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My friend, who is currently teaching an abstract algebra course, recently provided me with an example of an incorrect proof that I think showcases a few types of faulty reasoning that are common among students. I'm sharing it here with his permission. Proposition: Suppose $R$ is a ring and $I$ is a prime ideal in $R$. For all ideals $J$ and $K$ in $R$, if $...


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The ultimate for this, which is an entire curriculum, is "The Life of Fred" book series. It is fantastic, and you can get an entire math education, elementary to undergrad, just through Fred books.


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i'd like to recommend Isaac Newton and his Apple and Murderous maths series by Poskitt Kjartan (Author) and Philip Reeve (Illustrator). Such books explained many basic math concepts in lots of jokes. My son really loves it (10 out of 10, same as Roblox and icecream). Prof Richard Evan Schwartz's picture books especially Gallery of the Infinite, which ...


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Mathematics is often thought of as a bunch of clever people doing weird things with symbols for reasons that are difficult to relate to reality. Whilst this is not entirely false, it is for the most part (almost humorously so in my opinion), the antithesis of the actual role of mathematics in today's world. I challenge anyone to seriously tackle the world's ...


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Good list. One of the above comments is true. In the modern classroom, if you wait to get everyone’s attention, you won’t be able to teach anything. That is especially true in today’s math classrooms. Many students are not motivated to learn. Math is objective and cumulative. It is easy to see where someone is on the spectrum of math understanding. However, ...


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OP: "Refuse to teach without attention." In my role as chair, I attended an instructor's class where he really refused to advance until he was certain the students were all with him, via detailed verbal feedback. The students responded, stopped the presentations and asked questions. I've changed my own teaching as a result of watching how this can ...


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Here's a short grab-bag of ideas; things I've found useful. Design the test for gradeability. As the instructor, you have the power (hopefully) to design a test that you look forward to grading. Some of us get locked into legacy traditions from examples we've seen, or things mentors dictated. We don't need to necessarily follow those same habits if they're ...


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They are basic, friendly pieces of pedagogical advice. Most pre-college teaching is very much STILL in this mold. Where we fall down is in high-end universities and graduate schools, where pedagogy is less emphasized in the paradoxical belief that harder material should be learned with worse training methods. Or that smart students don't need/benefit from ...


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Grading may be tedious. But overly long answers can be averted. A student may write a lot, hoping that the mostly irrelevant text will contain whatever the teacher is looking for. But in doing so, the student demonstrates a lack of knowledge – and won't get full credit. No matter what truths are hidden in the sea of irrelevant wrapping. Students write this ...


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I have found that, for myself, implementing standards based grading has eliminated this frustration entirely. I now find grading to be enjoyable. I have a collection of standards for my course like "Evaluate the truth value of an expression such as $(T \Leftrightarrow F) \implies (F \wedge T)$" or "Give a Fitch style proof outline for a ...


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I actually get excited to grade my students exams. I see the test/exams as the whole point of the class: the chance for the student to demonstrate what they know or don't know about certain problems. It's like the chance to get inside of my students head and see "oh, that's what they were thinking." I also feel that grading is a responsibility that ...


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Overall, it can become tedious and even frustrating to grade math homework or exams. Do you share the same frustration, and how do you handle it in the best possible way? Some random ideas I have heard others use: Choose a small subset of proof questions to grade in detail. You're right that proofs can be long to write and difficult to parse for the grader. ...


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I grit my teeth and do it. Skimming long answers for the relevant parts is a skill. One way of handling the frustration is talking about it with someone. If that someone is also grading the same exams or homework, or was/is involved in teaching the course, this can even be genuinely useful. But really, on the scale of frustrations, this is not a big deal. At ...


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