It’s 9 a.m. on a Tuesday and Betsy Palmer’s seventh-grade students don’t understand that five-sixths is a bigger ratio than two-thirds — a comparison the Common Core says they should be able to make. She wants to know if this is a typical occurrence in grasping the concept of ratios.
How and when we learn has long been a subject of study. One area Educational Testing Service (ETS) researchers are exploring is that of learning progressions — the stages or steps that theory suggests most students go through as they progress toward mastering an important competency, like a key concept, process, strategy, practice or habit of mind. So far, ETS researchers have developed learning progressions in mathematics, English language arts and science.
“Researchers are trying to assemble a body of progressions that offer likely paths to proficiency in a significant portion of the domains that are taught in school,” says Randy Bennett, who holds the Norman O. Frederiksen Chair in Assessment Innovation at ETS.
For example, a learning progression for proportional reasoning (or ratios) starts at the first level with qualitative reasoning, where a student can make general judgments about ratios. Level two demonstrates progress to simple quantitative reasoning. By level three, the student can use multiplicative reasoning, and by level four, the student is able to flexibly select from a range of strategies to work with ratios.
When it comes to developing proportional reasoning, research shows that children might incorrectly believe that five-sixth is equal to two-thirds since the two quantities in each ratio differ by one, says Leslie Nabors Oláh, a Managing Research Scientist at ETS.
“It’s very important for teachers to understand the thinking behind this ‘wrong answer,’” Oláh says, “because they can then know how to address this misunderstanding with instruction.”
The ratio example shows how using developmental research can help teachers plan curricula better. Teachers also can gain information about their students’ progress that can help them better differentiate instruction.
In addition, assessments developed through a learning-progressions model can more accurately identify areas in which students may be struggling. This process helps teachers better understand what students need so that they can apply an appropriate intervention.
Learning-progressions information can be especially helpful for teachers of students who are underperforming. These teachers can find it “quite depressing” to view their students’ performance only through a standards-based test lens, says Oláh. “You talk about things like, ‘Oh, 80 percent of my kids are not meeting the standards.'”
On the other hand, learning progression tests can show that students do have some precursor skills and may be making progress so teachers can see areas of understanding from which to build.
However, not all — or even many — teachers know about learning progressions, says Caroline Wylie, Research Director at ETS. She says the subject is not often taught in schools of education, although ETS sometimes does professional development workshops for teachers on the topic.
“Often when we show learning progressions to teachers, there is this moment of recognition — ‘Oh, right! I’ve seen that!’ — but maybe they haven’t had a name for it,” says Wylie. “For me, essentially that’s what learning progressions are, a way of providing teachers with these schemas for not just how the topics connect together, but showing how expertise within the topic develops.”
ETS is working on developing more “teacher-facing” educational material about learning progressions, says Wylie.
“We want teachers to shift from, ‘This is a correct answer; this is an incorrect answer,'” she says, “to more nuanced thinking: ‘OK, so this is the kind of understanding that students have right now; how do I build on that understanding to move them along to deepen their learning?'”
Developing learning progressions is a time-consuming and painstaking process that can take several years, says Oláh.
First, researchers explore existing research. They look to see if a progression in a particular area needs to be added or revised. ETS researchers create an initial draft, then submit it for internal review. They take feedback from this step to create another draft, which they submit for review by content-area experts within ETS as well as recognized experts outside ETS. Researchers take these experts’ comments into account to revise the progression further. Then, they generate assessment tasks that denote each level in the progression and give those tasks to small numbers of students in the ETS Cognitive Testing Laboratory or in schools. Researchers study how students respond, which helps them further refine the learning progression and the tasks before being used in a large-scale assessment. Researchers also do statistical analyses to make sure the tasks are accurately measuring the progression and that the progression is a plausible pathway toward mastery.
Another part of ETS’s research into learning progressions maps them to standards, such as the Common Core State Standards or alternative state standards. Learning progressions and state standards are not the same, says Oláh. “The standards are where you need to get to,” she says. “The learning progressions are a way to think about how students get there.”
It can be challenging to align to the standards sometimes, because there is “not a grade-to-grade equivalent” with learning progressions, says Cara Laitusis, Senior Research Director at ETS. Students may be expected by the Common Core to know particular elements of fractions by a certain grade, for example, but conceptually that might be more challenging than other aspects at a later grade.
Going forward, ETS researchers are looking at how to identify and expand lower levels of progressions to help underserved and underperforming students, says Bennett. When a learning progression is created, it describes the skills and understandings that students are expected to have at each stage on their path to mastery. Bennett would like to see the skills and understandings broken down into more specific information about what the student has mastered and what he or she still needs to know.
“We’d like to be able to try and differentiate students who are at level one more finely,” says Bennett, “so that we can better describe to teachers what it is they know, and are able to do, and what it is that might be valuable for them to work on next.”
ETS is developing systems that deliver tests and tools for students from grades 3–12 in mathematics and English language arts, says Oláh. In the future, more content areas will be provided.
“We have resources for teachers that articulate what learning-progression skills are and how they develop,” says Wylie. “And we have tasks to give teachers that go along with those resources that are not just worksheets for rote learning — but problems that students can more deeply engage with.”
A big advantage of learning progressions is that they reflect student abilities “across a wide continuum of achievement levels, whether a student is on grade-level or not,” says Laitusis. “You can’t advance education or assessment without the building blocks of where you are going and what the purpose is.
“Learning progressions,” Laitusis continues, “provide a framework for identifying and arranging those building blocks.”