Given the major school disruptions we experienced over the past few school years, you may be noticing that students' preparedness to jump into grade-level math work this fall varies widely.
While it may seem right to try to address all of the content that students missed, the priority should be spending as much instructional time as possible focusing on rigorous, grade-level work, and incorporating support with prerequisite concepts when necessary and relevant.
We wanted to return to our blogpost on unfinished learning from last year to reflect our latest thinking on the topic and highlight the resources we have created to support teachers with this challenge.
One important way the conversation around unfinished learning has shifted is by focusing on acceleration instead of remediation. TNTP distinguishes these two concepts in the following way:
Spending significant time in below-grade level content before moving into new learning
Connecting unfinished learning into the context of new learning
… isolated from grade-appropriate learning
… covering many objectives or standards from prior grades/units (usually extending to a month or more of instruction)
… usually with greater than 50% of time on procedural fluency
... just-in-time to grade-appropriate learning (whether in core or extended time)
… integrating a few lessons from prior grades/units
… always with an appropriate balance of fluency, conceptual understanding, and application work
We want to help teachers use a learning acceleration approach to address unfinished learning in math in a way that focuses on grade-level content and makes the most of their prep and teaching time, while remaining as flexible as possible given all the other unknowns of the coming months.
Just-in-Time Instead of Just-in-Case
The inclination in your planning may be to think about the progression of the previous grade and which of the topics weren’t adequately covered last year. One way to start the year would be to try to cover, in an expedited fashion, the content that students missed last year before moving on to any grade-level content.
We would call this a kind of “just-in-case” review. Remediating for remediation’s sake in this way is going to start the year with an unnecessary deficit mindset, frustrate kids right off the bat by focusing on what they maybe didn’t learn in the previous grade that they should have, and eat up time in a year when time is going to be at a real premium.
Of course in order for students to be able to access grade-level content, they are going to need to have the foundational skills in place. And especially after the range of experiences they had last year, we know there will be concepts that need attention before moving on to grade-level instruction.
So perhaps a diagnostic test at the beginning of the year could help shape your review in a more data-driven way?
Maybe, but there are a few things to consider:
- You might be overwhelmed by how much your students don't know or recall, especially as they are coming back from many months away from school.
- You might think that there's so much content you need to re-teach that it’s best to just go with the full-scale “just-in-case” review from above.
- Students’ understanding can change throughout the year, so if you give a diagnostic in September that includes content you won’t teach until April, remediating for it in the early months of the school year might not be the best time to help it stick for your students.
This last point is one of the best arguments for “just-in-time” support.
A just-in-time approach focuses forward on the current grade-level content, rather than backward on the skills missing from the prior grade. It gives your students the chance to feel some learning momentum, as they continue to acquire new skills and understanding.
To take an example from the Fishtank curriculum, 3rd Grade Unit 6 focuses on fractions. This is very important content that, given its place in the 3rd grade sequence, may not have been given the time and attention it requires. Those foundational fraction skills will be needed in 4th grade, and will likely need some review to feel solid before launching into new content...but not until Unit 4.
And just-in-time planning considers content unit by unit, to help you determine your students’ needs at the time when it’s going to be most helpful.
If you delay starting any 4th grade content to re-teach fractions, you might find yourself needing to re-teach again several months later, or perhaps running out of time before even getting to this grade-level content. Even if you have an additional intervention block, addressing this content “just-in-case” and separate from grade-level content may not be the best use of that time. A just-in-time approach would assess student’s knowledge of the foundational standards that are important for understanding 4th Grade Unit 4 just before the unit begins, and plan for support accordingly.
Just-in-time support asks three questions that guide the way we plan for and teach each new unit: what, how, and when.
What to Integrate for Just-In-Time Support
When we look at a unit, deciding what students need support with should be rooted in the standards of the unit. We determine foundational standards of each unit and list them in the Standards section of the unit page, like this from 4th Grade Unit 4.
To form this list, we rely in part on Student Achievement Partners’ Coherence Map, a dynamic visualization of how the Common Core Standards relate and build upon each other from grade to grade. We then identify the skills and concepts embedded in these foundational standards, along with any other soft skills or conceptual underpinnings that students will need coming into the unit. Instruction Partners calls these the “load-bearing walls” for grade-level content; they need to be strong in order to be ready for the content that will be laid on top of it.
Another place to gather information about foundational content is in the Content Connections section of each unit's Unit Launch, offered as part of the Fishtank Plus package. Here, teachers can build their own content knowledge of foundational standards and look at problems from prior grade-levels.
Now it’s time to gather student data. For this, we’ve developed pre-unit assessments, also a Fishtank Plus feature, which include questions to diagnose foundational understandings before the unit begins.
Looking again at a Fishtank example, 6th Grade Unit 6 covers equations and inequalities. Given the timing of this unit, it may have been rushed at the end of the year. Since this unit covers major work of 6th grade that is part of the progression towards middle school algebra, it may be tempting as a 7th grade teacher to want to go back and teach or re-teach this content right away.
Looking at the full 7th grade course, however, you’ll see that Unit 4 is where equations and inequalities come in. This is the best place to diagnose and address gaps from 6th Grade Unit 6.
Our 7th grade pre-unit assessment for Unit 4 contains several problems that reach back and look at 6th Grade Unit 6 content. For example, this problem assesses students’ procedural skills in solving one-step equations before they encounter two-step equations in 7th grade.
Solving one-step equations (6.EE.7)
In 6th grade, students solved one-step equations first by using diagrams and balances, and then generalized their actions to solve equations algebraically. Students should understand that in the process of solving for a variable, whatever is done to one side of the equation must also be done to the other side in order to maintain the balance and equality. In 7th grade, students will extend this work of maintaining a balance using inverse operations to solve two-step equations of the forms $$𝑝𝑥 + 𝑞 = 𝑟 $$ and $$ 𝑝(𝑥 + 𝑞) = 𝑟$$.
You’ll see that the pre-unit assessment teacher guide identifies the standard being targeted by the questions (6.EE.7), and provides context for how the skills required relate to the content of the unit ahead.
Our pre-unit assessments are short, designed not to take away from precious instructional time. The questions can also be split up and incorporated into a problem set or warm up in advance of the new unit, as long as you are cognizant of gathering the results back together to analyze.
A free resource that can also help you gauge students' comfort with foundational skills is our pre-unit student self-assessment. This tool gives students the opportunity to reflect on the prior-grade-level standards, shared in student-friendly language, in advance of beginning a new unit. Check out the pre-unit student self-assessment from 7th Grade Unit 4, and find others in the Assessment section of Units 1–4 in 3rd–8th Grade. Additional units will be added on a rolling basis this fall.
How and When to Integrate Just-In-Time Support
With this student data in hand, you’ll now be able to make informed decisions about incorporating support into the unit.
Some concepts will need class-wide support, and some may only need reinforcement with a select group. If you know what standard was being assessed in the diagnostic phase, you can reach back into prior grade levels of Fishtank curriculum (often easiest to search by standard) to find lessons or practice material that addresses the standard.
You might decide to provide the material as a do-now if the students need more teacher-led facilitation around skills that they don't have, or you might have students play a fluency game in pairs if you think they mostly have it but they just need a little extra practice. You might also try a jigsaw structure, incorporating student-led teaching to encourage variety of student voice and engagement.
Just-in-time integration should still be the goal even if you have a separate intervention block, extended time, or tutoring program. Pre-unit assessment data can inform what content to address during this time for the duration of the upcoming unit. If this block is taught by a different teacher or a set of tutors, you could meet after students take the pre-unit assessment to decide what unfinished learning needs to be addressed and in what portion of students’ days.
As TNTP notes, however you decide to integrate this work, it’s important to strike an appropriate balance of fluency, conceptual understanding, and application work, rather than focusing too closely on procedural practice.
As far as when goes, if you know that a skill or content area is a prerequisite for a specific topic within the unit, then that key previous grade-level content should be woven in just prior to starting that topic.
We have a few resources that provide some of these answers for you:
- In the pre-unit assessment teacher guide, we offer a potential course of action for student support, depending on how students do on each question. For the 7th grade solving one-step equations example above, the suggestions are:
Potential Course of Action
- If needed, this concept should be addressed before or during the first four lessons of the unit as students work towards solving two-step equations algebraically.
- For example, include a couple of problems on solving one-step equations, similar to above, in a warm up for Lesson 1 or a homework for Lesson 3. Simple equations addressing specific misconceptions can be included as needed throughout the unit.
- Note that Lesson 1 includes review of solving one-step equations.
- Find problems and other resources in these Fishtank lessons:
This year you may find that rather than just adding a bit of review time to an existing lesson day, you need to insert a whole day or two into your sequence to cover prior-grade-level concepts. Our Scope and Sequence Adjustment Guides, found on each unit page and in our Learning Acceleration Teacher Tool, give suggestions of lessons that can be combined or eliminated to make time for these more extensive support days, without sacrificing student understanding of the highest priority grade-level content.
Some Anchor Problems, or even whole lessons, build in review of prior-grade-level work, and are indicated as such. The first anchor problem in 7th Grade Unit 4 Lesson 8 is a good example. Once you have identified the topics that need re-teaching, it is worth the time to check whether any of the Anchor Problems or lessons in the unit incorporate this review for you.
We hope that this approach to “just-in-time” support will make the challenge of addressing unfinished learning this school year feel a bit more manageable. We invite you to learn more about our pre-unit assessments and the rest of the enriching and time-saving features offered with a Fishtank Plus subscription.
Sarah Britton is the Senior Curriculum Director for K–5 Mathematics. Ms. Britton began her career in education through Teach For America Massachusetts, where she taught 7th and 8th grade mathematics. She then joined the staff at Teach For America as a manager of teacher leadership development, supporting and coaching their new math teachers of all grade levels. She has a Bachelor's degree in mathematics from Union College and a Master's degree in curriculum and teaching from Boston University.
Jami Therrien Wells is the Managing Director for Math Curriculum. She began her career at Roxbury Preparatory Charter School, where she served for 10 years teaching 8th grade math and 5th grade special education. Prior to joining Fishtank, Ms. Therrien Wells also worked at the Achievement Network as the managing director of the math assessment team. She holds a Bachelor’s degree in Mathematics from the University of Rochester, and a Master’s degree in teaching from Tufts University.