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How and What We Grade Matters: Grading for Mastery

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December Professional Development-- DEC. 8th

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December Professional Development-- DEC. 8th

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Google Keep: Full Teacher Tutorial (2022) | Tech Tips for Teachers

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One philosophy of reading, often referred to as leveled reading, assumes that the best way to teach students is to match them to books they can already understand and get through easily, and slowly build up their capacity from there.

Professor and literacy expert Tim Shanahan taught reading like this, too, when he was a young primary school teacher. Mostly, he did so because that's how reading had traditionally been taught: "It is hard to change ancient traditions on the basis of research or anything else," he reflected more recently. "It's even hard to envision how instruction could be different."

But Shanahan says that if we are serious about higher reading achievement, we need an evidence-based shift in mindset-encouraging and helping students to read, struggle, and ultimately comprehend more complex texts.

"Grade level texts or higher are the best choice for most students," Shanahan wrote in 2020. "Those are often the texts that students can't already read well. The purpose of a reading lesson then is to guide students to make sense of a text that they cannot succeed with on their own and to develop the abilities to deal with such texts."

Shanahan notes that many teachers shy away from this approach, fearing that challenging students might undermine their motivation to read altogether. But he argues that students will become motivated as they see themselves making progress on more and more challenging texts, growing and strengthening their muscles as readers in the process. "When kids are challenged and their learning is obvious, you won't need to worry about discouragement or a lack of motivation," he says.

In previous posts, we've argued for a balanced reading diet: Students should regularly be exposed to challenging texts, but have the latitude to read at or even below grade level periodically. In the end, the need to push students towards texts that are just beyond their reach is strongly supported by research on literacy-and learning more broadly. Encouraging students to read for pleasure makes sense, as well, to send the signal that reading is not always utilitarian, and not always difficult.

In a recent webinar covered by EdWeek, Shanahan, who has spent much of his career touting the benefits of students consistently engaging with complex texts, highlighted three strategies teachers can use to do this effectively in their classrooms.

Ask Students to Read Above Their 'Level'
Beginning readers (Pre-K to Grade 2) benefit from reading easy to understand books full of common words with repetition- Green Eggs and Ham, or Brown Bear, Brown Bear, What Do You See?, for example. But by the second grade, Shanahan said, research shows students who have mastered basic decoding skills make faster progress by grappling with texts slightly out of their reach.

In a recent study, 3rd graders struggling with reading outscored their more proficient peers when working with teachers on texts two to four grade levels above their reading level. "When all assessments were considered, assisted readers reading texts two grade levels above their instructional levels showed the most robust gains in oral reading fluency and comprehension," researchers noted.

In his blog, Shanahan cautions that aiming for incremental, linear progress-inching kids forward day by day as readers-leads to bad teaching decisions. The mindset, instead, should be to expose kids to challenging textual features like figurative language, advanced vocabulary, and text structure so that they can learn the tools to read challenging work on their own. That means that "grade-level texts or higher" should be front and center as students learn how to decode unfamiliar text, how to use context clues to make enough sense of new vocabulary to keep reading (or re-read to clarify and comprehend), how to follow complex syntax and punctuation, and how to identify and interpret more sophisticated literary devices.

Advanced texts "provide students with an opportunity to learn-to learn the unknown words, to learn how to untangle the complex syntax, to learn to track the subtle connections across a text, and so on. If students can already read texts reasonably well, there isn't much for them to learn from those texts," Shanahan writes.

Background Knowledge, Plus Upfront Preparation
Scaffolding by teachers throughout the process is imperative. In his webinar, Shanahan highlights the importance of background knowledge for readers. According to research, a poor reader who has an understanding about the subject they're reading-say, for example, baseball, or the evolution of dinosaurs-can often make up for low comprehension by relying on this background knowledge.

To set the table for learners, teachers can scaffold comprehension, asking students to recall knowledge they might have about a text or topic by asking them to brainstorm, or to respond to prompts that tease out what they already know about ancient Rome, volcanism, or ecosystems, for example.

Alternately, teachers can design quick exploratory activities that allow kids to become familiar with a time period or new subject matter before they take on reading challenges.

Other instructional strategies Shanahan suggests on his blog include being forthright with students about the goal of the challenging texts you're putting in front of them. "Explain to students what you're up to when you intentionally place them in texts they cannot already easily read," he writes. "They need to know what the goals are and how they can recognize if they are improving in their ability to handle these texts. Give the students some sense of self determination."

He also suggests giving students agency in selecting complex texts. For example, you might present them with two or three options of books or passages to choose from. To make complex texts easier to parse, Shananan recommends teachers divide a text into smaller bits for students to work through and "take on parts of it rather than trying to digest it all in one bite."

Get Strategic About Vocabulary Gaps
According to Shanahan, you can easily spend too much time on vocabulary. While he believes that it's important to increase students' knowledge of words, he recommends focusing on about 150 words over the course of the school year that are different from ones they've previously learned in other grade levels, but appear frequent enough in texts for them to be of use. He also recommends teaching students a list of key morphological elements that are most frequent for their grade level, such as "pre-", "able-", "-re", and "-ment."

Although not possessing the requisite academic vocabulary is a common problem for struggling readers, Shanahan's webinar promotes an approach that is equal parts tactics and strategy: Teachers and students tackle a limited set of new vocabulary terms, but spend more time learning useful strategies to help them recognize gaps in comprehension and utilize strategies to decode new words that aid in comprehension.

Rather than pre-teaching an extensive vocabulary list for a complex text, then, Shanahan recommends teaching students how to recognize and be honest with themselves about when they don't know the meaning of a word and lean on strategies to infer its meaning enough to continue reading, or look them up in the dictionary if the texts don't provide enough context clues.

"An important part of vocabulary learning is developing an ability to use context to determine meanings of unknown words," Shanahan writes in his blog. "Good readers can both figure the meanings of words they've never encountered previously, and they can decide which of a word's meanings is the relevant one in a given context."

Encouraging students to re-read a passage or section of a text to get a better understanding of words they don't have a grasp of is also useful, Shanahan notes, and comes with its own benefits according to research he cites-such as improved reading fluency, improved comprehension and improved literary appreciation.

Most importantly, he writes, students need to be taught how to persist when encountering headwinds in the form of unfamiliar words and, more broadly, to embrace the messy process of trying to make sense of something difficult to do.

"Sometimes readers just need to power through, making sense of as much of a text as possible, accepting that they aren't getting it all since they don't know all the words," Shanahan writes. That means discussing or modeling that reading behavior with students and explaining that while perfect understanding is ideal, very challenging texts often push even advanced readers beyond their limits. "Sometimes 50% understanding just has to be better than 0%. Too many readers encounter a couple of unknown words and call it a day."

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How to Help Readers Grapple With Challenging Texts

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Instead of matching students to texts they can breeze through, literacy guru Tim Shanahan says that students should be engaging with challenging texts that push them out of their comfort zones.

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Anonymously sharing students’ math mistakes can generate valuable discussions about problem-solving.

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Anonymously sharing students' math mistakes can generate valuable discussions about problem-solving.

As I was grading my class's algebra quizzes, I noticed that a conceptual error kept appearing on multiple students' papers. I pulled out my phone and snapped photos of various students' solutions-some with mistakes, some without. The next day in class, I displayed selected photos as a guide to start a whole-class conversation about the various solutions. (The identities of the students whose work was displayed were not revealed to the class.)

Here are some of the responses from the eighth graders as we viewed the photos:

"Oh, I see how they used the equation from the table of values to identify the slope."

"Why did they multiply 0.5 by 14? I did something different."

"Yes, I see the mistake there. They assumed the y-intercept was zero."

"I like how they showed the common difference in the table."

Why share photos of student work? All of the above student comments about the sample of student work contributed to the learning of the concept. I could have re-created each student's solution on the board; however, students benefit from seeing each other's work rather than only the teacher's.

Expecting and Respecting Mistakes

What if a student does not want their work shared?

Yes, even though the identity of the student is not revealed, another classmate might recognize the handwriting. This is why it's imperative to establish a class culture of collegial encouragement and respect. I would never display egregious mistakes that would run the risk of embarrassing a student if their identity were known. The teacher can preface the student work sample with "This was a common error; however, I chose this sample because they clearly started off with the correct approach. Let's discuss how we can learn from this example."

While students are working in groups at their desks, snap photos that will kick off a meaningful class discussion. I ask the student if they would be willing to discuss their work with the class. If they would rather not, I ask if it's OK for another student to come to the board to interpret and explain the process and steps. When one student explains another student's work, both the explainer and the solver practice clear mathematical communication.

If students are working at the whiteboards in groups (also referred to as vertical non-permanent surfaces, or VNPS, in Peter Liljedahl's book Building Thinking Classrooms in Mathematics), then everyone can see the group's work if you have them present or take a gallery walk. Occasionally, I deem a group's work worthy of future reference, and I snap a photo for the other sections to see (otherwise, the whiteboard work will be erased and never seen again).

In an article in Mathematics Teaching in the Middle School, " Examining Mistakes to Shift Student Thinking," the authors suggest displaying mistakes that are "worthy" of discussion. Worthy mistakes can be computational, conceptual, or procedural in nature. A worthy mistake will deepen the understanding of the mathematical goal of the lesson for all students-not just the one who made the error.

Desmos Classroom, a free online graphing calculator website that also includes digital activities, has a feature that enables teachers to snapshot student responses during an activity. By adding these snapshots to an album, the teacher can display students' work side by side to spark a discussion about student thinking. There is a field at the top of the presentation screen to ask the class a guiding question about the displayed student work. (Desmos also features an "anonymize" option to display student names as famous mathematicians' names.)

Below is an actual example of a photo I used in my algebra class. (The student's identity was not shared with the class.) This image led to a discussion of the multiple methods to compare an equation and table of values. Many students struggled with this problem on their assessment for many different reasons. My goal was to share a sample of how to interpret a table of values as an equation.
Courtesy of Crystal Frommert
First, I asked the class what they noticed about the equation written above the table. "How did they calculate the slope and y-intercept? What communication could be added here to clearly communicate the calculation of the slope?" At this point, a student might come to the board to annotate the table with common difference or the slope formula.

The side arithmetic could also lead to an interesting discussion about calculating decimals; however, because this was not the focus of the lesson, I did not follow that path of a potential conversation.
Courtesy of Crystal Frommert
As you teach your math classes, keep your eyes open to samples of student work that could further the understanding of the lesson. These images could be taken from both formative and summative assessments such as homework, classwork, group work, exit tickets, and/or quizzes/tests.

To curate which photos are best for the whole class discussion, consider which mistakes are discussion worthy. I frequently announce during these discussions, "This is my favorite mistake!" Then follow up with how the mistake helps everyone in the class gain a better understanding of the concept.

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Highlighting 'Good' Mistakes in Student Work

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Anonymously sharing students' math mistakes can generate valuable discussions about problem-solving. As I was grading my class's algebra quizzes, I noticed that a conceptual error kept appearing on multiple students' papers. I pulled out my phone and snapped photos of various students' solutions-some with mistakes, some without.

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A strategy called hexagonal thinking provides students with an effective way to launch project-based learning.

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A strategy called hexagonal thinking provides students with an effective way to launch project-based learning.