Why we need vertical alignment in mathematics

Cheyenne Mills
Cheyenne Mills

By Cheyenne Mills

When I was in elementary school, I was excellent at math. I won numerous accolades and was altogether very proud of myself. I was excellent at math – until I wasn’t anymore.

In 8th grade I started Algebra I, and much to my chagrin, I was horrible at it. Come to find out, I hadn’t been excellent at math, I had been excellent at memorizing.

It is, of course, up to us as math teachers to prevent this from happening. We don’t want our students to make it through to Algebra I without proficient problem-solving abilities and a deep conceptual understanding of mathematics concepts. We must design assessments that probe for this understanding and lessons that encourage it to be developed.

In math, perhaps more than any other subject, it is absolutely essential we ensure that our curriculum is vertically aligned within our elementary schools. Vertical alignment helps us to make sure that teachers within a school or district are on the same page with their curriculum. Teachers work together to ensure that their strategies and content help to prepare students for higher level material.

Math is a subject that builds. The Kentucky Academic Standards for Mathematics were designed with exactly this progression in mind.

Our job as mathematics teachers is to give the necessary foundational understandings at every grade level to move on to higher level math. Contrary to what many think, the Kentucky Academic Standards do tell us what to teach, but not how to teach it. That is why it is still up to us, as teachers, to use effective instructional practices to help our students meet the depth and breadth of our standards.

Our standards are no longer “a mile wide and an inch deep,” as the saying goes. There are fewer standards per grade level, but they are more focused and coherent. The standards maintain a balance of conceptual, procedural fluency/skills and application that enable students to make sense of mathematics. While the standards are designed to prepare students for gradually more challenging content, teachers within a school need to work together to make sure that they are addressing all standards – and in an order that helps students build on prior knowledge and understanding.

It is important for teachers within a school or district to have conversations across grade levels in order to be on the same page when it comes to how students model with mathematics in the classroom. Through conversation, teachers can work on maintaining consistency throughout the grade levels and building upon the modeling that students have done in the previous grades. In the Standards for Mathematical Practice, practice 4 encourages students and teachers to model with mathematics and show their work by creating diagrams and pictures. By creating an awareness of how educators in other grade levels are accomplishing this work, teachers will be better prepared to serve their students and help them model in ways that they are familiar with.

Teachers also should be aware of and trained on the standards progressions themselves. Most elementary school educators teach one grade level, and many teach that grade level for several years at a time. They develop an intimate understanding of the math standards for students in their year. However, many teacher are unaware of what math students are being asked to do in other elementary grades.

In order to fully prepare students for their future math classes, teachers must be keenly aware of those higher standards and the requisite skills they require. They also need to have a close understanding of the work that students did prior to entering their classroom and the strategies the students learned to master that work. This way, teachers are better able to use students’ prior knowledge schemas in order to scaffold them to new learning.

Throughout this year, I have been involved in an amazing Kentucky teacher initiative, Classroom Teachers Enacting Positive Solutions (CTEPS). I have spent the year researching best practice for enacting vertical alignment solutions within schools and districts, and where our mathematics vocabulary usage crosscuts this idea. In my school, we have begun to dig deep into vertical alignment in this past year.

As a 5th-grade teacher last year, having just one conversation with the 6th-grade teachers in my district changed the way that I taught that year. In our meeting, we discussed patterns and inconsistencies they had noticed among students, common misconceptions and gaps in learning. I was able to better address these issues after being made aware of them, and after those students went on to 6th grade, I was told by their teachers that they were better prepared than any class they had seen. Just opening up our rooms for these important conversations can change our entire year!

An article from Kentucky Teacher details the work that Kentucky Core Advocates have done to develop a professional learning community (PLC) module for vertical alignment and coherence in math instruction. The module encourages conversation about developing coherence in our mathematics instruction across grade levels. Using this module, teachers can lead their peers through a series of PLCs that will help them discuss the strategies they are using and the order in which they are teaching content. I would highly recommend that all schools work through this module in order to facilitate and guide these helpful conversations. We will be working through them in my school this year as well.

These conversations must be had in our elementary schools for our students to reach peak success. Currently, in most schools, PLCs are conducted among same grade level staff and administrators. I argue that subject-based PLCs should be implemented across grade levels for teachers to become better acquainted with both the standards across grade levels, as well as the teaching styles and strategies of their cohorts.

According to research conducted by Promoting Student Success in Algebra 1, a project funded by the U.S. Department of Education’s High School Graduation Initiative, the key to promoting student success in Algebra 1 is in ensuring students have the requisite skills and understandings needed to be successful. The best way to ensure this is through vertical alignment conversations. I have realized through the CTEPS program just how powerful a conversation between teachers can be when everyone comes to the table seeking what is best for students. We have so much to learn from each other.


Cheyenne Mills is a 4th-grade math and science teacher at Woodlawn Elementary School (Boyle County). She earned her bachelor’s degree in elementary education from the University of Kentucky and is now pursuing her master’s degree in STEM education from UK. She is a member of the 2016-17 Kentucky CTEPS team.