Research-informed classrooms.

Read the research on which EMBRS is based.

The EMBRS Core Principles

Explicit Teaching

Students need clear, structured teaching following a systematic framework.

Immediate Feedback

Immediate feedback strengthens understanding and accelerating mastery. Unassisted learning or long periods without feedback can be counter-productive.

Acquisition Comes First

Students shouldn’t be asked to apply learning before they’ve had a chance to acquire it.

Practice Builds Fluency

Like any skill or sport, regular, structured practice is key to developing speed, accuracy, and confidence in math.

Research-Based, Classroom-ready.

Our Research Base

This compilation of research synthesizes evidence-based practices for mathematics instruction. This research represents everything EMBRS is built on. This is EMBRS.

What the Research Says

The EMBRS Approach

  • “Model and practise conceptual [and procedural] understanding as part of solving mathematics problems.”1
  • EMBRS lessons follow a gradual release model, with the base of each lession being Instructional Loops using the TEACH-TALK-TRY format. This scaffolded form of Explicit Instruction allows students to build skills incrementally and with confidence.
  • “Model and practise algorithms [while considering] factors important for computation with algorithms, such as mathematics fact skill, working memory, or processing speed.”1
  • EMBRS Math emphasizes skill automation. If students develop automaticity with the basics, they can use their working memory for more complex tasks.
  • “Be sure students have a firm understanding and error-free application of requisite skills to solve novel problems.”1
  • Students can’t apply skills before they develop them. EMBRS gives ample opportunity for consolidation and feedback so students develop mastery.
  • Segment skills, use clear language, [and] allow for high levels of opportunities to respond.1
  • Lessons are designed with clear, precise language using the Minimum Viable Explanation. These explanations are recorded and ready to play via an audio link on each slide. This provides a high quality base of instruction that teachers can elaborate on, or replay, if necessary. The recordings are available in 5 languages.
  • Have instructional scaffolds in place that can be removed if or when students no longer need them.”1
  • Each lesson is built in a scaffolded way, so students can progress with competence and confidence. If additional scaffolding is required (for small groups OR the whole class), each lesson is accompanied by an ON-RAMP, which has two Instructional Loops reaching back to the pre-requisite skills for the lesson at hand.
  • “Although unguided or minimally guided instructional approaches are very popular and intuitively appealing…minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process.”2
  • With EMBRS, solving complex problems is important! But asking students to do this without the pre-requisite skills is inefficient – and in some cases, leads to increased inequity in our classrooms.

An example of Explicit Instruction according to the IES at the US Department of Education.

  • 1. States clear expectations at the start of instruction
  • 2. Starts instruction with a relatively easy instructional example
  • 3. Limits the number of instructional examples
  • 4. Uses consistent wording throughout the activities
  • 5. Provides clear demonstrations and step-by-step explanations
  • 6. Provides frequent practice opportunities
  • 7. Uses math manipulatives to build conceptual under-standing
  • 8. Offers ongoing academic feedback
  • 9. Provides cumulative review at the end of the third activity3
  • Each lesson is built on solid Explicit Instruction principles as indicated here.
  • “Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.“4
  • While Explicit Instruction is an important feature, it is equally important to be teaching the right things at the right time. EMBRS is both structured and systematic, ensuring students meet key benchmarks with an intricately weaved skill progression spanning from K to 12.
  • “Include instruction on solving word problems that is based on common underlying structures.”4
  • Schema-Based-Instruction is a key feature of EMBRS. Students are given ample opportunities to solve complex word problems but they’re not left to their own devices to figure out how to solve them. Using a proven SBI approach, students are given Explicit Instruction on answering different problem types so they can approach problems with confidence.
  • “Teachers should model each step in the process of reaching the solution to a problem and think aloud about the strategies they use during problem solving. Students must also be given many opportunities to solve problems using the strategies being taught, and should receive corrective feedback from the teacher when they experience difficulty.”5
  • Our Instructional Loops mirror this structure. During the TEACH phase, teachers use worked-examples and think alouds to demonstrate skills and call attention to certain mathematical elements. During the TALK phase, students respond (individually, in partners, or groups) to prompts including error-detection and examples/non-examples. During the TRY phase, students independently work on a small number of scaffolded examples on whiteboards, so the teacher can pinpoint what learning has occurred and what learning needs to happen next.
  • “We hypothesize that carefully sequenced examples are probably beneficial for initial learning of skills, while a range of examples helps students transfer their newly acquired skills to new performance situations.”5
  • The TRY section has thoughtfully scaffolded questions allowing for the initial acquisition of skills, while the PRACTICE section (following the lesson) ends with a range of questions leaning into the application of the previously learned skill.
  • “Providing teachers with information about students’ math performance led to gains in proficiency. Even stronger impacts were observed when teachers also received instructional tips and suggestions that helped them decide what to teach, when to introduce the next skill, and how to group/pair students, as informed by performance data.”5
  • The EMBRS AI-Marking-Assistant provides teachers with an at-a-glance quantitative data set to combine with their classroom observations. The AI-Marking-Assistant not only compiles marks, but it provides individual and class-wide insights so teachers can respond to students effectively.
  • “Sequence instruction so that the mathematics that students are learning builds incrementally.”6
  • The EMBRS Scope and Sequence was thoughtfully built on scaffolds that ensure students can reach benchmarks by following a systematic structure of skill progression.
  • “Provide immediate, supportive feedback to students to address any misunderstandings.”6
  • Students are actively learning throughout the EMBRS lesson. While students listen to and observe the teacher during the TEACH section, they are actively participating and receiving individual feedback in the TRY and TALK sections of the Instructional Loops.
  • “Teach clear and concise mathematical language and support students’ use of the language to help students effectively communicate their understanding of mathematical concepts.”6
  • Each lesson starts with schema-building-vocabulary that students use to describe their mathematical thinking.
  • “Use a well-chosen set of concrete and semi-concrete representations to support students’ learning of mathematical concepts and procedures.”6
  • The progression of Concrete-Representational-Abstract can be found throughout EMBRS lessons, with each HOOK in each lesson having a concrete learning component.
  • “Use the number line to facilitate the learning of mathematical concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics.”6
  • Number lines are one of several key instructional tools that provide students with representational supports leading to learning acquisition.
  • “Provide deliberate instruction on word problems to deepen students’ mathematical understanding and support their capacity to apply mathematical ideas.”6
  • We want students to be able to solve complex word problems independently! Many students aren’t ready to do this on their own. We make this possible through structured modeling, discussion, and guided practice before independent application.
  • “Those [instructional tactics] include, for example:
    • modeling correct and incorrect responding,
    • providing the response opportunities that help the child discriminate correctly
    • providing graduated prompting and support
    • and maintaining close contact with the learner so that errors can be detected and immediate corrective feedback can be provided.”7
  • After each brief TEACH section, students are given structured “response opportunities”. First, they’re given low-stakes response-opportunities during the TRY section, as they initially grasp concepts and discuss with partners, before moving to a more structured TRY section on individual whiteboards. Teachers can easily see student answers during the TRY section to provide individual and whole-class corrective-feedback.
  • “At the fluency-building stage of learning, instruction must shift to emphasize practicing productive skills by delivering a high dosage of opportunities to respond using well-controlled practice materials.”7
  • Active learning is essential for students to develop their skills. That is why 65% of every lesson is comprised of students working on expertly-scaffolded questions and performance tasks.
  • “The most critical tactic to mitigate math anxiety is to build skill with supportive instruction.”7
  • Students feel successful when they build on their learning incrementally and meet with success. EMBRS makes every student believe they are a “math person”.
  • “Critical Features of Instruction
    • Clarity of objective
    • Teaching one skill at a time
    • Using manipulatives and representations
    • Explicit instruction
    • Provision of teacher examples
    • Adequate practice opportunities
    • Review of prerequisite mathematical skills
    • Error correction and corrective feedback
    • Vocabulary
    • Progress monitoring”8
  • The very basis of Instructional Loops, each TEACH-TALK-TRY instructional loop includes these features.
  • “For novice learners, studying worked examples should be superior to solving problems.”9
  • Elementary math students, even quick learners, are still novices. That is why EMBRS includes worked examples in every TEACH section of an Instructional Loop.
  • “In the early school years, individual differences in intellectual abilities, basic memory capacities, general memory strategies, and metacognitive knowledge may influence memory performance even more than individual differences in the (scarce) knowledge base.“10
  • When entering Kindergarten (or any grade), students come with a wealth of experience learning and interacting with numbers. Counting their Halloween candy, dividing up snacks, asking how many minutes are left on a drive home…each student has their own experiences.

    Although some may have more than others, a major differentiating factor in successful outcomes is student variation in intellectual ability.

    For that reason, EMBRS was designed using the elements of UDL as an inclusive curriculum in several ways.
    • Instructional Loops are short, reducing the need for strong working memory to follow along and build skills
    • The general scaffolding approach of the EMBRS curriculum allows for all students to meet with success and gives teachers the precision they need for targeted feedback if a student is struggling
    • All lessons start with a HOOK that includes a concrete component with manipulatives or semi-concrete representations
    • Each lesson has an ON-RAMP that provides 2 Instructional Loops to help students with pre-requisite skills if they are not fully ready for the grade level lesson. ON-RAMPS can be used with the whole class or with a small group

  • Optimizing for Cognitive Load
    • Focus content only on the learning objectives, taking into account learner knowledge and prior experience.
    • Utilize visual aids that emphasize imagery rather than text.
    • Rehearse the session in advance.
    • Activate prior learner knowledge.
    • Limit the amount of material to be covered.
    • Align content with learner level and experience.
    • Tailor content to flow from simple to complex.
    • Utilize schema to present information.
    • Chunk information in meaningful ways.
    • Incorporate concept mapping
    • Decrease the level of support as learners advance.11
  • Opportunities for practice and feedback occur every few minutes
  • The Minimum Viable Explanation, meaning the simplest way to explain a concept with clarity, is provided in the teacher guide AND in a sound recording attached to every slide. This ensures that students have an opportunity to have high quality explicit instruction repeated if necessary. The sound recording of explicit instruction is on every slide and it is available in 5 different languages to make sure Multi-Language Learners (ESL) meet with success regardless of their level of English acquisition.
  • “If working memory is overloaded, there is a greater risk that the content being taught will not be understood by the learner…and will not be effectively encoded in long-term memory…The limitations of working memory can be overcome by schema construction and automation.”12
  • The explicit teaching of algorithms and the Schema-Based-Instructional approach to teaching how to problem solve are two examples of how EMBRS embraces Cognitive Load Theory.
  • “The Redundancy Effect: Students do not learn effectively when their limited working memory is directed to unnecessary or redundant information.”12
  • In addition to the Minimum Viable Explanation that is provided as a sound recording on each slide, the design of the slides is intentional in reducing distractions and ensuring students can focus on the task at hand.
  • “We see problem solving as central to school mathematics: Problem solving should be the site in which all of the strands of mathematics proficiency converge. It should provide opportunities for students to weave together the strands of proficiency and for teachers to assess students’ performance on all of the strands.”13
  • All students should be able to solve complex math problems. However, one does not get better at solving problems by repeatedly (and unsuccessfully) attempting math word problems.
  • When a child wants to become a good hockey player, we set them up for success with: skating lessons, passing drills, shooting practice, etc. It would be non-sensical to just throw them on the ice as novices and have them try to “play” without any explicit instruction. BUT, “playing” hockey is the eventual goal.
  • With EMBRS, solving complex problems is the goal. We believe that skill acquisition is essential, so we provide opportunities for students to build skills and then apply them weekly in problem-solving-focused lessons.
  • “Textbooks and other instructional materials should support teacher understanding of mathematical concepts, of student thinking and student errors, and of effective pedagogical supports and techniques.”13
  • EMBRS is as easy to implement as a unit from Teachers Pay Teachers. The difference is that EMBRS helps teachers become better at teaching math with job embedded professional learning-as-they-go. The structural support built into EMBRS ensures that every teacher is a great math teacher as their baseline.
  • “Activities and strategies should be developed and incorporated into instructional materials to assist teachers in helping all students become proficient in mathematics, including students low in socio-economic status, English language learners, special education students, and students with a special interest or talent in mathematics.“13
  • The inclusiveness EMBRS was previously mentioned, stating how the Instructional Loops support all students, including those with Executive Functioning difficulties and those who are Multi-Language Learners.

    What about those with a special talent in mathematics?

    Each lesson comes with a self-paced ACCELERATOR, allowing students who are ready to take the next steps to reach their full potential.

    Inclusive Instructional Loops, ON-RAMPS, recorded explanations, translations into 5 languages, CRA progressions, and ACCELERATORS – this is how EMBRS supports the whole class.
  • “Feedback information needs to be actionable…Feedback comments need to be provided at a time that learners are best able to use them…Enable learners to use feedback by explicitly designing connected assessment tasks.”14
  • EMBRS helps teachers provide just-in-time feedback in the Instructional Loops.
  • EMBRS teachers don’t lecture – they explain with clarity and then give students an opportunity to demonstrate their learning.
  • The use of student individual whiteboards gives teachers and insight into class-wide thinking in the TALK and TRY sections of each loop.
  • “High-information feedback contains information on task, process and (sometimes) self-regulation level. Its effect is very large, which suggests that students highly benefit from feedback when it helps them not only to understand what mistakes they made, but also why they made these mistakes and what they can do to avoid them the next time.”15
  • The Instructional Loops were designed so students could have bite-sized instructions and ample opportunities to receive feedback. Immediately after every TEACH section, students receive feedback as they work through the increments in the TRY and TALK sections.
  • “In formulating effective feedback the teacher has to make decisions on numerous occasions, often with little time for reflective analysis before making a commitment. The two steps involved, the diagnostic in interpreting the student contribution in terms of what it reveals about the student’s thinking and motivation, and the prognostic in choosing the optimum response: both involve complex decisions, often to be taken with only a few seconds available.”16
  • Each time students are asked to demonstrate their learning during the TALK and TRY sections, teachers are on high-alert for common errors and misconceptions. With tips provided in the teacher guide at each turn, teachers are almost never caught off guard with where a student’s thinking might be.
  • “The key take-away for school psychologists is to understand that
    • (a) procedural fluency and conceptual understanding emerge in concert around specific and connected skills
    • (b) high-quality fluency building instruction requires high doses of opportunities to respond (e.g., practice with feedback) that ensures high student engagement and occurs in frequent doses, and
    • (c) knowing whether students have attained fluency requires the use of brief timed assessments.”17
  • Student engagement. We know it makes a difference, but how do you achieve it? The Instructional Loops in EMBRS require students to be ready to respond to instruction so frequently that student engagement is seamless.
  • “Results indicated that different types of interventions led to improvements in the mathematics achievement of students experiencing mathematics difficulty, including the following:
    • (a) providing teachers and students with data on student performance;
    • (b) using peers as tutors or instructional guides;
    • (c) providing clear, specific feedback to parents on their children’s mathematics success; and
    • (d) using principles of explicit instruction in teaching math concepts and procedures.”18
  • EMBRS reduces teacher workload so they can focus on doing the most important work – helping students.
  • Instructional Loops reduce the planning workload on teachers, giving them an excellent baseline of instruction that is ready-to-implement from day one.
  • Our AI-Marking-Assistant instantly marks assessments and provides analysis, allowing teachers to focus on responding to students.

Sources:

1. Powell, S. R., Hughes, E. M., & Peltier, C. (2022). Myths that undermine math teaching. *Learning Disabilities Research & Practice, 37*(3), 155-164.

2. Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. *Educational Psychologist, 41*(2), 75–86.

3. Doabler, C. T., Fien, H., Nelson-Walker, N. J., & Baker, S. K. (2012). Explicit mathematics instruction: What teachers can do for struggling learners. *Intervention in School and Clinic, 48*(1), 31-38.

4. Gersten, R., Chard, D. J., Clarke, B., Baker, S. K., Vaughn, S., & Haager, D. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). *What Works Clearinghouse*.

5. Mastropieri, M. A., Scruggs, T. E., & Shiah, S. (2009). Mathematics instruction for secondary students with learning disabilities. *Learning Disabilities Research & Practice, 24*(4), 187-195.

6. Fuchs, L.S., Newman-Gonchar, R., Schumacher, R., Dougherty, B., Bucka, N., Karp, K.S., Woodward, J., Clarke, B., Jordan, N. C., Gersten, R., Jayanthi, M., Keating, B., and Morgan, S. (2021). Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (WWC 2021006). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.

7. VanDerHeyden, A. M., & Peltier, C. J. (2023). Best practices in school applications of the science of math. In P. Harrison, S. Proctor, & J. Grimes (Eds.). *Best Practices in School Psychology, 7th Edition, Volume 2* (pp. 253-264). Bethesda, MD: National Association of School Psychologists.

8. Bryant, B. R., Bryant, D. P., Kethley, C., Kim, S. A., Pool, C., & Seo, Y.-J. (2008). Preventing mathematics difficulties in the primary grades: The critical features of instruction in textbooks as part of the equation. *Learning Disability Quarterly, 31*(1), 21–35.

9. Sweller, J., Ayres, P., & Kalyuga, S. (2011). *Cognitive load theory*. Springer.

10. Case, R., & Griffin, S. (1990). Domain-specific knowledge structures and the development of children’s central conceptual capacities. In W. Schneider & F. E. Weinert (Eds.), *Interactions among aptitudes, strategies, and knowledge in cognitive performance* (pp. 111-135).

11. Jordan J, Wagner J, Manthey DE, Wolff M, Santen S, Cico SJ. Optimizing Lectures From a Cognitive Load Perspective. *AEM Educ Train. 2019 Oct 6;4*(3)

12. Cognitive load theory: Research that teachers really need to understand. SEPTEMBER 2017 Centre for Education Statistics and Evaluation – (https://education.nsw.gov.au/content/dam/main-education/about-us/educational-data/cese/2017-cognitive-load-theory.pdf)

13. National Research Council. (2001). *Adding it up: Helping children learn mathematics*. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

14. Henderson, M., Phillips, M., Ryan, T., Boud, D., Dawson, P., Molloy, E., & Mahoney, P. (2019). Conditions that enable effective feedback. *Higher Education Research & Development, 38*(7), 1401–1416.

15. Luke Mandouit, John Hattie, Revisiting “The Power of Feedback” from the perspective of the learner, *Learning and Instruction, Volume 84*, 2023, 101718, ISSN 0959-4752, [https://doi.org/10.1016/j.learninstruc.2022.101718](https://doi.org/10.1016/j.learninstruc.2022.101718).

16. Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. *Educational Assessment, Evaluation and Accountability, 21*(1), 5–31.

17. VanDerHeyden, A. M., & Codding, R. S. (2020). Belief-Based Versus Evidence-Based Math Assessment and Instruction: What School Psychologists Need to Know to Improve Student Outcomes. *Research-Based Practice; Commune, 48*(5), p. 1, 20-25.

18. Baker, S., Gersten, R., & Lee, D. S. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. *The Elementary School Journal,103*(1), 51-73.

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