What are /r/matheducation's favorite Products & Services?

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Hi everyone. Arithmagic is a math game I made over the span of two years, and I'm still working on it! I present it here to you all a potential educational resource.

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I built Arithmagic first and foremost as a game that uses math, and not a game that teaches you math. I didn't want the game to be just a calculator on the screen or a set of multiple choice questions, so I tried to design a mechanic that feels fun to play and yet also practices your arithmetic. I believe I have achieved that.

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I'd love to hear everyone's thoughts. If you want to find out more about the game, here are the store links:

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Google Play

App Store

I would strongly recommend either geogebra or desmos. They're both free. I prefer geogebra but Desmos seems to have what you want (for free) with a smaller learning curve.

Believe it or not, integration was developed long before differential calculus. Check out the book infinite powers, by steven strogatz. He talks at length about how these concepts in calculus were initially developed and how the founders thought about them. It might give you some fresh ideas for how to deliver the information.

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You also didn't specify the age of the kid. There's a book called Introductory Calculus for Infants, which I've never read, but I've heard it's surprisingly good.

I have read it and it shapes how I teach. As much as possible, I try to put students in the situation where they have questions to ask instead of just answering my questions. For a very concrete way this is done in a high school class, check out Dan Meyer's TED talk.

I teach at the college level so I don't have the tests to teach to. However, I do need to make sure the students are prepared for future classes. The thing is, you really have to be willing to give up some control of your class. This can be very difficult and scary at the beginning. I think as you get used to it, you realize you never really had control of what they were thinking to begin with!

Brilliant's Logic course is used by many teachers, you can share it for free with your students once you get your free educator account.

Ahh this is a great project, I just finished doing it with my class. If your students have access to technology, using Desmos is going to make things really easy on them. I haven't uploaded the results from my class, but here is a few that I found to show my students: Link 1 and Link 2

The only bad thing I found was that a few students (4 or 5) copied their project straight from a website, so you will have to check for plagiarism!

I'd start discussing it with your colleagues and signal your supervisors. Chances are, this is a structural problem at your school (district?), and in the long run you need a better strategy than a quick local fix, which are a stopgap at best. Of course, that doesn't help you now.

The problem with a lot of quick fixes is that even if the students start to appear to start to "get it", chances are their understanding is superficial and mostly procedural. They might be less of a drain on your instructional means and time, which is better for the other students, but I fear that you're just pushing the problem to the next module's teacher. Still, what else are you to do?

I have no idea, but I can offer some remarks:

• having them catch up with the rest of the students while they continue to learn will be hard on them and you. If possible at all, it would mean they would have to do extra work and, chances are, they aren't the most motivated and don't have the best situation at home to stimulate and support their learning. Furthermore, often such a fundamental lack of understanding does not come alone, and other subjects might be as problematic as well.

• teaching them a separate specialized curriculum to get them somewhat on the way while you continue the original curriculum with the other students will be hard on you and probably problematic to the students that get the alternative curriculum.

• a more computational approach might support them. A (free) CAS tool such as maxima can be a great help for them and you to explore and learn mathematical concepts together.

GeoGebra Tube has a huge number of proofs and interactive demonstrations. Not an app but it runs well on tablets. I haven't tried it on a phone. https://www.geogebra.org/materials/

I found this video (the bit where he's drawing a few things on the board) pretty good fo realising what was going on : http://channel9.msdn.com/Series/Sketchbooktutorial/Trigonometry-for-Designers-Dont-Panic

If you already know LaTeX (or are willing to learn), the TikZ package will make gorgeous pictures...with some effort. Typically when I want to make something in TikZ, I find somebody else's example that's close to what I need and tweak it. But then I only have to do it a couple times a year so I never really learned the syntax well.

Why not use Euclid's Elements? I motivate the study of constructions by thinking about the practical tasks that would have faced an architect or builder in Ancient Greece. Plus, it's good for the students to get a sense of how this truly is ancient knowledge. You can have fun deciphering the sometimes overly detailed proofs and they can see how many of the words they use in geometry originated with this, the foremost mathematical textbook of all time. There are free versions on The net, eg https://www.gutenberg.org/files/21076/21076-pdf.pdf

My kids are finishing up this exact project on Friday! I have a google doc made to organize their links. Later tonight or tomorrow morning I'll strip the document of their names and attach it here!

Here's one for right now: https://www.desmos.com/calculator/oopmnyldkq

Nice job, they look great. I just wanted to let you know that geogebra has a lot of this functionality built in via their commands: https://www.geogebra.org/m/sdsabkjv

Just looking at their respective websites (1 and 2) I would say say there is a pretty obvious response. That TeXmacs have either not spent much project time on branding, or, are determined to brand themselves as intended for the niche of open-source enthusiasts (obviously they may be other reasons, but they probably aren't too far from either of these). I would claim that the branding of Jupiter is more inclusive.

you could try using lyx. Its a program that uses LaTex and allows you to use a much more "Word-like" window.

When you have time/learn more about LaTex, you can view the source code for your document and edit things on that level as well.

I really was happy to have this program on my side when I started writing papers in college. It allowed me to learn LaTex while still producing great looking documents (even though its the content that really matters ;))

The literal answer to your question for the US would be fairly boring: two major textbook series would be Saxon (common among homeschoolers and private schools) and McDougal-Littel (pdf link).

But u/jessamina has already given the best answer you can get. All of AoPS is perfect for what you're talking about. You can also look up MathCounts, the U.S. middle school entry-level competition that eventually leads to the Olympiad level in high school. For even more advanced levels, I love Concrete Mathematics by Donald Knuth.

I haven't read it myself, but some of the other math consultants that I work with have really been enjoying the book. So while I can't personally endorse it, I know consultants who would and already have.

I've been going through Rough Draft Math by Amanda Jansen. I haven't finished it, but I've been enjoying it. It de-emphasizes getting the right answer and focusing on the process of developing understanding.

There is also the Mindset Mathematics series by Jo Boaler which provides some really interesting activities that you can do with your students, regardless of skill level. Her website also offers activities that you can find in her books.

I really like OneNote! I've only used it on Windows, but they do have an Android version that seems very fairly priced: first 500 notes are free, then pay a one-time fee of 4.99USD for unlimited notes.

Can you please clarify why you wrote this? I like his ability to write clearly, in the same spirit of books written by mathematicians that do math, unlike textbooks written by numerous authors that attempt to please everyone and loose a real flow of narrative or dialogue.

His dialogue with high school students is a model for teachers, see Math!: Encounters with High School Students, he seems adept at engaging students that are not advanced, but everyday kids.

Not answering your questions, but I would suggest, if it is withing your means, for you to buy a digital drawing table. There is some pretty inexpensive models like this one (the one I have) that would be enough to improve your videos drastically. Writing just using a mouse will usually result in some nasty handwriting, which doesn't affect the value of the actual subject you're addressing, but will inevitably affect the experience of watching your videos.

Corwin publishing released a book this year called “The Formative 5”. I’m currently reading it and it is helping to clear up my confusion on what kind of formative assessments to use, when I should use them, and how to maximize my understanding of students with them. I think it might help you out. https://www.amazon.com/Formative-Assessment-Techniques-Classroom-Mathematics/dp/1506337503/ref=nodl_

I never said you have to use PC to be able to run Latex. There are tons of Android Latex quick edit apps on the app store (e.g QuickTeX)

And if just want a quick share of your work, just write it down and take a pictures. The last time I check all smart phone have at least one camera.

I had a directed research my senior year in college that was a presentation and 20 page paper. If you enjoyed Linear Algebra, I would recommend the topic of researching the linear algebra behind Google Page Rank. There are lots of resources but here is a book to look into if you’re interested! My professor recommended it for me and I very much enjoyed it. Ask your professors for suggestions and let them know what math class was your favorite, they may have recommendations!

hmm it should work, is it android or ios?

could you try this links?

android

ios

Sam the Sumbot is a demanding mathematical game, which stands out with its unique hand-drawn style. The game does not only test your mathematical skills but also challenges your reflexes. How good are you when you have to calculate and manoeuvre at the same time? Not only sums, but also subtraction, multiplication and fractions are being tested throughout the different stages, making each a different challenge. Are you a pro in multiplication but have difficulties in adding fractions? Improve yourself in the fraction stage!

And here are the links for Android and iOS.

We did test this game within school classes and the feedback was very good. The pupils had fun playing it while improving their mental arithmetic skills.
If you like the game, please rate and share it. Hope somebody enjoys it :D

https://smile.amazon.com/Mathematicians-Delight-Dover-Books-Mathematics/dp/0486462404

Mathematician's Delight is an inexpensive gem.

Not sure which book you are thinking of.

Absolutely. You need to believe that you can achieve your goals as long as you work hard. Some people will need more or less time and effort, but the key is to keep going. In some ways you have a head start since you have some idea of what you want to do. If you need some more specific suggestions, you might look at this book:

https://www.amazon.com/Complete-Guide-Study-Maths-Physics-ebook/dp/B0825DV7RJ/

Another great book to give a road map of where you are going is Garrity, All the Math You Missed (But Need to Know for Graduate School).

>To know the answer to that question of whether allowing proofs in mathematics curriculums is too much for kids, we would have to look at psychological studied and papers in mathematics education.

Well, to me kids can handle some simple proofs. Generalising shouldn't be that difficult.

https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/1493927116 is a very concise book about real analysis.

You can use a few of the proofs there as reference.

As a general rule, steer as far away as possible from the traditional model of teaching most/all of each topic in a big block. It might seem easier for the kids that way, but retention stinks when a topic is largely ignored after a block is finished. It's much better to cover all of the topics a little at a time over a larger time frame. Ideally, you want to circle back to topics at a time when students are just on the edge of forgetting some things. The brain doesn't decide memories are worth strengthening when recall is easy; it strengthens them when the need for stronger connections is evident.

I'm basing this on what I learned in the book Make It Stick by Peter Brown (https://www.amazon.com/Make-Stick-Science-Successful-Learning/dp/0674729013/). That book probably did more to improve my teaching than about anything else I ever read. It's not really targeted for primary classrooms, but the principles should still serve you well.

There's a well-known book you might find interesting for working on proving things. It's called How to Prove It, by Daniel Velleman. It covers three things:

1. The basics of formal logic that are used in proofs, such as logical connectives and quantifiers.
2. Some proof strategies that occur throughout many branches of mathematics. For example, it will tell you about proofs by contradiction, induction, etc., as well as provide strategies for searching for proof strategies structurally from the statement you want to prove.
3. It also covers some of the really universal ideas from mathematics in a proof-oriented setting: basic set theory, functions and relations and their properties, and a little bit of number theory just because elementary number theory is a good setting for some practice on proofs.

If you do want to work up to your math studies over the summer and feel weak on proofs, then I think it would be a great choice for someone in your position.

Yes! And context is so important, including historical context... I never really saw that until college and it's one of the reasons I even considered studying math.

Another TED Talk that talks about the change in teachers - the difference between information distributors and... everything else.

Among the trove of math apps and tech, I urge you to not underestimate the one technology that has yet to find its master: pen and paper! Invite your kids to draw, sketch, scribble, use colors, and lead by example. So much of math can be represented and thought through pictorially, instead of pages and pages of symbols.

Instrumentwise:

• Blackboard: Intuitive interface, great contrast, easy undo. But you have to turn your back to the class or have stand awkwardly, often hiding the view.
• Whiteboard: same as blackboard, minus the contrast.
• Smartboard: Ugh. Presently I cannot recommend any of them. The interfaces are clunky and yank you out of your train of thought, and the whole class with it. Whatever they can show dynamically or interactively may look good in a demo, but is still a far cry from useful in a real lesson.

My current setup is a laptop + projector with a portable visualizer. I also use the Desmos calculator app instead of T-Rex Instruments.

Another piece of technology you should look into are Nonpermanent Vertical Surfaces (NPVS): a tongue-in-cheek acronym for student whiteboards. Have your students write not in their personal notes, but give them larger surfaces and markers – hell even the tables. This invites collaboration and the willingness to take risks, because they can simply wipe their mistakes away. Plus they can share their work easily with the rest of the class.

>I'm going to assume that there are 'buzzwords' to know.

To know and to use! You don't want to fill your statement with this stuff and then just come in and lecture every day. If you're looking for terms to google, inquiry-, group-, and project-based learning are good places to start, also flipped classrooms and technology integration are big. There's also a Coursera class starting soon that I've heard good things about. This kind of stuff is a lot more work than lecturing, but in my experience the students really benefit.

>Is that a thing that goes on a CV? "I went to this one talk once"?

Depends on how hard-up you are to pad yours out. I didn't have many papers or talks, so I added a section on conferences that I recieved funding to attend. I think it couldn't hurt and that it shows that you're an active member of the math ed community, but others might disagree.

I saw your reservations about high school, but another option is alternative certification programs. Most states are so desperate for math teachers that they'll grant temporary certification while you work towards a certificate. The down side is you may have to work at a school that is either rural or inner-city.

I wish you the best of luck. I know how hard it is out there!

https://dictionary.cambridge.org/us/grammar/british-grammar/about-adjectives-and-adverbs/adjectives-forms

In the English language their are only a couple of words that change in meaning in an adjective suffix and they are VERY much flagged.

......

Warning:

Adjectives ending in -ic and -ical often have different meanings:

The economic policy of this government has failed.

A diesel car is usually more economical than a petrol one.

.....

And 'false' is NOT one of them.

Websters SPECIFICALLY reference Falsifiability on the SAME PAGE as falsify for a reason.

https://www.merriam-webster.com/dictionary/falsify

The dominating opinion that matters when it comes to humanities education would be the businesses that run the economy, and government tailors the education system for it. Hence STEM being put forward hugely. For this reason programming is gaining HUGE traction here in the UK, ICT curriculum is changing to encompass this. I could easily see it make its way into maths, if you argue the economy reason.

Logic & Mathematical thinking maybe too. Mathematical thinking is already done at Further Maths A-level though - a very, very small number of the population get to experience this. It's a shame and should be done earlier. It's really at the core of what maths is really about and instead you get a view that it's just computation, because computation maths is all you do (came about predominantly for Engineering for the economy I think) Speaking of mathematical thinking... this is an excellent coursera course that just started

Anyway, as for philosophy in the education system, well why? What value does it provide to (this capitalist) society?:

You'd need to argue the benefit to the economy - which would be the argument of creative/different ways of thinking in society.

You could also argue that it could make people more empathetic, with moral philosophy.

However, both these values can be met by Humanities in general (performing arts, visual arts) can provide them too. Also these values evidenced by humanities are a thing that employers do to differentiate candidates after the core technical knowledge for the job is met.

So to argue philosophy in the core education system, you'd have a hard time getting its unique selling point that other humanities already do & are established.

See if your college has anything like a Math Education or STEM education program or something.

I'd also say try taking at least one higher level math class to see what it's like. Calculus is great and is probably the highest you'd ever have to teach in high school, but honestly, it's sort of just the gateway material to lots of higher level stuff. Look for a 'Logic and Proofs' class, or something like this.

I used FreeCAD, which is free, and the file is here (if that file host works). You will need to double-click on the Sketch (in the left panel) and open the Sketcher workbench (up the top).

Because it has two degrees of freedom, you would need two additional pieces of information (eg: two of the angles that are not stated in the problem).

Are you required to solve this problem using power series? If not you can solve it purely using trig identities and then l'hopital. I was able to simplify it to 2x/(sin(4x)) and then applying l'hopital i got 2/(4cos(4x)) as x approaches 0 which is equal to 1/2

Here is a graph showing my simplification is equivalent

Oh, like something on the tip of the line segment? You can long press the dot to the left of the object (a,b) and a window pops up to change it from a dot to an empty circle or an x

https://www.desmos.com/calculator/j4efcajcqh

Would be cool if you could set it up as an arrowhead that rotates based on the line segment leading to it, but I get why that's a whole extra level of computing

edit-you could make the arrow head out of line segments with slopes defined in terms of the slope of the vector, but I'm not feeling the holy spirit's will to tinker that much with desmos right now. Looks like this guy came up with something, though.

Khan Academy for the basic refresher.

Coursera offers a Course called "Introduction to Mathematcial Thinking" that is good as well, and the textbook can be found pretty cheap on Amazon. It's not running now, but seems to be offered at least once or twice a year.

There is also a book called "Mathematics for the Nonmathematician" by Morris Kline that I enjoyed and found helpful.

I'm in a similar position - was horrible at math, went back to college as an adult and am majoring in Information Systems Security & Computer Engineering, and those were the basics I used to help prepare for my math classes.

I also used a copy of Algebra for Dummies and the workbook with extra problems to go through and practice before enrolling in my Precalculus calss, because it covered a lot of Algebra. I used tiger-algebra.com to review the answer and steps for thigs I had problems with and kept practicing util I was answering most of the problems correctly on my own.

One way to learn a little bit more about higher level math is to read the 'Math Girls books by Hiroshi Yuki'. The first book in the sequence is at https://www.amazon.com/Math-Girls-Hiroshi-Yuki/dp/0983951306/ref=sr_1_2?keywords=math+girls&qid=1638650140&sr=8-2

There are currently 5 books in the sequence (book 5 on galois theory just came out last week).

Even though you might think that these books are just stories with some math thrown in, I think they are some of the best books to introduce people to higher level math. The math is introduced very well and I wish these books were around when I studied math 20 years ago when I got a degree in math.

As mentioned in another post, the Art of Problem Solving books are great as well. The calculus book and intermediate counting and probability will really give you some idea of higher level math as well.

NRich from Cambridge University has some early learning resources, including a large Activities and Games archive that might be fun for what we call Primary Students. Parent and Teacher resources can also be found there.

Meanwhile you as parent might like [the sister resource Plus](edited by Marianne Freiberger and Rachel Thomas), run by Marianne Freiberger and Rachel Thomas.

Before these colouring books were invented I got my start in Maths by colouring-in my times-tables in and uncovering pretty patterns.

Can't think of any books. It might be fun to play about with the scratch programming language though.

http://scratch.mit.edu/galleries/view/6423

Obviously need to pitch it at the right level, but could be useful for visualizing concepts and learning programming.

Edit: Bit of an explanation on scratch here

I second the teacher.desmos.com rec but also check out learn.desmos.com for all kinds of PD resources.

Here is a little demo of a cool way to use sliders on a parabola while also using a point you can manipulate directly. On the right side note that m uses a list instead of a slider to show multiple versions of that form.

What else did you have in mind?

You can think about the hyperbola as trace of the intersections of two expanding circles. Since one circle is larger than the other, they don't meet in the center, but meet along a curve. Look at this demo for more.

(this means that it is possible to have students construct a hyperbola's points using a ruler and compass -- might be good if they did constructions in geometry!)

I did something like this with my class a few weeks ago. Some got really into it and created some great stuff, some did not.

Here's the one I made as an example.

Good luck

Absolutely. Brilliant Premium has courses for anyone, from fundamental math to multivariable calculus. I think the best way to describe it is a educational website/app for people that genuinely care about their education.

1. As I said, anyone from an elementary/primary schooler to a college student can learn something from Brilliant.
2. They have many courses at different levels, and they gradually progress (kinda like the education system in that regard) in accessibility. He could very well know how to take the derivative of a function before he starts high school, if he wanted to. You brought up statistics, so we'll use that as an example. Brilliant's probability/statistics courses range from basic probability fundamentals to statistics and quantitative finance. So, to answer your second question: Yes, Brilliant teaches just about everything. As a matter of fact, each course has a prerequisite/going further graphic at the bottom of each course (I can't attach images in a comment, but go see for yourself; they put a lot of effort into designing their courses).

If he's bright and/or passionate about math (or science in general), then I would strongly recommend getting a premium subscription (maybe not lifelong, yet).

If you get really comfortable with the tools, you can totally design something exactly how you want it. But there's already a wealth of similar activities built and shared by others that you can browse through: https://www.geogebra.org/search/congruent%20triangles

Illustrative mathematics MS curriculum is going up on GeoGebra for free. https://www.geogebra.org/m/ckm3ffqh Besides free, it is the best, what I would recommend for anyone.

Use spherical coordinates to convert those lat/long angles into cartesian coordinates. Form two vectors from the two points using the center of the sphere as the base for each vector. Use the dot product to calculate the angle between these vectors. Use that angle in the formula (angle x radius) to find the arc length of that arc of the great circle.

(This assumes the Earth is a perfect sphere, a more accurate idea would be to use an elliptic coordinate system to convert to cartesian. Then use those two points and the center to find the equation of a plane. Find the curve of intersection between the plane and the sphere, and parametrize the geodesic between the two points. Then use calculus to find the arc length of that geodesic.)

I made a geogebra applet which does what I said: https://www.geogebra.org/3d/ukhdxedm The radius of this planet is = 1, so just convert the angle given to radians and multiply by the radius of Earth.

I have to recommend a Desmos competitor: Geogebra

• Eons better geometry tools
• Step-by-step construction/creation protocol available to show students how something works
• Exam capabilities through app window locking
• Active development of classroom solutions this year
• They are testing Augmented reality visualization capabilities for smartphones (currently only iPhones though I believe)
• Variety of phone applications availabe - From simple scientific, through 3D geo, to full fledged Geogebra suite, which is nearly at feature parity with the Desktop version. Desktop version runs on All: Windows, macOS and virtualy and Linux distro you can think of. Meaning, you can build on the PC and then the files you share can simply work on their smartphones

Geogebra depending on the age of the kids. It's free and amazing once you learn how to use it a bit. Great for experimenting.

https://www.geogebra.org/

It supports spanish language. Try some tutorials on youtube.

The absolute gold standard book for this is How to Solve It. Essentially, it covers a 4 step process on how to tackle math problems. It then continues to explain common heuristics for problem solving and has socratic dialogs between Polya and an imaginary student.

It doesn't talk about lesson plans or any of the more administrative details of teaching. However, it gives you a lot of specific details about how to lead students through problems in a way that makes them feel like they could have come up with the answer.

Note: the example problems range from basic geometry to writing proofs so some of them might be unhelpful if you haven't taken those classes yet. But they can be skipped.

I love Proof, Logic, and Conjecture by Wolf: https://www.amazon.com/Proof-Logic-Conjecture-Mathematicians-Toolbox/dp/0716730502/ref=mp_s_a_1_2?dchild=1&keywords=proof+and+conjecture&qid=1628461206&sr=8-2

With this app, you can practice linear algebra very easily https://play.google.com/store/apps/details?id=com.app.mathschallenger

https://www.amazon.com/gp/product/013446916X/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=013446916X&linkCode=as2&tag=themathsorc0e-20&linkId=b479343d20b014aadfd45299d11cdefa

This was recommended to me for an absolute beginner. It says college algebra though... would you say that its a good place to start for someone without any experience in algebra?

https://www.amazon.ca/Cartoon-Guide-Algebra-Larry-Gonick/dp/0062202693

Larry Gonick is great. This, in combination with explanations and extra practice from this free courseware https://courseware.cemc.uwaterloo.ca/41 will get you where you want to be.

Hopefully, there will be more groups online. I think that is happening as a consequence of covid. Your local university would be a good place to start. Good luck.

In case you are interested this book describes the circles (also many problem books are available): https://www.amazon.com/Mathematical-Circles-Russian-Experience-Genkin/dp/8173711151

My professor wrote this book, it's a great start to the funner parts of geometry, number theory, etc, even without a math background: https://www.amazon.com/Mathematics-Human-Flourishing-Francis/dp/0300237138

This site does use texts. They're online but they can be bought in printed form as well and relatively cheaply. But mostly the learning will be in doing problems and having someone tell you that they're wrong.

If you like a physical text, I recommend an older edition of something that is recommended for adults who need to review from basics.

I looked for "developmental mathematics" on amazon. These texts typically start with pre-algebra and go through algebra 2 if worked conscientiously. I found this book which I have no personal experience with but the reviews are really good. I can say (because I have reviewed them) that the Bittinger/Beecher, Lial, Martin-Gay, Rockswold, Sullivan texts are all solid textbooks. My favorite one is Sullivan but I don't see a cheap copy of it and it's not ENOUGH better to make it worth spending that much money on. A lot of people I work with love Martin-Gay. If you get old used ones, it's hard to go wrong -- honestly, buy a couple of the $5 ones and see how you like them.

If you work through one of these, you'll be ready to do a college algebra/trig book or a precalculus book. Then give Lang another shot.

i think for memorize flash card is good enough it can apply to android flash card Anki. Khan Academy maybe also can help your problem.

Public school, so all types of kids, some below grade level, some advanced, like any public school. The vision is limited by the administration and standards and the need to provide said books to students, so the books would need be purchased. So I'm looking for possible replacement of the usual textbooks with what might be better.

We have some room to change, so currently we either stick with the normal Algebra I, Geometry, Algebra II with trigonometry, then Calculus, or try Alg I, then II, then Geo/Trig, lastly Calculus, or Pearson's Integrated math years 1-4, which is almost identical to the usual except the topics are a little mixed around, so each year has some algebra, geometry, even probability is not relegated to the end of the book, but it's really not innovative. There is also the possibility to revise the curriculum a bit more, pick truly better books. One classic Algebra text I'd consider is Dolciani's Algebra: Structure and Method but it appears only Book 1 is available and I'm not even sure about that.

Our district is currently piloting a similar course using the text Financial Algebra by Gerver and Sgroi. It definitely uses some Algebra II level concepts, as well as geometry and statistics, but uses them in consumer math scenarios. In one of the accompanying documents, the authors suggest using chapters 1-6 for exactly the type of course you posted about.

Financial Algebra by Gerver and Sgroi

Most hobbies that I can think of involve at least one of three different components: developing a skill, producing something, and enjoyable busywork. It might be helpful to think about which of those are priorities in order to come up with something that works for you. The other question is do you want to lean in to your STEM-sensibilities, or would you rather tap the other half of your brain?

For me, it's mostly guitar and video games. My interest in both fluctuates a lot, but I've managed to avoid boredom while hardly leaving my house for the last 6 months. I also just happen to have gotten a dog in January, and while I'm not sure it's appropriate to call caring for a pet a "hobby", there does seem to be quite a bit of overlap.

For a STEM flavored hobby, you could try Arduino. I got this little project kit last year that had pretty clear instructions for a few dozen different things. I kind of lost interest after I finished with the kit, but I definitely had fun while I was doing it, and I might come back to it some day. If that seems like a near-miss, you can find lots of other gadget building kits online.

Most hobby shops are all about kits for building models or remote control cars/planes/boats.

I really enjoyed (no pun intended) "Geometry for Enjoyment and Challenge" Amazon link in high school. A couple of the early proof chapters drag a bit, but the book provides plenty of challenging problems. Bad news; even a used copy is about $80.

So I might actually suggest a 'math for elementary teachers' book for yourself (alternate here), so that you can get an idea of how to approach these kinds of problems with visual aids, such as what kinds of ways you can draw pictures of long division, etc. In other words, most people don't use textbooks with 4th/5th graders, but a lot of worksheets and packets, with activities and explorations drawn from curricula like this.

You can get little self-adhesive Velcro squares (or tape if you have more patience for cutting) that have the hooks on one side and the loops on the other. Then put the hooks on one of each pair and the loops on the other, so completed matches can stick to each other, even inside an envelope or plastic storage bag.

EDIT: I have no idea if this brand is any good, but here's the sort of thing I'm talking about. https://www.amazon.com/Vkey-500pcs-Diameter-Adhesive-Compatible/dp/B012EWJIXG/

I like the Safe-T compass

https://www.amazon.com/Learning-Resources-Safe-T-Compass-Pack/dp/B07NC7RBDQ/ref=sr_1_2?crid=32L0V4XMMQUO6&keywords=safe-t+compass&qid=1558482307&s=industrial&sprefix=safe-t+com%2Cindustrial%2C127&sr=1-2

Khan academy sucks for this reason. I strongly recommend this book if you are spending a lot of time piecing things together https://www.amazon.com/College-Algebra-7th-Robert-Blitzer/dp/013446916X/ref=zg_bs_13887_88?_encoding=UTF8&psc=1&refRID=P6E5V44ND250Y76AW1S0

It walks you through everything with plenty of practice. There are other books in the series

Nice list! Would you consider putting my game in it? I created a number puzzle called Mathemechanic that's inspired by Sudoku. It teaches how to count, subtract and requires you to think ahead. You can check it out on the Play Store if you have an android device.

https://play.google.com/store/apps/details?id=com.buckriderstudio.mathemechanic

It sounds like you are dealing with a heavily reinforced chunk of self-concept. I've been reading Transforming Your Self: Becoming Who You Want to Be. Any time you give him one example of him not being good at math, his brain immediately calls up 20 examples of him being bad at math and then overrules your example.

Unfortunately I haven't gotten far enough into the book to give useful advice, but if all else fails, give it a read.

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https://www.amazon.com/Math-Through-Ages-History-Teachers/dp/188192954X

This was my text for History of Math. Very nicely laid out, has a general thematic history and then twenty-some sketches of the development of various ideas.

I'm going to go against the grain here and recommend, strongly, that if you are allowed to take Calc 1 that you take Calc 1. In general people do not master the math that they learn until after two semesters of building on top of it. Any skills you're lacking from pre-calc you will refine and master after taking three semesters of calculus. Anything you don't master in Calc 1 you'll master in later semesters of Calc and differential equations.

Google "remedial math courses in college". There's plenty of evidence that students who go straight to college-level courses (even though they didn't place into them on assessment) ultimately fair better than those who decided to go into the remedial courses. If you take pre-calc, you will probably be grinding out tedious algebraic manipulations to prove things like trig identities. It will be boring, most of it redundant to what you already know, and you'll be paying a lot of money for it and further push back your graduation date. Even if you take the pre-calc course, there's no guarantee that Calc 1 won't be full the next semester (or you may have a scheduling conflict), so you may be put even further behind.

Lastly, if you're interested in philosophy then I highly recommend this book: More Precisely: The Math You Need to Do Philosophy

I realise this is from a while ago, but I've remembered the answer. I think you mean the book 'Arithmetic Arithmetic' by Martine Perry https://www.amazon.co.uk/Arithmetic-Martine-Perry/dp/1899618147

I recommend How to Teach Mathematics by Steven G. Krantz

Check out Thinking Mathematically and Betterexplained.

I agree that Khan Academy is a good resource--another one I always recommend to my students who struggle with math basics is this book. A lot of people are embarrassed by their poor math skills. Unfortunately, there are plenty of bad math teachers and since it builds on itself, you can miss one concept and have trouble with so many other things further down the line. Don't get too down on yourself about it! It's not who you are, it's just one aspect of what you know, and with the right teacher/book/explanation, you can understand it.

This set from Learning Resources is nice - you can use something like sand or rice and actually see that the volume of a cone will fit into a cylinder 3 times: http://www.amazon.com/Learning-Resources-Folding-Geometric-Shapes/dp/B006RQ8TW2/ref=sr_1_3?s=office-products&ie=UTF8&qid=1446487860&sr=1-3&keywords=learning+resources+folding+geometric+shapes

I teach a general Math Topics course. I cover a bunch of random topics. We don't have a book for that course, but I use a college algebra book, a stats book, a precalc book, and this consumer book as references.

If you like books: I used Number Theory Through Inquiry in one of my courses. It's got a lot of (all?) the classic theorems, but requires you to write all of the proofs. I enjoyed it. Elementary Number Theory by Underwood Dudley was also nice and is well-liked.

I made an app for teaching a basic math concept. PEDMAS

Released it in October but it has not got the traction I had thought it might have.

It is basic but provided an unique interactive way to see PEDMAS.

thanks Martin

Well you can try MalMath, it covers, Integrals, Derivatives, limits, Logarithms, etc.. You write the problem, and press solve, the app solves it and shows you the steps, on how it solved that.