The science
Established measurement methods, published standards and a catalog of how students actually get things wrong, explained in plain terms.
Item Response Theory
SubjectPath estimates each student’s ability with Item Response Theory (IRT). It uses a Rasch-family model with a guessing floor for multiple-choice questions, which accounts for the chance of picking the right answer by luck.
is the student’s ability, is the question’s difficulty, and is the guessing floor (zero for questions that can’t be guessed).
After each answer, the diagnostic updates its estimate and picks the next question expected to tell it the most. A session ends when another question would add little precision.
Beyond a single number
Each Path maps its standards framework as a graph of prerequisites, so the diagnostic can follow a gap back to where it starts.
Answer choices are written to reveal specific misconceptions, each drawn from a controlled catalog rather than written ad hoc.
Questions go where they are most informative for this student.
Research
Published studies about how students learn and how teaching works. They are not studies of SubjectPath.
Black and Wiliam’s review of classroom research found several studies in which efforts to strengthen the frequent feedback students get about their learning, the heart of formative assessment, led to gains in learning.
How SubjectPath applies this: SubjectPath’s diagnostic uses each answer to choose the next question and to locate where a student’s gap begins.
Black & Wiliam (1998)Bloom reported studies in which students in mastery learning classes, with regular checks and corrective help before moving on, outperformed students in conventional classes, and tutored students did better still.
How SubjectPath applies this: Students work through lessons and skill checks, and move past a skill once they show they know it.
Bloom (1984)A meta-analysis by Kulik and colleagues found that mastery learning programs had positive effects on exam performance from upper elementary school through college.
How SubjectPath applies this: SubjectPath starts each student’s practice at the skill where their gap begins.
Kulik et al. (1990)Doignon and Falmagne’s knowledge space theory describes what a learner knows as the set of problems they can solve, and frames assessment as efficiently finding that set among the possible ones.
How SubjectPath applies this: SubjectPath’s prerequisite graph is a related idea: it maps which skills build on which, so a gap can be traced back to where it starts.
Doignon & Falmagne (1985)By subject
Published studies about how students learn and how teaching works. They are not studies of SubjectPath.
Siegler and colleagues found that elementary students’ knowledge of fractions and division predicted their algebra knowledge and overall math achievement in high school, even after accounting for other math knowledge, general ability and family background.
Siegler et al. (2012)Booth and Newton found evidence that middle school students’ understanding of fraction size was related to their readiness for algebra, more so than their understanding of whole-number size.
Booth & Newton (2012)Knuth and colleagues found that many middle school students did not fully understand the equal sign, and that students with a stronger understanding of it solved equations more successfully, even accounting for overall math ability.
Knuth et al. (2006)The van Hiele theory describes levels of geometric thinking that run from recognizing shapes by their overall appearance, through reasoning about their properties, to deductive proof.
van Hiele (1986)Senk found that secondary school geometry students’ van Hiele levels were associated with their achievement in writing geometry proofs.
Senk (1989)Posner and colleagues’ model of conceptual change proposes that students give up an existing idea when they become dissatisfied with it and a new idea seems understandable, plausible and able to explain more.
Posner et al. (1982)Bishop and Anderson found that many students in a college non-majors biology course thought traits change because organisms need them, overlooking variation within a population.
Bishop & Anderson (1990)Sadler and colleagues found that, on questions with a popular wrong answer, middle school physical science students made larger gains when their teachers could identify that common misconception, not just the correct answer.
Sadler et al. (2013)Hestenes, Wells and Swackhamer reported that students’ commonsense beliefs about force and motion conflict with Newtonian ideas in most respects, and they developed an inventory for detecting those beliefs.
Hestenes et al. (1992)Nakhleh’s review of chemical misconceptions describes how students’ ideas about core topics such as the particle nature of matter often differ from accepted chemistry, and what that means for teaching.
Nakhleh (1992)Recht and Leslie found that junior high students who knew more about a topic recalled and summarized a passage about it better, whether they were stronger or weaker readers.
Recht & Leslie (1988)Scarborough described skilled reading as the intertwining of word recognition and language comprehension, with comprehension drawing on background knowledge, vocabulary, language structures, verbal reasoning and literacy knowledge.
Scarborough (2001)Cummins distinguished everyday conversational skills, such as fluency and accent, from the academic language proficiency that school learning draws on, and proposed that this academic proficiency is shared across a learner’s first and second languages.
Cummins (1979)A national panel review edited by August and Shanahan found that teaching the key components of reading is necessary but not enough for students learning English: oral proficiency in English is critical too.
August & Shanahan (2006)The ACTFL Proficiency Guidelines describe what individuals can do with a language at each level of proficiency in speaking, writing, listening and reading, in real-world situations.
ACTFL (2024)Each question’s difficulty starts as an expert estimate on a common scale. These estimates have not yet been refined with student response data.
The studies on this page are about the approaches SubjectPath uses, not about SubjectPath itself. We’ll share our own results once pilots produce them. Ask about a pilot
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