Geometry Class Rules And Procedures: Fill & Download for Free

Thoughtfully and respectfully, with lucid attention to what you are trying to reinforce.I don't agree that operant conditioning has no place in K-12 education or homeschooling. I'd contend that regardless of whether you believe it should happen, it happens on a level that parents and teachers may not be conscious of, because there often are unconsidered adult behaviors that reward or punish the children's behavior (whether the adult intends it or not).There are two levels on which I see this applying to my class:Classroom management, in the form of establishing procedures and setting the toneAcademic behaviorsClassroom management is all about organizing the class environment, time, and activities to maximize learning and growth. Part of this is establishing a safe and respectful environment with open communication channels, and some procedures play into that. From my class, some examples are:When you (the student) see me standing silently by the board, it means I'm ready to speak to the whole class and am waiting for attention; I want you to face front and listen quietly.When you are checking homework in class, you read through your answers with a partner and circle any problems on which you and your partner disagree or aren't 100% sure of the right answer.During work time, you work on something that is useful to your math learning (which may be an assigned task; if it's not appropriate for a student I offer other options), until the end of class. Packing up early is not OK.By "academic behaviors", I mean (roughly) student behaviors that will help them solve problems, learn the content, and get work done. In my math classes, some examples are:Making diagrams and labeling parts clearlyAsking the meaning of unknown words and phrasesIdentifying known facts and desired goalsTrying examples (like specific numbers or shapes) to get a feel for a problemThese may seem like little details, or things you take for granted in your work, but they must be learned; many students do not default to these behaviors. Importantly, at the level I'm teaching -- high school geometry -- nearly everyone can do them; they aren't a challenge, and require no creative insight, leaps of faith, or magical thinking. (And, for a student who has difficulties with them, I'm prepared to break them down into smaller constituent behaviors that the student can definitely handle.)So, given the set of behaviors I'm working with, how does conditioning apply?Positive reinforcement -- reinforcing a behavior by reward -- is my main tool, and most often is verbal. Most people want to help others, so this is sometimes as simple as:"Thank you for your attention.""I'm glad you asked that question! I saw from everyone's papers that lot of your classmates have the same question, so thanks for making sure we cover it.""Thanks" is the key word here. See, it doesn't even have to be praise to be positive reinforcement; I can reserve serious praise for when it's truly warranted. For a lot of us, thanks and acknowledgement go a long way.Negative reinforcement -- reinforcing a behavior by removing an aversive stimulus -- is a bit subtler and less obvious. In math class, I can think of two kinds of aversive stimulus:Uncertainty and perplexity about a problem for which the students really want to know the answer. This is frustrating, and solving the problem is its own reward! Yet this is where our math books suck! They take potentially fascinating problems, and rework them into a form that has no suspense and no drama, and is totally patronizing to our students. I won't rant further here; check out Dan Meyer's writing on "Three-Act Math" at http://blog.mrmeyer.com if you want to hear more. The point is that good problems (at the right difficulty) engage and tantalize us, and we get immense satisfaction and relief from solving them.Boredom with repetition. When a student has learned a technique thoroughly, it's no longer interesting. When they express frustration that a technique is boring, they're primed and ready for learning a more powerful technique that can do away with the repetition. For example, think about rectangle area. We first learn this by counting squares in a rectangle on graph paper. Eventually that's boring and slow, and we are relieved to notice that we can just multiply width and height. That's what I call productive laziness. Kids love to learn to be lazy in the right way, and work smarter.Here, the key ideas are relief and satisfaction, and the key word is "Congratulations!" You did X, and got Y to happen! You've solved a frustrating problem, or found a way to avoid doing needless boring work! I'm just highlighting the consequences of the student's actions now, and explicitly connecting it to the academic behaviors I observe, to be sure it's not lost on the students.It is challenging to engineer situations where the right mix of perplexity and attain ability occur. But boy, does it pay off in motivation.Positive punishment of actions -- a negative stimulus as a consequence of student behavior -- I use very sparingly, and always in conjunction with instructions of what I do expect. I don't think I ever do this regarding academic behaviors. Regarding class rules and procedures, once we've established a positive relationship -- and I do a lot of work towards that, early on -- it's usually sufficient for the kids to know that I'm not happy and I don't approve. Example:A student starts sharpening a pencil while a classmate is speaking. [Disapproving tone:] "Josh, we can't hear Lisa. Would you please wait until she's done talking." (I use the polite wording, but clearly end that sentence with a period and not a question mark.)If I needed to escalate a situation to the level of involving the school's discipline process, I would, but that's only happened maybe twice in the past eight years, and only for things way more out of line than the procedural stuff I'm talking about.Negative punishment -- withholding a desired result as a consequence of student behavior -- I can think of only one example of this, and that is this rule:If you pack up early while everybody is still working, you leave after everyone else leaves.Even in these circumstances, everything has got to be grounded in mutual respect.It had been a long time since I last tried articulating my thoughts on this subject. Thanks for asking the question! I hope the answer is as useful to you as the time to reflect on my practices has been for me. It took me a long time to learn to manage a classroom well.

Speaking as an aspiring mathematician, on a more ideological level, mathematics is not taught how a mathematician would do it. Mathematics is presented in a very dull and boring manner. The purpose of mathematics is not to simply solve problems, but understand them. Something which our education system does not seem to value.This isn't helped by a culture which assumes that it's okay to be bad at math. People say it almost pridefully! Imagine if people said with pride “oh yeah I SUCK at reading!” — somehow it's okay to say this for mathematics.Mathematics is truly about logic and creativity. The current public school system has taken it upon themselves to remove both components from a math education. Most students never get to see the beauty of simple geometry, or the amazing symmetries that elementary group theory models so well.Instead, students are left to solving polynomials, with no clue why they are doing it, and no clue why the method they have been taught works. They are not taught abstraction and reasoning skills. The concept of a proof does not exist. Yet since proofs are central to mathematics, what then are they learning? Equation solving. The mathematical education of the US is equation solving. There's not much else but a brief and disconnected stint in geometry, which entirely never fails to disappoint the student, as it becomes the subject of proving obscure results whose significance is never understood.As the mathematician Edward Frenkel says,“What if at school you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it...Of course this sounds ridiculous, but this is how math is taught.”How truly sad our mathematics education is! Our mathematical education “becomes the mental equivalent of watching paint dry.”One mathematician, Paul Lockhart, has given a very detailed criticism of the mathematical education system in the US in a document titled “A Mathematician's Lament” which can be found athttps://www.google.com/url?sa=t&source=web&rct=j&url=https://www.maa.org/external_archive/devlin/LockhartsLament.pdf&ved=2ahUKEwjfqoik59TbAhWpuVkKHeRPD1UQFjAOegQIABAB&usg=AOvVaw1-8EksPe3CjESJf4g-GoVETowards the end, he gives a paraphrase of the US math education. I will include it here, as it is quite clear:“LOWER SCHOOL MATH. The indoctrination begins. Students learn that mathematics is not something you do, but something that is done to you. Emphasis is placed on sitting still, filling out worksheets, and following directions. Children are expected to master a complex set of algorithms for manipulating Hindi symbols, unrelated to any real desire or curiosity on their part, and regarded only a few centuries ago as too difficult for the average adult. Multiplication tables are stressed, as are parents, teachers, and the kids themselves.MIDDLE SCHOOL MATH. Students are taught to view mathematics as a set of procedures, akin to religious rites, which are eternal and set in stone. The holy tablets, or “Math Books,” are handed out, and the students learn to address the church elders as “they” (as in “What do they want here? Do they want me to divide?”) Contrived and artificial “word problems” will be introduced in order to make the mindless drudgery of arithmetic seem enjoyable by comparison. Students will be tested on a wide array of unnecessary technical terms, such as ‘whole number’ and ‘proper fraction,’ without the slightest rationale for making such distinctions. Excellent preparation for Algebra I.ALGEBRA I. So as not to waste valuable time thinking about numbers and their patterns, this course instead focuses on symbols and rules for their manipulation. The smooth narrative thread that leads from ancient Mesopotamian tablet problems to the high art of the Renaissance algebraists is discarded in favor of a disturbingly fractured, post-modern retelling with no characters, plot, or theme. The insistence that all numbers and expressions be put into various standard forms will provide additional confusion as to the meaning of identity and equality. Students must also memorize the quadratic formula for some reason.GEOMETRY. Isolated from the rest of the curriculum, this course will raise the hopes of students who wish to engage in meaningful mathematical activity, and then dash them. Clumsy and distracting notation will be introduced, and no pains will be spared to make the simple seem complicated. This goal of this course is to eradicate any last remaining vestiges of natural mathematical intuition, in preparation for Algebra II.ALGEBRA II. The subject of this course is the unmotivated and inappropriate use of coordinate geometry. Conic sections are introduced in a coordinate framework so as to avoid the aesthetic simplicity of cones and their sections. Students will learn to rewrite quadratic forms in a variety of standard formats for no reason whatsoever. Exponential and logarithmic functions are also introduced in Algebra II, despite not being algebraic objects, simply because they have to be stuck in somewhere, apparently. The name of the course is chosen to reinforce the ladder mythology. Why Geometry occurs in between Algebra I and its sequel remains a mystery.TRIGONOMETRY. Two weeks of content are stretched to semester length by masturbatory definitional runarounds. Truly interesting and beautiful phenomena, such as the way the sides of a triangle depend on its angles, will be given the same emphasis as irrelevant abbreviations and obsolete notational conventions, in order to prevent students from forming any clear idea as to what the subject is about. Students will learn such mnemonic devices as “SohCahToa” and “All Students Take Calculus” in lieu of developing a natural intuitive feeling for orientation and symmetry. The measurement of triangles will be discussed without mention of the transcendental nature of the trigonometric functions, or the consequent linguistic and philosophical problems inherent in making such measurements. Calculator required, so as to further blur these issues.PRE-CALCULUS. A senseless bouillabaisse of disconnected topics. Mostly a half-baked attempt to introduce late nineteenth-century analytic methods into settings where they are neither necessary nor helpful. Technical definitions of ‘limits’ and ‘continuity’ are presented in order to obscure the intuitively clear notion of smooth change. As the name suggests, this course prepares the student for Calculus, where the final phase in the systematic obfuscation of any natural ideas related to shape and motion will be completed.CALCULUS. This course will explore the mathematics of motion, and the best ways to bury it under a mountain of unnecessary formalism. Despite being an introduction to both the differential and integral calculus, the simple and profound ideas of Newton and Leibniz will be discarded in favor of the more sophisticated function-based approach developed as a response to various analytic crises which do not really apply in this setting, and which will of course not be mentioned. To be taken again in college, verbatim.***And there you have it. A complete prescription for permanently disabling young minds— a proven cure for curiosity. What have they done to mathematics!”… Sigh…***EDIT***To address some of the remarks with regards to the importance of calculus and unimportance of more mathematicians, Lockhart does address this in his paper:“How many students taking literature classes will one day be writers? That is not why we teach literature, nor why students take it. We teach to enlighten everyone, not to train only the future professionals. In any case, the most valuable skill for a scientist or engineer is being able to think creatively and independently. The last thing anyone needs is to be trained.”—“But don’t we need people to learn those useful consequences of math? Don’t we need accountants and carpenters and such?How many people actually use any of this “practical math” they supposedly learn in school? Do you think carpenters are out there using trigonometry? How many adults remember how to divide fractions, or solve a quadratic equation? Obviously the current practical training program isn’t working, and for good reason: it is excruciatingly boring, and nobody ever uses it anyway. So why do people think it’s so important? I don’t see how it’s doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them. It might do some good, though, to show them something beautiful and give them an opportunity to enjoy being creative, flexible, open-minded thinkers— the kind of thing a real mathematical education might provide.”—“But don’t you think that if math class were made more like art class that a lot of kids just wouldn’t learn anything?They’re not learning anything now! Better to not have math classes at all than to do what is currently being done. At least some people might have a chance to discover something beautiful on their own.”

"Make dungeons!" was one recommendation I'd heard millions of years ago (literally: 20 years ago). So far away that resources such as the Interwebz or very digital tools did not exist. So I picked other people's systems, added blocknote paper (you know, with squares on it, the ones we used for Geometry classes), drew a labyrinth, put traps, monsters, damsels in distress, shapechanger baddies disguised as damsels in distress, warrior damsels, loots. Add dice, "Player's Handbook", 3-4 willing sacrifices whom you will "DM"*, and then play it out.Fun?Not quite the first time, unless you have preternatural disposition to be being an awesome storyteller from the get-go.[*DM: Dungeon Master - look it up]Fun later?Quite a lot of it - so much that you'll never be able to "play" anymore, but you'll be "DM'ing" all the time.Once you and your players are having FUN (what games are all about), does this make you a game designer? To some extent, yes. For a tad bit more insight for your question, read here too: How do I plan out a concept for a video game?Other than that, nowadays there are some good schools that can teach you "procedurally" how to become a game designer. I wish we had those in my time too, but look them up. They should also give you the opportunity to use the theoretical skills they teach in application as well. Oh also, learn to use, wait for it, Excel! Numbers & formulas mean a lot to game design. So do charts. Learn them love them, know that match matters and know that making a scoring design is HARD WORK! I mentioned DM'ing: You wanna see numbers in game design, look into pen & paper rpgs.You should also make a conscious observation of games you yourself like: How many if X are there in this game? Why? What does X give me in this game? How does Y work X in this game - why have both? How is a submachine gun different than a revolver in this game? Why? Try to look at everything you play from a critical perspective.Read actual game designers' blogs and articles. Hit up Gamasutra and enjoy the articles written by industry people. (See how much math plays into it!)A game's rules are always somewhat of a puzzle in their intricacies, but they should be very clear - easy to learn hard to master. It's hard work all of this