CAASPP Results: The Middle-School Math Mindset

After a rather lengthy delay, CAASPP results were finally released today… and our 6th grade math results are consistent with the past 3 years: highest percentage of “met/exceeded standard” students in the school district, and higher than expected performance for an at-risk demographic (82% Hispanic, and 74% free or reduced lunch.)

Here are the district-wide results:

At first glance, you might be thinking: “Hmmm… what’s to be so proud of? That doesn’t look so great. Less than half of the students passed! Only 47% proficiency?”


  1. I take particular ownership and pride in these results, because this year I was the sole math teacher for 6th grade.  In previous years, results were a combination of all 6th grade classes, since we had self-contained classes of all subjects. This year, we did “middle-school style” subject period rotations, and I was in charge of math (which is not to say some other people didn’t also have an impact: other 6th grade teachers and volunteers who helped, for example, at our after-school homework center, or with before-school tutoring.) This is also why I’m focusing on Math scores in this post, as it is something I can speak directly about, regarding strategies that may have contributed (for better or worse) to the results seen here…
  2. The great (fun? I hesitate to call it that, but it can be) part of math is that it allows us to use the numbers to dig deeper, to solve a mystery…
    In short, numbers can be used to lie, but they can also be used to discover truths that are not apparent on the surface… and that is the case here….

The problem with taking a quick glance at a data visualization like the column chart above is that it is missing important information; it is data “in a vacuum,” but the real world (and especially the world of education) does not work that way. As much as people want to believe that test scores are the sole result and responsibility of the teacher, and a pure indicator of quality of education given, that is not true. Research has shown that all of the following factors can create an “at-risk” population of students:

  • Race/ethnicity
  • Primary language spoken in home (ie. English as a second language)
  • Socioeconomic status
  • Level of proficiency / prior knowledge students have at the beginning of the year

I would like to place a particular emphasis on that final one. It seems like a no-brainer, but many people seem to assume that the level of proficiency a student has when entering a grade level has no bearing or affect on what a teacher can achieve with that student. It is true (as I will prove through the data), that deficits in knowledge can be overcome through effective strategies and interventions… but it does have an impact, and it does limit success, and it isn’t easy. I would also say that there are limits to what can actually be done; a student starting out the year one grade level behind has a significantly better chance of being rehabilitated than one entering 3 or 4 (or even more) grade levels behind in the prerequisite skills they are expected to have. But GROWTH MINDSET is something I believe in, and something that is important; what it tells us is that deficits can be overcome (it’s just, in many cases, a matter of effort… and time.)

So, if we are talking growth mindset, we should be looking at the data not as a snapshot, but from a growth perspective.  For example, when you glance at the results, it appears that both the 4th grade and 6th grade teams found success… and this is true. We work under the same conditions, at the same school, with the same demographic. So, an achievement of close to 50% proficiency, given the circumstances, is a feat.

However, where I am particularly pleased with the 6th grade results is due to the sheer growth that occurred.  If, for example, you look at the 4th grade math scores from a growth model, it looks like this:

As you can see, there was great growth in some ways (for example, a significant increase in “standard exceeded” as well as a significant reduction in “standard not met”), but it must also be noted that the students actually also entered the year with a good deal of preparation from 3rd grade: 51% of students met or exceeded standard. At the end of 4th grade, 45% met or exceeded standard.

On the other hand, the 5th grade test scores do not look great, with only 23% of students meeting or exceeding standard. If you look at growth, however,  you will see that this is actually an improvement from last year (only 21% met/exceeded standard at the end of 4th grade)! In fact, 5th graders were the only ones in the district (aside from my 6th graders) to show positive growth in the number of students who met/exceeded standard compared to the previous year…

This all just goes to show why boiling things down to a single metric or visual can be misleading, and is insufficient for drawing conclusions. You need more than a simple number to tell a whole story.

Which brings me to why I am proud of my (and my students’, and my 6th grade team’s) hard work last year: Although we fell short of my initial goal of 50% proficiency… the results still came close to that, and are significantly higher than would be expected: not only was the statewide proficiency rate for socioeconomically disadvantaged Hispanic students only 20%, but this particular cohort of students also entered my classes with very low proficiency: only 28% of students had passed the CAASPP test. More challenging was the fact that a large number of them (41%!) were not only slightly below (standard nearly met), but significantly below grade level proficiency upon entering 6th grade: 

To visualize this another way, this would be the chart that shows how much this particular cohort of students actually grew during my 2016-2017 school year:

These were statistical “non-movers” for multiple years, some showing small gains in proficiency in 5th grade, but others falling even further behind in math abilities.

  • 96% of these students had an increase in raw test scores
  • 79% increased at least one full proficiency level (several of the students jumped two proficiency levels!)
  • Overall, there was an 85% growth in number of students who met/exceeded standard compared to the previous year!

To put it another way… this is the chart that shows how much students actually grew/improved in proficiency (met/exceeded standard) at each grade level, compared to previous year CAASPP results:

This level of growth is why I am proud of these results, and why I feel like… well, I feel like I actually have figured out some of the secrets of success for teaching math (and, I hate to tell all you Jo Boaler fans out there… if you want to achieve similar results, I suggest that you ignore about half of what she recommends, much of which is actually antithetical to what the cognitive and education research actually shows. I elaborate on that in the next post... )

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