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Alignment Supports Achievement: Why we need vertical alignment in mathematicsBy Cheyenne Mills
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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 eighth 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 that, in order to meet these goals, we ensure that our curriculum is vertically aligned within our elementary schools.
Math is a subject that builds. The Core Standards were designed with exactly this progression in mind. “Mathematics is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts.” (Notes on Courses and Transitions, n.d.) Our job as mathematics teachers is to give children the requisite skills to move on to higher level math. In an ideal world, any math teacher would be able to do this effectively using the common core standards as their guide. In reality, the standards, while a vast improvement on older standards, are still left open to interpretation, on some level, and often intentionally so.
The standards are more skill focused than knowledge based. But debate and ambiguities exist amongst teachers on the best way to teach skills. Some teachers prefer not to teach the standard algorithm until it is required, some teachers want to teach it as soon as possible. Some teachers like the cross-multiplication method for comparing fractions, while others prefer students to draw a model. It is important for teachers within a school or district to be on the same page when it comes to these differences, so that their math students can have a consistent learning experience and not hear contradictory, confusing messages from their teachers.
Teachers should also be aware and trained on the standards progressions themselves. Most elementary school teachers teach one grade level, and many teach that grade level for several years at a time. These teachers 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 work that will be done in the future, the teacher must be keenly aware of that work and the requisite skills it requires. Teachers should also 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.
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. An article from Kentucky Teacher details the work that Kentucky Core Advocates have done to develop a PLC module for vertical alignment and coherence in math instruction. The module encourages conversation about developing coherence in our mathematics instruction across grade levels. (Why engage in professional learning communities/teams?, 2016)
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” (PSSA), a project funded by the U.S. Department of Education High School Graduation Initiative, the key to promoting student success in Algebra 1 is in ensuring that students have the requisite skills and understandings needed to be successful. (Curricular Alignment to Support Student Success in Algebra I, 2014) 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.
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 that, in order to meet these goals, we ensure that our curriculum is vertically aligned within our elementary schools.
Math is a subject that builds. The Core Standards were designed with exactly this progression in mind. “Mathematics is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts.” (Notes on Courses and Transitions, n.d.) Our job as mathematics teachers is to give children the requisite skills to move on to higher level math. In an ideal world, any math teacher would be able to do this effectively using the common core standards as their guide. In reality, the standards, while a vast improvement on older standards, are still left open to interpretation, on some level, and often intentionally so.
The standards are more skill focused than knowledge based. But debate and ambiguities exist amongst teachers on the best way to teach skills. Some teachers prefer not to teach the standard algorithm until it is required, some teachers want to teach it as soon as possible. Some teachers like the cross-multiplication method for comparing fractions, while others prefer students to draw a model. It is important for teachers within a school or district to be on the same page when it comes to these differences, so that their math students can have a consistent learning experience and not hear contradictory, confusing messages from their teachers.
Teachers should also be aware and trained on the standards progressions themselves. Most elementary school teachers teach one grade level, and many teach that grade level for several years at a time. These teachers 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 work that will be done in the future, the teacher must be keenly aware of that work and the requisite skills it requires. Teachers should also 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.
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. An article from Kentucky Teacher details the work that Kentucky Core Advocates have done to develop a PLC module for vertical alignment and coherence in math instruction. The module encourages conversation about developing coherence in our mathematics instruction across grade levels. (Why engage in professional learning communities/teams?, 2016)
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” (PSSA), a project funded by the U.S. Department of Education High School Graduation Initiative, the key to promoting student success in Algebra 1 is in ensuring that students have the requisite skills and understandings needed to be successful. (Curricular Alignment to Support Student Success in Algebra I, 2014) 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 & science teacher at Woodlawn Elementary School in Danville, KY. She lives in Lexington, KY and 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 as well. She is a member of the 2016 - 2017 Kentucky CTEPS team.
Use Cheyenne's infographics to support math vertical alignment.
