Error analysis – Educational Aspirations

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My fourth grade students took their first unit assessment of the year last Wednesday. This is the first class to take an assessment this school year. The unit took around four weeks and explored topics such as area, volume, number sentences, and a few different pre-algebra skills. This year I’ve been approaching student reflection and unit assessments differently.

Students were given their study guide during the first couple days of the first unit. The study guide included questions that covered topics that would be taught throughout the unit. At first students were confused about how to complete items that we haven’t covered yet. Eventually students became more comfortable with the new study guide procedure as we explored topics and they completed the study guide as the unit progressed. There were a couple of students that lost their study guides, but they were able to print it off from my school website. I reviewed the study guide with the class the day before the test. It took around 10-15 minutes to review, instead of around 40-50, which has been the norm in the past.

After students finished the study guide the class reviewed the skills that were going to be assessed. Students informally rated where they were at in relation to the skill. I decided to move in this direction as I’m finding that reflection on achievement or perceived achievement doesn’t always have to happen after the assessment.

Students took the test and I passed back the results the next day. Like in past years, I have my students fill out a test reflection and goal setting page. This page is placed in their math journals and I review it with each student. I decided to use Pam’s idea on lagging homework/coding and add this to my student reflections. Last year my students used a reflection sheet that indicated problems that were correct or incorrect and they developed goals based on what they perceived as strengths and improvement areas. This year I’m attempting to go deeper and have students look at not only correct/incorrect, but also at error analysis.

So I handed back the tests and displayed an image on the whiteboard.

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I told the students that we’d be using coding in math today. I reviewed the different symbols and what they represented with a test that was already graded. Each question would be given a code of correct, label / calculation error, misconception, or math explanation. I gave multiples examples of what these might look like on an assessment. I spent the bulk of my time introducing this tool to the misconception symbol (or as some students say the “X-Men” symbol) to the students. After a decent amount of time discussing what that looks like, students had a good feel for why they might use the math explanation symbol.

I then passed out the sheet to the students.

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Students went through their individual test and coded each question based on the key. At first many students wanted to use the label/ calculation error code for wrong answers, but then they stopped and really looked at why their answer didn’t meet the expectation. In some cases, yes, it was a label issue. Other times it was an insufficient math explanation. Most of the students were actually looking at their test through different lens. Some were still fixated on the grade and points, but I could see a shift in perception for others. That’s an #eduwin in my book.

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After students filled out the top portion of the reflection sheet they moved to the rest of the sheet.

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Students filled out the remaining part of the reflection sheet. They then brought up their test and math journal to review the entry. At this time I discussed the students’ reflection and perception of their math journey and I made a few suggestions in preparation for the next unit.

At some point I’d like create an “If This Than That” type of process for students as they code their results. For example, If a student is finding that their math explanations need improvement then they can ________________ . This type of growth focus might also help students see themselves as more owners of their learning. I’m looking forward to using this same process with my third and fifth grade classes next week.

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One of my goals this year was to have students analyze their own work, make observations and improve. These observations have improved this year by a light margin. For example, students get back their graded paper and look over how they did. Most students look at the top for their points or some type of feedback. Some look for where something was marked incorrectly, while others look for a place in their binder to place the paper. The good news is that students are looking at their graded papers with a more critical eye. That’s a win in my book. Students are starting to observe where they needed to elaborate or change a procedure. That’s good, but the time spent looking at what to change is still minimal.

This year I introduced the NY/M model. Students were a bit hesitant at first, but I’m finding some pockets of success. Those pockets are not just related to the new model, but also a whole range of opportunities that have been put in place for students to understand where a mistake might’ve occurred. Ideally, I’d like to have students identify how the mistake or error happened and to curb that action in the future. Don’t get me wrong, I’m all for making mistakes in order to learn, but some errors impact an entire answer and I’d like students to be able to identify where that’s happening. Being able to self-reflect in order to improve is a beneficial skill.

In an attempt to provide multiple opportunities for error analysis, I’ve intentionally planned for students to identify their own math misconceptions. This has taken many different forms. I believe that students that can identify math misconceptions may be better able to proceed without making them in the future. Three tools/strategies that have been helpful in this endeavor are found below.

Nearpod has been a useful too this year. Specifically, having students show their work using the draw tool has helped other students identify misconceptions within their own understanding. Displaying the work on the whiteboard without a name has been especially helpful, as a student might not be embarrassed, yet the class can still learn from that particular person. I’ve used this as an opportunity to look at positive elements of student work and also look for areas that need some bolstering.

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Lately I’ve been giving feedback on student papers and incorporating that into my agendas. Before passing back the papers I review the misconception list and answer questions then. I then pass out the papers and students complete the NY/M process. Generally, students make very similar errors and I attempt to address this while reviewing the agenda. This has decreased the amount of questions that students ask related to why/how to improve their answer to receive a M.

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On the paper I’m making a renewed effort to write feedback on homework and projects. The feedback takes many different forms and isn’t necessarily in a narrative form. Sometimes I ask question and other times I might circle/underline a specific portion that needs strengthening. This method often elicits student questions as it’s not as clear-cut as other methods. Regardless, it’s another way for students to analyze their work, make changes and turn it back in a second time.

Why is this important to me? Well, I believe that students should be provided additional opportunities to showcase their understanding. At times, I feel as though there’s a gap between what math work they show and what they’re capable of showing. Giving feedback, along with another opportunity to improve, tends to help my students show a real-time understanding of a particular concept. Ideally, this would seamlessly work and all students would move from an NYàM. It’s not all roses though. I’d say at least 50% of the students improve on their second attempt, but I’d like to see more. I believe we’re making progress and have more to go, but I believe we’re on the right track. I’m encouraged to see that this model is slowly and slightly changing the review, redo and improve cycle. This has me thinking of how to expand on it for next year. Stay tuned!