16

Here's a silly example: Give students collections of the same type of thing, where each collection contains "good" objects and "bad" objects -- for example, a stack of Pokemon cards with both rare and common cards. We might assume common cards are worth $1$ and rare cards are worth $5$. Have ready another stack of cards that are all common -- call this the "...


13

I found out about the Prisoners' Dilemma as a kid from a book about the Harry Potter phenomenon, which had a chapter about the problem, but presented as a story about Harry and Draco being accused of breaking school rules. Each was offered the same deal as in the original problem, formulated with House Points being taken away instead of a prison sentence. ...


10

Since no one's posted an answer I will get things started with some general advice. Calculus 3 is my favorite course to teach, but it can be a bear to wrestle with the first few times. Some more specific information about your situation would be helpful (are you at Community College? Ivy League? Are the students Engineers? Math Majors? Is the class 20 ...


8

I like Nick C's idea more than modifying the typical formulation. The notion of snitching on a friend, regardless of the severity of the "crime", has real-world ramifications beyond the punishment put out by the authorities. Depending on your student population, that is possibly going to spur a conversation that will overshadow the objectives of your ...


7

You may find the SageMath knot and links capabilities useful for computation and visualization. The Knot Atlas might be a bit more comprehensive than you are looking for but is certainly a reference to be quite aware of.


6

I've heard very good reviews of the 2017 book, "An Illustrated Theory of Numbers" by MH Weissman. The book's main site is here; a write-up, along with some reviews, by the American Mathematical Society can be found here. To quote from the latter (emphasis added by me): An Illustrated Theory of Numbers gives a comprehensive introduction to number ...


5

The Open Syllabus Project presents a large amount of data about books listed on syllabuses of courses taught around the world (especially in the USA and not only about math/science). I think that it is not possible to ensure that the presented textbooks are indeed the most adopted (or bought or sold or used or read). However, they probably are (at least) ...


5

Euclid the game is a set of challenges built in Geogebra. It allows the student to progress through the elements gaining additional tools as they go or solve each using only straight edge and compasses. It is accessible and enjoyable. I have used it with students from the age of 12. I don't know whether you were looking for something more formal.


5

I don't know much about knot theory but I know that Meike Akveld taught knot theory at both high school and university level. Here's a bibliography of one of her courses at ETH Zürich: https://www2.math.ethz.ch/education/bachelor/lectures/fs2015/math/knot/bibliography_FS2015.pdf It includes Englisch and German books both for high school and university ...


5

The folks at Art of Problem Solving have what you need. It's not cheap ($559), but they work with many students like you, and are highly recommended. I think you will find it worth what it costs, if you can afford that. (And if not, ask them for a scholarship. I don't know if they'd do it or not...)


5

This won't help the OP for the summer of 2017, but let me put this here for future readers of this site: Michigan Virtual High School is (as I write these words) developing its own online Algebra 2 curriculum. The curriculum, which is expected launch in September 2017, consists of two separate half-courses (Algebra 2A and Algebra 2B) which can be taken ...


4

I personally would prefer a textbook recommendation I can download or pick up that is [preferably] not old and does not make trigonometry intimidating to approach (especially one that emphasizes understanding proofs behind properties/theorems). I don't have textbooks to recommend, but I can recommend an approach to doing trigonometry that facilitates ...


4

Maybe a visual approach could supplement your study? There are many such resources available on the web, not in textbooks. E.g., Trig Intuitively:                     Note: the labels show where each item "goes up to." Another: Interactive Unit Circle. Another: Inverse Trig Functions.


4

Schaum's outlines are very practical in general and cheap. Well suited to an older learner. Often the answers are right after the problems versus at the end. And you get all the answers, not the odd/even gyp. Thus suited to self learning. I like this one, overall and own it: https://www.amazon.com/gp/product/0070026505/ref=...


4

The Florida Virtual School offers high school level classes in all subjects, including Algebra 2, and is very well regarded. They're considered a school district within the Florida school system so I would expect a course from them to be considered acceptable by another public or private high school. If you don't live in Florida, you can still take classes ...


3

(In before the close!) I'd say the PDE course looks more like a traditional course than the prob/stats course. Look at the hours expected, for example (~6.5 versus ~1.5), each times 8 weeks. The PDE course looks like a solid half to two thirds of a semester of a normal, engineering support course. You cover a couple of the 3-4 major equations. And get ...


3

It sounds like you wish to protect your students from the violence and greed of the adult world, while still making the dilemma real enough to keep them engaged. To that effect, I offer two solutions. One, replace prison with detention. Make the crime something like using cell phones in class or throwing spitballs. Two, have them arbitrarily grade each ...


3

A1/ I'm not sure why you would need a companion to Euclid. Euclid is already a textbook and you can progress through it as leisurely as you like... I prefer Sir Thomas Heath's version. But the two most popular works back in the 19th century (when Euclid teaching was at its height in the UK) were Todhunter's The Elements of Euclid for Schools and Colleges ...


3

I think the OP asks a difficult question that will not have a succinct answer. Permit me to point to one publication, Schoenfeld, Alan H., ed. Assessing Mathematical Proficiency. Mathematical Sciences Research Institute Publications. 53. Cambridge University Press, 2007. (PDF download of book.) which addresses the question of what constitutes mathematical ...


2

Short answer: (migrated from comments by request) Hung-Hsi Wu (Berkeley) has a home page full of links to writings of this ilk. Two specific examples that may fit the bill are ones I mentioned back in MESE 1857 (April 2014); in particular, links to a text on Pre-Algebra (pdf) and an Intro to School Algebra (pdf). Further comments: Some of H.H. Wu's ...


2

As a software engineer, the book "concrete mathematics" by Graham, Knuth and Patashnik is a must. Chapter 4 is on number theory.


2

Perhaps: You and another classmate are together in an obstacle course. If you both make it to the end within a minute, you each get a free day off from school. If just one of you makes it to the end in a minute, they get a whole week off. You know that if you had the other student's help, you could easily finish in a minute, but without it, you won't finish ...


2

Use of performance-enhancing drugs in sports is a good example. However, why the objection to money and capitalism? Real-life actors value money very much and it affects their behavior greatly. A very realistic and applicable example involving money is what happens when a group of friends goes dining, depending on whether each friend pays for themselves or ...


2

My suggestion would be to look at the existing literature. Blake, Rand, Tingley, and Warneken (2015) "introduce a novel implementation of the repeated Prisoner's Dilemma (PD) designed for children to examine whether repeated interactions can successfully promote cooperation in 10 and 11 year olds." Dealing with younger children (ages 6-11), Fan (2000) ...


2

Your list seems like overkill to me. As far as geometry, Kiselev is basically a rehash of Euclid, so I don't see the point in studying both. Just pick one. I don't think you need the solid geometry parts of either. If using Euclid: -- Euclid contains stuff like number theory done in an ancient style that is now only of historical interest, so if using Euclid,...


2

One of my favorite resources has been the shell center’s mathematics assessment project. They have both lessons and more traditional assessment scenarios, however the rubrics provided focus on ways to give formative feedback rather than a strictly point based approach. https://www.map.mathshell.org/


1

The Art of Problem Solving has plenty of problems involving pre-calculus tools, some of them quite challenging. However, the best way forward might not be computationally challenging exercises. You said they lack mastery. Please correct me if I'm wrong but I interpret this as they cannot reliably perform said computations and use said pre-calculus tools ...


1

Perhaps the problems of "make up" and "traffic" could also be used. Make-up: Assuming that the chemicals etc., damage your skin in the long run, we may state that constant make-up is "bad". And contrarily no make-up is better in the long run since your skin remains "naturally beautiful". Given any two individuals with the option of applying make-up or ...


1

The field of mathematics does not have a central regulatory board, like many computing platforms do (e.g., the IETF RFC's). Definitions of terms become standardized only through common use and consensus -- it is very common for different textbooks, papers, etc. to define the same term differently. There is no site for "official" definitions. One example of ...


1

Here is a book that should fit the bill: Camp Logic, by Mark Saul and Sian Zelbo. [Disclaimer: This comes from my publisher. I am guessing that it's good.]


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