> ## Documentation Index > Fetch the complete documentation index at: https://docs.learningcommons.org/llms.txt > Use this file to discover all available pages before exploring further. # New Meridian Mastery Statistics > Empirically derived mastery thresholds that estimate how difficult each math learning component and standard is to master. [Dataset last updated Nov 10, 2026.](#dataset-release-history) ## Overview > [!NOTE] > > The New Meridian Mastery Statistics dataset uses learning components > [entities](https://docs.learningcommons.org/knowledge-graph/schemas/learning-components.md#masterythreshold) and > [relationships](https://docs.learningcommons.org/knowledge-graph/schemas/learning-components.md#hasmasterythreshold). The New Meridian Mastery Statistics dataset assigns mastery thresholds to Math [learning components](https://docs.learningcommons.org/knowledge-graph/schemas/learning-components.md) and [standards](https://docs.learningcommons.org/knowledge-graph/schemas/standards.md). Lower threshold values mean "easier"; higher values mean "more difficult". Each threshold value describes the overall math proficiency a student needs before they are expected to master that learning component or standard. It predicts a student's score on a calibrated set of items – it is NOT a measure of conceptual understanding. See [Mastery thresholds](#mastery-thresholds) for more information. | | | | :- | :- | | **Source** | [New Meridian Corporation](https://newmeridiancorp.org/) ↗\[!NOTE] The reference population is the 2015 PARCC Spring operational administration in Arkansas, Colorado, Washington, D.C., Illinois, Louisiana, Maryland, Massachusetts, Mississippi, New Jersey, New Mexico, Ohio, and Rhode Island. If your users are mostly in non-PARCC states, you can still use the thresholds to classify students if you can produce [summative scores](#linked-summative-scores) and weight your sample to resemble the 2015 sample. For high school, the reference population is the 12,282 students who took the 2015 Integrated Mathematics II assessment. The sample is large, but it is not nationally representative. This dataset is on the PARCC scale (now New Meridian Summative), not the Smarter Balanced (SBAC) scale, which uses a different item bank and scale.Provider: Learning Commons Licensed under [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/) ↗ | | **Subject** | Math | | **Supported grades** | 3–8 (individual grade bands) and high school (one grade band) | | **Includes** | **New Meridian Mastery Statistics** Open | | **Dataset dependencies** | | ## Use cases Mastery thresholds work best for decisions about content (e.g., what order to teach standards and learning components in). Decisions about individual students require [student data on the same scale](#using-with-student-data) and mastery thresholds that pass the [required checks](#checks). | Use case | Examples | | :- | :- | | **Sequence content by difficulty** | For a grade and a set of learning components and standards:
  1. Tag each learning component or standard based on its [`MasteryThreshold`](https://docs.learningcommons.org/knowledge-graph/schemas/learning-components#masterythreshold)
  2. Sort all **Acceptable** and **Low evidence** tags by `masteryThreshold50` (basic mastery) or `masteryThreshold67` (stronger mastery) in ascending order
  3. Sort **Off-scale** tags by the same field and add to the end of the list
| | **Scaffold a standard** |
  1. Create a list with the target standard's supporting learning components, then its connected standards, and then the target standard itself.
  2. Use the **Sequence content by difficulty** steps above to sort each group in place
| | **Pick a next step after a student has mastered a standard** | | | **Pick review content when a student hasn’t mastered a standard** | Fetch the standard’s supporting learning components and standards, sort them using the **Sequence content by difficulty** steps above, and then assign them to students in the sorted order | | **Check whether a student has mastered a standard** | Requires [calibrated items or linked summative scores](#using-with-student-data)Requires additional student data
  1. Fetch the [`MasteryThreshold`](https://docs.learningcommons.org/knowledge-graph/schemas/learning-components#masterythreshold) - if it fails the [required checks](#checks), return "not enough evidence"
  2. Use the student's standard error as the band when it is known, otherwise use 0.3
  3. Compare their θ to `masteryThreshold50` (basic mastery) or `masteryThreshold67` (stronger mastery). If their θ is at or above the threshold plus the band, they have mastered it. If their θ is at or below the threshold minus the band, they have not mastered it. Otherwise, return "not enough evidence".
With calibrated items, compare the student's percentage score to 0.50 or 0.67 the same way, using a margin of a few percentage points. | | **Track mastery over time** | Requires [linked summative scores](#linked-summative-scores)Requires additional student data
  1. Compare a student's score to a learning component or standard's `masteryThreshold50` (basic mastery) or `masteryThreshold67` (stronger mastery) and record the result
  2. Track the student's mastery of learning components and standards across a grade over time
| ## Schema The data attaches mastery thresholds to existing [learning components](https://docs.learningcommons.org/knowledge-graph/schemas/learning-components.md) and [standards](https://docs.learningcommons.org/knowledge-graph/schemas/standards.md) using the [`hasMasteryThreshold`](https://docs.learningcommons.org/knowledge-graph/schemas/learning-components#hasmasterythreshold) relationship. ![Data model diagram: LearningComponent entities connected to StandardsFrameworkItem by the supports relationship](https://mintcdn.com/czi-60a2a443/UoQ2sR1ZTSo_L1ZG/images/knowledge-graph/new-meridian-mastery-statistics.jpg?fit=max\&auto=format\&n=UoQ2sR1ZTSo_L1ZG\&q=85\&s=57f3d67fc5eb37dd85222a1b7ddcaac0) | | | | :- | :- | | **Entities** | | | **Relationships** | | ## Accessing the data > [tab] Local files > > Download the dataset: > > * From the Dataset catalog: [New Meridian Mastery Statistics](https://platform.learningcommons.org/dataset-catalog) ↗ > * [Using direct links or `curl`](https://docs.learningcommons.org/knowledge-graph/using-knowledge-graph/local-files#download-using-direct-links-or-curl) > > The catalog subset contains only this dataset's nodes and edges. To resolve the edges, also download [Math learning components](https://docs.learningcommons.org/knowledge-graph/datasets/learning-components/math-learning-components.md) and [U.S. academic standards](https://docs.learningcommons.org/knowledge-graph/datasets/standards/us-academic-standards.md) (Math). The dataset is included in the all-open Knowledge Graph downloads. > [tab] REST API > > Check out the [API Reference](https://docs.learningcommons.org/api-reference/overview.md) for more information. > > | File | API endpoints | > | :- | :- | > | **New Meridian Mastery Statistics** | Not yet supported | > [tab] MCP server > > Check out the [MCP server](https://docs.learningcommons.org/knowledge-graph/using-knowledge-graph/mcp-server.md) for more information. > > | File | MCP tools | > | :- | :- | > | **New Meridian Mastery Statistics** | Not yet supported | ## Mastery thresholds > [!WARNING] > > * **Don't compare thresholds across grades.** Each grade band has its own scale, and there is no scale linking grades. > * **Off-scale thresholds may be inaccurate.** A threshold of exactly 4.5 or −4.5 means the estimate hit the edge of the scale, and the true value may be more extreme. > * **Don't use thresholds to make high-stakes decisions.** Don’t use thresholds as the only or deciding input for promotion or retention, grades of record, graduation or course access, gifted or special education placement, or discipline or funding. Use them for low-stakes, reversible recommendations like “try this next.” > * **Don’t compare demographic groups.** Thresholds describe how hard a learning component or standard is, not how able any group of students is. > * **Protect student data.** Treat student mastery results as student education records (e.g., under FERPA). Keep them in the instructional context and don’t send to third-party analytics, advertising, or disciplinary or administrative systems without proper authority. The dataset itself contains no student data. ### Theta scale The dataset scores students, learning components, and standards on the same θ (theta) scale, which follows a bell curve from -4.5 to 4.5 (average 0, standard deviation 1): * **For students** - Student's overall math proficiency in their grade * **For learning components and standards** - Minimum threshold a student must have before being expected to master the learning component or standard This scale treats mastery as a line – students who master harder targets are expected to master easier ones in the same grade. > [!NOTE] > > Students are often stronger in some areas than others. A student's result on a specific learning component or standard can differ from what their θ predicts. Treat student thresholds as "expected to master," not "has mastered". ### Cutoffs The dataset contains mastery thresholds at 2 cutoffs: | Cutoff | Property | Description | | :- | :- | :- | | **Basic mastery** | `masteryThreshold50` | Threshold at which a student is expected to score 50% or higher on the aligned items Suited to low-stakes calls such as "ready to attempt" | | **Stronger mastery** | `masteryThreshold67` | Threshold at which a student is expected to score 67% or higher on the aligned items Suited to instructional decisions like "ready to move on to harder materials" | ### Using with student data > [!TIP] > > If you do not have calibrated items or linked scores, use thresholds to order > content only – not to classify students. | If you have | You can | You cannot | | :- | :- | :- | | **No linked student data** | Order content by mastery threshold. | Compare a student's score on your own edtech platform to a mastery threshold. | | **[Calibrated items](#calibrated-items) aligned to learning components or standards** Requires additional student data Items aligned to specific [learning components](https://docs.learningcommons.org/knowledge-graph/schemas/learning-components.md) or [standards](https://docs.learningcommons.org/knowledge-graph/schemas/standards.md) and calibrated to the New Meridian Summative item bank | Classify a student from their percentage score on the aligned items. | Use your own items unless they have been calibrated to the same θ scale. | | **[Linked summative scores](#linked-summative-scores)** Requires additional student data Scale scores from a summative test you can convert to the 2015 PARCC θ scale | Convert each student's score to θ and compare it to a mastery threshold. | Treat the converted θ as exact for an individual student. | > [!NOTE] > > Leave room for student measurement error. > > A student whose θ or percentage score sits close to a threshold could be on either side of it. Classify a student as having mastered a learning component or standard only if their estimate clears the threshold by its margin of error, and as not mastered only if it falls below by that margin. Otherwise report that there is not enough evidence. > > If you do not have a standard error for the student's θ, ±0.3 is a reasonable default. #### Calibrated items * Items aligned to a specific learning component or standard * Items drawn from or psychometrically linked to the New Meridian Summative item bank – Released SBAC items are on a different scale and do not qualify * 3+ items on your own form, and more when several learning components support it (\~3 per supporting learning component) - This is separate from the dataset's `alignedItemCount`. Then compare the student's percentage score on those items to the [cutoff](#cutoffs). A student scoring 67% on easier, uncalibrated items is not at the 67% threshold. #### Linked summative scores To convert scale scores to θ, you need: * Summative test with documented scale score properties * Sample of your data that approximates the 2015 calibration sample That sample can be a stratified proportional systematic random sample with final weights (base weight × post-stratification weight), or all of your data adjusted with post-stratification weights. Convert in two steps: ```text theme={null} θ_sample = (X − M_X,w) / S_X,w θ_2015 = (σ_2015 / S_θ,w) · θ_sample + (μ_2015 − (σ_2015 / S_θ,w) · M_θ,w) ``` * `X` - Student's scale score * `M_X,w` - Weighted mean of scale scores in your sample * `S_X,w` - Standard deviation of scale scores in your sample * `M_θ,w` - Weighted mean of `θ_sample` * `S_θ,w` - Standard deviation of `θ_sample` * `μ_2015` - 0 * `σ_2015` - 1 > [!NOTE] > > * This is concordance, not equating. Converted scores match on average, not for each student. > * The conversion does not carry the student's measurement error. Students near a threshold may fall on either side of it. > * If your test's content differs a lot from PARCC math, weighting your sample will not fix that. Treat the converted θ as a rough anchor. ### Checks * **Student's grade must match the threshold's grade band** * Thresholds are grade-specific – there is no scale linking grades * **Threshold should not be off-scale** (i.e. exactly 4.5 or −4.5) * More common in the high school band * If off-scale, use thresholds for ordering only (no student classification) at the end of the list * **Threshold should be stable and reliable** * Thresholds with `alignedItemCount` >= 3 are stable * Thresholds with `reliability50` or `reliability67` >= 0.80 are reliable * 27-40% of learning components and 5-15% of standards do not meet these 2 requirements, depending on the grade band and cutoff * If these 2 requirements are not met, use thresholds for ordering only (no student classification) at the end of the list | Property | Description | | :- | :- | | `alignedItemCount` | Number of items used to estimate the threshold | | `reliability50` and `reliability67` | Classification accuracy at each [cutoff](#cutoffs) New Meridian simulated 5,000 students, generated their answers to every aligned item, and classified each student twice: once from their simulated percentage score and once from their θ compared to the threshold. Reliability is the share of students whose classifications agree. | > [!NOTE] > > `alignedItemCount` and `reliability50` / `reliability67` are related but not > interchangeable. Check both properties before using a threshold. ## Dataset release history | Date | Changed | | - | - | | Nov 10, 2026 | First release | ## Related topics > [card] [Learning components schema reference](https://docs.learningcommons.org/knowledge-graph/schemas/learning-components.md#masterythreshold) > > Review property definitions for `MasteryThreshold`. > [card] [Math learning components dataset](https://docs.learningcommons.org/knowledge-graph/datasets/learning-components/math-learning-components.md) > > Thresholds attach to learning components in this dataset. > [card] [U.S. academic standards dataset](https://docs.learningcommons.org/knowledge-graph/datasets/standards/us-academic-standards.md) > > Standard thresholds attach to Common Core Math standards in this dataset.