Acceleration as a Means of Catching Up
by Charlene Marchese
As students settle into the 2021-2022 academic year, the world is still in the midst of a pandemic and continued uncertainty. We know that students’ school experience over the last 18 months has been challenging and that there is overwhelming worry among teachers that students have entered their mathematics classrooms without exposure to and/or mastery of previous grade-level mathematical skills and concepts. While there is a great deal of variability in the learning students have brought with them and significant unpredictability about more school disruptions to the school year, one thing is certain: schools need to address students’ unfinished learning while engaging the whole child in grade-level content.
The tendency to address unfinished learning – which the Achievement Network defines as concepts students have not yet mastered and are necessary to grasp upcoming ideas – is often to “remediate” and spend the first weeks and maybe first few months of school teaching and reteaching previous grade level standards. This method only continues to enhance a skills-deficient approach that can be disheartening for students. As an alternative we suggest engaging students in what is called “learning acceleration”. While the word acceleration may sound like speeding things up, in this context it refers to providing time for instruction to support any unfinished learning as students engage in grade level content. One can think of this process in three steps:
1) deeply acquainting yourself with the concepts embedded in grade level content and how these concepts develop over the years;
2) pre-assessing students to determine what, if any, previous skill(s) need to be reinforced; and
3) providing ‘just in time ‘ instruction on those skills. There is strong evidence that learning acceleration successfully provides students with the understandings they need for accessing grade-level content (TNTP, 2021; Rollins, 2014; Hirsh, 2020; Takabori, (n.d.)) .
Let’s walk through an example of learning acceleration in a 4th grade unit on multiplication.
STEP 1a: Identify the standard or standards being addressed in instruction. This could be related to content being taught over one or two weeks (and pre-assess only for that content as part of STEP 2).
Standard 4.NTB.5 Common Core Standards Mathematics (p.29)
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
An example of multiplying a two digit by two digit number:
Build an array to represent and solve
Two equations to represent the multiplication problem:
12 x (30 + 5) = 420
12 x 30 + 12 x 5 = 420
STEP 1b: Identify the previous grade-level content students will need to be successful in learning the grade-level standard. This is a similar process to Math for All’s listing the demands of a task, limited to the content demands.
The content below is critical for students to know in order to access the fourth grade content in discussion:
- Fluently multiply and divide within 100, know from memory all products of two one-digit numbers
- Use an understanding of place value to decompose numbers into hundreds, tens and ones
- Understand the distributive property in the context of single digit multiplication, such as: 8 x 7, i.e. 8 x 7 as 8 x (5 + 2) and (8 x 5) + (8 x 2) and its connection to the array
Understanding the mathematical trajectories for the specific content is essential. For support on the critical math standards for each grade refer to the Focus by Grade Level documents from Achieve the Core. For an understanding how those standards develop over the grades refer to the University of Arizona’s Progression Documents.
Once we understand what we can about the content standards both at and prior to current grade level, we are ready for Step 2.
STEP 2: Determine students’ readiness for grade-level work by creating a short pre-assessment to understand what students know and what needs to be reviewed, practiced or learned. Then analyze the data to group students based on the prerequisite skills that need targeted instruction.
For our 4th grade example, this pre-assessment could include asking students to:
- Break apart numbers by place value, such as 35, 236, 1254;
- Create an array to solve 12 x 5;
- Determine which equations (4 options) that represent 8 x 7.
STEP 3: Begin instruction with on-grade-level content for all students while inserting key ideas from previous grades to support unfinished learning. This could be anything from providing a temporary support like a multiplication chart and/or a calculator to access basic facts or starting with a few targeted activities from the prior year as a bridge to grade-level content. It is key that prior grade-level activities connect directly to the current grade-level standards – i.e. “just in time”.
These prior grade activities could be infused in teacher-led small group instruction and math stations throughout the unit to provide support for students who need it. For example, in a small teacher-led group, students can be supported in building arrays and writing equations for 2-digit by 1-digit multiplication problems (15 x 4) prior to building an array for larger numbers (42 x 56). In math stations, games and activities utilizing basic fact array cards, such as arranging square tiles into rectangles, can connect one-by-one digit arrays to facts as students strengthen automaticity. Sending these games and activities home engages care-givers in the students’ goal of getting their basic facts to memory and understanding the connection of a multiplication fact and its array as they work on the 4th grade level content of using models to multiply large numbers.
This unit by unit approach to accelerated learning provides students with experiences in grade-level content while assessing and addressing unfinished learning with just in time instruction. More help for planning accelerated learning could be found in supplemental instructional materials recently added by publishers. Returning to normalcy in school will take time, an accelerated learning approach is one tool that may help in this process.
Accelerate, don’t remediate. (2021, May 23). The New Teacher Project.
Hirsh, S. (2020, September 1). How to accelerate learning for all students in the 2020–21 school year. Carnegie Corporation of New York.
Rollins, S. P. (2014). Learning in the fast lane: 8 ways to put all students on the road to academic success. Association for Supervision and Curriculum Development.
Takabori, A. (n.d.). Learning acceleration, not remediation, for a fantastic school year. Carnegie Learning.
What is unfinished learning? (2019, October 23). Achievement Network.
Math for All is a professional development program that brings general and special education teachers together to enhance their skills in
planning and adapting mathematics lessons to ensure that all students achieve high-quality learning outcomes in mathematics.