Mathematics Resource Landscape
What happens between one math screening and the next?
Across Canada and the United States, more students are being screened for mathematics difficulty, and more systems are expected to act on the results. This page explains the three functions involved, why the third is the least defined, and how to evaluate what any vendor will tell you about it. It draws on four decades of published research on short learning cycles, summarized near the top.
Last updated October 26, 2026
Who wrote this. Knowledgehook offers a product in this category. Its own product and evidence are described only in the section About Knowledgehook.
Who it is for. Ministries, state agencies, school boards, districts and others working out what math intervention supports should look like.
The research case for short learning cycles
Closing a gap quickly, in class, by the teacher who found it, is one of the best-attested ideas in education
The term is the literature’s, not ours. Wiliam and Thompson (2008) distinguish long-cycle formative assessment, across terms; medium-cycle, across units; and short-cycle, within and between lessons, minute by minute and day by day. Leahy, Lyon, Thompson and Wiliam (2005) describe what that looks like in a classroom.
Five research strands that rarely cite each other arrive at the same finding: mathematics outcomes move when the loop between evidence and instruction is short, specific to a concept, and run by the classroom teacher. The table maps each step of that loop to its evidence.
Effect size when teachers measured progress frequently and adjusted instruction, across 21 studies. Fuchs and Fuchs, 1986.
Mean effect of mastery learning across 108 controlled studies, larger for lower achievers. Kulik, Kulik and Bangert-Drowns, 1990.
Additional progress from high-quality feedback, at the Education Endowment Foundation’s highest evidence rating.
Feedback interventions that lowered performance across 607 effect sizes. Specificity decides. Kluger and DeNisi, 1996.
| Step | What the evidence supports | Key findings and sources |
|---|---|---|
| 1. Check | Frequent, concept-level checks for every student; the check itself strengthens retention | Black and Wiliam’s 1998 review of about 250 studies reported effect sizes of 0.4 to 0.7 for formative assessment, largest for students who had done poorly. Roediger and Karpicke (2006) and Dunlosky et al. (2013) show that being tested on material improves retention more than restudying it. |
| 2. Reflect | Teachers reading item-level patterns with decision rules; gains depend on the teacher acting on the data | Fuchs and Fuchs’ 1986 meta-analysis found an effect size of 0.70 when teachers measured progress frequently and adjusted instruction. Stecker, Fuchs and Fuchs (2005), reviewing 18 experiments in reading and mathematics, found gains only when teachers used the data to change what they taught. |
| 3. Intervene | Task-specific, explanatory, timely feedback and explicit instruction aimed at the identified gap | Hattie and Timperley (2007) and the EEF Toolkit place feedback among the strongest influences on achievement; Kluger and DeNisi (1996) show it works only when aimed at the task. The US Institute of Education Sciences practice guides for struggling mathematics students (Gersten et al., 2009; Fuchs et al., 2021) recommend explicit instruction and progress monitoring for identified students. |
| 4. Measure | Re-checking the same objective after corrective instruction, spaced over days, before moving on | Kulik, Kulik and Bangert-Drowns (1990) found the mastery effect larger when the check was followed by corrective instruction. The EEF Toolkit rates mastery learning at about five months and notes the effect falls for programs longer than about twelve weeks. Cepeda et al. (2006) show spaced re-checks beat massed ones. |
Why short
Three separate literatures point the same way. Kulik and Kulik (1988) found immediate feedback beat delayed feedback in classroom studies. Mathematics is cumulative, so a gap left open at one unit becomes a prerequisite failure at the next. And Yeh (2007) found rapid formative assessment several times more cost-effective per unit of gain than class-size reduction, vouchers or increased spending.
Who runs it
Across every strand, the effect appears when the teacher acts, not when a system reports. Data collected and not used produced nothing in Stecker’s review; teacher learning communities, not materials, carried the EEF’s 2018 randomized trial across 140 schools. The research supports tools that make the loop fast enough for a teacher to run inside a lesson, not tools that take it away from them.
The honest version of the numbers
Later meta-analyses found smaller averages: Kingston and Nash (2011) pooled the studies that met strict criteria and reported a mean effect of 0.20, and 0.17 in mathematics. The reason is the argument for the cycle: averaging across loosely defined programs washes out the effect, and the studies that held up were the ones where the evidence changed what the teacher did next.
What the evidence does not say
No independent trial yet isolates a four-step, teacher-run, same-concept cycle as a unit. The strands support each step and the short-cycle principle; any vendor’s claim about a specific design rests on that vendor’s own evidence, and should be judged by the tests further down this page.
Why this matters now
Systems will soon know who is behind. Few have defined what happens next.
Across Canada and the United States, screening for mathematics difficulty is expanding, results are being reported upward, and legislatures are attaching mandates to them. What most systems do not yet have is a defined approach for what happens between one screening and the next.
Alberta now requires numeracy screening for every student from Kindergarten to Grade 5. Grades 4 and 5 were added in 2026-27, with a fall whole-class screen and a spring re-screen, and the province will publish its first provincial report in 2027-28.
Arkansas requires a written math intervention plan for every student in grades 3 to 8 who scores below proficient. Texas requires accelerated instruction for every student who does not meet the standard on its state assessment.
Florida now maintains a state-examined and approved list of mathematics intervention programs, after a 2023 statute recognized intervention materials as their own category.
Each of these produces a count of students who are behind. Whether those students are still behind at the next screen depends on what happens in classrooms in between. That is the function this page is concerned with.
The three functions at a glance
Each function answers a different question. None can substitute for the others.
| Screening assessments | Targeted instruction resources | Core instruction resources | |
|---|---|---|---|
| Question it answers | Which students may need support, and in which broad areas? | What exactly is this student missing, what should the teacher do about it, and has it been resolved? | What does the whole class learn next, and how? |
| Focus | Every student, briefly | The individual student and the specific concept | The whole class |
| Timing | Fixed windows set by the jurisdiction | Continuous, between screening windows | Daily, paced through the year |
| Measured against | Norms for the grade or age | The same concept, checked again after instruction | The curriculum’s learning outcomes |
| Produces | A flag of risk and possible areas of need | A diagnosis, an instructional response, and a re-measure of the same concept | Lessons, practice and assessment for the class |
| Does not | Instruct, or close the gap it finds; further assessment is usually needed to locate the precise gap | Replace core instruction or screening | Respond to every gap individual students carry, although many include differentiation; rarely returns a student to grade level on its own |
| Maturity as a category | Established; mandatory in many jurisdictions | Varies widely; least defined | Established; often centrally approved |
These are working descriptions. Some products combine roles, so the useful test is the function a resource performs, not the label it carries.
Screening and core resources
Neither is built to close a specific student’s gap on its own
Isn’t the screener already a diagnosis?
The two terms are often used interchangeably, but they describe different instruments with different jobs.
A screener is brief, given to every student, and scored against norms. Its job is early warning: it tells a school which students may be at risk and in which broad areas. Precision about an individual student’s thinking is not its purpose.
A diagnosis identifies the specific misconception or missing prerequisite behind a student’s difficulty. Two students flagged in the same domain can need very different responses. One may not understand place value beyond whole numbers; another may understand it but not yet see fractions as numbers on a number line. A screener result alone does not distinguish them.
This matters most in the upper elementary grades, where screeners are often given to whole classes to keep them efficient. A teacher receiving results for several flagged students still has to determine what each one needs. That step sits with targeted instruction, not with screening.
Don’t core resources already do this?
Core resources, such as textbooks and daily programs, are the foundation of daily instruction. They sequence the curriculum, pace the class through it, and give teachers lessons, practice and assessment aligned to the learning outcomes. Many jurisdictions approve or provide them centrally.
Many core resources include differentiation, and they serve every student. Because they are built for the whole class, they are rarely sufficient on their own to return a student who has fallen behind to grade-level pace. The class moves on to the next unit; the student’s gap can move with them.
Many core resources now include adaptive practice, which adjusts the difficulty or selection of practice items for each student. That serves a different purpose from identifying a specific misconception, giving the teacher a response to it, and re-measuring the same concept to confirm it has been resolved.
What targeted instruction does
Targeted instruction resources complete the cycle that screening begins
They act on what screening identifies, and they run continuously between screening windows. A complete resource supports four steps:
- Check understanding of one concept. A short check pinpoints the concept the student has not grasped, or the prerequisite knowledge they are missing.
- Reflect on the pattern. Whoever runs the cycle, usually the classroom teacher, reads the pattern of responses and decides what the gap is, which students have it, and what to do next.
- Intervene. Give the teacher a concrete instructional response matched to that gap, usable within the school day.
- Re-measure the same concept. Confirm within weeks, not months, whether the gap has closed, and adjust if it has not.
A resource that does only the first step is another assessment. A resource that does only the third is more practice. The value lies in completing all four, repeatedly, for the students who need it.
Consider a Grade 5 class
The fall screen flags several students in number. Core instruction continues for the whole class. A closer check then shows that one flagged student is missing place value with decimals, while another has not yet understood fraction equivalence. The teacher responds to each gap within regular instruction, and a student with a larger gap may also receive small-group support. A few weeks later, the same concepts are checked again. By the spring re-screen, the school knows not only who was behind, but which gaps were closed and how.
Relationship to existing intervention resources
Some ministries and states provide intervention lessons alongside their screeners, often focused on foundational number skills in the early grades. Where such resources exist, a targeted instruction resource should extend them, not duplicate them. The upper elementary curriculum introduces content, such as fractions, decimals and multiplicative reasoning, where the range of possible misconceptions widens considerably.
Who runs the cycle
Targeted instruction resources differ most in who interprets the evidence, teaches, and checks again. Some products and programs combine these types.
| Design | How it works | Who runs the cycle | Designed for |
|---|---|---|---|
| Classroom-based, teacher-led resources | The teacher checks understanding of specific concepts, responds, and re-measures as part of regular instruction | The classroom teacher, supported by the resource | Responding to gaps across a class within daily teaching, and building teacher practice over time |
| Adaptive practice software | Adjusts tasks to each student’s responses, typically during independent practice; teachers may assign and review it | The software, with the teacher assigning and reviewing | Practice matched to each student’s level, with data on where students are struggling |
| Tutoring and intervention programs | Structured additional teaching, often by a second adult in small groups or a pull-out setting; some operate within class | A specialist, tutor or educational assistant | Intensive, focused support for students with significant gaps |
The types share questions about outcomes and access, but differ in staffing and instructional purpose. Many schools use more than one.
Questions to ask
What separates a strong answer from a weak one is specificity
Of your own system
Before looking at any resource, it helps to be clear about what the system wants to know and who would act on it.
- What would we want to know at the spring re-screen that we cannot know now?
- When a student is flagged in the fall, who decides what happens next, and how soon?
- Which concepts in the upper elementary curriculum account for most of the gaps we see?
- Who would act on information about a specific gap: the classroom teacher, a specialist, or both?
- How would we know, by spring, whether the gaps identified in the fall had closed?
Of any targeted instruction resource
Targeted instruction resources vary more than screeners or core resources, so these questions are where the variation shows. An answer can be clear about a limitation and still be useful.
| Question | A strong answer | A weak answer |
|---|---|---|
| How does it fit with the screener and core resources schools already use? | Traces a screening result to a teaching action on a specific curriculum concept; states alignment to the jurisdiction’s curriculum or standards, grade by grade, including recent revisions; explains data transfer, including manual steps, compatibility limits and overlap with existing materials. | Says “curriculum aligned” or “integrates seamlessly” without an example. |
| Does it extend intervention resources the jurisdiction already provides? | Explains how it builds on those resources and covers outcomes they do not. | Duplicates them, or does not know they exist. |
| Does it support the full learning cycle? | Shows one cycle end to end: a check on a specific concept, what the teacher sees, the response, and a later check of the same concept; identifies any steps supplied by others and the time between checks. A tutoring program can show this through session records and re-assessment; adaptive software through item-level reports the teacher acts on. | Shows separate features without explaining how they connect. |
| What evidence is there that students who were behind improved? | Names the cohort, starting point, number of students, measure, period and comparison; reports who remained behind, missing results and limits on attribution; offers educators who can confirm it. | Testimonials, usage counts, averages or growth percentages with no baseline or comparison. |
| What is the teacher’s role, and does it build their capacity or reduce it? | Shows the decisions teachers make, what is automated and how teachers can override it; describes workload and any evidence of change in teachers’ practice. | Promises teacher empowerment or time savings without showing the work. |
| What staffing does it assume beyond the classroom teacher? | States the staffing model and the time per cycle or session; where a design relies on small-group time with a second adult, addresses the scheduling and staffing that come with it. | Describes flexibility without saying who does the work or when. |
| Will it show schools, districts and the ministry or state whether identified students are closing their gaps? | Shows learning progress and remaining gaps at each level, with dates and numbers of students; explains who can access what, how data is aggregated, and the limits of what it can report. | Reports usage and logins; cannot show whether students who were behind caught up. |
| Does it meet language and data requirements? | Available in the jurisdiction’s languages of instruction, such as French for francophone and immersion programs in Canada; states where student data is stored and under which privacy legislation. | Language support or data location and handling unclear. |
Different designs answer these questions differently. Tutoring programs typically lead on the intensity of small-group instruction; adaptive software on the depth of item-level diagnostic data; classroom-based resources on how often the cycle can run within regular teaching.
How to judge any vendor’s efficacy claims
Did students who were behind improve, and how much of that can be linked to the resource?
No single test below proves causation; together they show how much weight a claim can bear.
- Same concept, before and after. A claim that a specific gap closed should show comparable measures of that concept before and after, with the interval stated.Repeating the same items can overstate learning, and closing a specific gap is not the same as reaching overall grade-level proficiency.
- A comparison. Students with similar starting points who did and did not receive the intervention, or the same system’s prior years.Prior-year comparisons give context but are less able to isolate the resource’s effect; check for changes in teaching, cohorts and assessment.
- Dose and response. Whether greater use, such as more completed cycles, coincides with greater improvement.Ask how use was measured and whether starting points and other supports were considered. Teacher engagement can also explain the pattern.
- An external measure. Results on an assessment the vendor does not control, such as the jurisdiction’s own screener or provincial or state assessments, carry more weight.The assessment must measure the learning being claimed, and an external measure does not by itself make a study independent.
Not sufficient on their own
- Usage figures
- Satisfaction scores
- Growth percentages with no baseline
Usage describes participation; satisfaction describes experience; an unexplained percentage does not establish learning.
Two checks that cost nothing
- Call a superintendent or principal in a system the vendor cites.
- Ask the vendor for a result that disappointed them.
Discuss what was delivered, who improved, who did not, and what changed. References add context; they do not replace a study.
What a rollout involves, and what comes back
Targeted instruction resources only produce outcomes when teachers run the cycle regularly
So a rollout has to fit the timetable and the people available.
Teacher preparation, class time and elapsed time per cycle, kept separate; the cycles per term the evidence is based on, the range across classrooms, and what is known about lower use.
Rollouts already delivered, kept separate from planned capacity; time from decision to first classroom use; who in the school does the work; training, help channels, response times, and availability in the languages of instruction.
What the resource needs from student information systems and screening results, and what it sends back; data minimisation, storage location, access, retention and deletion; applicable privacy legislation and accessibility standards.
What a principal sees about their school and what a district sees across schools, with cohort sizes, missing data and dates. Any reporting to the ministry or state depends on authorised purposes and appropriate aggregation.
A system that invests in targeted instruction should be able to say, at the end of the year, which students caught up, on which concepts or measures, who still needs support, and what the investment produced, and be clear about what the evidence cannot attribute to that investment.
How other systems have described this function
No one has named this category yet. Several have described the function.
The public documents below are the closest we found, four American, linked so they can be read in the original. None describes any one vendor’s model, and some bundle functions this page separates.
Bridgeton Public Schools, New Jersey
RFP 27-012, Mathematics Assessment and Intervention, August 2026. Prerequisite skill gaps, differentiated lessons, ongoing monitoring of intervention effectiveness, and reporting for teachers and system leaders.
Boundary: bundles universal screening with intervention in one request.
Pittsburgh Public Schools, Pennsylvania
K to 12 Digital Interventions for Mathematics, 2024. Frequent diagnosis of unfinished learning, support for teachers in progress monitoring, and adjusting instruction to student need through the year.
Boundary: emphasizes adaptive digital learning; does not require re-measuring the same concept.
Florida Department of Education
Specifications for the 2024 to 25 adoption, Grades K to 4 Mathematics Intervention. A state recognizing intervention materials as their own category, with next steps for instruction, targeted assessment with item analysis, and evidence of effectiveness.
Boundary: a broad materials category; not specific to any delivery model.
Edinburg CISD, Texas
RFP 25-51, Reading and Math Intervention, February 2025. Assessment for placement and differentiation, progress reporting, and guidance to teachers on using assessment information, with training and ongoing PD.
Boundary: grades 6 to 12, print-based despite the title, with an end-of-year post-assessment rather than short cycles.
Read together, the four US documents ask for the same four things in different words: identify the learning need, connect assessment to action, monitor the response, and support effective use. The specific loop described here is one way to deliver those functions, not the only one.
One-page checklist
Evaluating targeted instruction resources
Use this when reviewing a resource intended to close the specific gaps that screening finds.
Before looking at any resource
- What do we want to know at the spring re-screen that we cannot know now?
- When a student is flagged, who decides what happens next, and how soon?
- Who acts on a specific gap: the classroom teacher, a specialist, or both?
- How will we know by spring whether the fall gaps closed?
What a strong resource should show
- It finds the specific gap, not just a broad area
- Teachers can act on it within the school day
- It re-checks the same concept within weeks
- Its results show which students caught up
Questions for the provider
Eight questions to use when reviewing any targeted instruction resource.
| Question | A good answer includes |
|---|---|
| How does it connect to the screener and core resources we use? | A screening result traced to a teaching action on a specific concept; alignment to our curriculum or standards, including recent revisions |
| Does it extend the intervention resources we already have? | What it covers that they do not |
| Does it run the full cycle? | One concept shown end to end, with the time between checks |
| Did students who were behind improve? | Cohort, starting point, measure, comparison, and who stayed behind |
| What does the teacher decide and do? | What is automated, the workload, and the effect on practice |
| What staffing does it assume? | The staffing model and time per cycle or session |
| Can we see whether identified students are closing gaps? | Progress and remaining gaps by school and district, with dates and student numbers |
| Does it meet language and data requirements? | The languages of instruction we need; where data is stored and under which privacy legislation |
Checking evidence claims
Ask whether the evidence shows:
- the same concept measured before and after, and how far apart
- a comparison with similar students, or with the same school’s prior years
- more improvement where the resource was used more
- results on a measure the provider does not control, such as our screener or provincial or state assessments
About Knowledgehook
Everything above applies to us, and we expect to be held to it
Knowledgehook is a Canadian K to 10 mathematics company. Its product, ClassOS, is a classroom-based, teacher-led resource.
ClassOS runs a Short Learning Cycle in the classroom: a check for understanding, teacher reflection, a targeted response, and a re-measure of the same concept. The teacher runs the cycle; the system supports it. ClassOS is used in nearly 100 education systems across Canada, the United States and Latin America, including 64 of Ontario’s 72 school boards.
Evidence. Our results are set out in the Knowledgehook Impact Report 2025-26 (Ontario), which names the systems, grades and measures, including results on EQAO provincial assessments such as those at Niagara Catholic District School Board. We will connect any reader with the educators and system leaders who saw these results.
Work underway. We are completing a dose-response analysis with the Toronto District School Board, and building independent validation of our results through academic partners, separately from our own reporting.
We are glad to talk through the category or anything on this page.
Sources
Screening and policy context
- Government of Alberta, Literacy and numeracy screening
- Government of Alberta, More supports for math and reading, September 10, 2026 (as republished by Education News Canada)
- EdCan Network, Minding the Gap in Mathematics
Research on short learning cycles
- Black, P., and Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education, 5(1), 7–74.
- Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., and Rohrer, D. (2006). Distributed practice in verbal recall tasks: a review and quantitative synthesis. Psychological Bulletin, 132(3), 354–380.
- Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., and Willingham, D. T. (2013). Improving students’ learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4–58.
- Education Endowment Foundation (2018). Embedding Formative Assessment: evaluation report. London: EEF.
- Education Endowment Foundation. Teaching and Learning Toolkit: Feedback; Mastery learning. London: EEF.
- Fuchs, L. S., and Fuchs, D. (1986). Effects of systematic formative evaluation: a meta-analysis. Exceptional Children, 53(3), 199–208.
- Fuchs, L. S., et al. (2021). Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (WWC 2021006). Washington, DC: Institute of Education Sciences.
- Gersten, R., et al. (2009). Assisting Students Struggling with Mathematics: Response to Intervention for Elementary and Middle Schools (NCEE 2009-4060). Washington, DC: Institute of Education Sciences.
- Hattie, J., and Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112.
- Kingston, N., and Nash, B. (2011). Formative assessment: a meta-analysis and a call for research. Educational Measurement: Issues and Practice, 30(4), 28–37.
- Kluger, A. N., and DeNisi, A. (1996). The effects of feedback interventions on performance. Psychological Bulletin, 119(2), 254–284.
- Kulik, J. A., and Kulik, C.-L. C. (1988). Timing of feedback and verbal learning. Review of Educational Research, 58(1), 79–97.
- Kulik, C.-L. C., Kulik, J. A., and Bangert-Drowns, R. L. (1990). Effectiveness of mastery learning programs: a meta-analysis. Review of Educational Research, 60(2), 265–299.
- Leahy, S., Lyon, C., Thompson, M., and Wiliam, D. (2005). Classroom assessment: minute by minute, day by day. Educational Leadership, 63(3), 18–24.
- Roediger, H. L., and Karpicke, J. D. (2006). Test-enhanced learning: taking memory tests improves long-term retention. Psychological Science, 17(3), 249–255.
- Stecker, P. M., Fuchs, L. S., and Fuchs, D. (2005). Using curriculum-based measurement to improve student achievement: review of research. Psychology in the Schools, 42(8), 795–819.
- Wiliam, D., and Thompson, M. (2008). Integrating assessment with learning: what will it take to make it work? In C. A. Dwyer (ed.), The Future of Assessment: Shaping Teaching and Learning (pp. 53–82). New York: Lawrence Erlbaum Associates.
Other systems
- Bridgeton Public Schools, RFP 27-012, Mathematics Assessment and Intervention, August 2026
- Pittsburgh Public Schools, K to 12 Digital Interventions for Mathematics, 2024
- Florida Department of Education, Specifications for the 2024 to 25 adoption, Grades K to 4 Mathematics Intervention
- EdWeek Market Brief, Edinburg CISD RFP 25-51, Reading and Math Intervention, February 2025