections they need to achieve the standards of mathematics they need to move forward.

I agree opportunity loss is a better description. I plan on using desmos and Peter Liljedahl’s new book Building Thinking Classrooms to bring students into a state of thinking about the math. Give them math headaches and let them create the asprins. The content will come.

You love to hear it. Let's go!

First, by assuming that teachers taught “less” because they used fewer lessons is a mistake. This year, I pulled from a variety of helpful online resources to make my math instruction more engaging both online and in-person. The biggest challenges for me were reduced opportunities for social learning when in-person and assessing individual student learning when remote. I taught first grade, so handing in work was harder for them without parent assistance and the available tools for documentation/observation/communication were insufficient. Social learning is so crucial, especially for less confident learners who start to feel “stupid” if they feel they’re asking the teacher for help all the time. We couldn’t let kids work as partners or small groups until restrictions eased to 3 feet apart near the end of the school year. Despite the challenges of teaching under COVID conditions, I taught everything “we were supposed to” based on district priorities and benchmarks. I also taught more because I’m not a fan of the depth not breadth movement and think math learning should meet students practical daily needs, like making change, telling time, keeping score, and estimating space. Many of these skills have been marginalized at the expense of extensive focus on counting, addition and subtraction. I hated the math program my district used so I was actually gleeful when parents neglected to pick up their children’s workbooks when we went remote. I used it as an excuse to teach my own way and either create my own materials or use fun interactive activities I found online. It was a good opportunity for me to explore what’s out there. So, don’t assume teachers taught less because they didn’t use your lessons. We’re not robots, we’re professionals. Published programs are a convenient tool, not a curriculum and certainly not a “how to” when it comes to teaching.

I'll continue to use low floor-high ceiling tasks, such as 3 Act Math or Open Middle problems. These have multiple entry points and can me identify starting points for learning and misunderstandings. Students will continue to be met where they are at in their learning.

The Opportunity Myth goes into some good data on the importance of teaching grade-level content. Gaps continue to widen if we try to address content from previous grades. Moving Forward article talks about the importance of identifying essential understanding and supporting prerequisite knowledge. That will be our focus this year.

Last year, many students spent less time learning about things from the narrow band of "what math teachers teach," and so probably learned less of it. Which means there are more times where we may have to say, "We can't learn some things this year, because we didn't learn the prerequisite things last year, for whatever reason." The more we can minimize the importance of "prerequisite" knowledge in our courses, the less we have to worry about this.

First a follow up question on your data- if you restrict teachers to exclude those using the curriculum for the first time what does that do to your median? My hypothesis is that teachers were learning so many other new things that something had to give for first time users.

In answer to your question- Having used the curriculum for the first time myself this summer with students who had struggled during the school year, the readiness checks were a great guide to what previous topics needed to be woven in. The curriculum is so inviting that there was 100% zero need to teach a unit of missed material. They could all find a way in to that first lesson. But it did find myself going much slower than I had anticipated as I wove in things that showed up in the readiness check to our class discussion and supported social emotionally scarred students who were so afraid to engage deeply. Other teachers from my team plowed through at the originally planned pace and had more mixed feelings about how much they had helped students to recover from the previous year.

I don't have all the answers for next year but I think it starts at grade level with adjusted scaffolds as the needs show themselves.

> The curriculum is so inviting that there was 100% zero need to teach a unit of missed material. They could all find a way in to that first lesson. But it did find myself going much slower than I had anticipated as I wove in things that showed up in the readiness check to our class discussion and supported social emotionally scarred students who were so afraid to engage deeply.

Love to hear the first part. Sad to hear the second. Do you think that scarring was primarily COVID-related or more related to the kinds of math trauma we often see in students in summer school?

It was a mix. A few students with extreme anxiety around people in general, and more whose self worth had taken a beating when they failed 3 or more classes last year.

But there was also alot of joy as students exclaimed out loud "Hey I am smart!" or to a partner "we are so good at this!"

Hopefully, most teachers start the year finding out what their students know and where they are, and then moving them forward from this point. This year will be no different, although the starting points for kids may be very different from what we are used to.

Perhaps we'll find out new things as we move forward - maybe some kids will benefit from being introduced to certain concepts later rather than earlier. Maybe students will have learned to be more independent in their learning. I am looking forward to seeing how this year unfolds, knowing that I will need to be flexible, just as in years past (this past year and a half in particular!). Plus, I have a few more tools in my pocket now as a result of online learning time!

Flagging for myself comments like this:

"This year will be no different, although the starting points for kids may be very different from what we are used to."

Where teachers like you are identifying this upcoming year as _continuous_ rather than _discontinuous_ with other years.