Assessing and Tracking Progress in a Math Class by Mr. Kaldawi

Any math teacher will tell you that mathematics is an interconnected web of topics that heavily relies on the fundamentals of previous years. In order to solve systems of equations, some basic knowledge of linearity is required. Linearity links back to rate of change. Rate of change involves knowledge of multiplication facts and long division, and it can be made easier with some number theory basics with factors and multiples, and working with decimals and fractions in math as a whole is unavoidable. We could go on forever, but it’s easy to see how one deficiency could be catastrophic for higher-level skills, especially in a challenging step up like Algebra, which I teach at Seven Hills. If we don’t ensure that sturdy foundation, anything we try to build upon it falls apart quickly, and one struggle compounds into several more.

As I welcome new students to my classroom each year, I’m always thrown for a loop as to what their background in math looks like. For my Bridge Math class, they’re all coming from different schools with vastly different levels of mastery in a variety of skills. Some already know everything I’m teaching them, while others have no idea what I’m talking about. For my Algebra students in 7th and 8th grade, however, I have an idea of what was taught and what wasn’t from their previous teacher, but I typically don’t know how much they’ve retained from Pre-Algebra, or to what level of mastery they have reached in specific skills/topics. This is often exacerbated by the learning loss that results from three months away from doing math in summer break.

Over the past two years, I’ve had three major goals in the forefront of my mind:

1. Bridge the gap between the previous year, the current year, and the upcoming year by laying out and documenting what students know and don’t know on a skill by skill basis.

2. Use that information to better reinforce current skills and keep a running tab on what the students know and where they leave off after their time with me is over.

3. Communicate this information to students in an actionable, constructive way.

Goals 1 and 2 can be accomplished through talks with fellow teachers, but I’ve developed a system and routine to have this data easily accessible for years to come. This system also serves to satisfy Goal 3 with very little modifications, and it has become the backbone for the way I assess and give feedback to students and communicate trouble spots as needed.

After each assessment, I record details of skill-by-skill mastery in a spreadsheet that I keep on the backend. Observe Figure 1.

(Figure 1: A sample of my backend spreadsheet to indicate how students are doing when working with specific skills)

Each page of the spreadsheet is dedicated to a different unit. Each column represents a key skill I want the students to take away from this unit. Each cell is color-coded based on level of mastery, with the following key to help read it:

• Green: Mastered – fully understands the material and can apply the skill flawlessly or nearly flawlessly.

• Blue: Proficient – understand the material and can apply but with some minor errors here and there.

• Yellow: Developing – has an inkling of understanding but is inconsistent in application. This is sometimes due to gaps in prerequisite knowledge.

• Red: Needs Review – does not understand the material well enough to apply the skill; the student should review this topic.

In addition to the color coding, specific commentary can be added to each cell to give context to a trouble spot. If the obstacle preventing a student from reaching mastery is one specific step, or if there is a clear gap in a past skill that is hindering success now, this is a good place to include it. If the skill is fully mastered, there often isn’t any further comment needed, so those get left blank and are only colored green.

This spreadsheet makes grade report writing and feedback for families a breeze. It also has the added benefit of aiding future teachers within Seven Hills as to where we left off in each topic and where each student is at in each skill category. This better informs future remediation and communication with families so that we teachers can better meet students where they are.

This goal serves to accomplish goals 1 and 2. Goal 3 piggybacks off of this strategy in the form of a rubric given to students at each assessment. I don’t show them or tell them a letter or number grade at any point in the school year except for report cards; instead, they see a skill-by-skill analysis of what they’ve done well on and what areas they still need to work on. Figure 2 illustrates what this might look like.

(Figure 2: A sample rubric, unfilled, that a student would get after an assessment.)

We have four columns indicating the four levels of mastery seen previously, and each row is dedicated to individual skills found in the assessment. The numbers in parentheses indicate which questions on the test the skill is being tested on. The boxes aren’t just checked off; much like the spreadsheet, they also contain specific feedback about a student’s ability in that skill, especially if the weakness or struggle is something specific like a deficiency in a prerequisite skill or a single consistent step that they are doing incorrectly. Figure 3 has some examples of what these rubrics might look like after being filled out.

(Figure 3: Filled-in rubrics)

You can see that their appearance mirrors the back-end spreadsheet. The language is similar and the color-coding parallels the four classifications of skill mastery. While the rubrics are a new addition to my strategy this year, I have already noticed a shift in student attitude towards aiming for mastery rather than just “getting an A”.

These steps have also led me to reconsider how to better assist students who consistently hover in the “developing” and “needing review” categories. While I don’t have any one-size-fits-all solution, being able to see a full picture helps me better communicate with families, and it helps me decide on the best way to remediate. Sometimes, I hand the student the test back, ask them to look it over, and orally present corrections, mostly unassisted, to show proficiency in the topics they struggled with. Other times, I pull the student for a remediation session and ask them to retake the test at a later date. With a goal of skill mastery at the forefront, it helps in the effort to fill in as many gaps in math knowledge as possible before they move on to more advanced math classes in the future.

These steps towards building a more connected math space and a different approach to aiming for mastery are definitely not the end-all, be-all solutions for struggles in math. However, it’s steps like these that allow us to better support our students, pinpoint the roots of trouble spots, track progress, and communicate which skills students need to work on for continued success in math in middle school and beyond.