In 2014 I did some action research for the Governor’s Teacher Network. I was researching perseverance in elementary students, and I created a plan to gather data every few weeks.
I developed a rubric for perseverance, and I was clear with my 4th grade students about how I would be scoring their math assessments. I scored every problem separately, using a 4, 3, 2, 1 system:
That was it. Clearly explaining how they could score points on every problem encouraged students to put forth effort so effectively that it almost ruined my research project.
Why? Because on the very first assessment, before I could implement the other aspects of my plan, the students out performed any normal group of beginning-of-year 4th graders. Almost all of them tried to earn a “4” on every problem, attempting to solve each problem with two strategies.
So why does explaining this simple grading rubric to students work so well?
For many students, grading is a mystery.
Combine that mystery with a fixed mindset of “I’m not great at math,” and you have students who look like they’re not willing to try for that “A,” but they actually just don’t know how. They feel that the “A” is not for them. Clearly explaining how students earn points invites more of them to try.
It’s not just students who feel that grading is a mystery. Many teachers are overwhelmed by creating their own grading system. And parents LOVE the clarity of this rubric.
With this rubric, all strategies are valued equally… with a few caveats.
I gave students a “4” for accurately using ANY two strategies; abstract, representative, and concrete strategies were OK. Even on assessments, students could use hands-on tools, like base ten blocks, counters, or other manipulatives.
This practice does not only improve the number score on their assessments, it makes use of every moment of math class for students to practice problem-solving and self-differentiating. This helps students grow faster as mathematicians. By allowing a student who only understands a concept in a concrete way to use a concrete solution, he is not being left out.
Caveats: as the year progressed, I was clear about changing expectations. For example, by the end of 4th grade, the Common Core Standards require 4th graders to use the standard algorithms for addition and subtraction. Therefore, by the end of the school year, I required students to use the standard algorithm as one of their two strategies in order to earn a 4. Also, throughout the year I continually showed students when strategies were too similar to count as 2 different strategies. Dividing 84 by 4 by separating 84 ones blocks into 4 groups and then drawing the same process did not count as 2 strategies (even though that step of moving from concrete to representative is important and valuable during math practice!).
Solving problems with 2 strategies is a better accuracy check than using the inverse operation.
Have you seen some of the end of grade test questions elementary students need to solve these days? They can be REALLY complex, and more often than not they are multi-step problems.
Checking solutions with inverse operations works well sometimes, but kids get mixed up working backwards from their solution to a multi-step problem. Also, sometimes kids miscopy the numbers from their word problems, and checking with the inverse operation won’t help them find that mistake.
Students catch many of their mistakes when they solve a problem once with one strategy, and then start all over again with a different strategy.
This is especially helpful for advanced students who sometimes rush through solving problems or those who are overly confident and don’t check their work. When they know that the only way they can get the highest score is to solve the problem twice, they are more likely to catch mistakes they made the first time. Also, pushing these students to come up with a second strategy is a great way to engage those students who sometimes feel bored with problems they think are “too easy.”
When students use multiple strategies, they make strong connections between operations… and this makes the teacher’s life easier.
Students who are frequently asked to use 2 strategies begin to see patterns and structures in math that make sense to them. They begin to understand how numbers work.
Over and over again, I see students using place value-based methods throughout the operations. Once students realize they can break down an addition problem by place value, they try a similar method for subtraction. They break up multiplication problems by place value, and when division is introduced they break apart place value again.
I notice similar trends for students who like using math tools, like base 10 blocks. They realize that using manipulatives turns the abstract into concrete… the numbers in equations become blocks, and the operation symbols become actions (separating blocks, bringing them together, etc.).
These connections are exactly what’s missing when students rely mostly on standard algorithms. When they use multiple strategies regularly, students begin to see the relationship between all 4 operations on their own, which cuts down on teaching time.
I hope that using this simple grading rubric helps you as much as it’s helped me. It’s all about empowering students, right? If they know how to reach their goals, they’re much more likely to try.
Freebie: Find a free assessment reflection that fits this rubric on my Teachers Pay Teachers page. Just click the Download Now button under the words Free Download.