## Key Ideas > [!abstract] Core Concepts > > - **Push for excellence**: Don't accept partially correct answers (require complete, precise responses) > - **Student does the work**: Avoid filling in gaps yourself; make students develop complete understanding > - **Build mathematical vocabulary**: Require precise terminology rather than informal language ## Definition **Don't Round Up**: The practice of pushing for complete, accurate responses rather than accepting partial answers and filling in gaps yourself, ensuring students develop genuine understanding and precise communication. ## Overview Teachers may be tempted to "round up" partial student responses by accepting approximate language or completing students' incomplete reasoning to maintain lesson momentum. This practice can create situations where the teacher performs the critical thinking whilst the student contributes fragments, creating an illusion of understanding. "Don't Round Up" describes strategies to resist this tendency, encouraging students to develop precise mathematical language, complete reasoning processes, and genuine understanding. When teachers consistently require complete responses, students learn to monitor their own thinking and develop precision in mathematical communication. ## Connected To [[Check For Understanding]] | [[Culture of Error]] | [[No Opt-Out]] | [[Cold-Call]] | [[Wait Time]] | [[Responsive Teaching]] --- ## What does "rounding up" look like? Rounding up occurs when teachers accept imprecise language and translate it into mathematical terminology themselves. When a student says "you cancel them", the teacher might respond "yes, we divide both numerator and denominator by the common factor", losing the opportunity for the student to develop precise mathematical language. Similarly, "it goes down" becomes "right, the gradient is negative", and "you flip it" becomes "exactly, we find the reciprocal". In each case, technical vocabulary remains the teacher's responsibility rather than the student's. A subtler version involves the teacher doing the thinking. A teacher might ask "what's the first step in solving this ratio problem?" and accept "find the total" as sufficient, then immediately add "so we add 3 + 2 to get 5. What is 3 plus 2?" The student responds "five" and the teacher continues "exactly! Okay, so what do I do next?" Here the teacher provides all critical insights whilst the student contributes only minimal computation. ## Why teachers round up Teachers round up for understandable reasons. Filling gaps yourself saves time in the moment, keeps the lesson flowing, and feels supportive. Students appear successful and avoid frustration. However, these short-term benefits create long-term problems. Students do not develop independence, develop a false sense of understanding, and miss opportunities for productive thinking. The costs extend beyond individual interactions. Students think they understand when they do not, become dependent on teacher support, fail to develop precise mathematical language, and miss opportunities to recognise their own gaps. Teachers receive false data about student understanding, need to re-teach concepts repeatedly, see standards gradually decline, and watch students fail to develop independent thinking. ## Strategies to resist rounding up Resisting the urge to round up requires deliberate strategies that maintain high standards whilst keeping students engaged and supported. Teachers can build mathematical vocabulary systematically by requiring students to develop precise terminology rather than accepting informal language. When a student says "you flip the fraction and times it", the teacher can ask "what's the mathematical term for 'flip'?" and continue prompting until the student produces "you find the reciprocal of the second fraction and multiply". Follow-up questions like "what's the proper term for 'cancelling'?" or "can you be more precise with your language?" push students toward accuracy. Teachers should address incomplete responses by identifying imperfections: informal language ("cancel" instead of "divide"), problematic methods that sometimes fail, unclear answers with ambiguous terminology, and half-finished responses missing units or reasoning. Response strategies include upgrading language by pushing for mathematical terminology, completing the method by asking students to walk through all steps, adding precision by asking "what exactly do you mean by...", and including context by questioning vague quantities like "five what?" When students genuinely cannot provide more, teachers have several options. They can check what students do know ("what do you understand about ratios?") to build from existing knowledge, use no opt-out techniques ("listen to me explain, then repeat it back") to ensure engagement, sample the class ("I'll ask three others, then come back to you") to gather more information, or provide a frame ("I'm going to explain this, then ask you a related question") to scaffold appropriately. ## Balancing high standards with support Michael Pershan's principle captures the balance: end every conversation with the student saying something smart. This approach pushes for excellence whilst maintaining supportive relationships, making students feel genuinely capable rather than artificially praised. Teachers balance high expectations with high support to create genuine understanding rather than false confidence. Scripts help maintain this balance. For incomplete answers, "that's a good start, let's make it even better" encourages whilst pushing. For informal language, "you've got the right idea, now let's use the mathematical term" builds vocabulary. For partial understanding, "you're thinking well, can you take it further?" extends thinking. For wrong approaches, "I can see your thinking, let's refine the method" provides supportive correction. ## Integration with other strategies "Don't Round Up" combines with other teaching strategies to create a classroom culture of precision and genuine understanding. With culture of error, teachers must maintain high standards whilst keeping the environment safe for mistakes. The message becomes: mistakes are valuable learning opportunities and we will work together to reach excellence, but being wrong is safe whilst being sloppy is not acceptable. No opt-out provides complementary support. No opt-out ensures participation whilst don't round up ensures quality participation. Both maintain high expectations with high support. Cold-call techniques enhance questioning. Teachers use cold call to get initial responses, use don't round up to push for complete understanding, then follow up with additional cold calls to check listening. Wait time enables patient excellence. Teachers give students time to improve their responses, resist rushing to fill gaps with explanations, and allow processing time for complete thoughts. ## Common challenges Teachers face several obstacles when implementing this approach. The time concern is legitimate: avoiding rounding up initially takes longer. However, long-term benefits include less re-teaching, students developing independence, higher quality thinking becoming habitual, and standards remaining high across all interactions. Student frustration can be managed by framing the work as "improving together", celebrating incremental progress, using encouraging language like "let's make this even better", and maintaining a supportive tone whilst pushing for excellence. When other students switch off, teachers can include checking for listening throughout interactions, keep exchanges moving with clear prompts, engage multiple students in building complete responses, and use "relay" explanations between students. When a student genuinely does not know more, teachers should use no opt-out techniques first, sample other students then return, teach explicitly then ask the student to repeat back, or provide a scaffold then require application. ## References Black, P., & Wiliam, D. (1998). Assessment and classroom learning. *Assessment in Education: Principles, Policy & Practice*, 5(1), 7-74. https://doi.org/10.1080/0969595980050102 Lemov, D. (2015). *Teach like a champion 2.0: 62 techniques that put students on the path to college*. Jossey-Bass. Rosenshine, B. (2012). Principles of instruction: Research-based strategies that all teachers should know. *American Educator*, 36(1), 12-19, 39. Rowe, M. B. (1986). Wait time: Slowing down may be a way of speeding up! *Journal of Teacher Education*, 37(1), 43-50. https://doi.org/10.1177/002248718603700110 Wilson, K., Raven, M., & Loaiza, V. (2019). *Active student responding: The big 5 instructional practices that promote student success*. SafeSchools. ---