Make Math Moments Academy › Forums › Full Workshop Reflections › Module 6: LongRange Planning and Assessment to Make Math Moments That Matter › Lesson 62: What is Spiralling & Spacing › Lesson 62: Question
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Lesson 62: Question
Kyle Pearce updated 1 week, 1 day ago 95 Members · 122 Posts 
Share any questions, thinking, and comments on your spiralling and spacing here.

I have used my “warmups” as spiral reviews but I have never tried to spiral the whole curriculum. Something that stuck with me was the idea that spiraling can solve the problem of kids moving from one school to another, absences, moving from one class to another, etc. I found the following especially interesting the ideas that kids who missed one part of our content will have the opportunity to go over it later and that students who already had contact with the material will have the chance to deepen their understanding.

This is exactly how I have always done my spriralling as well. I have always struggled to spiral within core content. I am very interested in the Ontario and Chicago links that are provided in the resources.
 This reply was modified 7 months, 1 week ago by Jeremiah Barrett.


Unlike the mathematics curriculum in North America, I had been exposed to spiralling since my primary and secondary education. I have been using spiralling in teaching since I first taught in my current secondary school in Hong Kong.
Spiralling seems to be unnecessary and boring parts for top students and students with good memory of what they have learnt in the past. However, it’s definitely good for the majority of the average and weaker students. They tend to forget what they have learnt and it’s important for teachers to embed or even integrate the previous knowledge with the new knowledge so that students can revisit and apply the previous knowledge in a new context.
I used to give a summative test after teaching one topic by giving a mark. Most students show fear and emotions when receiving their test with an unsatisfactory mark. After this module, I’ll try not to put a mark on their test paper so that students can focus on my feedback/suggestions instead of focussing on the marks.
Thanks for giving us an opportunity to reflect on our current practice!

One takeaway from this is that students learn a concept more deeply and have better retention with spiraling than with blocking the material in units and chapters. I can remember being so relieved once I completed my college course on statistics and how I never wanted to engage with that type of math again. If statistics had been introduced early on and woven into my math classes, I would have been less apprehensive and more open to learning the concepts. As a teacher, I notice that many of my students struggle with retention of previously taught math concepts if they did not have enough time or exposure to interact with the concepts. I also like the concept of using tests to study rather than study for a test.

I am so excited to hear about spiraling again. When I was student teaching 18 years ago, we were using a math program (I believe it was Saxon?) that spiraled. I absolutely loved this way of teaching math and I just thought that was how math was taught. As the years have gone on, I have become more and more frustrated with the math programs that are out there and how much they only teach using blocking, rather than spiraling. They also rely so much on test taking as a way to know if a student has mastered a concept. However, being a special education teacher, I promise you this is not an ideal way to teach. My student work so hard to try to understand a concept for test day and then the second a new concept is taught that are unable to recall most of the preivously taught information. They are definietly not learning through wondre and curiosity. They are just trying to survive and move concept to concept. I see this with both special education and general education students. They definitely are only developing that surface level learning in most cases. Often times when I ask a student to recall a previously taught skills, they will act as if I am speaking a foreign language. Usually after some reteaching the skill starts to come back, but imagine how powerful that would be if that skill was revisited over and over again every 35 days. I’m so excited to think there’s a possibility that more spiraling may be occuring in the future and that more of these kids may have a shot at being successful with math.


Last summer I led some work with a team of teachers from each grade level K5. We put all textbook sources aside, and only looked at the CCLS domains, clusters, and standards at each grade level. We had vertical conversations about priority big ideas, traditional student areas of strength and weaknesses, and connected big ideas within the grade levels. Teams then used these conversations to connect ideas within their grade levels, and then sequence the learning in a way that made sense for kids, considering pacing as well. This was our first step as a district to move away from the idea of just teaching from the textbook, and hints at your idea of sequencing.
Now, having gone through part of a school year with these changes, I will be anxious for us to gather again (possibly over the summer) to reflect on this work and its impact on kids. I do think that we can do better at making more connections between big ideas and create a more effective spiraling effect, so I will be using this learning to help guide this future work.

I have been doing a lot of reading and research on spiralling over the past year or so. I started this process this semester and in all of my classes. It was going well and I was seeing how following the ideas presented here by Jon and Kyle here is making things go well. I look forward to being able to see how spiralling works over a complete semester.

I am a big promoter of spiraling. In fact, on an informal level, I liken it to looping. The teacher that loops can offer continuous learning as s/he knows the students and the content that was presented to them previously. I felt solid this year looping with content, as I had been teaching 4th grade math and now teach 6th. I know what they had been presented. I also know that skipping an entire year of concepts, as is set up through the Common Core Standards (which, by the way, do not endorse spiraling), has detrimental effects on students.

Spiralling math is a great way to mix the math units that way the students are always coming back to previous lessons/stragtegies. Every year I see students work hard to understand and learn math topics, only to forget it by the end of the school year. Spiralling these topics can make it so they are exposed to the topics all year long and not just for a month. By giving the class multiple lessons throughout the year makes it so they can retain the information easier.

I am such a huge fan of spiralling but have been hesitant due to my inexperience with the courses I am teaching (I’m a new teacher). I’ve promised myself to get my bearings with traditional massed practice and then hop straight into spiralling when I’m feeling more versed. I’ve been slowly seeding in these moments throughout this last year, prepping my self for the future. It’s very exciting. The one thing that I have noticed about my own practice is the fear of having to “go back”. There’s a strange feeling of failure (?) associated with going back to “reteach” certain concepts, or a feeling of broken contenuity when you deviate from the overall unit plan. I have been actively trying to fight back on these feelings and tell myself it is absolutely okay to loop back over and revisit a concept by from a different or more nuanced angle.

I am always excited about trying to spiral, however the expectations of performance on district assessments and the expectation of each teacher being in the same place are things that hold me back. I do have excellent teammates, but we don’t always agree about how and when to teach material. I need to continue to look for ways to still integrage this into my teaching. I know it is best for the kids.

I have often been frustrated by how quickly students forget concepts that they have “mastered” based on a topic assessment. I’ve done various things in class to keep students practicing topics, (10 question drills, adding looped problems to their daily practice of current topics) but never with consistency nor could I justify spending the time on these activities when I would look at everything I “had to teach” in the course of a year. I also struggled with how to include the assessment of this spiraling in the gradebook. Grading and reporting out student “achievement” based on standards never felt comletely accurate. I often felt the grades I reported for many students that “mastered” a standard were misleading because I knew given a similar task a month later would cause many to struggle even though they had “mastered” that standard according to their grades in the gradebook. The idea that a test is really an opportunity to access stored knowledge is mindblowing for me. I talk so much with my students about connections in our brains. I make them put their hands on their heads to “wake up” stored knoweldge and constanlty ask them to look for patterns or information in problems that might help them problem solve based on something they see that triggers a concept they may have learned before. It gives me legs to defend spiraling and now has me questioning what I want to include in my gradebook.

We use CPM curriculum and one of their pillars is mixed, spaced practice (=spiralling). So my students tests after each chapter contain 70%+ on previous chapters and only about 2030% on the “newest” concept they’ve learned. So, they don’t get a chance to “forget” because the homework problems have been spiralled and so are the tests!

I totally agree with the importance of spiraling, however, the work required to do that would seem very overwhelming to my teachers (I am an instructional coach). Is this something that I can do? I bet this will become clearer as I progress through this Module!

I Have been interested in using Spiralling but having access to a curriculum or resource, would be very helpful in making my administration see how it will work and someone else has done it before.
Thank you for sharing this !

We use Everyday Math in our district and love the spiral! However, so many teachers are stuck on the teach to mastery and move on thinking that they don’t follow the spiral of the curriculum, but supplement and stay in one spot until students show a temporary fluency that is often mistaken for learning. Most people either love or hate Everyday Math curriculum, and though it isn’t perfect I love it!

Every year students forget what they learnt the previous year or the previous term. They just think about learning a topic, doing the assessment and it’s done!! Spiralling math is really important for students to connect the different strategies and strands. I will be using this learning and reflect over the summer on how to move forward for next September.

Spiraling is something that I’ve known about for a long time, but I usually think of it at concepts that come back in future years, not as something that happens in my class during one school year. I love this idea of teaching in a spiral way throughout the year, and totally see how it can help students retain.
Things I question are how my students will do on our district benchmark assessments, which are very blocked in nature, as well as what the balance would be between giving kids enough time with a concept to develop some understandings, but not siloing at the same time. I’m sure the idea is not to stop the units to just bounce around randomly day to day, but I’m not sure where that balance lies.

I do not know anyone who teaches in a spiraling format! A lot of traditionalists in our school. I definitely plan on using spiraling in the fall. Thanks for the websites that have plans in place for spiraling. That will give me a place to start!

Keep us posted on how the planning and implementation goes!


I had heard about spiraling and we were always told we were doing it by beginning class with review questions. Now I have a deeper meaning of what spiraling really means and how it is a form of interleaving. I like the messiness of it, even though it complicates matters for me for it is much more like how people really learn best, as the researchers stated. I loved Cary’s admonition to “Let go” of the all the paced, repetitive, ritualistic type of teaching and learning we’ve been steeped in for so long. My students have been asking for more wonderful and curiosityinspiring lessons and I intend to respond to the call by spiraling and taking on what I am learning through this course!

I’m really excited to put spiraling into full practice this year. I have tried to begin with baby steps this year (moving certain topics around to make them flow better and pull things like statistics in early to connect to proportional reasoning, etc…). I really love the idea that if a student comes into my classroom later in the year, by spiraling they will be able to see the concepts that they may have missed because we will come back to it. I am hoping to spend the summer trying to plan out what the spirals will look like for 7th and 8th grade, and I will definitely look at the resources you posted. So excited to learn more about this and how to actually put it into practice!

Our Lower School uses Everyday Math so spiraling in middle school is a natural follow on for our students.

I have only taught Everyday Math once when I taught fifth grade for a single year. I’ll be returning to this program (in grade 4 this time) this coming year. In my district, it has a bad review by most. Colleagues put it down because they feel the students can’t focus on a topic and find mastery before doing a different topic. It’s good to hear the research backing the set up and spiraling involved and gives me a positive outlook for next year!

I used Everyday Math in 5th grade as well very early in my career, now over 10 years ago. I remember loving the concept of spiraling, but also struggling with what you say some teachers mention – the spiraling felt ineffective because kids often couldn’t retrieve skills needed and because there were not multiple examples on one topic, I couldn’t figure out a way to teach them without “giving away answers” or taking on the majority of thinking. Now in reflection I think what held it back was the lack of depth and connections to make the spiraling effective.

What I find we need to keep in mind is that we not only spiral content but we also need to spiral the “release of responsibility”. I often direct learning through tasks early and then gradually let that go as students become more familiar and more confident.
Spiralling is a large topic and we just hint at it here (in the workshop). In our Academy (your next step) we have a course that dives into more depth plus case studies with teachers working through problems of practice. https://learn.makemathmoments.com/courses/spiralling/


I heard this idea of retrieval practice on a couple of different podcasts that I listen to. I like brining that idea into the spiraling of the math order of concepts.

Prior to my current central position, I was weaving together different mathematic strands to avoid being stuck at the end of the term in not teaching a unit that I needed a grade for the report card; not realizing that this technique was called Spiralling the Curriculum. I’ve also used the TIPS4MATH website for ideas to integrate within my lessons, such a great resource.

When I first started teaching, I would either follow the textbook or teach strand blocks which I always found myself struggling in getting all the necessary grades needed to have to finalize the report cards. Then I was starting to weave together different mathematics strands together as I planned units; this greatly helped me to ensure that I had all of the grades necessary for the report cards. However, I would rarely go back and review the expectation throughout the school year which is why I really like the concept of Spiralling the Curriculum. It not only helps the students to understand and retain their learning but helps the teacher know which concepts that needs to be reviewed throughout the year. I’ve also used the TIPS4MATH website for ideas to integrate within my lessons, such a great resource.
 This reply was modified 1 year, 6 months ago by Tracy Martel.

Thanks for the website! ‘ll be going there this afternoon for research!

I haven’t used a spiraled curriculum but it’s interesting to hear the research supports it. Before I started teaching at my school, Everyday Math was the elementary curriculum and the teachers did not feel it provided sufficient practice of the concepts; they did not think the students developed automaticity. Likewise, when we were reviewing new curriculum, other teachers who had taught using Saxon math (which is very purposefully spiraled) felt that there were some students were left behind by the constant switching between strands; Saxon, however, may be more inflexible than other spiraled curricula. I’m taking this workshop to shake up some of my wellingrained thoughts and habits so I’m open to learning more about this.

I am aware of spiraling because I worked for one year at a school that “used” Saxon math. I can see how this would be beneficial for average to struggling students and can help to eliminate the “oh I totally forgot how to do that” comments. Unfortunately, I did not feel comfortable with spiraling yet because 1) it was my first year of teaching, but 2) the students’ previous teachers had seriously neglected to do their job. Due to their lack of background knowledge it did not seem feasible to jump around from topic to topic because often they did not have the prerequisite skills that we would be building on from and we had to do a lot of pivoting to fill in all the gaps.
The point of that aside is to explain my feeling that spiraling can be extremely successful if done over successive years. As a teacher who works with the same students for 68 I would be able to make this happen. But I hesitate to implement this for the students in 8th this year who do not like change much and already are a very strong class with things as is. I wonder if/what the varying degrees of implementation are? I also am unsure about the ordering/organizing of lessons because I do think there are some skills/units that need to be mastered before others.
I feel bad that I am not totally on board yet!

Does anyone know if Illustrative Mathematics has spiralling built into its framework? It does claim to incorporate the 5 Practices! I feel like I need some training wheels!

Having taught FDK, I feel like spiralling Math has become a natural means of teaching for me. I strongly believe that this method is a good way to mix the different units. This will help students to get a refresher and/or review of previously taught lessons and/or strategies. I think it is very important to use this method, especially with very young learners, so that they can retain the information easily.

I have students that come and go frequently, so spiraling seems like a great way to make sure my students don’t totally miss out on an important concept.

I have a workbook that does a great job of spiraling. As a fourth grade teacher, I used it for our warm up. Now that I’m moving to 5th grade and have a smaller amount of time, I am going to try to shorten the daily exercises. I love that it allows me to see the concepts students are already comfortable with and allows me to teach and go in depth where students most need it. I have seen many benefits to having the standards spiraled. Students get multiple chances to practice and it has helped with retention of skills.

I teach 5th Grade in North Carolina. I would love to have someone to collaborate with on long range plans. I am also pursuing my National Board Certification.


When I taught 4th grade, we used Saxon Math. Saxon spirals the curriculum daily. I wish I had one of my old textbooks. All of the assessments were spiraled too.

I love TIPS4Math and have used it for years. Did I realize that it was already a “spiralling” math program? Yes and no. I knew it integrated many math ideas but I’m wondering why in the the fervour for everyone to spiral math, no one is talking about it in any of the chat rooms? Everyone seems to be focussed on creating something from scratch. I know we have a new math curriculum in Ontario can the government tweak TIPS to match it so we have a resource for September?

This past school year I tried to spiral my plans. It was tricky! Students would work on different math strands as bell work (their first task after attendance). I loved that it brought up great conversations and we usually discussed the morning work as part of a number talk later in the morning. However, the tricky part was that if students were unfamiliar with the content presented that day, they would just make their best guess and put very little effort into the task (during bell work, I wasn’t normally available to work one on one with students to help them through the task). I guess it would work better if we ALWAYS spent time afterwards discussing solutions and strategies. But this took too much time. Or perhaps be available to those who need help, by gathering as a small group as needed.
I think a lot of educators, myself included, find spiraling to be intimidating as we don’t know how to progress through the concepts in a gradual way throughout the year. We also are very accountable to writing report cards and having a grade for each strand, so I think we often feel rushed.
I do love the idea of spiraling though, and this year I’ll give it another try, perhaps use the Throwback Thursday idea, using 1 day of the week to explore a different strand than we are currently focusing on.

My school uses Everyday Math. They do an okay job with spiralling, but it’s heavily worksheet based, so I add my own things. Spiralling can also happen outside of the math class. Science is a great way to bring in previously learned skills. If you use the NGSS standards, each unit tells you which Common Core math standards apply to that unit.

Questions

How do you assess with spiraling?

You mentioned Everyday Math, which our district uses up to grade 5; what curriculum(s) spiral for grades 68?
In past years I have used what I call forgetmenots for Spiral Review on Fridays to start the class. It can include concepts that are current or not so current. But this type of spiraling is not the type of spiraling that I need to be doing, am I correct? I need to do more focused concept lessons over spiraling, yes?

Luanne,
Great questions. I’d say that “review” Friday’s is a form of spiralling and a great way to get started. We also encourage 510 minute starter activities that link to learning goals that might not be apart of that days Lesson.For assessment we’re building out our course Assessment For Growth in the Academy and you currently have access to module 1. Have a look there for some guidance.


Thank you for this informative lesson. I have a lot to ponder about how to make spiraling a more integral part of my curriculum.

I am super excited to learn about spiralling. I also used to think that a warm up of mixed review at the begininng of class was a good spiral. But am now ready to move on. I am also excited to start putting my classes together. I teach 6,7,8 at a small school and teach one class of each grade – all of them. This type of math program will allow me to really spiral over the 3 years as well! It makes me wonder about increasing my work load (!) to make recording documents closer standards mastery and check them off as I go along. And am just NOW thinking about changing the grading to move toward standards based grading! There is a lot to do in a short amount of time! I am also on my school´s committee for reopening in the fall. At least we get summers ¨off¨…

I’m very excited about spiraling. It makes so much sense to me. Not that I have a plan for how yet . . . .

The concept of spiralling is important. I know from my 12 years of teaching 4th/5th grades that many students do not retain concepts and skills from earlier in the year or previous years. However, if your district does not have a math program that has spiralling built in, do you have suggestions for resources that can help? Otherwise, creating content that spirals tends to become more and more time consuming. Additionally, we have to be aware of what kind of spiralling we are doing. I don’t think mindless drill and kill formats are not valuable. I’m excited to find out more about spiralling in the next lesson and within the academy. I think that one of the ideas that will help me moving forward is just being mindful of going back to standards and concepts at times. Maybe incorporating previously learned concepts into warm ups. With a blended learning format that we are tentatively going to pursue in the fall, I could also try to weave in some spiralling when students are in the remote setting.

I don’t think you can gain enough experience with algebra without some massing. And a lack of fluency can make students feel disheartened or bored. Those are concerns that I have with constant spiraling. But generally mixing it up and going back to prior concepts is good. I feel that more about sixth grade than advanced Algebra 1 or PreCal

All though we don’t spiral at our district, I plan on implementing this principle by adding problems from other content areas other than the one we are doing at the moment in my warm up.

I am really game to try to spiral the curriculum this year! Looking forward to learning more in the next lessons.

My district used to use Everyday mathematics as our K5 math curriculum. I could see how much sense the spiraling of concepts made for the kids. It alleviated a lot of stress and pressure for struggling students – they knew we would come back to the concepts again. I could see the deeper retention happen. Unfortunately when we went to CCSS spiraling went by the wayside to cover blocks of standards. This reminds me of the need to do some spiraling of my own for those concepts I know will take more to retain.

Since I began teaching elementary school, we have always used a spiraling curriculum. I really enjoy it, because students bring more to the table each unit and seem to really make deeper connections and grow exponentially. For example, our intro to multiplication focuses on the idea of multiplication, equal groups, and repeated addition. By the time we revisit it a few units later, students are moving to faster strategies and answering facts with confidence.

I can now see how spiraling is a very good and important approach in math. It is true that once students move to a new academic year, most of them forget what they have learned in the previous year. I will use the spiraling method this coming year and I will think of ways of weaving related expectations from different strands together. I want my students to retain all important concepts that they learn.

I’m all aboard the spiraling train. Meaningful repetition, spaced out, gives kids a chance to apply their learning. Hopefully the concept stuck, and even if it did not, students are in a lowpressure situation where they can take time to rethink, look up, and review concepts.

I can see how this would help especially the students in my Resource math classes. I am planning this year as I type I will be doing a way better job with this in the up coming year.

Great to hear so many folks committed to trying to implement spiralling in some shape or form this coming year!
Let us know what you all come up with!

I have never done formal spiralling in my math classes. I see the benefit of it and glad that you shared research to support it. I have included review problems and tasks during the school year in my classes, but it was not spirally because we did not dive deeper. I did these review problems/tasks to remind students of previous content. It was helpful to students who had mastered the content pretty well in the first place, but was fairly meaningless to the students who hadn’t. I am interested in learning more about spiralling particularly with regard to related concepts so that students can make deeper connections within the content.
One question I have is how do you get administrators on board with spiralling if it isn’t something that the school has already adopted? I will be teaching at a new school in a new district this fall so I don’t want to rock the boat.

I try to spiral content through the use of warmups or morning work. We also have an online program where I can give students assignments tailored individually for them. Our program claims to spiral because we will have a unit focused on say multiplication , then one on measurement, then it goes back to multiplication but with bigger numbers. But it does not spiral in the way you have described in these videos.

I agree with the idea of spiraling and giving students continued exposure to concepts over time. However, I also feel like I’m one of those people who are tied to the idea of using units to organize material for my course (and maybe that’s just it – I need to feel a sense of organization in what I’m doing and teaching my students).
So I guess my question is, how do you commit to unblocking your content and still feeling like you are doing things in a somewhat organized manner?
Similarly, what do assessment cycles look like in this type of classroom? Weekly quizzes and cumulative exams at regular intervals? Although I may not completely shift my class to this style this year, I’m curious about how to make the shift for the future!! 🙂

I feel that my district does a good job with spiraling, as well as the curriculum that we use. I feel that it allows our students to practice, gain understanding, make connections and show growth. I’m excited to see how 4th grade will take concepts taught and 3rd and expand on the knowledge.

I am very lucky that in my district we implement Math RTI, Response To Intervention, everyday! This is an extra time that all students get extra work on what they need. Some do work with a teacher and some are independent.
In these groups we are able to spiral what our students need. We usually focus on a concept during each 6 week block. This allows us to spend time working on the topics and teaching to the students needs.
I am excited to put into practice what we have learned here into Math RTI as well as core.

This was great to listen to and I believe everyone in my math department should.
So when planning your tasks and spiraling, I have a few questions.
How do you know how many tasks you should plan for each standard? For example, with our Number Sense Standard there are two sections to cover where in our Equations Standard there are 7 sections. I do understand that everything can change as the year goes on as lessons are being conducted, but I am just trying to get a general sense of how determine all the lessons.
How do figure what order to do everything since you are interweaving all the concepts/standards?
Thanks

I have tried spiralling grade 9 math class before and it works really well with the intermediate curriculums. I really struggle with the idea of spiralling senior level math courses, specifically the preuniversity courses. Anyone tried spiralling 11th or 12th grade math courses?

I love this and definitely want to use it. It’s something I’ve used without actually realising but I’m glad to have back up for not following a textbook!
My only issue is timing, I find it hard to plan ahead enough to fit everything we need to cover into my term or year. I have groups right now that are all at different stages of this spiral idea (year 2s NZ) but feel that this means that my kids who are back at the beginning of the spiral will never reach where they need to be at the end of the year. There are obviously other things involved but, for me, I don’t want them to miss out but I also feel pushing them on would be building on sand without full understanding of beginning concepts.

I love this idea and think it will be helpful especially this year with some of the prior grade curriculum not being taught due to Covid19 school closures and remote learning.

Makes so much sense. And I can see how all learners can benefit from this. The strong student has the opportunity to be challenged with new topics more frequently to avoid becoming bored with a particular big idea. The notas strong student, will have multiple encounters with difficult concepts, but not in one dreadful and intimidating 2week block. And the time in between (spiraling) will help all learners have time to reflect.

I like the idea of spiralling, particularly when each concept is built on when revisited. I will have a look at the TIPS programme and see how I can incorporate this in my planning.

It definitely takes a bit to get your head wrapped around things! Keep in mind that with the New Ontario Curriculum, TIPS hasn’t been “rearranged” yet to match (boo). BUT – it might still be worth exploring to get a sense.


I have heard of spiraling in the past but it seems that it was from year to year, as opposed to being integrated content that allowed for multiple diverse experiences. It also had the same type of math problems through out the book, all year long, but without remediation on the content, the student still misses the same concept over and over again.
This planning unit is a gift. The philosophy and science coupled with the stepbystep recommendations and tools is changing how I approach the learning in our classroom.

Perhaps you should spiral the lessons in this workshop.

Touché!
That probably would be a great idea – however, I’d argue that most of what we do in this 6 module course is all interconnected whereas in math, for example, some concepts are completely avoided outside of specific units.
I’m still going to think on that and see if there is something that could be done to interleave while keeping this connected.
Your Unit 1 is sort of an intro to everything, but it was missing a lot of what was going to be covered later such as spiraling and assessment.
It’s nice to bounce around through all the units while going through the workshop. I first got in the habit of doing this while reading expository books because I grew impatient with the covertocover approach. It’s nice to get a good idea of everything first, and then slowly grind down into the nittygritty of each topic.
 This reply was modified 7 months, 1 week ago by NICHOLAS SMITH.

Glad that you’re finding what you’re looking for as you bounce around!



I thought this video focused primarily on what was wrong with blocking but not enough on how to Spiral within a curriculum. I am looking forward to checking out both the Ontario and Chicago links that are being promoted as resources.

I just previewed lesson 63, and it looks like you are going to get into more detail on how to do Spiralling. I should have anticipated that…….
 This reply was modified 7 months, 1 week ago by Jeremiah Barrett.

Yes – dive into lesson 3… some approaches to consider. Of course, there are many different ways.
For specific examples, you might consider checking out our units here:
learn.makemathmoments.com/tasks
The units are pretty “blocked” but the idea would be to explore each new unit in an interleaved sort of way.


I’m thinking that since Ontario has chosen to move elementary reporting to just “math” versus forcing teachers to report based on each strand, that spiralling just got easier to manage. Although we can still comment on all of those strands, the one mark means that assessment could have come from many directions and avenues!

The link kylep.ca/surfacedeeplearn gives a 404 error. Is there a better link?

I never thought about spiraling my whole content! Light bulb moment! I can’t wait to research this and see how I can change my teaching to better support my students.

I was a student who was considered good at math because I could learn the formulas and get an A on the test. But I did not retain the information from year to year. It wasn’t until I started teaching third grade 4 years ago that I really started to understand the basic of why some math works. My curriculum is divided into Units and material from the previous unit is integrated into the next unit. For example, we learn measurement in Unit 3 and then in the next several units many of the word problems include some form of measurement concept in them. My district requires us to complete and submit Module Assessments within a given week for each grade level. How would I address the Module Assessments if I am spiraling the curriculum? I may not cover everything on the District assessment by the given date.

kylep.ca/surfacedeeplearn from the video is a broken link from the States.

Spiralling really does work. Thankfully the Algebra curriculum in my district spirals naturally because students struggled with solving equations and domain and range. Every moment I had an equation, we solved it and I would ask guiding questions about the operations needed to solve it. If there was a graph, we talked about domain and range. The district massed content into units, but I didn’t care about the district tests. I told my principal I was playing for the end game, the state assessment. I kept spiraling and building, and those kids did really well. I am grateful to see that research supports it and that there is more to learn about it.

Fantastic to hear that you observed positive impacts on student learning through spiralling! Definitely in it for the long game (for us, that is students building confidence and a deep understanding)


This is the first year I have heard about spiraling and was intrigued. Your explanation and science behind it have sold me on using it in a classroom.

I have tried MANY different spiraling methods in the past and have not had a lot of success. It has been workintensive for me and the students with the payoff not being what I was hoping for. Next year I am going to try to spiral within the current lesson as opposed to doing a ‘warmup’ or secondary activity with the purpose of spiraling. By doing this, the students won’t feel as if they are being asked to lump in one more thing into the already packed classes and the math in the spiraling will have context and meaning because it will be a part of something they are currently engaged in. This has me excited to see how it works out.

Spiralling a curriculum can be likened to introducing the taste bud to various delicatessens. For one, it eliminates boredom, and provides multiple opportunities to pivot to a different topic while maintaining focus on the concept. In addition, spiralling provides students with resources for generating prior knowledge.
It is not by chance that you, dynamic duo of Kyle pearce & Jon orr, spaced this workshop to allow the organic process of presenting information in chunks, while consistently revisiting the concept of the 3part framework throughout the modules.

I was introduced to the concept of spiraling math learning when a previous district I taught in adopted Everyday Math. I will be honest… At first I was thrown off by the way it was structured because we didn’t get any training about the “Why” it was like that. Most of us complained that it felt like we were constantly skipping around instead of “really teaching” a concept. Our math specialist at the time said that she also didn’t get training, but was supposed to tell us to “TRUST THE SPIRAL.” I taught second grade the year it was adopted, and kids had significant gaps since they didn’t have the same curriculum structure in K and 1. They had forgotten most of what they had learned, especially concepts that were only visited at the beginning of the previous year.
However… by the end of the sevenyear curriculum adoption cycle, we were all loving it!! It was less stressful for kids, and they were having better retention. Then when the seven years were up, we adopted a blocked curriculum resource. By then I was teaching fourth grade, so I didn’t get a chance to really compare apples to apples as far as material retention was concerned.
In this same district, another seven years later, another new curriculum was adopted called Origo Stepping Stones. It is deeply based in the research of Dr. John Hattie. The most profound difference is the elegant spiraling that is its structure. Another big part of Origo curriculum is the social sharing that is built in. I was still teaching fourth grade when it was adopted, and I will say that my students were fearless sharers and were so very confident!! Unfortunately this was the year of COVID, so we were cut short. Now I’m no longer in that district.
I think the main reason that districts keep returning to blockstyle curriculum choices is that it is easier to make common districtwide assessments for all students in a grade level when the units are chunked. For example, all elementary students in every grade do everything number sense first, and the whole district takes the same assessment on number sense by a specified date. It’s much harder to keep everyone together, accountability wise, when there’s a spiraled approach.
 This reply was modified 6 months, 1 week ago by Terri Bond.

I guess, before going through this lesson, I thought spiraling and spacing were not really the same thing. My view of spacing was that you revisit material that had been previously taught as you proceed through your curriculum either through warmups or additional practice, without necessarily reteaching the concept at a deeper level, although the problems could be more complex as students’ understanding of that concept deepens. From this lesson, it seems that spiraling is briefly touching on a priority standard or concept before moving to the next, until you have progressed through those standards, and then you start over at a deeper level.
My district adopted CPM for middle and high school, in part due to how teaching tools like “the Giant 1” and the “generic rectangle” can be developed for the different levels of math, helping them to make connections to their previous learning. The first chapter at every level introduces concepts that will be taught during the year in greater depth in the chapters. Due to this, these lessons should basically provide exposure to what is coming and it isn’t something students are expected to fully grasp. If I understand spiraling, it seems that this would be a great way to start the year, but instead of progressing through the chapters after that, I would develop each concept again at a little deeper level and then start the process over again. Is this accurate?
I find it extremely difficult to work through this first chapter with many students because it has been so ingrained in them that they are expected to know the content being presented and if they don’t, they see themselves as stupid and stop trying. Also, as you move through the concepts again is there an approximate time frame or number of lessons that should be covered during each rotation? I’m thinking about solving multistep equations including the distributive property and combining like terms, which many of my students struggle with because they don’t have a solid foundation solving one or twostep equations. Then they are also expected to check their answers with substitution, which adds another level of confusion.

The importance of spiraling has been ingrained into my brain by my college professors and the district I work for. This was the most challenging aspect of teaching during my first year as a teacher. With a new school year and new grade level, I have been reflecting how I can be more successful when it comes to spiraling content. For example, I plan on implementing bell work, embedding content into morning meetings, centers, small group work, and daily lessons that foster opportunities to practice retrieving prior knowledge. My goal for next year is to avoid the mistakes I made last school year (a.k.a my first year teaching).

Our district has a unitbased curriculum. I have been a curriculum specialist/coach for our district. This summer I am trying to post a written curriculum for an Algebra/Geometry concepts course. This course is often taken by students in grades 9 and 10. I am hoping to build in more spiraling back and using tasks to spark curiosity and provide relevance. I am a little overwhelmed by where to start.

My district is very big on benchmark testing and curriculum checks. The district has been working to make the curriculum map and pacing guide the same across campuses so if a student transfers we are all on a similar page. Any suggestions on how to teach organically yet move along at a similar path? Would it make sense to follow the map and guide loosely as more of a check list? I’m just concerned that they will not be prepared for their 9 weeks Curriculum Check if we are not digging deep into the unit before moving on.
I do believe that this spiral method would work best, especially for students who think they are bad at math but really they just need to learn it a little at a time and use those small parts while making their connections. Some of the connections I ask them to see are things that took me until adulthood because I would get it in a large amount during class and then brain dump as I moved to the next unit. When I was studying mathematics in university and had multiple math classes each semester is why I finally had these concepts over a long enough period of time for it to finally start connecting.

I teach at an alternative high school and our school year is divided into 8 minterms instead of 4 quarters. I get new students almost every miniterm. I can see how spiralling can be helpful, but I am concerned about the students who come into the class 3/4 of the way through the school year. Are they going to feel lost?

@marjorie.allred this is a super common wonder. We feel like spiralling actually helps with this. Here’s a video of us chatting about this https://learn.makemathmoments.com/courses/qacalls/modules/june232021howcanieffectivelyusethetasksintheacademy/lessons/howdoihelpstudentswhoareabsentordontretaintheinformationfromthedaybefore/
How do I help students who are absent or don’t retain the information from the day before?

Thank you. The more I think of it, the better I like the idea of spiraling because as we come back to ideas, the new ones can pick up things and the ones who have been in the class are strengthened and can go deeper in their understanding.



This year our math team has a professional development grant to rework our curriculum map to reflect spiraling… I’m excited to take what we have/what we know/what we want and create a new more well developed grade 7 and 8 math curriculum that will spiral the content to benefit student long term learning!

I have never thought of spiraling the teaching of math. It always seem like a reading thing. I see so much of math as skills that build on each other. I have always spiral math in the warmups and assessment pieces. This is something that I will need some time with.

Growing up I was taught with Saxon, which while incredibly dry was spiraled well, in my opinion. You always had questions from the past pop up and you knew where to go if you needed help with them. I love the idea of spiralling in class, however I echo others with questions of longterm planning and assessment. I look forward to learning more!

I have resisted resources that are pure spiral, because in my opinion, they lack depth. But upon reading the materials and reflecting on my students’ experience, I realize that to an extent, I am often spiralling, and when I don’t, my students struggle.
Effectively spiralling is the practice of an effective teacher — I will definitely increase my practice this year!

Last year my PLC focused on interleaving and we saw a dramatic increase in our student’s learning and retention of that learning. We also have students analyze their own test data before completing an intervention assignment in their own specific areas of weakness. Does anyone else have some suggestions as to how to use the test as an opportunity to study?

I agree that Spiralling is a topic very much spoken of, but I haven’t yet had the opportunity to apply it in my classes. I think these next lessons will show me some tips and examples to add to my understanding of Spiralling. Thank you!

I teach in Alberta, Canada, and one of my colleagues had spoken to me about spiralling her math course in grades 34. I had wanted to try it out this year, but between suddenly being online for the year, a new grade, and everything else, I was more on survival mode than trying out new things mode.
This year, in grade 2, as this course is reinforcing my belief that spiralling would be ideal, I want to go ahead and try it out. Following my friend’s idea, I may start with a version of this schedule: Monday numbers, Tuesday patterns and relations, Wednesday shapes and space, Thursday statistics and probability. Then, on Fridays, we can use threeact math or games to review what we’ve learned over the week.
I am debating whether maybe my “week” should start on Fridays with a Notice and Wonder or Threeact math so I can then see where my students’ thinking is headed and I can plan more accordingly for the following week. Or am I creating more work for myself?

Like a lot of other people, I use warmups that spiral concepts throughout the year. More recently I try to identify “promise standards” and set aside time to revisit these concepts more deliberately than in just the beginning of class. Being a math coach this year helps me see how larger concepts are touched on throughout the grade levels as well. Something else that stuck out from the video is how testing can be used as formative.. even when it is generally a summative assignment.

I wonder if many who have tried spiralling have had less success because the focus in on content coverage rather than “big ideas.” If we see the big ideas and how the task now and the task later have the same big idea but also connect ideas to it, we’d probably be more likely to see the strength of spiralling.
Following a textbook that spirals is not a great idea imo since it’s really about the teacher monitoring and adjusting based on their understanding of their students and the big ideas. What I’m trying to say is that, to spiral takes a deep understanding of the big picture, the small pieces and the students and the teacher needs to have lots of flexibility like bamboo in the wind…

I’ll be honest my first reactions are all over the place. I do believe this is more helpful for students and that just teaching one topic at a time seems like a better idea because it is more focused it is likely most helpful to teachers. Other than “this seems like a lot of work to plan effectively for a whole year” … I’m also wondering how and when summative assessments would work. I have some ideas already but it might be something that year two might end up working better than year one.

Every part of me wants to jump right in and begin spiraling, but I am very nervous and overwhelmed. I look forward to learning more in the next few lessons to ease my worries and doubts.

I haven’t heard much about spiralling – maybe it’s not such an Australian thing, or maybe just because i’m not a Math specialist – but the research shown here seems pretty solid. I think we lean towards blocking because of that idea that it gives students a chance to build each day on the concepts learned the day before, but hearing about that “illusion of fluency” gives a strong counter argument to that. If I didn’t arrange lessons by blocking of concepts I’m not sure how I’d arrange them – everything would feel a bit piecemeal and like you are just jumping around? I’d love to know how Jon and Kyle plan a yearlong curriculum – how do you get a feeling of continuity? Also, we have been keeping students on the Autism Spectrum at the front of our planning recently and we are told that ASD students need to know what the learning is going to be about to fulfil their need for routine – how do balance that with a spiralling curriculum? Thanks!

Our most recent approaches to spiralling follow something more like a chunk of an idea which is how we plan our problem based units (https://learn.makemathmoments.com/tasks). Check those out for a feel of length. Usually about 5 days or so and then head off into a different unit and shift the concept/content.
