A few years ago Tracy Zager wrote a wonderful article called “How Not to Start Math Class in the Fall” where she shared the pitfalls of starting the year with diagnostic tests and instead gave a more positive and productive path which included setting a positive tone for learning mathematics and gathering useful formative data. While the article was a powerful reminder about what we should value and how we can help start the year off on a positive note, the article might be more important this year than most for us to consider.

The ending of the 2020 school year was (is) not ideal for many students (as we all know). Many students did not participate in learning from home platforms, and for those who did, many did not participate regularly. And even for those who did participate regularly – with no fault at all placed on teachers or schools – the ability to give students experience to learn new materials, to observe students’ thinking, to ask timely guiding questions, to monitor student progress, to know how/when/what to consolidate….. were not ideal or equitable (or possible in many cases) making learning mathematics difficult.

From conversations I have had with various teachers, I think we can all agree on a few things here:

- Learning over the past few months has not been ideal for many students;
- Learning about our students’ thinking has been difficult, at best, for us, making it difficult to sequence learning, consolidate big ideas, and use various students’ thinking to drive conversations; and
- There will be a huge discrepancy between how much / what students have learned over the past few months

Because of these three points, when students finally get back into classrooms we will likely have many eagre to attempt to make the best of things. However, what first moves we make when school returns matters more this year than ever. This leads me to wonder, will our decisions be driven by thoughts of how to fill gaps or how to build a community of learners?

Whether or not things will go back to normal in the fall, even if we are back in schools, what we value and what we believe is important will have huge effects on the experiences our students have in our classrooms. For those who might be pushing a “Gaps Driven” message, I would like us to recognize the multitude of equity issues that surround this approach in normal circumstances. NCTM’s new resource Catalyzing Change in Elementary and Early Childhood Mathematics offers some advice:

At the early childhood and elementary school levels, the use of pre-assessment data at the start of a unit or mathematics workshop to create flexible ability groups might seem harmless on the surface and even helpful. Proponents say that this practice allows teachers to figure out children’s learning needs, then tailor the content and pace of instruction to children’s varying levels of performance. However, flexible groups often lead to differentiated learning expectations and experiences and thus, differentiated learning outcomes. Students are perceptive and soon realize they are usually put in the same groups with the same other students. Any ability grouping in mathematics education is an inequitable structure that perpetuates privilege for a few and marginality for others.

Catalyzing Change in Elementary and Early Childhood Mathematics, 2020

The idea that many of our students will be in different places academically will be at the front of our thinking, however, there are many issues that we need to be thoughtful about. Families that have been able to support children from home this spring are at a direct advantage in the fall. Students from economically disadvantaged homes, or are from families that have limited access to technology or have mental health concerns, or students that have struggled with motivation or self-monitoring…. are at a particular disadvantage right now, and potentially in the fall.

So, how could we start the fall productively? Somehow, the first few weeks need to be a time to build community, engage in rich learning experiences where we can notice student thinking and create opportunities for collaboration and discussion norms. Dr. Yeap Ban Har might have said it best:

We have no idea what next year will look like. So, whatever time we do have in classrooms, we need to build the kinds of relationships and norms that will help us in case we are expected to once again learn from home.

## How TO Start?

If we really are worried about gaps in prior learning, thinking about how to start all new learning with experiences that will help bridge current understandings with what your students will be learning will need to be a focus. Instead of starting with a test that quantifies learning or sorts kids, how about you:

- Start with a diagnostic Task for each new concept
- Choose a specific notice and wonder image as a shared experience where you can build important discussions about key concepts
- Use an open problem that is highly accessible. Then share specific examples with the group that lead to relationships between prior and new learning
- Choose a spatial task to help students learn to persevere when challenged
- Ask students to share what they know on a frayer model which can be updated throughout upcoming days
- Play a game that uses the concept you want to address so you can watch students’ in action, then bring up what you have noticed with the class
- Anything to get your students DOING so you can NOTICE their current thinking and WONDER about what to do next.
- Anything that gets kids thinking, talking, sharing, testing ideas, playing with concepts, making conjectures, noticing patterns, building, representing…..

Content will come. Focusing on our kids as thinkers and doers of mathematics needs to come first. Doing so in ways that builds relationships and learning norms is where I would start!

## A few things to reflect on:

- Some students have missed a lot of school / learning. Beyond content, what other aspects of learning math might be a struggle in the fall?
- How do you see equity playing a role in all of this? Pinpointing and focusing on student gaps often leads to inequities in experiences and outcomes. So, how can the ideas above help reduce these inequities?
- What you do the first few days/weeks will show your students what you value. What will your first days/weeks say about you as a teacher and the subject of mathematics to your students?
- If you noticed a lack of engagement this Spring, how can we better prepare for future disruptions by building the right kinds of relationships, norms and routines? What will you do in your first few days/weeks to start down this path?
- Maybe if you can see that some of the above strategies can really help you get to know your kids personally and mathematically, you might realize that a test might not be as valuable as you had thought.

As always, I’d love to hear your thoughts. Leave a reply here on Twitter (@MarkChubb3)

Timely and though-provoking. Thank you!

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On Fri, 22 May 2020 at 04:32, Thinking Mathematically wrote:

> Mark Chubb posted: ” A few years ago Tracy Zager wrote a wonderful article > called “How Not to Start Math Class in the Fall” where she shared the > pitfalls of starting the year with diagnostic tests and instead gave a more > positive and productive path which included setting a ” >

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Thanks for an important post. I think the challenge will be helping students realize that any “gaps” in their math background due to COVID are not any more significant that gaps due to: vacation, illness, not focusing due to distraction or being preoccupied with other issues or any other host of reasons why a lesson was lost on you. Reassure students that this year through rich deep meaningful problems they will have lots of opportunities to encounter the math their are required to know and more. Ban from your lips the phrases, “You have missed a lot of content” or “We have a lot of catching up to do”! Just DON’T say or think things like that. Instead, as you mentioned just start by building that math community where students talk and share their thinking. Allow yourself to be open to being surprised by what they DO know.

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I’m hoping that we can start to see new possibilities. Some teachers just teach grade level content (i.e., here is the algorithm to calculate…), but lack idea of learning differences. Other teachers try to sort students into ability groups, they recognize differences, but their choices lead kids down different paths promoting those who are privileged. I’m suggesting that we get better at beginning new learning by starting with kids’ ideas. We can get what’s best about both approaches, without the issues either extreme has.

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Thank you for this. I want to help student fill in these perceived gaps, but the intentions aren’t pure. The student driven approach definitely strives towards student learning, not checking off standards. I forgot about this. Thank you for the timely reminder.

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This is such a timely article. Our team is meeting shortly to go over what standards need support next year and this is such good information to keep in mind.

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Very interesting article that fits every country

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Insanely informative article with strong and relevant links. This comes from a Family and Consumer Science instructor. I will be using these ideas in my class to help students learn and succeed. Thank you for sharing.

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Boosting the signal. Sharing your post with mathematics education in Michigan via the Michigan Council of Teachers of Mathematics. Thank you — well thought out and valuable information for our members.

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This article is a good read. I am a second grade teacher. This is my favorite quote: “Students are perceptive and soon realize they are usually put in the same groups with the same other students. Any ability grouping in mathematics education is an inequitable structure that perpetuates privilege for a few and marginality for others.” 100% students realize where the fall in the land of “smarts” (student comment I have heard). Because small group happens in reading, I do agree that does help students who need support get it and grow throughout the year, to be grouped almost all day is sad for most. Our curriculum does encourage a skill assessment with each new unit. However, instead of grouping right away, I teach the whole group lesson. Math is a unique topic. Where some are strong, others need support. And that is fluid because some students love geometry while others are problem solvers and love it. You also see students lightbulbs go off based on teaching strategies and I chose to give that student who came into my room with little to no knowledge a chance to “get it.” Once the skill has been modeled, practiced and played; if that student is still struggling, my small group day occurs. My reteach get more focused instruction and my ready for a challenge kids get that. Next topic/lesson begins with a whole group and the cycle begins again.

Where to begin? A lot of what we do in the classroom is driven by curriculum and schedules of testing. So while the suggestions of other options of activities are well thought out, it needs to be presented to our curriculum writers. I would suggest to primary parents to focus on numbers sense and basic facts. If a student enters second grade with a concept of what the number 4 or even 24 means, it makes math easier for that student. If they can quickly add 2 + 3, it will make other calculations easier.

I am hoping that we will begin our year in the classroom. If it does not, we will just do what we usually do, adapt and do what is best for our students.

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Thanks for your comment!

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These are such helpful tips for how to start in the fall. Thank you for this!

https://mathsux.org/

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Hello. I am looking for a way to contact Mark Chubb to request permission to use a co-teaching graphic for training purposes. The 6 models of co-teaching referenced in this older post: https://buildingmathematicians.wordpress.com/2017/09/28/co-teaching-in-math-class/ – Thank you!

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Hi Sarah. The graphic was not created by me. In my post I reference where it came from and the authors. Hope that helps.

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Thank you! One of the presenters pointed me back to you. I’ll keep searching. Thanks!

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Those images are from Marilyn Friend’s classic work on coteaching. She has many books and articles that use the same models. Sincerely, a special ed professor!

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Thank you Rachel. I will adjust the credit appropriately.

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Thank you both! I was able to find this reference: Adapted from “Co-Teaching: An illustration of the complexity of collaboration in special education,” by M. Friend, L. Cook, D. Hurley-Chamberlain, and C. Shamberger, 2010, Journal of Educational and Psychological Consultation, 20(1), p. 12.

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I am looking for some good blog sites for studying. Life is a mathematical problem. To pick up the most, you need to realize how to change over negatives into positives. Take some time to visit my blog on Reasons Why Studying Math Is Important

Regards

Jerry

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Math is necessary for everyone to learn. You think that its lessons and topics might not be as useful in everyday life but in reality, it revolves around everything.

You may also check this blog

Relevance of Mathematics to Everyday Life

Hope this will help. Thank you.

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Several things are true:

-math is all around us

-it is a useful tool to help us understand our worlds

-math is beautiful

-mathematics is fun

Hopefully you hear the message in my article that we should start learning by engaging in rich learning experiences, aiming for us to learn about how our kids think…and try to avoid the trap of looking for deficits. For many this is how they start to disconnect from math.

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The author is saying that we should ditch diagnostic tests at the beginning of the year in favor of beginning to build a community of learners. I agree that community is very important. Our Sec Math 1 class is remedial, and we’ve already focused greatly on community-building in that class. I’m glad we’ll have longer class periods to work on that this year! Sec 1 will NOT have a diagnostic test.

I also teach Sec 3, which is an advanced course for college-bound students. There is a lot of challenging content, and if students aren’t prepared with the foundational skills, we’re not doing any favors by keeping them in the wrong level of class. There is not enough bandwidth in the year to teach them Sec 2 and Sec 3. So I’ll administer a diagnostic test to be certain they have skills to succeed in Sec 3. If not, we’ll reccommend a re-take of Sec 2. We will not test them to determine ability-grouping, which is what the author was mainly opposed to.

We will also benefit from building a community of learners in Sec 3 as the school year progresses.

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