In her book, Feedback: The Hinge That Joins Teaching and Learning, Jane E. Pollock makes the claim that feedback is one of the most powerful tools an educator has in the classroom. Her book is certainly worth a read and I will likely reference it often on this blog but I want to reexamine when and how I use feedback in the math classroom.
Discovery One of my favorite discovery lessons I teach involves having the students discover the formulas for the areas of rectangles, triangles, parallelograms and trapezoids. In a very real way, students have an opportunity to be an Archimedes or Pythagoras and develop the formula for the areas of these figures. This is no hyperbole. Feedback in this type of lesson should involve consistently asking students to "tell me more." Answers, or even hinting questions, destroy a once in a lifetime discovery. Students only have a chance to discover this once. After that, they're just reciting or memorizing a skill someone else already figured out.
DOK 1 and 2 Typical math lessons involve an opportunity for students to practice a skill on their own. These practice questions would typically fall in the DOK 1 and 2 types of questions and for this, a different approach is required. In my classroom, I provide students with an answer key to 100% of the questions in their practice book. No practice has more radically shaped my math classroom providing my students with an answer key. Now, students have the tool they need to instantly find out if they are on the right or wrong track. My students self monitor, their progress and seek additional feedback if necessary from their math notebook (self feedback), from their peers (peer feedback) or even from me. I cringe reflecting on the time when my students would work for 20 minutes on practice questions only to find out they were on the wrong track the entire time. This should not happen. On a side note, this is one of the reasons I am a firm believer in programs like Khan Academy. This is what computers are great at! Students can receive feedback on whether their answer is right or wrong instantly and can proceed forward on the correct path. For me see my post on the Case for Khan.
DOK 3 and 4 Practice questions are great for refining and mastering a specific tool or skill, but the heart of math is in application. For these types of questions, a different feedback approach is required. Recently my students worked to catch cars speeding and fine them based on a drone footage clip I had captured the weekend before. As one of my groups worked through their calculations, I would stop and ask them to explain what was going on in one area of their calculations. This is similar to the type of feedback I would give in a discovery lesson ("tell me more"). After one student explained their thinking, I realized there was a fundamental misunderstanding of how to convert the units in their ratio. I shared that their thinking here was incorrect and proceeded to give a similar example with a different values. I then had the group explain my thinking then go back and correct their work. The feedback I provided here was a combination of the first two types of feedback I shared earlier. I first encouraged the group to explain to me their thinking (in the hope they would discover the mistake themselves.) Had they caught the mistake, I would have known it was more of a careless mistake instead of a gap in their understanding. When I realized it was the latter, I shared with them their answer was incorrect and provided a short mini-lesson on converting units in ratios. I then had the students explain to me my thinking and could have provided additional feedback if it was required.
We spend a majority of our day giving feedback. It's worth evaluating the types of feedback we provide students, when to provide feedback to students, and how to build in other sources of feedback like self and peer. Want to know more about how and why I give my students 100% of the answers during practice time? Email or comment below and I would love to follow up.
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When you hear the name Khan Academy, most remember a collection of YouTube videos on how to do everything from arithmetic to solving for z. Today, however, Khan Academy has become so much more. Khan Academy now provides students and teachers with:
In my 6th grade classroom, each student has a unique account that is a part of my Khan classroom. Students can select skills that I have recommended based on what we are currently studying, review skills that we have previously learned, or try their hand at skills we haven't yet started. Using my teacher account, I am able to see exactly what students are working on, what their excelling at, and what they are struggling with. Best yet, students can see a percent on their dashboard that shows them exactly what percent of the 6th grade curriculum they have masted and what skills they still need to work at. Not sold yet? I'm glad you brought up the price because Khan Academy is 100% free and, according to Sal Khan (the founder) it always will be. I've provided several links below on how to set up your own account. The videos are specific to 6th grade at Penn Manor but many of the steps are the same no matter your school. I've also provided several images for you to see what both the teacher and student would see when they are logged in to Khan Academy. While this may sound like a paid endorsement, know that it is only because I believe firmly that every student in America should have access to either Khan Academy or another digital program for mathematics. Programs like Khan Academy provide students an opportunity to try, fail, and try again until they can demonstrate a skill with success. Students receive instant feedback on the mistakes they are making so they can continue working at it until they have reached mastery. Sal Khan, the founder of Khan Academy and whose voice you remember you hear in most of the tutorials, spoke at a TED conference in 2016 where he made the case of teaching to mastery--not test scores. While most teachers would agree with the premise, most view it as a pipe-dream to believe we can teach a class to 100% mastery. Khan Academy empowers students to take control of their own learning and know that through hardwork and perseverence, they can demonstrate 100% mastery of every skill they need in every K-12 grade. If you have any questions or need assistance in any way in setting up Khan Academy for your students, do not hesistate to send me an email and I will work to help you empower your students through Khan.
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