UDL Week: Day 7 - Direct / Explicit Instruction and pre-teaching new vocabulary
Welcome to the final day of UDL Week here at the AutSide. We’ve been diving into a rigorous and fast paced geometry lesson to see where students with IEPs, language learners, twice-exceptional, gifted, and students with unfinished learning might struggle … and how best to help them. What an amazing week it’s been.
I’ve saved the toughest and most controversial topic for last - Direct / Explicit Instruction. In the professional development sessions supporting the implementation of the curriculum, direct / explicit instruction is not only downplayed but shown as an inferior route to mastery of maths concepts. When I pushed back to say that IEPs often require direct / explicit instruction of new topics and/or vocabulary, the hosts quickly dismissed my concerns as trivial or irrelevant. Surely all these kids require is a bit of a nudge, right?
What is Productive Struggle?
Productive struggle was first introduced in a chapter by Hiebert and Grouws from the 2007 Handbook of Research on Math Teaching and Learning, where they discussed the notion of struggle as useful effort towards solving a problem, not needless frustration. It is an instructional approach that allows students to grapple with mathematical concepts and persist through challenges before providing scaffolds and supports. This technique is rooted in social constructivist learning theory, which emphasizes actively building understanding rather than passively receiving it. The influential work of Piaget highlighted that cognitive growth occurs when learners encounter disequilibrating situations that disrupt their existing schemas and force construction of new, more adequate schemas.
Similarly, Vygotsky’s Zone of Proximal Development described the ideal level of task difficulty as just beyond students’ current solo abilities but achievable with support. Productive Struggle purposely elicits this beneficial cognitive dissonance. Students must wrestle with perplexing problems in order to reconcile the disconnect between previous knowledge and new ideas. This is said to consolidate learning at a profound level.
Many math curricula adopt a Productive Struggle approach because it is thought to allow students to reason, persevere, collaborate, and experience authentic mathematical behaviours. However, teachers must still monitor students’ frustration levels and provide assistance when appropriate. The goal is a developmentally optimized balance of productive challenge versus detrimental floundering. With careful implementation, and the “right” student population, Productive Struggle can spark tenacity, creativity, and deep understanding - the foundations of math proficiency.
Why not productively struggle?
Students who benefit from direct, explicit instruction per their IEP may have difficulty with a primarily student-driven discovery approach. Without clear explanations and modeling from teachers, the ambiguous nature of Productive Struggle activities may cause confusion and frustration. These students thrive when teachers transparently introduce new concepts and vocabulary, think aloud, scaffold each step, offer examples, and check frequently for understanding.
Additionally, gestalt language processors (GLP) grasp information most easily when concepts are presented visually rather than through dense verbal explanations. Without visual aids, manipulatives, diagrams, and other graphic supports to make sense of new ideas, unguided Productive Struggle may overwhelm gestalt learners. These students (like me) require focused, orderly input of new material to form complete pictures of learning objectives.
Lastly, students with or at risk for emotional and behavioural disorders (ED / EBD) may become easily aggravated by the intense cognitive dissonance of Productive Struggle lessons. The inherent challenge and initial ambiguity can heighten anxiety, erode self-confidence, and escalate negative reactions. These students benefit from direct behaviour coaching and a high degree of academic and emotional scaffolding to remain regulated (thus my love of the Self-Regulation Strategy Development methodology). Too much disconnect without adequate support risks disengagement or poor behaviour.
Whilst potentially very useful for many, Productive Struggle requires thoughtful adaptations to ensure equity and inclusion for all. Teachers must carefully monitor student frustration, provide cognitive graphic tools, teach coping strategies, and know when to offer more explicit guidance. The level of struggle must be individually calibrated to stimulate, not discourage.
The IEP is a legally binding contract between the school and the parents
It is imperative to remember that an Individualized Education Program (IEP) is a legally binding document under federal law. An IEP outlines the individual supports, services, and accommodations necessary for a student with disabilities to access a free and appropriate education (FAPE). This includes accommodations like direct / explicit instruction and/or pre-teaching essential vocabulary.
These are not mere suggestions, but rather binding requirements schools and teachers must fulfill. Failure to consistently implement IEP accommodations constitutes a denial of a free, appropriate public education for students with disabilities. This is a violation of their rights under the Individuals with Disabilities Education Act (IDEA).
Therefore, teachers and administrators have a legal duty to provide ALL IEP services with fidelity. Overlooking or disregarding legally mandated accommodations can make a school district vulnerable to state complaints, Office of Civil Rights investigations, and due process lawsuits. The consequences for noncompliance can be substantial and may include monetary judgments, mandated corrective actions, and reimbursement of parents’ legal fees.
Thus, the accommodations written in a student’s IEP are non-negotiable. Whilst Productive Struggle has merits, it cannot override individual disability rights. Educators should thoughtfully adapt techniques like Productive Struggle to align with each student's IEP and avoid discriminatory exclusion or violations that would rightfully prompt legal action by families. Remember, an IEP is a binding contract to be followed, not optional suggestions.
What direct / explicit instruction can look like in our lesson
First of all, here are a few ways students with IEPs who have accommodations for direct/explicit instruction and pre-teaching of new vocabulary may struggle with this lesson:
The lesson jumps right into sample student responses and an activity without clearly stating the learning goals upfront. Students who benefit from direct instruction may have difficulty following along without clear learning objectives provided at the start.
There are several new mathematical terms introduced such as “slope ratio,” “flared sides,” “ADA guidelines,” etc. without explicit pre-teaching. Students who need vocabulary pre-taught may not understand these key terms.
The lesson moves through multiple activities and routines like MLR8, aspects of mathematical modeling, draw it etc. without explaining what these routines are. Students requiring explicit instruction may get lost switching between different structures.
The synthesis asks students to make connections between angles, ratios, and similarity but these connections are not explicitly taught. Students needing more direct guidance may struggle to make those conceptual leaps independently.
Remember, GLPs often fall under the SLD eligibility for special education services. I’ve yet to see an SLD IEP that does not call for direct / explicit instruction and pre-teaching of new vocabulary. Here are some ways GLPs may struggle:
There are several multi-step verbal instructions provided without accompanying visuals/models. Gestalt processors may have difficulty following complex verbal descriptions.
The lesson emphasizes verbal discussion, sharing, and explanation without a focus on visual/symbolic representations. GLPs often benefit from visual aids and manipulatives.
The language used includes some complex vocabulary and sentences. GLPs may get overwhelmed by dense verbal information.
The cool-down exercise relies heavily on verbal reasoning without visual support. GLPs may struggle to work through this independently.
Providing visual models, manipulatives, graphic organizers, explicit teaching of key concepts/vocabulary, and opportunities to process concepts visually before verbally could help address some of these challenges. Checking in frequently with struggling students is also important.
Why pre-teaching new vocabulary is essential for GLPs
Gestalt language processors, like me, comprehend best when we can form a complete mental / visual representation or picture of new concepts. We struggle to extract meaning from individual abstract words presented serially without context. For example, hearing terms like “slope,” '“ratio,” and “flared sides” without visual models would provide little meaning. However, pre-teaching key words using images, diagrams, graphic organizers, and real-world examples allows gestalt learners to integrate new terms into an existing knowledge framework, and into the theatre of our minds.
Seeing a ramp diagram labeled with “vertical rise” and “horizontal run” begins to build an understanding of slope. Looking at proportional triangles helps conceptualize “ratios.” Watching a video clip of a wheelchair maneuvering “flared sides” makes the words tangible. Providing these embodied visualizations ahead of time equips GLPs with the mental pictures necessary to grasp new language and content within the geometry lesson.
Rather than relying solely on verbal definitions, GLPs benefit tremendously when teachers explicitly link unfamiliar vocabulary to engaging visual representations. This context and imagery make the words memorable. Pre-teaching terms in gestalt-friendly ways transforms confusing labels into meaningful pieces that help complete the learning picture.
What’s good for GLPs is often good for ELLs and EBs
The visual vocabulary strategies that support gestalt processors also provide valuable benefits for English Language Learners (ELLs) and Emerging Bilinguals (EBs).
Like gestalt processors, ELLs and EBs build understanding best when new terms are made comprehensible through multi-modal input. Seeing words illustrated with pictures, diagrams, performances, and graphic organizers builds the mental scaffolding to make connections to prior knowledge. This is especially true when images reflect students' cultural backgrounds and real-world experiences.
Additionally, explicitly linking new vocabulary in English to translations in students' home languages helps cement meaning. Providing bilingual word walls, picture dictionaries, and reference sheets can reinforce retention.
Allowing collaborative activities to pre-teach terms also validates the assets ELLs/EBs bring to learning. Peer-to-peer teaching in students’ dominant languages expands comprehension.
Just as for gestalt learners, pre-teaching vocabulary for ELLs/EBs using visuals and first language connections reduces cognitive load, boosts retention, and makes new words meaningful within a complete concept picture. This equity-based practice ensures all students have the tools to engage with grade-level content.
Bringing it all together - the week in review lesson plan
To get a hint at what RSP teachers like me do every day, here’s a scaffold lesson plan overlay for our geometry lesson.
Minutes 0-5:
Warm-up: Preview key vocabulary terms (e.g. ratio, slope) using bilingual word wall and visual diagrams. ELLs/gestalt processors benefit.
Minutes 5-10:
Explicitly explain new concepts and math thinking routines students will experience. IEP accommodations for direct instruction.
Show exemplar ramp design and model process step-by-step. Support for gestalt processors.
Minutes 10-15:
Small group work: Provide adapted materials (larger print, pictures) for ELLs/IEPs. Partner students. Teacher / RSP circulate and check for understanding.
Minutes 15-20:
Provide manipulatives and calculators for hands-on support. Benefits ELLs, IEPs, gestalt learners.
Build in stretch break and sensory tools to help focus. Helps IEPs.
Minutes 20-30:
Monitor student frustration levels closely during Productive Struggle. Provide direct guidance to IEP/behavioural students if needed.
Minutes 30-40:
Allow students to present ramp designs in varied modes (oral, drawing, demo). Choices for gestalt/ELLs/IEPs.
Provide sentence frames to facilitate discussion for ELLs/IEPs.
Minutes 40-50:
Make explicit connections between old and new concepts. Give graphic organizers. Assists IEPs/gestalt/ELLs.
Minutes 50-55:
Provide oral instructions and visual models for cool-down. Read aloud problems for ELLs/IEPs. Allow oral responses.
The key here is layering in multiple research-based supports to reduce barriers and provide access to all learners. Adjustments can be made to further tailor to individual needs.
What about our twice-exceptional (2e) and gifted students?
This lesson on designing and analyzing ramps lends itself well to allowing gifted students to take leadership roles and guide peers. For example, advanced spatial thinkers could be asked to create building templates or model ramps for groups to reference. Students with strengths in mathematical reasoning could circulate to help explain concepts like ratios and angle measurements. Talented artists and designers could put their skills to use visualizing creative, aesthetically pleasing ramps. And gifted communicators could be trained as peer tutors to provide vocabulary assistance and explain problem-solving approaches.
Empowering these students as “math coaches” boosts their self-confidence and makes them invested in the learning process. Meanwhile, their classmates benefit from helpful explanations and models provided by trusted peers. The wisdom of leveraging these exceptional capacities instead of having gifted students work in isolation is twofold - harnessing their abilities enhances engagement for them while simultaneously advancing understanding for others. With thoughtful facilitation and training, 2e and gifted students can be invaluable collaborative partners in unlocking success for all.
Equity Grading and Instruction
It should be noted that the geometry class in which I’m a co-teacher features the Equity Grading and Instruction (EGI) model (formerly called Mastery Grading). The detailed lesson plan and leveraging of peer supports noted above align well with key principles of mastery grading and the equity grading model in several ways:
The plan provides scaffolded instruction, differentiated supports, and multiple modes of representation to ensure all students can access the geometry concepts. This enables genuine mastery-based grading grounded in equitable opportunity.
The peer tutoring roles allow 2e students to showcase and extend their knowledge whilst assisting struggling learners in reaching mastery goals. This embodies the spirit of equity grading where all contributors become partners in learning.
Checking frequently for understanding and explicitly connecting old and new learning promotes mastery by ensuring students have strong foundations before moving forward. Misconceptions get addressed in real-time.
Presenting concepts concretely, allowing manipulatives, and giving oral assessment options help remove non-essential obstacles to demonstrating mathematical understanding. This allows grades to better reflect mastery of essential skills.
Accommodations aligned to IEPs/504s ensure disabled students can exhibit their full capacities. This prevents grades from being clouded by unrelated barriers.
In short, intentionally designing an accessible, supportive lesson makes mastery and meaning-making possible for all. And tapping students’ diverse abilities to collaborate toward understanding improves outcomes and enthusiasm. The thoughtfully inclusive nature of the plan (I don’t mind telling you) promotes mastery-based grading’s aim of maximizing each learner's inherent potential.
Conclusion
I sincerely hope that you’ve enjoyed this week’s articles as much as I’ve enjoyed writing them. They’re both an artifact of my frustration - my being an autistic gestalt language processor (aka, non-verbal) educator working within a system that is not only not designed with me in mind but doesn’t even believe that people like me exist - and my desire to help things go right for my colleagues and you, dear reader.
This series also hints at my other passion project. The work this week closely mirrors Chapter 5 of my upcoming book, Holistic Language Instruction (out next year). There, I deal with cross-curricular issues in language instruction … or how maths, science, arts, and so on can support students on their language learning journey. Here, this week, we expanded upon what it might look like to fully support students in a rigorous, standards-based geometry lesson.
Thank you for joining me on this journey. If you’ve found any value in what you’ve read, I encourage you to support my work by becoming a paid subscriber.